COMPUTATIONAL MODELING OF HIP JOINT MECHANICS

by

Andrew Edward Anderson

A dissertation submitted to the faculty of The University of Utah

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

Department of Bioengineering

The University of Utah

April 2007

Copyright © Andrew Edward Anderson 2007

All Rights Reserved

ABSTRACT

The hip joint is one of the largest weight bearing structures in the human body.

While its efficient structure may lend to a lifetime of mobility, abnormal, repetitive

loading of the hip is thought to result in osteoarthritis (OA). The etiology of hip OA is

unknown however, due to the high loads this joint supports, mechanics have been

implicated as the primary factor. Quantifying the relevant mechanical parameters in the

joint (i.e. cartilage and bone stresses) appears to be central to an enhanced understanding

of this disease. Experimental studies have provided valuable insight into baseline hip

joint biomechanics but they require a protocol that is inherently invasive. Numerical

modeling techniques, such as the finite element method, open the possibility of predicting

hip joint biomechanics noninvasively and could revolutionize the way pathological hips

are diagnosed and treated. Unfortunately, hip finite element models to date have used

simplified geometry and have not been validated. It can be credibly argued that prior

computational models of the hip joint do not have the ability to predict cartilage and bone

mechanics with sufficient accuracy for clinical application.

The aim of this dissertation is to develop and validate methods that will facilitate

patient-specific modeling of hip joint biomechanics. Toward this objective, subject-

specific FE models of the pelvis and entire hip joint were developed. The accuracy of

model geometry, i.e. cortical bone and cartilage thickness, was assessed using phantom

based imaging studies. FE predictions were compared directly with experimental data for

purposes of validation. The sensitivity of the models to errors in assumed and measured

model inputs was quantified. Finally, recognizing that acetabular dysplasia may be the

single most important contributor of hip joint OA, the validated modeling protocols were

extended to analyze patient-specific models to demonstrate the general feasibility of the

approach and to quantify differences in hip joint biomechanics between a normal and

dysplastic hip joint. The developed modeling methodologies have a number of potential

longer-term uses and benefits, including improved diagnosis of pathology, patient-

specific approaches to treatment, and prediction of the success rate of corrective surgeries

based on pre- and post-operative mechanics.

v

To my father: Richard E. Anderson

“It matters not how long we live but how” Philip James Bailey

TABLE OF CONTENTS

ABSTRACT....................................................................................................................... iv LIST OF TABLES............................................................................................................. ix LIST OF FIGURES .............................................................................................................x ACKNOWLEDGEMENTS............................................................................................. xiii CHAPTER 1. INTRODUCTION ...................................................................................................1 Motivation................................................................................................................1 Research Goals.........................................................................................................4 Summary of Chapters ..............................................................................................5 References................................................................................................................8 2. BACKGROUND ...................................................................................................10 Forward ..................................................................................................................10 Hip Joint Structure and Function ...........................................................................11 Pelvic and Femoral Bone ...........................................................................11 Cartilage.....................................................................................................13 Labrum, Capsule, Ligaments, Muscles......................................................15 Hip Joint Pathology................................................................................................20 Osteoarthritis..............................................................................................20 Hip Dysplasia.............................................................................................22 Experimental Hip Joint Biomechanics...................................................................25 Bone Material Properties ...........................................................................25 Cartilage Material Properties .....................................................................27 In-Vitro Studies of Hip Joints ....................................................................29 In-Vivo Studies of Hip Joints ....................................................................32 Numerical Modeling of Hip Joint Biomechanics ..................................................35 Analytical Modeling of the Hip Joint ........................................................35 Computational Modeling of the Hip Joint .................................................36 References..............................................................................................................43

3. A SUBJECT-SPECIFIC FINITE ELEMENT MODEL OF THE PELVIS: DEVELOPMENT, VALIDATION AND SENSITIVITY STUDIES......................................................................................58 Abstract ..................................................................................................................58 Introduction............................................................................................................60 Materials and Methods...........................................................................................63 Experimental Study....................................................................................63 Geometry Extraction and Mesh Generation ..............................................66 Position-Dependent Cortical Thickness.....................................................69 Assessment of Cortical Bone Thickness....................................................71 Material Properties and Boundary Conditions...........................................72 Sensitivity Studies......................................................................................73 Data Analysis .............................................................................................75 Results ....................................................................................................................76 Reconstructions of Pelvic Geometry .........................................................76 Cortical Bone Thickness ............................................................................77 Trabecular Bone Elastic Modulus..............................................................80 FE Model Predictions ................................................................................80 Discussion..............................................................................................................85 References..............................................................................................................92 4. FACTORS INFLUENCING CARTILAGE THICKNESS MEASUREMENTS WITH MULTI-DETECTOR CT A PHANTOM STUDY..........................................................................................97 Abstract ..................................................................................................................97 Introduction............................................................................................................99 Materials and Methods.........................................................................................102 Phantom Description................................................................................102 CT Imaging Protocol................................................................................105 Image Segmentation, Surface Reconstruction, and Measurement of Thickness ......................................................................106 Error Analysis ..........................................................................................109 Results ..................................................................................................................110 Contrast Enhanced Scans.........................................................................110 Non-Enhanced Scans ...............................................................................115 Discussion............................................................................................................117 Study Limitations.....................................................................................119 Practical Applications ..............................................................................120 References............................................................................................................122

5. VALIDATION OF FINITE ELEMENT PREDICTIONS OF CARTILAGE CONTACT PRESSURE IN THE HUMAN HIP JOINT...........................................................................................126 Abstract ................................................................................................................126 Introduction..........................................................................................................128 Methods................................................................................................................130 Experimental Protocol .............................................................................130 Computational Protocol ...........................................................................133 Sensitivity Studies....................................................................................136 Data Analysis ...........................................................................................137 Results ..................................................................................................................140 FE Mesh Characteristics ..........................................................................140 Peak Pressure, Average Pressure, Contact Area......................................141 Contact Patterns .......................................................................................142 Misalignment and Magnitude Errors .......................................................145 Sensitivity Studies- Cartilage Material Properties and Thickness...........147 Sensitivity Studies- FE Boundary Conditions .........................................149 Discussion............................................................................................................152 References............................................................................................................159 6. PATIENT-SPECIFIC FINITE ELEMENT MODELING PROOF OF CONCEPT .......................................................................................165 Abstract ................................................................................................................165 Introduction..........................................................................................................167 Methods................................................................................................................170 Subject-Selection .....................................................................................170 CT Arthrography......................................................................................170 Image Data Analysis and Segmentation ..................................................171 FE Mesh Generation, Cartilage Thickness, Material Properties..............172 FE Boundary and Loading Conditions ....................................................174 Sensitivity Studies....................................................................................175 Data Analysis ...........................................................................................175 Results ..................................................................................................................177 Discussion............................................................................................................182 References............................................................................................................189 7. DISCUSSION......................................................................................................195 Summary ..............................................................................................................195 Limitations and Future Work...............................................................................200 References............................................................................................................205

LIST OF TABLES Table Page 3.1. Models studied for sensitivity analysis ...............................................................75

3.2. Reconstruction errors for simulated cortical bone ..............................................78

3.3. Results for all sensitivity models ........................................................................84

5.1. Misalignment and magnitude errors of FE predicted cartilage contact pressures ................................................................................146 5.2. Differences of center of pressures between FE and experimental results ...................................................................................146 6.1. Differences in FE predicted mechanics between a normal and dysplastic hip joint .........................................................................179

viii

LIST OF FIGURES Figure Page 2.1. Photograph of plastic hip joint............................................................................12

2.2. Histological cross-section of cartilage ................................................................14

2.3. Illustration of hip joint with labrum....................................................................16

2.4. Illustration of hip joint capsule ...........................................................................17 2.5. Illustration of iliofemoral ligament.....................................................................18 2.6. Volumetric CT scan of patient with acetabular retroversion ..............................24 3.1. Schematic of pelvis loading fixture ....................................................................65

3.2. 3D reconstruction of pelvis from CT image data................................................67

3.3. Finite element mesh of pelvis with close-up of acetabulum...............................68 3.4. Schematic illustrating the special cases considered in in determination of cortical thickness .................................................................70 3.5. Cortical bone thickness phantom........................................................................71 3.6. Schematic showing length measurements obtained from cadaveric pelvis and accuracy of geometry reconstruction.................................................76 3.7. Contours of position dependent cortical bone thickness of the pelvis.........................................................................................................79 3.8. Distribution of pelvic Von-Mises stress .............................................................82 3.9. Finite element predicted vs. experimentally measured strains for subject-specific and sensitivity models .........................................................83

4.1. Schematic of phantom used to assess accuracy of cartilage thickness reconstructions ...............................................................104 4.2. Simulated cartilage RMS and mean residual reconstruction errors for the transverse contrast enhanced CT scans as a function of agent concentration......................................................................111 4.3. Simulated cartilage RMS and mean residual reconstruction errors for the transverse contrast enhanced CT scans as a function of imaging direction and resolution .................................................112 4.4. Simulated cartilage RMS and mean residual reconstruction errors for the transverse contrast enhanced CT scans as a function of joint spacing, agent concentration, imaging direction and resolution ......................................................................114 4.5. Simulated cartilage RMS and mean residual reconstruction errors for the transverse non-contrast enhanced CT scans as a function of imaging direction and resolution .................................................116 5.1. Experimental setup for loading of hip joint ......................................................132 5.2. Finite element mesh of the entire hip joint in the walking position with a close-up of the acetabulum.......................................................135 5.3. Contours of cartilage thickness.........................................................................140 5.4. Finite element vs. experimentally measured average pressure and contact area ..................................................................................141 5.5. Qualitative comparison between finite element and experimentally measured contact pressure .......................................................143 5.6. Finite element predicted pressures relative to the femur and acetabulum .................................................................................................144 5.7. Percent changes in peak pressure, average pressure and and contact area due to changes in cartilage material properties and geometry......................................................................148 5.8. Percent changes in peak pressure, average pressure and and contact area due to changes in model boundary conditions..........................................................................................150

xi

5.9. Contours of cartilage pressure predicted by the baseline and rigid bone finite element models................................................................151 6.1. Fringe plots of acetabular and femoral cartilage thickness for the normal and dysplastic hip joints............................................................173 6.2. Comparison of finite element predicted acetabular cartilage pressures between a normal and dysplastic hip joint ........................................177 6.3. Finite element predicted acetabular cartilage pressures as a function of anatomical and joint reaction force orientation for the normal and dysplastic hip joint ...........................................180

xii

ACKNOWLEDGEMENTS

Financial support from the University of Utah Department of Orthopaedics,

University of Utah Funding Incentive Seed Grant, the Orthopaedic Research and

Education Foundation, and from NIH Grant #F31-EB00555 is gratefully acknowledged.

The University of Utah Department of Radiology (CAMT), Scientific Computing

Imaging Institute (SCI) and Brad Maker of Lawrence Livermore National Lab are also

given acknowledgement for their contributions.

CHAPTER 1

INTRODUCTION

MOTIVATION

The hip joint serves a very important biomechanical function. While supporting

the majority of the human body (~ 2/3 of total bodyweight) the joint must simultaneously

facilitate smooth articulation of the lower limbs to enable bi-pedal gait. During routine

daily activities, forces on the order of 5.5 times bodyweight are transferred between the

femur and pelvis [1-3]. While its efficient structure may lend to a lifetime of mobility,

abnormal, repetitive loading of the hip is thought to result in the breakdown of articular

cartilage, resulting in osteoarthritis (OA) [4-7].

Hip joint OA represents a significant burden to society via financial, social and

psychological effects. It is estimated that nearly 40 million Americans currently have

joint osteoarthritis (~18% of the population) of which nearly 3% of the cases originate at

the hip joint [8,9]. To alleviate pain and return the hip to at least the most basic

functioning state, nearly 193,000 osteoarthritic hips are replaced annually in the United

States by way of total hip arthroplasty (THA) [10]. While THA has enjoyed a high rate

of success in elderly patients (less than 10% require revision THA [10]), the surgery is

generally avoided in the younger population due to the limited lifespan of implants and

2

unfavorable results of revision THA. Although a common misconception by the general

public, hip OA is not confined to elderly patients. As detailed later, factors such as

abnormal joint geometry (i.e. hip dysplasia), body weight, occupation, and prior injury

appear to play major roles independently of age [11-13]. Nevertheless, the etiology of

hip OA is unknown, in part because it takes so long to develop- a decade or more likely

passes before cartilage has fissured to the point where bone contact initiates pain [14].

However, due to the high loads this joint supports, mechanical factors have been

implicated as a primary causes [4-7]. Thus, quantifying the relevant mechanical

parameters in the joint (i.e. cartilage and bone stresses) appears to be central to an

enhanced understanding of this disease [14].

Research on the biomechanics of the hip is not new to orthopedic medicine.

While previous studies have provided valuable insight into baseline hip joint

biomechanics, they require a protocol that is inherently invasive. Unlike experimental

investigations, computational modeling opens the possibility of predicting hip joint

biomechanics noninvasively. In particular, the advent, increased availability and

resolution medical imaging modealities provide a means to develop detailed

computational models that are based on individual patient geometry. These attractive

points, along with a tremendous evolution of computing power, have lead to substantial

growth in the field of computational biomechanics.

Although computational models have provided substantial additional insight to

hip biomechanics above and beyond that obtained via experimental studies, substantial

voids remain. In particular, simplifying model assumptions have often resulted in model

3

predictions that are inconsistent with experimental measurements. Most models have not

been validated by direct comparison with experimental data. For an analyst to develop

patient-specific models, without having to validate each model independently, it is

necessary to demonstrate that: 1) the computational protocol yields results that predict

known/measured quantities with sufficient accuracy, and 2) an assessment of model error

and uncertainty is accounted for in an effort to gauge how inaccuracies could be

propagated due to erroneous model inputs and assumptions.

4

RESEARCH GOALS

The overall aim of this dissertation is to develop and validate methods that will

facilitate patient-specific modeling of hip joint biomechanics. It is clear that patient-

specific computational models have the potential to revolutionize the way that disorders

of the hip joint are diagnosed and treated. However, first rigorous and validated

protocols that incorporate both computational and experimental techniques must be

established. In this dissertation research, model predictions are compared directly with

experimental data and errors in assumed and measured model inputs, i.e. material

properties, constitutive behavior, geometry, and boundary conditions, are discussed as

they pertain to errors in the developed model and in the context of future patient

modeling efforts. Second, recognizing that acetabular dysplasia may be the single most

important contributor of hip joint OA [17-20], the validated subject-specific finite

element modeling protocol is extended to analyze patient-specific models to demonstrate

the general feasibility of the approach and to quantify differences in hip joint

biomechanics between a normal subject and a patient with acetabular dysplasia. Finally,

limitations of the modeling protocol as well as unforeseen challenges in modeling

individual patients non-invasively are presented in the context of general hip joint

modeling applications but with special emphasis to the study of acetabular dysplasia.

5

SUMMARY OF CHAPTERS

The structure of this dissertation has been organized to answer the essential

questions that arise when developing a protocol to generate patient-specific models of the

hip joint. The primary objective of Chapter 2 is to provide a working knowledge base

that will serve as reference to the topics covered in the remaining Chapters. Chapter 2

discusses hip joint structure and function and provides further motivation for developing

computational models, in particular, by application of the finite element method. Topics

such as hip osteoarthritis, approaches to quantify hip biomechanics (experimental and

computational), and the importance of computational model verification, validation, and

sensitivity studies are presented.

In the context of hip joint OA, the most fundamental mechanics of interest are

bone and cartilage stresses and strains. In this dissertation computational models are

developed and validated to study the mechanics of bone and cartilage separately in an

effort to maintain simplicity and to control confounding factors (Chapter 3 and Chapter 5,

respectively). Chapter 3 discusses the development and validation of a subject-specific

finite element model of the pelvis. Computational predictions of bone strains were

validated by direct comparison to experimentally measured strains using tri-axial strain

gauges attached to the cortical surface of the pelvis. The influence of measured and

assumed model inputs was assessed using sensitivity studies and the geometrical

accuracy of the model, in particular, cortical bone thickness, was quantified.

Since computational models often use medical image data as the basis for creating

model geometry, it is crucial to demonstrate that the reconstructed geometry is an

6

accurate representation of the true continuum. Although this is important for all

computational studies, it becomes absolutely essential when modeling joint contact

mechanics between layers of articulating cartilage. Although volumetric computed

tomography (CT) data are often used as the basis for constructing joint models, the lower

bounds for detecting articular cartilage thickness and the influence of imaging parameters

on the ability to image cartilage have yet to be reported. Thus, it was necessary to

quantify the accuracy and detection limits of cartilage geometry with CT. To this end, a

phantom based imaging study was conducted and is presented in Chapter 4. While the

results of this study have application to subject-specific models using cadaveric joints

(Chapter 5), the primary focus of this work was centered around quantifying the accuracy

of CT arthrography since this procedure is required to visualize cartilage in live patients,

which has direct relevance to patient-specific modeling (Chapter 6). The results of this

study are discussed in terms of general clinical applications of CT for imaging articular

cartilage in diarthrodial joints.

Chapter 5 presents results for a subject-specific finite element model of the

mechanics of cartilage in the hip joint. Finite element predictions of cartilage contact

pressures were validated by comparing computational predictions to experimentally

measured contact pressures using pressure sensitive film. A physiological experimental

and computational loading protocol was employed in an effort to lay the groundwork

necessary for creating realistic patient-specific models. Sensitivity studies were included

in the analysis to determine the influence of measured and assumed model inputs on the

7

ability to predict cartilage contact pressures. Chapter 5 concludes with a discussion of

the model’s limitations.

As discussed in Chapter 2, acetabular dysplasia may be the primary etiology of

hip joint OA. Therefore, it was of interest to demonstrate the feasibility of the modeling

protocol developed in Chapters 3-5 for application to individual patients with dysplasia.

Chapter 6 presents two patient-specific finite element models: one for a normal volunteer

and one for a patient with acetabular dysplasia. Differences in computationally predicted

bone and cartilage mechanics are reported and clinical implications of these data are

discussed. Chapter 6 concludes with a discussion of the challenges involved with patient-

specific modeling and makes recommendations for circumventing these issues in the

context of future modeling efforts. Finally, Chapter 7 summarizes the entire dissertation

by highlighting the important contributions that were made to the field of hip

computational biomechanics along with a discussion of limitations and future research

directions.

8

REFERENCES

[1] Hodge, W. A., Fijan, R. S., Carlson, K. L., Burgess, R. G., Harris, W. H., and

Mann, R. W., 1986, "Contact Pressures in the Human Hip Joint Measured in Vivo," Proc Natl Acad Sci U S A, 83, pp. 2879-83.

[2] Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A.,

Strauss, J., and Duda, G. N., 2001, "Hip Contact Forces and Gait Patterns from Routine Activities," J Biomech, 34, pp. 859-71.

[3] Bergmann, G., 1998, Hip98: Data Collection of Hip Joint Loading on CD-Rom.

Free University and Humboldt University, Berlin. [4] Mankin, H. J., 1974, "The Reaction of Articular Cartilage to Injury and

Osteoarthritis (Second of Two Parts)," N Engl J Med, 291, pp. 1335-40. [5] Mankin, H. J., 1974, "The Reaction of Articular Cartilage to Injury and

Osteoarthritis (First of Two Parts)," N Engl J Med, 291, pp. 1285-92. [6] Mow, V. C., Setton, L. A., Guilak, F., and Ratcliffe, A., 1995, "Mechanical

Factors in Articular Cartilage and Their Role in Osteoarthritis," in Osteoarthritic Disorders. American Academy of Orthopaedic Surgeons.

[7] Poole, A. R., 1995, "Imbalances of Anabolism and Catabolism of Cartilage

Matrix Components in Osteoarthritis," in Osteoarthritic Disorders. American Academy of Orthopaedic Surgeons.

[8] Felson, D. T., Lawrence, R. C., and Dieppe, P. A., 2000, "Osteoarthritis: New

Insights. Part 2. Treatment Approaches," Ann Internal Med, 133, pp. 726-737. [9] Felson, D. T., Lawrence, R. C., and Dieppe, P. A., 2000, "Osteoarthritis: New

Insights. Part I the Disease and Its Risk Factors," Ann Internal Med, 133, pp. 635-646.

[10] AAOS, 2007,"Questions and Answers about Hip Replacement," National Institute

of Arthritis and Musculoskeletal and Skin Disorders. [11] Anderson, J. J. and Felson, D. T., 1988, "Factors Associated with Osteoarthritis of

the Knee in the First National Health and Nutrition Examination Survey (Hanes I). Evidence for an Association with Overweight, Race, and Physical Demands of Work," Am J Epidemiol, 128, pp. 179-89.

9

[12] Felson, D. T., 1994, "Do Occupation-Related Physical Factors Contribute to Arthritis?," Baillieres Clin Rheumatol, 8, pp. 63-77.

[13] Heliovaara, M., Makela, M., Impivaara, O., Knekt, P., Aromaa, A., and Sievers, K., 1993, "Association of Overweight, Trauma and Workload with Coxarthrosis. A Health Survey of 7,217 Persons," Acta Orthop Scand, 64, pp. 513-8.

[14] Macirowski, T., Tepic, S., and Mann, R. W., 1994, "Cartilage Stresses in the

Human Hip Joint," J Biomech Eng, 116, pp. 10-8. [15] Oberkampf, W. L., Trucano, T. G., and Hirsch, C., "Verification, Validation, and

Predictive Capability in Computational Engineering and Physics," presented at Foundations for Verification and Validation in the 21st Century Workshop, Johns Hopkins University, Laurel, Maryland, 2002.

[16] Anderson, A., Ellis, B. J., and Weiss, J. A., 2006, "Verification, Validation and

Sensitivity Studies in Computational Biomechanics," Computer Methods in Biomechanics and Biomedical Engineering, In Press Dec 2006.

[17] Harris, W. H., 1986, "Etiology of Osteoarthritis of the Hip," Clin Orthop, pp. 20-

33. [18] Murray, R. O., 1965, "The Aetiology of Primary Osteoarthritis of the Hip," Br J

Radiol, 38, pp. 810-24. [19] Solomon, L., 1976, "Patterns of Osteoarthritis of the Hip," J Bone Joint Surg Br,

58, pp. 176-83. [20] Stulberg, S. D. and Harris, W. H., "Acetabular Dysplasia and Development of

Osteoarthritis of the Hip," presented at Proceedings of the second open scientific meeting of the Hip Society, St Louis, MO, 1974.

CHAPTER 2

BACKGROUND

FORWARD

As discussed below, computational models have the potential to non-invasively

estimate hip mechanics for living subjects. However, based on the available in-vivo and

in-vitro experimental data, it can be credibly argued that most previous hip joint

computational models do not have the ability to predict cartilage and bone mechanics

with sufficient accuracy for clinical application. Furthermore, models that have included

more realistic geometries have not been validated by direct comparison to experimental

data. The purpose of this dissertation is to present novel methods to develop and validate

computational models of the hip joint that result in models that indeed have direct clinical

applicability to study diseases such as osteoarthritis (OA) and hip dysplasia. This chapter

presents the most relevant background information, including: hip joint structure and

function, hip pathologies, experimental hip joint biomechanics, and numerical modeling

of hip joint biomechanics.

11

HIP JOINT STRUCTURE AND FUNCTION

The hip is a ball and socket joint formed by the articulation of the spherical head

of the femur and the concave acetabulum of the pelvis. It forms the primary connection

between the lower limbs and skeleton of the upper body. Both the femur and acetabulum

are covered with a layer of cartilage to provide smooth articulation and to absorb load.

The entire hip joint is surrounded by a fibrous, flexible capsule to permit large ranges of

motion but to prohibit the proximal femur from dislocation. Several ligaments connect

the pelvis to femur to further stabilize the joint and capsule. Muscles and tendons

provide actuation forces for extension/flexion, adduction/abduction and internal/external

rotation.

Pelvic and Femoral Bone

The pelvis forms a girdle which protects the digestive and female reproductive

organs. It is formed from three bones: the ilium, ischium and pubis, which fuse together

to form the ox coxae, or innominate bone (Figure 2.1). At the point of fusing they form

the acetabulum (Figure 2.1). Joints adjacent to the pelvis include the sacroiliac (SI) and

pubis joint (Figure 2.1). Many large nerves and blood vessels pass through the pelvis to

the lower limbs.

The femur is the longest and strongest bone in the human body. It consists of a

head and a neck proximally, a diaphysis (or shaft), and two condyles (medial and lateral)

distally. The diaphysis of femur is a simplistic, cylindrical structure, while the proximal

femur is irregular in shape, consisting of a spherical head, neck and lateral bony

12

protrusions termed the greater and lesser trochanters. The trochanters serve as the site of

major muscle attachment. The lateral location of these structures offers a mechanical

advantage to assist with abducting the hip [2].

The bony structure of the pelvis is similar to a sandwich composite material,

consisting of a dense, stiff, thin shell of cortical bone (0.7 to 3.2 mm thick, [3]) filled with

much less dense trabecular bone. The spherical head of the femur has a thin layer of

subchondral bone where cartilage attaches, which is less stiff than cortical bone. Cortical

bone along the diaphysis of femur is much thicker (up to ~ 7 mm [4]) and supports the

large tensile and compressive loads that develop as a result of hip loading. Trabecular

Ilium

Fem

ur

Pubis Joint

Sacro-Iliac Joint

Pubis

Ischium

Acetabulum

Figure 2.1. Photograph of a plastic hip showing the individual bones and joints.

13

bone is found throughout the pelvis and proximal femur but is not as prevalent along the

diaphysis of the femur as this area primarily contains marrow.

Cartilage

Cartilage is composed of collagenous fibers and chondrocytes embedded in a firm

gel (Figure 2.2). Cartilage has remarkable mechanical properties in that it is strong but

flexible and has extremely low coefficients of friction [5]. Cartilage is avascular and

anueral [6]. Chondrocytes and their precursor chondroblasts are the only cells in

cartilage (Figure 2.2) [5]. Nutrients diffuse through the matrix by way of interstitial

fluid, which makes up nearly 60-80% of the total weight of cartilage [7]. In addition,

ionic charges in the fluid are thought to facilitate nutrient flow [8]. The solid matrix

represents nearly 60% of the dry weight and is composed of proteoglycans, which are

large proteins with a protein backbone and glycosaminoglycan (GAG) side chain [7].

The most common GAGs are keratin sulfate and chondroitin sulfate [7]. Matrix fibers

make up the remaining dry weight and are composed of collagen type II [7].

The acetabulum is covered with a horseshoe shaped layer of articulating hyaline

cartilage ranging from 1.2 to 2.3 mm thick in normal adults [9]. The entire head of the

femur is covered with a smooth layer of hyaline cartilage of varying thickness, except for

a small depression called the fovea capitis femoris that gives attachment to the

ligamentum teres. The thickness of femoral cartilage ranges from 1.0 to 2.5 in the normal

adult [9].

14

Figure 2.2. Through the thickness histological photograph of bovine articularcartilage (stained with Alician Blue). Chondrocytes appear as small dots.Copyright Lutz Slomianka 1998-2006.

Cal

cifie

d C

artil

age

Subc

hond

ral B

one

Cartilage Matrix

15

Labrum, Capsule, Ligaments, Muscles

The hip joint labrum is a ring of fibrocartilagenous tissue that surrounds the rim of

the acetabulum (Figure 2.3). It helps to guide normal motion, to prevent dislocation

between the femoral head and acetabulum and is thought to act as a seal to prevent loss of

interstitial fluid. An in vitro study where the labrum was removed have demonstrated

that cartilage is strained to a greater degree than joints with intact labrums for a given

load [10], suggesting that greater fluid flow in the latter scenario causes increased

cartilage matrix deformation.

The entire hip joint is surrounded by the hip capsule (Figure 2.4). The capsule

attaches proximally to entire periphery of the acetabulum, beyond the acetabular labrum.

It also covers the femoral head and neck like a sleeve, eventually attaching to the base of

the femoral neck. The capsule consists of two sets of fibers: longitudinal and circular

fibers. Circular fibers form a collar around the femoral neck whereas longitudinal

retinacular fibers travel along the neck and carry blood vessels.

The capsule is further defined by ligaments. The iliofemoral ligament attaches

from the pelvis to the femur and resists excessive extension (Figure 2.5). It is the

strongest ligament in the human body and allows one to maintain posture for extended

periods without extensive muscular fatigue. The pubofemoral ligament is the most

anterior and inferior portion of the fibrous capsule. It attaches to the pubic bone and

passes inferolaterally to merge with the iliofemoral portion of the fibrous capsule

(attaching to intertrochanteric line). Overabduction of the hip joint is prevented by this

ligament. The ischiofemoral ligament attaches from the ischial part of the acetabulum to

16

the femur and supports the posterior aspect of hip capsule. Finally, the ligament teres

connects the head of the femur to the acetabulum (Figure 2.3). Although it supports little

or no loads it may serve as an important conduit to supply blood to the head of the femur

in some individuals.

Labrum

Figure 2.3. Illustration of hip joint with labrum. Adopted from [1].

17

Figure 2.4. Illustration of hip joint capsule. Adopted from [1].

18

Figure 2.5. Illustration of iliofemoral ligament. Adopted from [1].

19

The hip can flex, extend, abduct, adduct, and rotate using several muscles

attached between the pelvis and femur. Many of the hip muscles are responsible for more

than one type of movement in the hip as different areas of the muscle act on tendons in

different ways. Hip joint flexors include the psoas major, iliacus, rectus femoris,

sartorius, pectineus, adductores longus and brevis, and the anterior fibers of the glutaei

medius and minimus. Hip joint extensors include the glutaeus maximus, assisted by the

hamstring muscles and the ischial head of the adductor magnus. The adductors include

the adductores magnus, longus, and brevis, the pectineus, the gracilis, lower part of the

glutaeus maximus, the glutaei medius and minimus, and the upper part of the glutaeus

maximus. The rotators that cause inward rotation are the glutaeus minimus, anterior

fibers of the glutaeus medius, tensor fasciae latae and the iliacus and psoas major.

Finally, inward rotators include the posterior fibers of the glutaeus medius, the piriformis,

obturatores externus and internus, gemelli superior and inferior, quadratus femoris,

glutaeus maximus, the adductores longus, brevis, and magnus, the pectineus, and the

Sartorius.

20

HIP JOINT PATHOLOGY

The hip is subject to disease due to improper development, acute trauma and

prolonged mechanical wear and tear. The most common disorders include arthritis

(rheumatoid arthritis, traumatic arthritis, osteoarthritis), avascular necrosis

(osetochondritis dissecans, Perthes disease), slipped epiphysis, bursitis, developmental

dysplasia of the hip and femoro-acetabular impingement. Osteoarthritis and hip dysplasia

are the primary thrust of this dissertation, and thus will be the focus of further discussion.

Osteoarthritis

Osteoarthritis is the most common type of arthritis in the hip and is intimately

associated with other disorders such as avascular necrosis, slipped epiphysis,

impingement and dysplasia. It is also the most common cause of musculoskeletal pain in

the United States [11]. Hip OA is a disorder of the entire joint, involving cartilage, bone,

synovium, labrum, and capsule [12]. OA is classically associated with more advanced

age but is being seen and treated more frequently in younger patients [12].

OA is characterized by a loss of articular cartilage in the predominately load

bearing areas of the joint, with eburnation of the underlying subchondral bone and a

proliferative response characterized by osteophytosis [13,14]. Gradual loss of the matrix

components is thought to be caused by a loss of proteoglycans, although some changes in

the integrity of collagen network may be necessary to initiate the disease [15]. It is also

thought that OA disrupts the mechanism for fluid support, which may exacerbate solid

matrix degeneration [12]. OA is further characterized by an increase in vascularity of

21

surrounding bone. Cysts often form within the surrounding bone and are accompanied by

changes to the joint margin. They may also cause outgrowths of cartilage as well as

osteophyte formation, which may lead to further degeneration. Therefore, the mechanics

of bone in areas adjacent to cartilage may be important to developing a comprehensive

understanding of hip OA.

OA was once thought to be primary or idiopathic in nature. However,

considerable clinical, epidemiological, and experimental evidence supports the concept

that mechanical demand greater than some critical level has a major role in the

development and progression of joint degeneration in all forms of OA. Surveys of

individuals with physically demanding occupations, including farmers, construction

workers, metal workers, miners, and pneumatic drill operators, suggest that repetitive

intense loading is associated with early onset of joint degeneration [16-18]. Excessive

mechanical stress can directly damage articular cartilage and subchondral bone and can

adversely alter chondrocyte function including the balance between synthetic and

degradative activity [19-25].

Although joint loading or overloading can lead to cartilage degeneration, the

precise mechanism remains controversial. Opinions differ concerning the relative

contributions of direct mechanical trauma to articular cartilage versus elevation of

articular stresses secondary to stiffening of subchondral bone. No experimental studies to

date have allowed one to directly separate the contributions of hydrostatic and deviatoric

stresses generated by joint loading. Therefore, it is unknown whether degenerative

22

changes are primarily due to excessive loads applied during normal activities or shearing

of cartilage during abnormal motions involving local instability.

In the elderly patient population, hip OA is treated by prosthetic replacement of

the hip joint. Nearly 193,000 total hip arthroplasties (THA) are performed each year in

the United States [26]. THA is highly successful in relieving pain and restoring

movement. However, ongoing problems with wear and particulate debris may eventually

necessitate further surgery, including replacement of the prosthesis. Men and patients

who weight more than 165 pounds have higher rates of failure [27]. The chance of a hip

replacement lasting 20 years is about 80% [27].

Hip Dysplasia

Developmental dysplasia of the hip (DDH) describes a broad spectrum of

problems, including hips that are unstable, malformed, subluxated (incomplete

dislocation), or completely dislocated [28]. In the broadest sense, DDH is a

developmental deformity characterized by malorientation and a reduction of contact area

between the femur and acetabulum [29]. Subluxation caused by dysplasia of the hip joint

is a primary cause of degenerative joint disease and clinical disability [30]. Subluxation

leads to increased stresses across the hip joint each time the hip is loaded during gait [31].

Consequently, it is thought that the altered biomechanics cause cartilage and bone of the

hip to break down prematurely, leading to early hip osteoarthritis. OA due to hip

dysplasia is commonly treated by THA. Surgical correction of the anatomic

abnormalities associated with hip dysplasia is performed on younger patients via pelvic

23

osteotomy, which preserves the hip joint and associated articular cartilage and delays the

need for prosthetic replacement of the hip. Redirectional acetabular osteotomy

(periacetabular osteotomy) involves cutting the socket free from the pelvis and rotating it

to a new orientation [32-37]. The most common type of dysplasia, referred to herein as

traditional dysplasia, can be diagnosed by evaluation of a 2-D planar radiograph of the

hip. Recently, a specific variant of dysplasia, referred to herein as retroversion of the

acetabulum, has been identified [38,39]. In the retroverted acetabulum, the acetabular

opening and its proximal roof lie at an angle of retroversion with respect to the sagittal

plane. Thus, posterior coverage of the femoral head is lost (Figure 2.6).

Retroversion is difficult to diagnose by the untrained clinician since a standard hip

radiograph shows that the hip is normal; nevertheless, the anatomy of the retroverted

acetabulum is still pathologic. It is likely that the obscurity of the retroverted acetabulum

has often persuaded the clinician into prescribing passive treatments for a potentially

aggressive pathology.

Several studies have shown that mild developmental dysplasia, in patients that

went unrecognized before, may indeed be the leading cause of osteoarthritis in the hip

[39-43]. Wilson and Poss [44] reported that deformity of the acetabulum is found in 25-

35% of adult cases of OA of the hip. Michaeli et al. [29] estimated that 76% of patients

with OA of the hip have some type of untreated acetabular dysplasia. In contrast to these

reports, other studies have failed to find a statistically significant relationship between

acetabular dysplasia and the risk of hip OA [45-49]. These discrepancies highlight the

need for an improved understanding of hip dysplasia.

24

Figure 2.6. Anterior (A) and Posterior (B) view of a volumetric CT scan from a patient with acetabular retroversion of the left hip. The patient’s right hip was considered normal. The lines indicate the edge of the acetabulum. Note excessive forward progression of anterior edge of left acetabulum in image A) and lack of posterior wall coverage of left femur in image B). Courtesy of Christopher L. Peters.

Left Right

LeftRight

AnteriorA)

B)

Posterior

25

EXPERIMENTAL HIP JOINT BIOMECHANICS

The contribution of muscles, ligaments, tendons, and hip capsule serve as vital

components when studying general hip joint biomechanics. However, the tissues of

primary interest in the context of studying OA and hip dysplasia are bone and cartilage.

In-vitro experimental studies are conducted using whole cadaveric hip joint bones or

individual tissue samples that are instrumented with sensing devices such as strain

gauges, pressure sensitive film, and force transducers. The objectives of these tests are to

ascertain material properties, to study the effects of interventions and diseases, and to

quantify normal cartilage and bone mechanics. In-vivo studies are difficult to conduct as

access to the hip joint is extremely intrusive. However, several studies have employed

instrumented hip prostheses implanted at the time of THA in patients with OA.

Bone Material Properties

Studies of the material properties of bone date back to the mid 1800s when

Wertheim measured the strength and elasticity of human cortical bone specimens [50]. In

the latter half of the 19th century Julius Wolff published pioneering work regarding bone

remodeling (termed Wolff’s Law, [51]) by stating that if loading on a particular bone

increases, the bone will remodel itself over time to become stronger to resist that

mechanism of loading. The converse was also stated to hold true.

In the mid 20th century Dempster and Liddicoat [52] demonstrated that cortical

bone exhibits different moduli of elasticity when loaded in different directions. The

dependence of the elastic properties on the basic lamellar unit of cortical bone was

26

recognized early by Evans et al. [53,54]. Building on this work, Lang et al. [55,56]

measured cortical bone moduli by assuming transverse isotropy (the plane normal to the

Haversian canals being the plane of isotropy). To investigate the transverse isotropy

assumption further, van Buskirk and Ashman [57] and Katz et al. [58] measured the

anisotropic moduli using ultrasound. They showed that, in general, cortical bone

possesses orthotropic elastic properties, but stiffness in various directions normal to the

Haversian canals did not deviate more than 10%. Direct mechanical tests further

confirmed that cortical bone can be reliably considered as a transversely isotropic

material [59,60]. The reported Young’s moduli for cortical bone have been shown to be

about 20 – 22 GPa along the axis of long bone and about 12 – 14 GPa transverse to it

[61,62].

It is widely accepted that trabecular bone exhibits orthotropic material behavior

(three preferred material directions) [63-65]. It has also been argued that trabecular

alignment corresponds to principal stress directions [51,66,67]. Early work by Chalmers

and Weaver [68] and Galante et al. [68] showed that porosity was far more important

than mineral content in determining material properties. Therefore, apparent rather than

calcium-equivalent densities are most often used to identify the remodeling state of bone

[65,69-74]. Dalstra et al. used dual-energy quantitative computer tomography (DEQCT)

to investigate the distribution of bone densities in pelvic bone, and nondestructive

mechanical testing was used to obtain Young's moduli and Poisson's ratios in three

orthogonal directions for cubic specimens of pelvic trabecular bone [75]. The combined

data made it possible to establish empirical relations between apparent density, calcium

27

equivalent density and elastic modulus for pelvic trabecular bone. Dalstra et al. found

that pelvic trabecular bone stiffness ranged from 100 – 250 MPa when using density as a

primary predictor [75].

Bone exhibits rate-dependent material behavior, suggesting that it a viscoelastic

material [76-79]. Linde and Hvid [78,79] demonstrated that the stiffness of trabecular

bone specimens increased significantly as the loading rate was increased incrementally.

Schoenfeld et al. [80] determined the relaxation of trabecular bone and Zilch et al. [81]

demonstrated the viscoelastic behavior of bone through creep and relaxation tests.

Cartilage Material Properties

Cartilage structure and function was described as early as 1743 when William

Hunter presented the paper “Of the Structure and Disease of Articulating Cartilage” [82].

He described the ability of cartilage to deform under pressure and to regain its original

shape when the pressure was removed. He further described how the collagen fibers

anchored in the underlying bone ran vertically through the cartilage as: “a mass of short

and nearly parallel fibers rising from the bone, and terminating at the external surface of

the cartilage”. Collagen fiber orientation was investigated further in the late 1800’s when

India ink studies demonstrated that cartilage split lines (i.e. path of collagen fiber

alignment) had a tendency to lay parallel to the articulating surface and to extend radially

[83]. Later work confirmed that collagen fibers are oriented nearly perpendicular to the

calcified interface and change orientation gradually until they are nearly parallel to the

articulating surface [84,85].

28

Experimental studies demonstrate that cartilage is an inhomogenous tissue.

Cartilage modulus varies extensively depending on the location on the articulating

surface [86,87] and through the depth [88-92]. In addition, cartilage is stiffer when

loaded along the split line direction compared to perpendicular to this direction [93-97].

Cartilage exhibits a tension-compression nonlinearity wherein cartilage has higher

stiffness values in tension than in compressive [88,89,95,98,99]. It is thought that the

higher stiffness in tension versus compression allows cartilage to resist radial expansion

under axial compressive loading and results in increased fluid pressurization and dynamic

stiffness [93,100-103].

Cartilage is viscoelastic due to its high water content and relative mobility of the

fluid phase relative to the solid phase [104-106]. The equilibrium modulus of cartilage is

very low, on the order of 0.3 – 1.5 MPa [104,107,108], yet contact stresses measured in-

vivo routinely exceed 2.0 MPa [109-111]. Several theories have been proposed to

explain how cartilage can routinely support loads higher than what the solid matrix can

withstand [112]. McCutchen proposed a self pressurizing, “weeping” mechanism

whereby synovial joints are supported mainly by the hydrostatic fluid pressure [113]. In

contrast, some have argued that fluid could flow into the cartilage during loading causing

a “boosting” effect [114]. Nevertheless, because cartilage in the normal joint is ~70%

liquid, which is essentially incompressible, and because the cartilage layers indeed

consolidate under load ~10% [115] it is more likely that fluid flows out of cartilage

layers, corroborating the original “weeping” mechanism [113].

29

Under cyclic loading at physiological frequencies, interstitial fluid pressures

remain elevated [116-118]. The dynamic cartilage modulus under these conditions is

orders of magnitude greater than the equilibrium modulus [117,119-121]. Park et al.

[105] demonstrated the rate response of cartilage tissue samples under load controlled

unconfined compression using frequencies ranging form 0.1 – 40 Hz. Stress strain curves

became markedly steeper, but still nonlinear, at higher loading rates. It was suggested

that the nonlinear stress response of cartilage under loading was in part due to the

tension-compression nonlinearity. Hysteresis (energy dissipation) was reported as zero at

40 Hz and was not substantial at rates higher than 1 Hz. Minimum and maximum moduli

ranged from 14.6 – 65.7 MPa, respectively. These data demonstrate the ability of

cartilage to routinely maintain physiological levels of contact stress [105].

In-Vitro Studies of Hip Joints

In vitro experimental studies have served to elucidate hip biomechanics on the

macro scale. These studies have helped to elucidate plausible modes of failure (e.g.,

during automobile side impacts or femur fracture in the elderly), implications of

prosthetic replacement (e.g., peri-prosthetic bone shielding), and magnitudes of normal

bone and cartilage stresses and strains. Studies with particular relevance to this

dissertation are related to the measurement of bone and cartilage stresses and strains in

intact hips or hips with simulated dysplasia as they provide baseline experimental data

and detail proven methodologies that can be useful when developing and validating

computational models of the hip joint.

30

Several studies have used strain gauges to quantify strains in the pelvis [3,122-

127]. Ries et al. [127] dissected four cadaveric pelvi free of soft tissue and instrumented

each hemipelvis with ten rosette strain gauges to measure normal pelvic strains in-vitro.

Static loading was applied through the intact hip joint to simulate single leg stance. The

medial portion of the pelvis was under tension directed vertically and the lateral ilium

was in compression. This strain pattern was consistent with bending applied to the ilium

from the action of the abductor and joint reaction forces. Finlay et al. [123] subjected

pelvi with 2.5kN of force directed from the femur into the joint. Normal pelvic

maximum principal stresses reached ~12 MPa assuming an elastic modulus of 6.2 MPa

and Poisson’s ratio of 0.3 for cortical bone.

Oh et al. [128] measured the distribution of strain in the proximal femur under

conditions of simulated single-leg stance using strain gauges applied to the cortex.

Strains decreased from proximal to distal in the intact femora under load, and the highest

values were in the calcar area. More recently, Kim et al. [129] affixed strain gauges in

the proximal femur and subjected it to loads of 900 N. Cortical bone strains ranged from

1700 – 2300 µE. In contrast to Oh et al., they found that strain increased from proximal

to distal in the intact femora under load.

Numerous in vitro studies have investigated cartilage hip joint stresses in the

intact hip joint [115,130-138]. These studies used pressure sensitive film [130,134-136],

piezoelectric sensors [131,132], or instrumented prostheses [115,133,137,138]. Pressure

sensitive film is often the measurement technique of choice as it is inexpensive,

accommodates various geometries when cut (i.e. spherical femoral heads), and has

31

proven to be reasonably accurate (± 10% error, [139]). Using pressure sensitive film, von

Eisenhart-Rothe measured peak contact stresses of ~9 MPa in intact femoral heads when

loaded directly into the acetabulum at 300% bodyweight [134,135]. Adams et al.

implanted eleven piezoelectric pressure transducers through the bone of the acetabulum

[132]. Maximum pressure ranged from 4.93 to 9.57 MPa at the interface between

acetabular cartilage and subchondral bone, suggesting that high cartilage stresses are

likely to occur throughout the thickness of hyaline cartilage in the hip joint.

Brown et al. [133] measured the time variant distributions of intra-articular

contact stress from direct measurement of seventeen grossly normal fresh cadaveric hips.

Local stresses were sensed by arrays of 24 compliant miniature transducers inset

superficially in the femoral head cartilage. Contact stress magnitude was usually found

to rise nearly linearly with applied joint loads in excess of about 1000 N. The sites of

maximum local stress were found to underlie the general region of the acetabular dome.

For a resultant joint load of 2700 N, the spatial mean contact stress and peak local contact

stress averaged 2.92 MPa and 8.80 MPa, respectively. The full contact stress patterns

were irregular and complex, but most commonly the general feature was a central band or

“ridge” of pressure elevation, oriented in an approximately anterior-to-posterior direction.

Rushfeldt et al. [138] measured the in vitro distribution of pressure on the cartilage

surface of the human acetabulum using a modified endoprosthesis with fourteen integral

pressure transducers. Peak pressures at 2250 N of load were ~11 MPa and decreased

with time while the contact area increased. The pressure distribution was neither uniform

nor axisymmetric about the load vector. It was concluded that the highly irregular

32

pressure profiles observed are due primarily to cartilage thickness distribution and

irregularities at the calcified cartilage interface. Macirowski et al. [115] used a similar

prosthesis to measure the total surface on acetabular cartilage when step-loaded by an

instrumented hemiprosthesis. Using a combined experimental and computational

protocol they found that, even after long-duration application of physiological force, fluid

pressure supported nearly 90% of the load within the cartilage network stresses. Their

results provided further support for the “weeping” mechanism proposed by McCuthen

[113].

One limitation of experimental studies is that measurements of stress and strain

are only obtained at the location of the sensing device. Therefore, a priori knowledge is

required to place sensors in meaningful positions. However, for studying specific

disorders this information may be unknown. Another limitation is that to analyze

individual disorders such as hip OA and dysplasia one would need to obtain cadaveric

specimens that exhibited the pathology of interest. Given the challenges of obtaining

donor tissue this task would be a very difficult, if not impossible endeavor. Based on

these limitations, in vitro experimentation may not be the most appropriate technique for

the study of specific hip pathologies.

In-Vivo Studies of Hip Joints

No known methods exist to measure pelvic and femoral bone strains in-vivo.

However, a considerable amount of work has been devoted to measuring hip joint contact

pressures and joint reaction forces using instrumented prostheses. Carlson et al. [140]

was one of the first to describe the development of a radio telemetrized femoral

33

prosthesis in 1974. In 1985 Hodge et al. [111] implanted a prosthesis into a patient and

measured contact stress at 10 discrete locations. Data were acquired during surgery,

recovery, rehabilitation, and normal activity, for longer than 1 year after surgery.

Pressure magnitudes were synchronized with body-segment kinematic data and foot-floor

force measurements to locate transduced pressure areas on the natural acetabulum and to

correlate movement kinematics and dynamics with local cartilage pressures. The data

revealed very high local (up to 18 MPa) and non-uniform pressures, with abrupt spatial

and temporal gradients.

More recently, Bergmann et al. implanted similar prostheses in 5 patients who

underwent THA surgery for treatment of hip OA [109,110]. Gait analysis was performed

on each patient and contact pressure data and equivalent joint reaction force were

evaluated in parallel with joint kinematics during a variety of daily activities such as

walking, stair climbing, descending stairs, and rising from a chair. Joint reaction forces

were as high as 5.5 times bodyweight when the subjects rose from a chair, but were

generally lower (2.5 times bodyweight) during walking, stair climbing, and descending

stairs. Their data also suggested that contact stresses and joint reaction forces correlated

well with foot-floor force measurements and demonstrated large inter-subject variation in

contact stresses, joint reaction forces and joint kinematics.

Data from instrumented prostheses have yielded contact pressure data that are

consistent with experimental studies, suggesting that this technique has the ability to

accurately measure hip joint mechanics in vivo. However, the procedure is invasive and

limited to a small sample of patients who have already undergone treatment to correct

34

OA. In addition, the technique is limited to the measurement of joint reaction forces

associated with implant contact mechanics rather than cartilage stresses [141]. Finally, as

with in vitro studies, data from instrumented prostheses only yield mechanical estimates

at the contact site rather than an estimate of the mechanics throughout the joint, which

may play a vital role in the development and progression of diseases such as OA and hip

dysplasia.

35

NUMERICAL MODELING OF HIP JOINT BIOMECHANICS

Analytical Modeling of the Hip Joint

Analytical approaches to predicting hip joint biomechanics generally use the

equations of statics to solve for resultant joint reaction forces. For clarity, “analytical”

studies will be described herein as those that can be solved using simplified mathematical

equations that do not require discretization of geometry or stipulation of material

properties. Several analytical models have been developed to estimate hip joint

mechanics [29,142-145]. In previous efforts, the geometry of the acetabulum and femur

was assumed spherical by calculating the average radius of the femur and acetabulum by

measuring 2-D radiographs [29,142-145]. The equivalent joint reaction force was

estimated by summing zero a vertical body force (generally 5/6 bodyweight) and non-

vertical abductor muscle force. Contact pressures were found by distributing the force

over the estimated area.

Two analytical models have been developed to compare mechanics between

normal joints and those affected by acetabular dysplasia [29,142]. Mavcic et al. used a

mathematical model of static, single-leg stance based on AP radiographs of normal and

dysplastic subjects [142]. Dysplastic hips had significantly larger peak contact stresses

than healthy hips (7.1 kPa/N and 3.5 kPa/N, respectively). Michaeli and co-workers also

demonstrated notable differences in the location and magnitude of contact stresses

between normal cadaveric pelvi and plastic pelvi with simulated dysplasia [29].

Although these studies further support the notion of pathological biomechanics

and in particular increased contact stresses in the dysplastic hip, they neglected several

36

important aspects of the biomechanics. For example, idealized geometry was used to

represent all or part of the hip articulation, neglecting the issues of regional and patient-

specific congruency between the femoral and acetabular cartilage layers. Ignoring

cartilage geometry and assuming joints to be concentric likely lead to erroneous estimates

(underestimation) of contact pressure.

Computational Modeling of the Hip Joint

For clarity, “computational” models will be described as a subclass of numerical

models, which requires the geometry of interest to be discretized into smaller

mathematical problems. Constitutive equations and boundary conditions also must be

stipulated during the development of a computational model. The use of computational

modeling is an attractive method for studying hip joint biomechanics. Computer models

have the ability to predict bone and cartilage stresses and strains throughout the

continuum of interest rather than at select measurement locations. With the advent and

availability of medical imaging techniques, individual patient models can be developed

by segmenting image data, which contains detailed geometry and estimates of mechanical

properties. Therefore, gross simplifying assumptions regarding hip joint geometry (i.e.

spherical geometry, concentric articulation of cartilage) are not necessary. Finally, with

the exception of radiation exposure during CT, computational models can be developed

noninvasively using living subjects, allowing the analysis of individual patients.

37

Constitutive Models for Bone and Cartilage

Besides providing insight into the contribution of different tissue components to

overall tissue material behavior, constitutive models are necessary to represent the

properties of tissue in computational models. Constitutive equations with particular

relevance to this dissertation will be discussed further.

Although viscoelastic, bone can be considered as an elastic material for many

applications [146]. Therefore, under the assumptions associated with linearized

elasticity, the material behavior is characterized by a fourth-order elasticity tensor C in

the generalized Hooke’s law that relates the Cauchy stress T to the infinitesimal strain

tensor ε :

: ij ijkl klT ε= ⇔ =T ε CC . (1.1)

In its most general form, the elasticity tensor involves 21 independent elastic coefficients

that must be determined experimentally. In the case of orthotropy, three orthogonal

planes of symmetry exist, leaving nine independent coefficients. The number of

independent elastic coefficients is reduced further to five for the case of transverse

isotropy and to two for the case of isotropy.

Cartilage has been modeled as isotropic-elastic [147], isotropic biphasic [99,148],

transversely isotropic biphasic [149], poroviscoelastic [150], and as a fibril reinforced

poroelastic material [103]. When cartilage is loaded instantaneously, the response is

equivalent to that of an incompressible material [99,102,148,151-154]. In such instances

the use of a linearized elastic constitutive model may be appropriate. However, the

accuracy of model predictions will degrade as strains increase since the assumption of

38

infinitesimal strain results in spurious strains when the continuum undergoes rigid

rotations. Hyperelasticity is based on the existence of a strain energy potential, which

generally results in a nonlinear relationship between stress and strain. Poroelastic

constitutive models describe the relative contributions of solid and fluid phases to the

overall material behavior of cartilage. They were originally developed to describe the

mechanics of soils [155,156] and were extended to cartilage using the biphasic theory

developed by Mow et al. [99].

Finite Element Modeling of Hip Joint Biomechanics

The finite element (FE) method is a proven technique that has been used

extensively to evaluate biomechanical systems. The FE method allows an analyst to

obtain a solution for the stress and strain distribution throughout a continuum when the

applied loads, boundary conditions and material properties are known. FE model

construction can be divided into three distinct steps: 1) pre-processing, 2) stipulation of

boundary and loading conditions, and 3) analysis and post-processing. Pre-processing

involves discretization of the geometry of interest into small finite elements and has

historically been the most challenging aspect when constructing FE models of human

joints. However, with the development of commercial segmentation programs this task

has become much less daunting as the process is generally automated [157,158]. Next,

loading and boundary conditions are applied to the model to govern displacements of

individual elements. Constitutive equations and associated material coefficients are

specified data. The discretized equations of motion, based on minimization of potential

energy, are solved to obtain the displacement field. Strains and then stresses are

39

computed from the displacement field. Finally, model predictions are post-processed to

facilitate visualization and data analysis.

A few 3D FE models have been developed to predict bone strains in intact hips

[3,159,160]. Oonishi et al. used measurements from a 3D coordinate measuring machine

to generate contours of the horizontal sections of the iliac bone. An FE mesh of the

pelvis was constructed using these contours. Simulated muscle forces and bodyweight

were applied. Peak cortical bone von-Mises stresses were well below 1 MPa. However,

they apparently made a mistake in calculating the magnitude of load from kgf to N

whereby instead of multiply by 9.8, they divided by 9.8, making their results almost a

factor of 100 too small [3]. Dalstra et al. [3] used CT image data to develop a realistic

3D model of the human pelvis. Cortical bone was assigned a spatially varying thickness,

based on measurements from CT image data. Strain gauges were attached to a pelvis to

experimentally measure cortical bone strains. FE predictions of cortical bone stress were

compared to those measured on the cadaveric pelvis for purposes of validating the model.

FE predictions of von-Mises stress were on the order of ±4 MPa and were in fair

agreement with experimental data although no statistical tests were conducted to quantify

model accuracy.

Nearly all FE hip joint modeling studies that have analyzed cartilage contact have

used two-dimensional, plane strain models [115,161-163] with either rigid [115,161] or

deformable bones [162,163]. The earliest FE contact model was reported by Brown and

DiGioia [162]. In this study predicted pressures were irregularly distributed over the

surface of the femoral head with values of peak pressure on the order of 4 MPa.

40

Rapperport et al. [163] developed a similar model based on geometry from a radiograph,

assuming femoral acetabular surfaces to be spherical and congruent. At 1000 N of

applied load peak, pressures were on the order of 5 MPa and a rather uniform contact

distribution was observed. Rigid bone models yielded predictions only slightly different

than the deformable bone model.

Macirowski et al. [115] utilized a combined experimental/analytical approach to

model fluid flow and matrix stresses in a biphasic contact model of a cadaveric

acetabulum. This is the only FE study to date to explicitly model the acetabular cartilage

thickness. The acetabulum was step loaded to 900 N using an instrumented femoral

prosthesis. At the instant load was applied peak contact pressures measured by the

prosthesis were on the order of 5 MPa. When the experimentally measured total surface

stress was applied to the FE model average predicted pressures (solid stress + fluid

pressures) were approximately 1.75 MPa. An important conclusion made in this study

was that even small variations in sphericity (up to 0.2 mm) likely influenced the cartilage

sealing process since during early step loading high local maxima and irregular, steep

pressure gradients were measured. This argument parallels that made by Rushfeldt et al.

who concluded that the highly irregular pressure profiles observed during an

instrumented prosthesis in-vitro study were likely due to the cartilage thickness

distribution and irregularities at the calcified cartilage interface [138].

With the exception of Macirowski’s study, it is evident that the cartilage contact

FE models developed thus far have a tendency to predict lower contact pressures when

compared to in-vitro studies that have loaded cadaveric joints with similar forces. The

41

discrepancy between predictions is most likely attributed to the fact that prior

computational studies assumed spherical geometry and concentric articulation. Although

the computational modeling literature suggests that normal joints may be modeled as

spherical structures with concentric articulation [164,165], it has been well documented

that the hip joint is neither spherical nor has cartilage with uniform thickness

[9,115,135,166,167].

Very recently patient-specific FE models have been developed to elucidate the

biomechanics of dysplastic hip joints [168]. Russell et al. [168] constructed patient-

specific, non-linear, contact FE models using CT arthrography image data. A normal

model was also generated which was based on geometry from the Visible Human Project

[169]. Peak contact pressures for dysplastic and asymptomatic hips (contra-lateral joints)

ranged from 3.56 – 9.88 MPa. There were significant differences between the normal

control and the asymptomatic hips and a trend towards significance between

asymptomatic and symptomatic joints. They concluded that bone irregularities caused

localized pressure elevations and that asymptomatic hips had pathological mechanics.

While these models represent the current state of the art for modeling patient-specific hip

joint contact mechanics it remains unknown if the predictions were accurate as the

computational modeling protocol was not validated.

Discrete Element Analysis

Discrete element analysis (DEA) (a variant of the FE method) has been used to

analyze hip joint contact mechanics [164,170,171]. Cartilage layers were represented

using a series of discrete compressive spring elements and tangential shear elements.

42

Yoshida et al. [171] developed a dynamic DEA model to investigate the distribution of

hip joint contact pressures using in-vivo data from the literature. The model assumed

spherical geometry for the femur and acetabulum and concentric articulation. Peak

pressures during simulated walking, descending stairs, and stair climbing were relatively

low in comparison to previous experimental measurements. In a similar study Genda et

al. [170] generated 3D contact hip DEA models using 2-D radiographs by assuming that

the femoral head and the acetabular surface were spherical in shape. They determined

that the joint contact area and normalized peak contact pressure were significantly

different between men and women. The normalized peak contact pressure was around 1.5

MPa, which again was substantially lower than experimental data form the literature

under similar loading conditions. For certain limited instances, DEA may be effective

[172]. However, because direct experimental validation has not been performed for this

technique, it is unclear whether or not DEA has the ability to accurately predict hip joint

contact mechanics. Furthermore, gross simplifying assumptions are made using this

technique (e.g. generation of 3D models from 2D radiographs), which provides an

explanation of why DEA estimates of peak pressure substantially underestimate peak

pressure when compared to experimental data.

43

REFERENCES

[1] Gray, H., 1918, Gray's Anatomy of the Human Body, 20 ed. Lea and Febiger,

Philadelphia. [2] Gore, D. R., Murray, M. P., Gardner, G. M., and Sepic, S. B., 1977,

"Roentgenographic Measurements after Muller Total Hip Replacement. Correlations among Roentgenographic Measurements and Hip Strength and Mobility," J Bone Joint Surg Am, 59, pp. 948-53.

[3] Dalstra, M., Huiskes, R., and van Erning, L., 1995, "Development and Validation

of a Three-Dimensional Finite Element Model of the Pelvic Bone," J Biomech Eng, 117, pp. 272-8.

[4] Ericksen, M. F., 1982, "Aging Changes in Thickness of the Proximal Femoral

Cortex," Am J Phys Anthropol, 59, pp. 121-30. [5] 2002, Mechanobiology: Cartilage and Chondrocyte vol. 2. IOS, Amsterdam, The

Netherlands. [6] 2004, Articular Cartilage Lesions- a Practical Guide to Assessment and

Treatment, vol. XIII. Springer New York, NY. [7] Mow, V. C. and Ratcliffe, A., 1997, "Structure and Function of Articular

Cartilage and Meniscus," in Basic Orthopaedic Biomechanics, V. C. Mow and W. C. Hayes, Eds. Lippincott-Raven, Philadelphia, pp. 113-177.

[8] Maroudas, A., 1979, "Physicochemical Properties of Articular Cartilage," in

Adult Articular Cartilage, M. A. Freeman, Ed. Pitman Medical, London, pp. 215-290.

[9] Shepherd, D. E. and Seedhom, B. B., 1999, "Thickness of Human Articular

Cartilage in Joints of the Lower Limb," Ann Rheum Dis, 58, pp. 27-34. [10] Ferguson, S. J., Bryant, J. T., Ganz, R., and Ito, K., 2003, "An in Vitro

Investigation of the Acetabular Labral Seal in Hip Joint Mechanics," J Biomech, 36, pp. 171-8.

[11] Felson, D. T., Lawrence, R. C., and Dieppe, P. A., 2000, "Osteoarthritis: New

Insights. Part I the Diease and Its Risk Factors," Ann Internal Med, 133, pp. 635-646.

44

[12] Callaghan, J. J., Rosenberg, A. G., and Rubash, H. E., 2007, The Adult Hip, vol. I, 2nd ed. Lippincott Williams and Wilkins, Philadelphia, PA.

[13] Radin, E. L., Burr, D. B., Caterson, B., Fyhrie, D., Brown, T. D., and Boyd, R. D.,

1991, "Mechanical Determinants of Osteoarthrosis," Semin Arthritis Rheum, 21, pp. 12-21.

[14] Radin, E. L., 1995, "Osteoarthrosis--the Orthopedic Surgeon's Perspective," Acta

Orthop Scand Suppl, 266, pp. 6-9. [15] Hardingham, T. and Bayliss, M., 1990, "Proteoglycans of Articular Cartilage:

Changes in Aging and in Joint Disease," Semin Arthritis Rheum, 20, pp. 12-33. [16] Heliovaara, M., Makela, M., Impivaara, O., Knekt, P., Aromaa, A., and Sievers,

K., 1993, "Association of Overweight, Trauma and Workload with Coxarthrosis. A Health Survey of 7,217 Persons," Acta Orthop Scand, 64, pp. 513-8.

[17] Anderson, J. J. and Felson, D. T., 1988, "Factors Associated with Osteoarthritis of

the Knee in the First National Health and Nutrition Examination Survey (Hanes I). Evidence for an Association with Overweight, Race, and Physical Demands of Work," Am J Epidemiol, 128, pp. 179-89.

[18] Felson, D. T., 1994, "Do Occupation-Related Physical Factors Contribute to

Arthritis?," Baillieres Clin Rheumatol, 8, pp. 63-77. [19] Radin, E. L., Martin, R. B., Burr, D. B., Caterson, B., Boyd, R. D., and Goodwin,

C., 1984, "Effects of Mechanical Loading on the Tissues of the Rabbit Knee," J Orthop Res, 2, pp. 221-34.

[20] Buckwalter, J. A., 1995, "Osteoarthritis and Articular Cartilage Use, Disuse, and

Abuse: Experimental Studies," J Rheumatol Suppl, 43, pp. 13-5. [21] Jeffrey, J. E., Gregory, D. W., and Aspden, R. M., 1995, "Matrix Damage and

Chondrocyte Viability Following a Single Impact Load on Articular Cartilage," Arch Biochem Biophys, 322, pp. 87-96.

[22] Setton, L. A., Mow, V. C., Muller, F. J., Pita, J. C., and Howell, D. S., 1994,

"Mechanical Properties of Canine Articular Cartilage Are Significantly Altered Following Transection of the Anterior Cruciate Ligament," J Orthop Res, 12, pp. 451-63.

[23] Atkinson, T. S., Haut, R. C., and Altiero, N. J., 1998, "An Investigation of

Biphasic Failure Criteria for Impact-Induced Fissuring of Articular Cartilage," J Biomech Eng, 120, pp. 536-7.

45

[24] Atkinson, T. S., Haut, R. C., and Altiero, N. J., 1998, "Impact-Induced Fissuring of Articular Cartilage: An Investigation of Failure Criteria," J Biomech Eng, 120, pp. 181-7.

[25] Loening, A. M., James, I. E., Levenston, M. E., Badger, A. M., Frank, E. H.,

Kurz, B., Nuttall, M. E., Hung, H. H., Blake, S. M., Grodzinsky, A. J., and Lark, M. W., 2000, "Injurious Mechanical Compression of Bovine Articular Cartilage Induces Chondrocyte Apoptosis," Arch Biochem Biophys, 381, pp. 205-12.

[26] AAOS, A. A. o. O. S., 2007,"Questions and Answers About Hip Replacement,"

National Institute of Arthritis and Musculoskeletal and Skin Disorders. [27] AAOS, A. A. o. O. S., 2007,"Hip Implants," American Academy of Orthopaedic

Surgeons AAOS. [28] Morrissy, R. T., 1991, "Congenital Dislocation of the Hip," in The Hip and Its

Disorders, M. E. Steinberg, Ed. WB Saunders, Philadelphia, PA. [29] Michaeli, D. A., Murphy, S. B., and Hipp, J. A., 1997, "Comparison of Predicted

and Measured Contact Pressures in Normal and Dysplastic Hips," Med Eng Phys, 19, pp. 180-6.

[30] Cooperman, D. R., Wallensten, R., and Stulberg, S. D., 1983, "Acetabular

Dysplasia in the Adult," Clin Orthop, pp. 79-85. [31] Bombelli, R., 1983, Osteoarthritis of the Hip. Springer-Verlag, Berlin, Germany. [32] Nozawa, M., Shitoto, K., Matsuda, K., Maezawa, K., and Kurosawa, H., 2002,

"Rotational Acetabular Osteotomy for Acetabular Dysplasia. A Follow-up for More Than Ten Years," J Bone Joint Surg Br, 84, pp. 59-65.

[33] Peters, C. L., Fukushima, B. W., Park, T. K., Coleman, S. S., and Dunn, H. K.,

2001, "Triple Innominate Osteotomy in Young Adults for the Treatment of Acetabular Dysplasia: A 9-Year Follow-up Study," Orthopedics, 24, pp. 565-9.

[34] Sanchez-Sotelo, J., Trousdale, R. T., Berry, D. J., and Cabanela, M. E., 2002,

"Surgical Treatment of Developmental Dysplasia of the Hip in Adults: I. Nonarthroplasty Options," J Am Acad Orthop Surg, 10, pp. 321-33.

[35] Takatori, Y., 2001, "Bernese Periacetabular Osteotomy," Clin Orthop, pp. 245-6. [36] Takatori, Y., Ninomiya, S., Nakamura, S., Morimoto, S., Moro, T., and Nagai, I.,

2000, "Long-Term Results of Rotational Acetabular Osteotomy in Young Patients with Advanced Osteoarthrosis of the Hip," J Orthop Sci, 5, pp. 336-41.

46

[37] Siebenrock, K. A., Leunig, M., and Ganz, R., 2001, "Periacetabular Osteotomy: The Bernese Experience," Instr Course Lect, 50, pp. 239-45.

[38] Bircher, M. D., 1999, "Retroversion of the Acetabulum," J Bone Joint Surg Br,

81, pp. 743-4. [39] Kim, W. Y., Hutchinson, C. E., Andrew, J. G., and Allen, P. D., 2006, "The

Relationship between Acetabular Retroversion and Osteoarthritis of the Hip," J Bone Joint Surg Br, 88, pp. 727-9.

[40] Harris, W. H., 1986, "Etiology of Osteoarthritis of the Hip," Clin Orthop, pp. 20-

33. [41] Stulberg, S. D. and Harris, W. H., "Acetabular Dysplasia and Development of

Osteoarthritis of the Hip," presented at Proceedings of the second open scientific meeting of the Hip Society, St Louis, MO, 1974.

[42] Solomon, L., 1976, "Patterns of Osteoarthritis of the Hip," J Bone Joint Surg Br,

58, pp. 176-83. [43] Murray, R. O., 1965, "The Aetiology of Primary Osteoarthritis of the Hip," Br J

Radiol, 38, pp. 810-24. [44] Wilson, M. G. and Poss, R., 1992, "Osteoarthritis: Diagnosis and

Medical/Surgical Treatment," R. W. Moskowitz, D. S. Howell, V. M. Goldberg, and H. J. Mankin, Eds. WB Saunders, Philadelphia, pp. 621-50.

[45] Croft, P., Cooper, C., Wickham, C., and Coggon, D., 1991, "Osteoarthritis of the

Hip and Acetabular Dysplasia," Ann Rheum Dis, 50, pp. 308-10. [46] Ali-Gombe, A., Croft, P. R., and Silman, A. J., 1996, "Osteoarthritis of the Hip

and Acetabular Dysplasia in Nigerian Men," J Rheumatol, 23, pp. 512-5. [47] Croft, P., Cooper, C., Wickham, C., and Coggon, D., 1992, "Is the Hip Involved

in Generalized Osteoarthritis?," Br J Rheumatol, 31, pp. 325-8. [48] Inoue, K., Wicart, P., Kawasaki, T., Huang, J., Ushiyama, T., Hukuda, S., and

Courpied, J., 2000, "Prevalence of Hip Osteoarthritis and Acetabular Dysplasia in French and Japanese Adults," Rheumatology (Oxford), 39, pp. 745-8.

[49] Lau, E. M., Lin, F., Lam, D., Silman, A., and Croft, P., 1995, "Hip Osteoarthritis

and Dysplasia in Chinese Men," Ann Rheum Dis, 54, pp. 965-9.

47

[50] Wertheim, G., 1847, "Memoire Sur Pelasticite Et Al Cohesion Des Principaux Tissus Du Corps Humain," Am. de Chim et de Phys, 21, pp. 385-414.

[51] Wolff, J., 1892, Das Gesetz Der Transformation Der Knochen. Hirschwald,

Berlin. [52] Dempster, W. T. and Liddicoat, R. T., 1952, "Compact Bone as a Non-Isotropic

Material," Am J Anat, 91, pp. 331-62. [53] Evans, F. G. and Vincentelli, R., 1969, "Relation of Collagen Fiber Orientation to

Some Mechanical Properties of Cortical Bone," J Biomech, 2, pp. 63-71. [54] Evans, F. G. and Bang, S., 1966, "Physical and Histological Differences between

Human Fibular and Femoral Compact Bone," in Studies of the Anatomy and Function of Bone and Joints, F. G. Evans, Ed. Springer, Berlin, pp. 142-155.

[55] Lang, S. B., 1970, "Ultrasonic Method for Measuring Elastic Coefficients of Bone

and Results on Fresh and Dried Bovine Bones," IEEE Trans Biomed Eng, 17, pp. 101-5.

[56] Lang, S. B., 1969, "Elastic Coefficients of Animal Bone," Science, 165, pp. 287-

8. [57] Van Buskirk, W. C. and Ashman, R. B., 1981, "The Elastic Moduli of Bone," in

Mechanical Properties of Bone, vol. AMD 36, S. C. Cowin, Ed. ASME, New York, NY, pp. 131-143.

[58] Katz, J. L., Yoon, H. S., Lipson, S., Maharidge, R., Meunier, A., and Christel, P.,

1984, "The Effects of Remodeling on the Elastic Properties of Bone," Calcif Tissue Int, 36 Suppl 1, pp. S31-6.

[59] Zioupos, P., Currey, J. D., Mirza, M. S., and Barton, D. C., 1995, "Experimentally

Determined Microcracking around a Circular Hole in a Flat Plate of Bone: Comparison with Predicted Stresses," Philos Trans R Soc Lond B Biol Sci, 347, pp. 383-96.

[60] Reilly, D. T. and Burstein, A. H., 1975, "The Elastic and Ultimate Properties of

Compact Bone Tissue," J Biomech, 8, pp. 393-405. [61] Yoon, H. S. and Katz, J. L., 1976, "Ultrasonic Wave Propagation in Human

Cortical Bone--Ii. Measurements of Elastic Properties and Microhardness," J Biomech, 9, pp. 459-64.

48

[62] Ashman, R. B., Cowin, S. C., Van Buskirk, W. C., and Rice, J. C., 1984, "A Continuous Wave Technique for the Measurement of the Elastic Properties of Cortical Bone," J Biomech, 17, pp. 349-61.

[63] Yang, G., Kabel, J., van Rietbergen, B., Odgaard, A., Huiskes, R., and Cowin, S.

C., 1998, "The Anisotropic Hooke's Law for Cancellous Bone and Wood," J Elast, 53, pp. 125-46.

[64] Wirtz, D. C., Schiffers, N., Pandorf, T., Radermacher, K., Weichert, D., and Forst,

R., 2000, "Critical Evaluation of Known Bone Material Properties to Realize Anisotropic Fe-Simulation of the Proximal Femur," J Biomech, 33, pp. 1325-30.

[65] Carter, D. R., Orr, T. E., and Fyhrie, D. P., 1989, "Relationship between Loading

History and Femoral Cancellous Bone Architecture," J Biomech, 22, pp. 231-244. [66] Pauwels, F., 1980, Biomechanics of the Locomotor Apparatus. Springer, Berlin. [67] Hayes, W. E. and Snyder, B. D., 1981, "Toward a Quantitative Formulation for

Wolff's Law in Trabecular Bone," in Mechanical Properties of Bone, vol. AMD Vol 45, S. C. Cowin, Ed. ASME, New York, NY, pp. 43-68.

[68] Chalmers, J. and Weaver, J. K., 1966, "Cancellous Bone: Its Strength and

Changes with Aging and an Evaluation of Some Methods for Measuring Its Mineral Content.Ii. An Evaluation of Some Methods for Measuring Osteoporosis," J Bone Joint Surg Am, 48, pp. 299-308.

[69] Beaupre, G. S., Orr, T. E., and Carter, D. R., 1990, "An Approach for Time-

Dependent Bone Modeling and Remodeling-Application: A Preliminary Remodeling Simulation," J Orthop Res, 8, pp. 662-70.

[70] Beaupre, G. S., Orr, T. E., and Carter, D. R., 1990, "An Approach for Time-

Dependent Bone Modeling and Remodeling--Theoretical Development," J Orthop Res, 8, pp. 651-61.

[71] Carter, D. R., Fyhrie, D. P., and Whalen, R. T., 1987, "Trabecular Bone Density

and Loading History: Regulation of Connective Tissue Biology by Mechanical Energy," J Biomech, 20, pp. 785-94.

[72] Huiskes, R., Weinans, H., Grootenboer, H. J., Dalstra, M., Fudala, B., and Slooff,

T. J., 1987, "Adaptive Bone-Remodeling Theory Applied to Prosthetic-Design Analysis," J Biomech, 20, pp. 1135-50.

[73] Jacobs, C. R., 1994,"Numerical Simulation of Bone Adaptation to Mechanical

Loading," Stanford University.

49

[74] Weinans, H., Huiskes, R., and Grootenboer, H. J., 1992, "The Behavior of Adaptive Bone-Remodeling Simulation Models," J Biomech, 25, pp. 1425-41.

[75] Dalstra, M., Huiskes, R., Odgaard, A., and van Erning, L., 1993, "Mechanical and

Textural Properties of Pelvic Trabecular Bone," J Biomech, 26, pp. 523-35. [76] Carter, D. R. and Hayes, W. C., 1977, "The Compressive Behavior of Bone as a

Two-Phase Porous Structure," J Bone Joint Surg Am, 59, pp. 954-62. [77] Ducheyne, P., Heymans, L., Martens, M., Aernoudt, E., de Meester, P., and

Mulier, J. C., 1977, "The Mechanical Behaviour of Intracondylar Cancellous Bone of the Femur at Different Loading Rates," J Biomech, 10, pp. 747-62.

[78] Linde, F., 1994, "Elastic and Viscoelastic Properties of Trabecular Bone by a

Compression Testing Approach," Dan Med Bull, 41, pp. 119-38. [79] Linde, F., Norgaard, P., Hvid, I., Odgaard, A., and Soballe, K., 1991, "Mechanical

Properties of Trabecular Bone. Dependency on Strain Rate," J Biomech, 24, pp. 803-9.

[80] Schoenfeld, C. M., Lautenschlager, E. P., and Meyer, P. R., Jr., 1974,

"Mechanical Properties of Human Cancellous Bone in the Femoral Head," Med Biol Eng, 12, pp. 313-7.

[81] Zilch, H., Rohlmann, A., Bergmann, G., and Kolbel, R., 1980, "Material

Properties of Femoral Cancellous Bone in Axial Loading. Part Ii: Time Dependent Properties," Arch Orthop Trauma Surg, 97, pp. 257-62.

[82] Hunter, W., 1743, "Of the Structure and Diseases of Articulating Cartilages,"

Philosophical Transactions, 42, pp. 514-521. [83] Hultkranz, J. W., 1898, "Uber Die Spaltrichtungen Der Gelenkknorpel," Verh

Anat Ges, 12, pp. 248-256. [84] Meachim, G., Denham, D., and Emery, I. H., 1974, "Collagen Alignments and

Artificial Splits at the Surfaces of Human Articular Cartilage," J Anat, 118, pp. 101-118.

[85] Meachim, G. and Stockwell, R. A., 1979, "The Matrix," in Adult Articular

Cartilage, M. A. R. Freeman, Ed., 2nd ed. Pitman, London, pp. 1-67. [86] Athanasiou, K. A., Agarwal, A., and Dzida, F. J., 1994, "Comparative Study of

the Intrinsic Mechanical Properties of the Human Acetabular and Femoral Head Cartilage," J Orthop Res, 12, pp. 340-9.

50

[87] Shepherd, D. E. and Seedhom, B. B., 1999, "The 'Instantaneous' Compressive Modulus of Human Articular Cartilage in Joints of the Lower Limb," Rheumatology (Oxford), 38, pp. 124-32.

[88] Akizuki, S., Mow, V. C., Muller, F., Pita, J. C., Howell, D. S., and Manicourt, D.

H., 1986, "Tensile Properties of Human Knee Joint Cartilage: I. Influence of Ionic Conditions, Weight Bearing, and Fibrillation on the Tensile Modulus," J Orthop Res, 4, pp. 379-92.

[89] Kempson, G. E., Freeman, M. A., and Swanson, S. A., 1968, "Tensile Properties

of Articular Cartilage," Nature, 220, pp. 1127-8. [90] Schinagl, R. M., Gurskis, D., Chen, A. C., and Sah, R. L., 1997, "Depth-

Dependent Confined Compression Modulus of Full-Thickness Bovine Articular Cartilage," J Orthop Res, 15, pp. 499-506.

[91] Wang, C. C., Chahine, N. O., Hung, C. T., and Ateshian, G. A., 2003, "Optical

Determination of Anisotropic Material Properties of Bovine Articular Cartilage in Compression," J Biomech, 36, pp. 339-53.

[92] Wang, C. C., Deng, J. M., Ateshian, G. A., and Hung, C. T., 2002, "An

Automated Approach for Direct Measurement of Two-Dimensional Strain Distributions within Articular Cartilage under Unconfined Compression," J Biomech Eng, 124, pp. 557-67.

[93] Huang, C. Y., Stankiewicz, A., Ateshian, G. A., and Mow, V. C., 2005,

"Anisotropy, Inhomogeneity, and Tension-Compression Nonlinearity of Human Glenohumeral Cartilage in Finite Deformation," J Biomech, 38, pp. 799-809.

[94] Kempson, G. E., Muir, H., Pollard, C., and Tuke, M., 1973, "The Tensile

Properties of the Cartilage of Human Femoral Condyles Related to the Content of Collagen and Glycosaminoglycans," Biochim Biophys Acta, 297, pp. 456-72.

[95] Roth, V. and Mow, V. C., 1980, "The Intrinsic Tensile Behavior of the Matrix of

Bovine Articular Cartilage and Its Variation with Age," J Bone Joint Surg Am, 62, pp. 1102-17.

[96] Woo, S. L., Akeson, W. H., and Jemmott, G. F., 1976, "Measurements of

Nonhomogeneous, Directional Mechanical Properties of Articular Cartilage in Tension," J Biomech, 9, pp. 785-91.

[97] Woo, S. L., Lubock, P., Gomez, M. A., Jemmott, G. F., Kuei, S. C., and Akeson,

W. H., 1979, "Large Deformation Nonhomogeneous and Directional Properties of Articular Cartilage in Uniaxial Tension," J Biomech, 12, pp. 437-46.

51

[98] Armstrong, C. G. and Mow, V. C., 1982, "Variations in the Intrinsic Mechanical Properties of Human Articular Cartilage with Age, Degeneration, and Water Content," J Bone Joint Surg Am, 64, pp. 88-94.

[99] Mow, V. C., Kuei, S. C., Lai, W. M., and Armstrong, C. G., 1980, "Biphasic

Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments," J Biomech Eng, 102, pp. 73-84.

[100] Cohen, B., Lai, W. M., and Mow, V. C., 1998, "A Transversely Isotropic Biphasic

Model for Unconfined Compression of Growth Plate and Chondroepiphysis," J Biomech Eng, 120, pp. 491-6.

[101] Fortin, M., Soulhat, J., Shirazi-Adl, A., Hunziker, E. B., and Buschmann, M. D.,

2000, "Unconfined Compression of Articular Cartilage: Nonlinear Behavior and Comparison with a Fibril-Reinforced Biphasic Model," J Biomech Eng, 122, pp. 189-95.

[102] Soltz, M. A. and Ateshian, G. A., 2000, "A Conewise Linear Elasticity Mixture

Model for the Analysis of Tension-Compression Nonlinearity in Articular Cartilage," J Biomech Eng, 122, pp. 576-86.

[103] Soulhat, J., Buschmann, M. D., and Shirazi-Adl, A., 1999, "A Fibril-Network-

Reinforced Biphasic Model of Cartilage in Unconfined Compression," J Biomech Eng, 121, pp. 340-7.

[104] Jurvelin, J., Kiviranta, I., Arokoski, J., Tammi, M., and Helminen, H. J., 1987,

"Indentation Study of the Biochemical Properties of Articular Cartilage in the Canine Knee," Eng Med, 16, pp. 15-22.

[105] Park, S., Hung, C. T., and Ateshian, G. A., 2004, "Mechanical Response of

Bovine Articular Cartilage under Dynamic Unconfined Compression Loading at Physiological Stress Levels," Osteoarthritis Cartilage, 12, pp. 65-73.

[106] Wong, M., Ponticiello, M., Kovanen, V., and Jurvelin, J. S., 2000, "Volumetric

Changes of Articular Cartilage During Stress Relaxation in Unconfined Compression," J Biomech, 33, pp. 1049-54.

[107] Arokoski, J. P., Hyttinen, M. M., Helminen, H. J., and Jurvelin, J. S., 1999,

"Biomechanical and Structural Characteristics of Canine Femoral and Tibial Cartilage," J Biomed Mater Res, 48, pp. 99-107.

[108] Mow, V. C., Holmes, M. H., and Lai, W. M., 1984, "Fluid Transport and

Mechanical Properties of Articular Cartilage: A Review," J Biomech, 17, pp. 377-94.

52

[109] Bergmann, G., 1998, Hip98: Data Collection of Hip Joint Loading on Cd-Rom. Free University and Humboldt University, Berlin.

[110] Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A.,

Strauss, J., and Duda, G. N., 2001, "Hip Contact Forces and Gait Patterns from Routine Activities," J Biomech, 34, pp. 859-71.

[111] Hodge, W. A., Fijan, R. S., Carlson, K. L., Burgess, R. G., Harris, W. H., and

Mann, R. W., 1986, "Contact Pressures in the Human Hip Joint Measured in Vivo," Proc Natl Acad Sci U S A, 83, pp. 2879-83.

[112] Furey, M. J., 1995, "Joint Lubrication," in The Biomedical Engineering

Handbook, J. D. Bronzino, Ed. CDC Press, Boca Raton, FL, pp. 333-351. [113] McCutchen, C. W., 1959, "Sponge-Hydrostatic and Weeping Bearings," Nature,

184, pp. 1284-1285. [114] Walker, R. S., Dowson, D. L., Longfield, M. D., and Wright, V., 1968, "'Boosted

Lubrication' in Synovial Joints by Fluid Entrapment and Enrichment," Ann Rheum Dis, 27, pp. 512-520.

[115] Macirowski, T., Tepic, S., and Mann, R. W., 1994, "Cartilage Stresses in the

Human Hip Joint," J Biomech Eng, 116, pp. 10-8. [116] Huang, C. Y., Mow, V. C., and Ateshian, G. A., 2001, "The Role of Flow-

Independent Viscoelasticity in the Biphasic Tensile and Compressive Responses of Articular Cartilage," J Biomech Eng, 123, pp. 410-7.

[117] Lee, R. C., Frank, E. H., Grodzinsky, A. J., and Roylance, D. K., 1981,

"Oscillatory Compressional Behavior of Articular Cartilage and Its Associated Electromechanical Properties," J Biomech Eng, 103, pp. 280-92.

[118] Soltz, M. A. and Ateshian, G. A., 2000, "Interstitial Fluid Pressurization During

Confined Compression Cyclical Loading of Articular Cartilage," Ann Biomed Eng, 28, pp. 150-9.

[119] Buschmann, M. D., Kim, Y. J., Wong, M., Frank, E., Hunziker, E. B., and

Grodzinsky, A. J., 1999, "Stimulation of Aggrecan Synthesis in Cartilage Explants by Cyclic Loading Is Localized to Regions of High Interstitial Fluid Flow," Arch Biochem Biophys, 366, pp. 1-7.

[120] Kim, Y. J., Bonassar, L. J., and Grodzinsky, A. J., 1995, "The Role of Cartilage

Streaming Potential, Fluid Flow and Pressure in the Stimulation of Chondrocyte Biosynthesis During Dynamic Compression," J Biomech, 28, pp. 1055-66.

53

[121] Sah, R. L., Kim, Y. J., Doong, J. Y., Grodzinsky, A. J., Plaas, A. H., and Sandy, J. D., 1989, "Biosynthetic Response of Cartilage Explants to Dynamic Compression," J Orthop Res, 7, pp. 619-36.

[122] Dietschi, C., Schreiber, A., Huggler, A. H., and Jacob, H., 1975, "Experimental

Investigation of Deformation of the Weight-Bearing Acetabulum," Acta Orthop Belg, 41 Suppl 1, pp. 153-7.

[123] Finlay, J. B., Bourne, R. B., Landsberg, R. P., and Andreae, P., 1986, "Pelvic

Stresses in Vitro--I. Malsizing of Endoprostheses," J Biomech, 19, pp. 703-14. [124] Jacob, H. A., Huggler, A. H., Dietschi, C., and Schreiber, A., 1976, "Mechanical

Function of Subchondral Bone as Experimentally Determined on the Acetabulum of the Human Pelvis," J Biomech, 9, pp. 625-7.

[125] Lionberger, D., Walker, P. S., and Granholm, J., "The Effects of Prosthetic

Acetabular Replacement on Strains in the Pelvis," presented at Proceedings of the 30th Annual Orthopaedic Research Society, Atlanta, GA, 1984.

[126] Petty, W., Miller, G. J., and Piotrowski, G., 1980, "In Vitro Evaluation of the

Effect of Acetabular Prosthesis Implantation on Human Cadaver Pelves," Bull Prosthet Res, 10-33, pp. 80-9.

[127] Ries, M., Pugh, J., Au, J. C., Gurtowski, J., and Dee, R., 1989, "Normal Pelvic

Strain Pattern in Vitro," J Biomed Eng, 11, pp. 398-402. [128] Oh, I. and Harris, W. H., 1978, "Proximal Strain Distribution in the Loaded

Femur. An in Vitro Comparison of the Distributions in the Intact Femur and after Insertion of Different Hip-Replacement Femoral Components," J Bone Joint Surg Am, 60, pp. 75-85.

[129] Kim, Y. H., Kim, J. S., and Cho, S. H., 2001, "Strain Distribution in the Proximal

Human Femur. An in Vitro Comparison in the Intact Femur and after Insertion of Reference and Experimental Femoral Stems," J Bone Joint Surg Br, 83, pp. 295-301.

[130] Afoke, N. Y., Byers, P. D., and Hutton, W. C., 1987, "Contact Pressures in the

Human Hip Joint," J Bone Joint Surg Br, 69, pp. 536-41. [131] Adams, M. A., Kerin, A. J., Bhatia, L. S., Chakrabarty, G., and Dolan, P., 1999,

"Experimental Determination of Stress Distributions in Articular Cartilage before and after Sustained Loading," Clin Biomech (Bristol, Avon), 14, pp. 88-96.

54

[132] Adams, D. and Swanson, S. A., 1985, "Direct Measurement of Local Pressures in the Cadaveric Human Hip Joint During Simulated Level Walking," Ann Rheum Dis, 44, pp. 658-66.

[133] Brown, T. D. and Shaw, D. T., 1983, "In Vitro Contact Stress Distributions in the

Natural Human Hip," J Biomech, 16, pp. 373-84. [134] von Eisenhart-Rothe, R., Eckstein, F., Muller-Gerbl, M., Landgraf, J., Rock, C.,

and Putz, R., 1997, "Direct Comparison of Contact Areas, Contact Stress and Subchondral Mineralization in Human Hip Joint Specimens," Anat Embryol (Berl), 195, pp. 279-88.

[135] von Eisenhart-Rothe R, A. C., Steinlechner M, Muller-Gerbl M and Eckstein F,

1999, "Quantitative Determination of Joint Incongruity and Pressure Distribution During Simulated Gait and Cartilage Thickness in the Human Hip Joint," Journal of Orthopaedic Research, 7, pp. 532-539.

[136] Sparks, D. R., Beason, D. P., Etheridge, B. S., Alonso, J. E., and Eberhardt, A.

W., 2005, "Contact Pressures in the Flexed Hip Joint During Lateral Trochanteric Loading," J Orthop Res, 23, pp. 359-66.

[137] Rushfeldt, P. D., Mann, R. W., and Harris, W. H., 1979, "Influence of Cartilage

Geometry on the Pressure Distribution in the Human Hip Joint," Science, 204, pp. 413-5.

[138] Rushfeldt, P. D., Mann, R. W., and Harris, W. H., 1981, "Improved Techniques

for Measuring in Vitro the Geometry and Pressure Distribution in the Human Acetabulum. Ii Instrumented Endoprosthesis Measurement of Articular Surface Pressure Distribution," J Biomech, 14, pp. 315-23.

[139] Hale, J. E. and Brown, T. D., 1992, "Contact Stress Gradient Detection Limits of

Pressensor Film," J Biomech Eng, 114, pp. 352-7. [140] Carlson, C. E., Mann, R. W., and Harris, W. H., 1974, "A Radio Telemetry

Device for Monitoring Cartilage Surface Pressures in the Human Hip," IEEE Trans Biomed Eng, 21, pp. 257-64.

[141] Mann, R. W., 2002, "Comment On "Quantitative Determination of Joint

Incongruity and Pressure Distribution During Simulated Gait and Cartilage Thickness in the Human Hip Joint"," Journal of Orthopaedic Research, 18, pp. 164-167.

55

[142] Mavcic, B., Pompe, B., Antolic, V., Daniel, M., Iglic, A., and Kralj-Iglic, V., 2002, "Mathematical Estimation of Stress Distribution in Normal and Dysplastic Hips," Journal of Orthopaedic Research, 20, pp. 1025-1030.

[143] Mavcic, B., Antolic, V., Brand, R., Iglic, A., Kralj-Iglic, V., and Pedersen, D. R.,

2000, "Peak Contact Stress in Human Hip During Gait," Pflugers Arch, 440, pp. R177-8.

[144] Ipavec, M., Brand, R. A., Pedersen, D. R., Mavcic, B., Kralj-Iglic, V., and Iglic,

A., 1999, "Mathematical Modelling of Stress in the Hip During Gait," J Biomech, 32, pp. 1229-35.

[145] Ipavec, M., Iglic, A., Iglic, V. K., and Srakar, F., 1996, "Stress Distribution on the

Hip Joint Articular Surface During Gait," Pflugers Arch, 431, pp. R275-6. [146] Van Rietbergen, B., Odgaard, A., Kabel, J., and Huiskes, R., 1996, "Direct

Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture," J Biomech, 29, pp. 1653-7.

[147] Hayes, W. C., Keer, L. M., Herrmann, G., and Mockros, L. F., 1972, "A

Mathematical Analysis for Indentation Tests of Articular Cartilage," J Biomech, 5, pp. 541-51.

[148] Mak, A. F. and Mow, V. C., 1987, "Biphasic Indentation of Articular Cartilage- I.

Theoretical Analysis," J Biomech, 20, pp. 703-714. [149] Mow, V. C., Good, P., and Gardner, T., "A New Method to Determine the Tensile

Properties of Articular Cartilage Using the Indentation Test," presented at Transactions of the 47th Annual Meeting of the Orthopaedic Research Society, 2000.

[150] Suh, J. K. and Bai, S., 1998, "Finite Element Formulation of Biphasic

Poroviscoelastic Model for Articular Cartilage," J Biomech Eng, 120, pp. 195-201.

[151] Armstrong, C. G., Lai, W. M., and Mow, V. C., 1984, "An Analysis of the

Unconfined Compression of Articular Cartilage," J Biomech Eng, 106, pp. 165-73.

[152] Ateshian, G. A., Lai, W. M., Zhu, W. B., and Mow, V. C., 1994, "An Asymptotic

Solution for the Contact of Two Biphasic Cartilage Layers," J Biomech, 27, pp. 1347-60.

56

[153] Bachrach, N. M., Mow, V. C., and Guilak, F., 1998, "Incompressibility of the Solid Matrix of Articular Cartilage under High Hydrostatic Pressures," J Biomech, 31, pp. 445-51.

[154] Brown, T. D. and Singerman, R. J., 1986, "Experimental Determination of the

Linear Biphasic Constitutive Coefficients of Human Fetal Proximal Femoral Chondroepiphysis," J Biomech, 19, pp. 597-605.

[155] Truesdell, C. and Toupin, R., 1960, "The Classical Field Theories," in Handbuck

Der Physik. Springer-Verlag, Berlin, pp. 226-793. [156] Terzaghi, K., 1943, Theoretical Soil Mechanics. John Wiley and Sons, New

York, NY. [157] Lee, C. F., Chen, P. R., Lee, W. J., Chen, J. H., and Liu, T. C., 2006, "Three-

Dimensional Reconstruction and Modeling of Middle Ear Biomechanics by High-Resolution Computed Tomography and Finite Element Analysis," Laryngoscope, 116, pp. 711-6.

[158] Wang, Z., Zeng, F., Li, H., Ye, Z., Bai, Y., Xia, W., and Liang, B., 2007, "Three-

Dimensional Reconstruction on Pc-Windows Platform for Evaluation of Living Donor Nephrectomy," Comput Methods Programs Biomed, 86, pp. 39-44.

[159] Goel, V. K., Valliappan, S., and Svensson, N. L., 1978, "Stresses in the Normal

Pelvis," Comput Biol Med, 8, pp. 91-104. [160] Oonishi, H., Isha, H., and Hasegawa, T., 1983, "Mechanical Analysis of the

Human Pelvis and Its Application to the Artificial Hip Joint--by Means of the Three Dimensional Finite Element Method," J Biomech, 16, pp. 427-44.

[161] Ferguson, S. J., Bryant, J. T., Ganz, R., and Ito, K., 2000, "The Influence of the

Acetabular Labrum on Hip Joint Cartilage Consolidation: A Poroelastic Finite Element Model," J Biomech, 33, pp. 953-60.

[162] Brown, T. D. and DiGioia, A. M., 3rd, 1984, "A Contact-Coupled Finite Element

Analysis of the Natural Adult Hip," J Biomech, 17, pp. 437-48. [163] Rapperport, D. J., Carter, D. R., and Schurman, D. J., 1985, "Contact Finite

Element Stress Analysis of the Hip Joint," J Orthop Res, 3, pp. 435-46. [164] Genda, E., Konishi, N., Hasegawa, Y., and Miura, T., 1995, "A Computer

Simulation Study of Normal and Abnormal Hip Joint Contact Pressure," Arch Orthop Trauma Surg, 114, pp. 202-6.

57

[165] Konishi, N. and Mieno, T., 1993, "Determination of Acetabular Coverage of the Femoral Head with Use of a Single Anteroposterior Radiograph. A New Computerized Technique," J Bone Joint Surg Am, 75, pp. 1318-33.

[166] Rushfeldt, P. D., Mann, R. W., and Harris, W. H., 1981, "Improved Techniques

for Measuring in Vitro the Geometry and Pressure Distribution in the Human Acetabulum--I. Ultrasonic Measurement of Acetabular Surfaces, Sphericity and Cartilage Thickness," J Biomech, 14, pp. 253-60.

[167] Bullough, P., Goodfellow, J., Greenwald, A. S., and O'Connor, J., 1968,

"Incongruent Surfaces in the Human Hip Joint," Nature, 217, pp. 1290. [168] Russell, M. E., Shivanna, K. H., Grosland, N. M., and Pedersen, D. R., 2006,

"Cartilage Contact Pressure Elevations in Dysplastic Hips: A Chronic Overload Model," Journal of Orthopaedic Surgery and Research, 1.

[169] Ackerman, M. J., Spitzer, V. M., Scherzinger, A. L., and Whitlock, D. G., 1995,

"The Visible Human Data Set: An Image Resource for Anatomical Visualization," Medinfo, 8, pp. 1195-1198.

[170] Genda, E., Iwasaki, N., Li, G., MacWilliams, B. A., Barrance, P. J., and Chao, E.

Y., 2001, "Normal Hip Joint Contact Pressure Distribution in Single-Leg Standing--Effect of Gender and Anatomic Parameters," J Biomech, 34, pp. 895-905.

[171] Yoshida, H., Faust, A., Wilckens, J., Kitagawa, M., Fetto, J., and Chao, E. Y.,

2006, "Three-Dimensional Dynamic Hip Contact Area and Pressure Distribution During Activities of Daily Living," J Biomech, 39, pp. 1996-2004.

[172] Brown, T. D., Rudert, M. J., and Grosland, N. M., 2004, "New Methods for

Assessing Cartilage Contact Stress after Articular Fracture," Clin Orthop Relat Res, pp. 52-8.

CHAPTER 3

A SUBJECT-SPECIFIC FINITE ELEMENT MODEL OF THE PELIVS:

DEVELOPMENT, VALIDATION AND SENSITIVITY STUDIES1

ABSTRACT

A better understanding of the three-dimensional mechanics of the pelvis, at the

patient-specific level, may lead to improved treatment modalities. Although finite

element (FE) models of the pelvis have been developed, validation by direct comparison

with subject-specific strains has not been performed, and previous models used

simplifying assumptions regarding geometry and material properties. The objectives of

this study were to develop and validate a realistic FE model of the pelvis using subject-

specific estimates of bone geometry, location-dependent cortical thickness and trabecular

bone elastic modulus, and to assess the sensitivity of FE strain predictions to assumptions

regarding cortical bone thickness as well as bone and cartilage material properties. A FE

model of a cadaveric pelvis was created using subject-specific CT image data.

Acetabular loading was applied to the same pelvis using a prosthetic femoral stem in a

fashion that could be easily duplicated in the computational model. Cortical bone strains

1 Reprinted from Journal of Biomechanical Engineering, Vol. 127, No. 3, Anderson, A.E., Peters, C.L., Tuttle, B.D., Weiss, J.A., “A Subject-Specific Finite Element Model of the Pelvis: Development, Validation, and Sensitivity Studies”, pp: 364-373, 2005, with kind permission from the ASME.

59

were monitored with rosette strain gauges in ten locations on the left hemi-pelvis. FE

strain predictions were compared directly with experimental results for validation.

Overall, baseline FE predictions were strongly correlated with experimental results (r2 =

0.824), with a best-fit line that was not statistically different than the line y=x

(Experimental strains=FE predicted strains). Changes to cortical bone thickness and

elastic modulus had the largest effect on cortical bone strains. The FE model was less

sensitive to changes in all other parameters. The methods developed and validated in this

study will be useful for creating and analyzing patient-specific FE models to better

understand the biomechanics of the pelvis.

60

INTRODUCTION

The acetabulum and adjoining pelvic bones are one of the most important weight

bearing structures in the human body. Forces as high as 5.5 times body weight are

transferred from the femur to the acetabulum during activities such as running and stair

climbing [1-3]. The structure of the pelvis is a sandwich material, with the thin layers of

cortical bone carrying most of the load. Despite its efficient structure, the pelvis can

become damaged due to altered loading. Side impact forces, such as those generated in

car accidents, are notorious for generating pelvic fractures. The fracture itself often

causes multiple internal trauma leading to a mortality rate on the order of 12 - 37% [4,5].

In addition to pelvic fractures, it has been hypothesized that subtle alterations in pelvic

geometry (i.e., pelvic dysplasia) lead to osteoarthritis [6-11]. In fact, secondary causes of

osteoarthritis, such as undiagnosed pelvic dysplasia, appear to be more prevalent among

candidates for total hip arthroplasty (THA) than primary arthritis [10-13]. Michaeli et al.

reported that nearly 76% of THA recipients exhibited signs of a dysplastic joint - a

condition that went unrecognized prior to surgery [3]. Nevertheless, the relationship

between pelvic dysplasia and osteoarthritis remains controversial since there is no direct

quantitative evidence linking the two together.

Simplified mathematical models, experimental contact analyses, and force

telemetry data have been used to estimate joint contact forces at the acetabulum [1-3,14-

21]. These studies provide valuable information concerning overall joint mechanics but

do not yield estimates of the surrounding bone stresses and strains. It would be wise to

develop methods capable of quantifying the mechanics beyond the acetabular contact

61

interface since there is evidence to suggest that the surrounding bone plays a pivotal role

in the progression of diseases such as osteoarthritis [22-24]. A better understanding of

the mechanics for the entire pelvis could lead to improved implant designs, surgical

approaches, diagnosis, and may present the framework necessary for preoperative

surgical planning. Specifically, an analysis of the stress distribution in and around the

pelvic joint may clarify the mechanical relationship between pelvic geometry and

predisposition to osteoarthritis.

It is difficult to assess the stress and strain distribution throughout the entire pelvis

using simplified mathematical models, implanted prostheses, or via experiments with

cadaveric tissue. An alternative approach to analyze pelvic mechanics is the finite

element (FE) method, which can accommodate large inter-subject variations in bone

geometry and material properties. The potential benefit of patient-specific FE analysis

becomes clear when one considers how difficult (if not impossible) it would be to

assemble a population of donor tissue that exhibits a specific pathology such as pelvic

dysplasia.

The objectives of this study were to develop and validate a FE model of the pelvis

using subject-specific estimates of bone geometry, location-dependent cortical thickness

and trabecular bone elastic modulus, and to assess the sensitivity of FE cortical strain

predictions to cortical bone thickness and bone and cartilage material properties. The

following hypotheses were tested: 1) A FE model of the pelvis that incorporated subject-

specific geometry, cortical bone thickness, and position dependent trabecular bone elastic

modulus would accurately predict cortical bone strains. 2) A subject-specific FE model

62

of the pelvis would be more accurate than models that assume average cortical bone

thickness and trabecular elastic modulus.

63

MATERIALS AND METHODS

A combined experimental and computational protocol was used to develop and

validate a subject-specific three-dimensional model of a 68 y/o female cadaveric pelvis

(International Bioresearch Solutions, Tucson, AZ). The pelvic joint was visually

screened for large-scale osteoarthritis prior to the study.

Experimental Study

The sacroiliac joint and all soft tissues, with the exception of articular cartilage,

were removed. A registration block and wires were attached to the iliac crest. The block

allowed for spatial registration of experimental and FE coordinate systems, while the

wires served as a guide to reproduce the boundary conditions used in the experimental

model [25]. A CT scan (512x512 acquisition matrix, FOV=225 mm, in-plane

resolution=0.44x0.44 mm, slice thickness=0.6 mm, 354 slices) was obtained in a superior

to inferior fashion using a Marconi-MX8000 scanner (Philips Medical Systems, Bothell,

WA). A bone mineral density (BMD) phantom (BMD-UHA, Kyoto Kagaku Co., Kyoto,

Japan), consisting of 21 rectangular blocks of urethane with varying concentrations of

hydroxyapaptite (0 - 400 mg/cm3, 20 mg/cm3 increments) was also scanned with the

same field of view and energy settings. CT data from the BMD phantom were averaged

over each block to obtain a relationship between CT scanner pixel intensity and calcium

equivalent bone density.

The mounting and loading of the pelvis followed a protocol similar to that

described by Dalstra et al. [26]. The iliac crests were submerged in a mounting pan of

64

catalyzed polymer resin (Bondo, Mar-Hyde, Atlanta, GA) to the depth defined by the

iliac guide wires. Ten three-element rectangular rosette strain gauges (WA-060WR-120,

Vishay Measurements Group, Raleigh, NC), representing 30 channels of data, were

attached to the left hemi-pelvis at locations around the acetabulum, pubis, ischium, and

ilium. Vertically oriented loads of 0.25, 0.50, 0.75, and 1.0 X body weight (559 N) were

applied to the acetabulum by displacing a femoral prosthesis, attached to a linear actuator

(Figure 3.1). The femoral implant was displaced continuously until the appropriate load

was reached at which time the displacement was held constant, allowing stress relaxation,

until the load relaxed to a value greater than 95% of the original with a load-time slope

less than 0.25 N/sec for at least 60 seconds. The average time to reach quasi-static

equilibrium for each loading scenario was 6 minutes. An average of the rosette gauge

readings (ε1, ε2, ε3) for the last 10 seconds of the equilibrium period was obtained and

then converted to in-plane principal strains (εP, εQ) using the relationship [27]:

1 2 21 3 ( ) ( ), 1 2 2 32 2P Qε εε ε ε ε ε+

= ± − + − . (3.1)

3D coordinates of the strain gauges and registration block were determined in a

laboratory reference frame using an electromagnetic digitizer (Model BE-3DX,

Immersion Corp., San Jose, CA). Geometric features of the pelvis were digitized to

determine the accuracy of the geometry reconstruction.

65

A

B

C

D E

F

G

LOAD

Figure 3.1. Schematic of fixture for loading the pelvis via a femoral implant component.(A) actuator, (B) load cell, (C) ball joint, (D) femoral component, (E) pelvis, (F)mounting pan for embedding pelvis, and (G) lockable X-Y translation table.

66

Geometry Extraction and Mesh Generation

Contours for the outer cortex and the boundary of the cortical and trabecular bone,

registration block, and guide wires were extracted from the CT data via manual

segmentation (Figure 3.2). Points comprising the contours were triangulated [28] to form

a polygonal surface, which was then decimated [29] and smoothed [30] to form the final

surface using VTK (Kitware Inc., Clifton Park, NY) [31] (Figure 3.2). A volumetric

tetrahedral mesh was created from the final surface to represent the outer cortex (CUBIT,

Sandia National Laboratories, Albuquerque, NM). A 4-node, 24 degree of freedom

tetrahedral element was used to represent trabecular bone [32]. This element has three

translational and rotational degrees of freedom at each node. Mesh refinement tests were

performed with this element using a model of a cantilever beam under a tip load with a

thickness that was 10% of the beam length. FE-predicted tip deflections reached an

asymptote of 4% error with respect to an analytical solution when at least 3 tetrahedral

elements were used through the thickness of the beam.

Cortical bone was represented with quadratic 3-node shell elements [33]. The

elements were based on the Hughes-Liu shell [34,35], which has three translational and

rotational degrees of freedom per node, with selective-reduced integration to suppress

zero-energy modes [36]. The geometry of the shells was based on the nodes of the

outside faces of the tetrahedral elements, on the outer surface of the pelvis. The shell

reference surface and shell element normal were defined so that the cortical thickness

pointed inward toward the interface between cortical and trabecular bone. This approach

resulted in an overlap of one cortical bone thickness between the tetrahedral solid

67

element and thin shell element. The elastic modulus for all tetrahedral element nodes in

this region of overlap was set to 0 MPa. Mesh refinement tests showed that the 3-node

shell was nearly as accurate as using three tetrahedral elements through the thickness of

the beam (< 5% error with respect to analytical solution).

Figure 3.2. A) - CT image slice at the level of the ilium, showing the registration block(arrow) and the distinct boundary between cortical and trabecular bone. B) - the original polygonal surface representing the cortical bone was reconstructed by Delaunaytriangulation of the points composing the segmented contours. C) - polygonal surface after decimation to reduce the number of polygons and smoothing to reduce high-frequency digitizing artifact. A - anterior, P - posterior, M - medial, L - lateral, I -inferior, S - superior.

P

A

M L

A) B) C)

68

The density of the FE mesh was adjusted until it was at or above the beam mesh density

required to achieve an error of 4%. The final surface mesh density was 0.5 shell

elements/mm2 with a volumetric density of 2.5 tetrahedral elements/mm3. The final FE

model consisted of 190,000 tetrahedral elements for trabecular bone and 31,000 shell

elements for cortical bone (Figure 3.3). Acetabular cartilage was represented with 350

triangular shell elements with a constant thickness of 2 mm, determined by averaging the

distance between the implant and acetabulum in the neutral kinematic position.

Figure 3.3. A) FE mesh of the pelvis, composed of 190,000 tetrahedral elements and31,000 shell elements. B) close-up view of the mesh at the acetabulum.

A) B)

69

Position-Dependent Cortical Thickness

An algorithm was developed to determine the thickness of the cortex based on the

distances between the polygonal surfaces representing the outer cortex and the boundary

between the cortical and trabecular bone. Vectors were constructed between each node

on the cortical surface and the 100 nearest nodes on the surface defining the cortical-

trabecular boundary. Cortical thickness was determined by minimizing both the distance

between the nodes of the surfaces and the angle of the dot product between the surface

normal of the cortical surface with that of each corresponding trabecular vector. In areas

of high curvature (such as the acetabular rim), special consideration of thickness was

necessary (Figure 3.4). When the above-described algorithm reported a thickness value

that exceeded 1.5 times the smallest distance between the nodes, the smallest distance

between nodes on the two surfaces was used. The minimum value of nodal thickness was

assumed to be 0.44 mm or the width of one pixel (FOV= 225, FOV/512 = 0.44

mm/pixel). The algorithm was tested using polygonal surfaces representing parallel

planes, concentric spheres, and layered boxes with varying mesh densities.

70

Figure 3.4. Schematics illustrating the special cases considered in determination ofcortical thickness. Both the distance between the surfaces and the angle of the dotproduct between the normal vector (n) with that of the vector created by subtracting thetrabecular and cortical node coordinates were considered. Nodes on the cortical surfaceare represented as open circles, while nodes on the trabecular surface are shown as filledcircles. Case A) the smallest angle of the dot product between the cortical node andnearest trabecular node neighbor yields the desired thickness measurement. Case B) the smallest distance between nodes provides the desired thickness measurement. Case C)the normal vector (n) from the cortical node does not intersect the trabecular surface. Forcases B and C, a weighting scheme was applied such that the smallest distance between the nodes was taken as the cortical thickness when the originally reported thickness valueexceeded 1.5 X the smallest distance between nodes on the two surfaces.

n

A) B) C)

n n

71

Assessment of Cortical Bone Thickness

A custom-built phantom was used to assess the accuracy of cortical thickness

measurements (Figure 3.5) [37]. Ten aluminum tubes (wall thickness 0.127– 2.921 mm)

were fit into a 70 mm dia. Lucite disc. The centers of the aluminum tubes were filled

with Lucite rods so that both the inner and outer surfaces of the tubes were surrounded by

a soft tissue equivalent material [38,39]. Aluminum has x-ray attenuation coefficient that

is similar to cortical bone [37]. The phantom was scanned with the same CT scanner

field of view and energy settings used for the cadaveric pelvis and bone mineral density

phantom. The z-axis of the scanner was aligned flush with the top edge of the tissue

phantom to prevent volume averaging between successive slices. The inner and outer

circumferences of the tubes were segmented from the CT image data using the same

technique to extract the pelvic geometry. The surfaces were meshed and the thickness

algorithm was used to determine wall thickness.

Figure 3.5. A) Tissue equivalent phantom containing 10 aluminum tubes used to simulatecortical bone with varying thickness. The phantom was scanned with a CT scanner andmanually segmented to determine the accuracy of cortical bone reconstruction. B) cross-sectional CT image of the cortical bone phantom. Changes in thickness can be seen forthe thicker tubes but become less apparent as the tube wall thickness decreases.

A) B)

72

Material Properties and Boundary Conditions

The femoral implant was represented as rigid while cortical and trabecular bone

were represented as isotropic hypoelastic. Baseline material properties for cortical bone

were E = 17 GPa and Poisson’s ratio (ν) = 0.29 [26]. A linear relationship was

established between CT scanner pixel intensity and calcium equivalent density using the

CT image data from the BMD solid phantom:

20.0008 0.8037 ( 0.9938)ca INT rρ = − =i (3.2)

Here caρ is the calcium equivalent density of trabecular bone (g/cm3) and INT is the CT

scanner intensity value (0 - 4095). Next, a relationship was used to convert calcium

equivalent density ( caρ ) to apparent bone density ( appρ ) [40]:

0.626

caapp

ρρ = . (3.3)

Finally, an empirical relationship was used to convert apparent density of pelvic

trabecular bone to elastic modulus for each node [40]:

( )2.462017.3 appE ρ= , (3.4)

where E is the elastic modulus (MPa) and appρ is the apparent density of the trabecular

bone (g/cm3). Nodal moduli were averaged to assign an element modulus. Acetabular

articular cartilage was represented as a hyperelastic Mooney-Rivlin material [41].

Coefficients C1 and C2 were selected as 4.1 MPa and 0.41 MPa, respectively with

Poisson’s ratio=0.4 [42].

73

A FE coordinate system was created from the polygonal surface of the

reconstructed registration block. A corresponding coordinate system was established for

the experimental measurements using the digitized coordinates of the registration block

[25]. To establish the neutral kinematic position, a transformation was applied to the FE

model to align it with the experimental coordinate system. Nodes superior to the iliac

guide wires and nodes along the pubis synthesis joint were constrained to simulate the

experiment. Contact was enforced between the femoral implant and cartilage while load

was applied to the implant using the same magnitude and direction measured

experimentally. Analyses were performed with the implicit time integration capabilities

of LS-DYNA (Livermore Software Technology Corporation, Livermore, CA) on a

Compaq Alphaserver DS20E (2 667 MHz processors). Each model required

approximately 3 hours of wall clock time and 1.1 GB of memory.

Sensitivity Studies

Sensitivity studies were performed to assess the effects of variations in assumed

and estimated material properties and cortical thickness on predicted cortical surface

strains. The assumed parameters were cortical bone Poisson’s ratio, trabecular bone

Poisson’s ratio, cartilage elastic modulus, and cortical bone elastic modulus. The

estimated parameters were trabecular elastic modulus and cortical bone thickness.

Variations in assumed parameters were based on standard deviations from the literature

(Table 3.1). The trabecular elastic modulus and cortical thickness were varied to reflect

the median and inter-quartile range estimated computationally. The FE models included

74

constant cortical shell thickness (CST), constant trabecular elastic modulus (CTEM),

constant shell thickness and elastic modulus (CST/CTEM) and subject-specific models

(position dependent trabecular elastic modulus and cortical thickness), with alterations in

cortical bone Poisson’s ratio (SSCV), trabecular bone Poisson’s ratio (SSTV), cortical

elastic modulus (SSCM), articular cartilage thickness (ACT) and articular cartilage

elastic modulus (ACEM). A sensitivity model (OVERLAP) was analyzed to determine

the cortical surface strain effects due to overlap between the cortical shell and tetrahedral

elements. For the overlap model the tetrahedral surface nodes were assigned the

maximum elastic modulus estimated from the cadaveric CT image data (3829 MPa). The

surface nodes were averaged to estimate the elastic modulus for the each tetrahedral

element as was done in the subject-specific model. The sensitivity of each model, S, was

defined as:

% change in slope% change in input parameter

S = . (3.5)

The numerator in (5) is the percent change in slope of the best-fit lines between the

sensitivity model and baseline subject-specific model. The denominator is the percent

change in the model input parameter between the sensitivity model and the baseline

subject-specific model. For those sensitivity models that investigated constant inputs

such as cortical thickness and trabecular bone elastic modulus, the change in constant

model input parameters was used in the denominator.

75

Type Models Analyzed Reference CST Thickness = ± 0, 0.5, 1 SD (0.49 mm) EXP

CTEM E = 45, 164, 456 MPa (Quartiles) EXP CST/CTEM Thickness = 1.41 mm, E = 164 MPa EXP

SSCV ν=0.2, ν=0.39 [57] SSTV ν=0.29 [55] SSCM E = ± 1 SD (1.62 GPa) [58] ACT Thickness = 0.0, 4.0 mm (Min/Max) EXP

ACEM E = 1.36, 7.79 MPa (Min/Max) [59] OVERLAP Surface Tet. Nodes = Max Trabecular Modulus NA

Data Analysis

FE predictions of cortical principal strains were averaged over elements that were

located beneath each strain gauge. A rectangular perimeter, representing each strain

gauge, was created on the surface of the FE mesh using digitized points from the

experiment. Strains for a shell were included in the average if at least 50% of its area

was within the perimeter. FE predicted strains were plotted against experimental strains.

Best-fit lines and r2 values were reported for each model at all loads. Statistical tests

(α=0.05) were performed to compare the slope and y-intercept of the subject-specific

best-fit line with the line y=x (Experimental Strains=FE Strains) to test the null

hypothesis: there was no significant difference between FE predicted strains and

experimental strains [43]. Statistical tests were used to test differences between the slope

of the best-fit line, and r2 values for each sensitivity model with the baseline subject-

specific model [43].

Table 3.1. Models studied for FE sensitivity analysis. Deviations in material propertiesand cortical thickness were taken from experimentally measured/estimated values (EXP)as well as data reported in the literature.

76

RESULTS

Reconstruction of Pelvic Geometry

The geometry reconstruction techniques yielded a faithful reproduction of the

measured geometric features of the pelvis (Figure 3.6). Correlation between

measurements on the cadaveric pelvis with the corresponding FE mesh was strong

(r2=0.998). There was no statistical difference between the slope and y-intercept of the

regression line and the line y = x.

Figure 3.6. A) schematic showing the length measurements that were obtained from thecadaveric pelvis with an electromagnetic digitizer. Measurements were based onidentifiable anatomical features of the iliac wing, ischium, obturator foramen, pubis, and acetabulum. B) excellent agreement was observed between experimental measurementsand the FE mesh dimensions, yielding a total error of less than 3%.

0 20 40 60 80 100 120 140 160 1800

20

40

60

80

100

120

140

160

180

y = 0.97x + 2.16, r2= 0.998

FE Measurements (mm)

Expe

rimen

tal M

easu

rem

ents

(mm

)

77

Cortical Bone Thickness

The thickness algorithm accurately predicted thickness using simple polygonal

surfaces with known distances between the surfaces. For parallel planes and concentric

spheres, errors were ±0.004%. For the layered boxes, the RMS error was ±2%. For all

surfaces, errors decreased with increasing surface resolution. The above errors are based

on polygonal surfaces with a resolution similar to the pelvis FE mesh.

The thickness algorithm estimated aluminum tube wall thickness accurately (less

than ±10% error) for tubes with thicknesses between 0.762 and 2.9210 mm (Table 3.2).

The reported standard deviation in nodal thickness for these tubes was also less than 10%

of the average nodal thickness (Table 3.2). Therefore individual nodal thickness values

did not deviate much from the average nodal thickness. However, errors in thickness

increased progressively for tubes with wall thickness between 0.127 and 0.635 mm.

Cortical bone thickness ranged from 0.44 - 4.00 mm (mean 1.41 ± 0.49 mm (SD))

(Figure 3.7). Cortical thickness was highest along the iliac crest, the ascending pubis

ramus, at the gluteal surface and around the acetabular rim. Cortical bone was thin at the

acetabular cup, the ischial tuberosity, the iliac fossa and the area surrounding the pubic

tubercle.

78

True Thickness (mm)

Estimated Thickness (mm)(mean ± SD) Error (%)

0.127 0.554 ± 0.094 336 0.254 0.669 ± 0.111 163 0.381 0.638 ± 0.089 67 0.508 0.815 ± 0.079 60 0.635 0.709 ± 0.071 12 0.762 0.825 ± 0.063 8.3 1.016 1.039 ± 0.088 2.2 1.270 1.317 ± 0.077 3.7 2.032 1.982 ± 0.078 -2.5 2.921 2.781 ± 0.108 -4.8

Table 3.2. Measurement of aluminum tube wall thickness from CT data. Errors in wall thickness were less than 10% for thicknesses greater than or equal to 0.762 mm. Errorsincreased progressively as the wall thickness decreased.

79

Figure 3.7. Contours of position dependent cortical bone thickness with rectangles indicating the locations of the 10 strain gauges used during experimental loading. A)anterior view, B) medial view. Cortical thickness was highest along the iliac crest, the ascending pubis ramus, at the gluteal surface and around the acetabular rim. Areas of thin cortical bone were located at the acetabular cup, the ischial tuberosity, the iliac fossa and the area surrounding the pubic tubercle. Cortical thickness beneath the surface of the strain gauges was similar to the average model thickness of 1.41 mm but deviated less.

Anterior Oblique Medial

2.75 mm

0.44 mm

A) B)

80

Trabecular Bone Elastic Modulus

Trabecular elastic modulus ranged from 2.5 - 3829.0 MPa (mean = 338 MPa,

median = 164 MPa, inter-quartile range = 45 - 456 MPa). Data were significantly

skewed to the right (positively skewed) so the median and bounds of the inter-quartile

range were used for sensitivity models rather than the arithmetic mean and standard

deviation. Areas of high modulus were predominately near muscle insertion sites and

within the subchondral bone surrounding the acetabulum. Areas of low modulus were

located near the sacroiliac joint, pubis joint, and along the ischial tuberosity and the

interior of the ilium.

FE Model Predictions

FE predicted von Mises stresses for the subject-specific model ranged from 0-44

MPa and were greatest near the pubis-symphasis joint, superior acetabular rim, and on

the ilium just superior to the acetabulum for each load applied (Figure 3.8). Baseline FE

predictions of principal strains showed strong correlation (r2=0.824) with experimental

measurements (Figure 3.9 A) and had a best-fit line that was not statistically different

than y=x (Experimental Strains=FE Strains), (Table 3.3).

Coefficients of determination and y-intercept values were not statistically

different than the subject-specific model for all sensitivity models analyzed (Table 3.3).

The sensitivity model with constant trabecular elastic modulus, representing the upper

bound (456 MPa) of the inter-quartile range, was significantly stiffer (lower strains) than

the subject-specific model (Figure 3.9 B) (Table 3.3). Although not statistically

significant, models representing the median (164 MPa) and lower bound (45 MPa) of

81

trabecular elastic modulus were also stiffer than the subject-specific model (Figure 3.9

B), (Table 3.3).

Changes in the thickness of the cortical bone had a profound effect on cortical

strains (Figure 3.9 C), for both ± 0.5, 1 SD (Table 3.3). Using a ratio of average

sensitivities, cortical surface strains were approximately 10 times more sensitive to

changes in cortical thickness than to alterations to trabecular bone elastic modulus (Table

3.3). The model with average cortical thickness predicted strains that were statistically

similar to subject-specific model results (Table 3.3). FE predictions were significantly

stiffer than the subject-specific model predictions when both average thickness and

trabecular elastic modulus were used (Table 3.3). Changes to the cortical bone elastic

modulus were significantly different than the subject-specific model for E=15.38 MPa

but were not for E=18.62 MPa. However, values of the sensitivity parameter for the

cortical bone modulus models were actually greater than those for changes to cortical

thickness. This suggests that the pelvic FE model was very sensitive to changes in

cortical bone modulus despite the fact that statistical significance was not obtained for

both models. On average, FE predicted strains were 15 times more sensitive to

alterations to the cortical bone elastic modulus than they were to changes in the trabecular

bone elastic modulus. The remaining sensitivity models had best-fit lines that were not

statistically different than the subject-specific model (Table 3.3). Sensitivity values for

the remaining models were also comparable to those of the constant trabecular bone

modulus, which suggests that FE predicted strains were not very sensitive to changes in

cartilage modulus, cartilage thickness, cortical bone Poisson’s ratio, and trabecular bone

82

Poisson’s ratio (Table 3.3). The best-fit line for the overlap sensitivity model was nearly

identical to the subject-specific model, which suggests that FE predicted surface strains

were not sensitive to overlap between the cortical shell and trabecular tetrahedral

element.

Figure 3.8. Distribution of Von-Mises stress at 1 X body weight. A) anterior view, B)medial view. Areas of greatest stress were near the pubis-symphasis joint, superior acetabular rim, and on the ilium just superior to the acetabulum.

0 MPa

5 MPa

Anterior Oblique Medial

A) B)

83

Figure 3.9. FE predicted vs. experimental cortical bone principal strains. A) subject-specific, B) constant trabecular modulus, C) constant cortical thickness. For the subject-specific model there was strong correlation between FE predicted strains with those that were measured experimentally with a best-fit line that did not differ significantly from the line y=x (Experimental strains=FE predicted strains). Changes to the trabecular modulus did not have as significant of an effect on the resulting cortical bone strains as did changes to cortical bone thickness.

A)

B)

C)

84

Model Type Value Best-Fit Line r2 SensitivitySubject-Specific NA y = 1.015x + 4.709 0.824 NA Const. Cortical Thick. (mm) 1.41 y = 1.054x – 2.823 0.754 NA 1.66 y = 1.193x + 2.265* 0.732 0.743 1.17 y = 0.890x – 2.820* 0.770 0.914 1.90 y = 1.395x – 2.059** 0.728 0.931 0.92 y = 0.720x – 2.248** 0.789 0.911 Const. Trabecular E (MPa) 164 y = 1.142x + 7.094 0.833 NA 45 y = 1.059x + 5.371 0.841 0.100 456 y = 1.272x + 8.370** 0.810 0.064 Const. Thick. & E (mm, MPa) 1.41, 164 y = 1.204x + 2.559* 0.767 NA Cortical ν ν = 0.2 y = 0.956x + 9.460 0.764 0.187 ν = 0.39 y = 0.898x + 3.294 0.788 0.334 Trabecular ν ν =0.29 y = 1.013x + 4.507 0.824 0.005 Cortical E (GPa) 15.38 y = 0.840x + 6.670** 0.777 1.82 18.62 y = 1.107x + 4.622 0.821 0.951 Cartilage Thick. (mm) 0.0 y = 0.952x + 12.294 0.780 0.062 4.0 y = 1.072x + 5.590 0.841 0.056 Cartilage E (MPa) 1.36 y =1.015x + 4.711 0.824 0.001 7.79 y = 1.019x + 4.715 0.827 0.004 Overlap (MPa) Esuface nodes = 3829 y = 1.024x + 5.119 0.832 NA

Table 3.3. Results for all FE models including best-fit lines, r2 values and sensitivity parameters. Best-fit lines were generated in reference to experimentally measured values of strain. Lines with slopes significantly different than the subject-subject model are indicated (* p < 0.05, ** p< 0.01). All r2 values were not significantly different than the subject-specific model. Y intercepts for all lines shown were not significantly differentfrom zero. Higher values of sensitivity indicate a greater sensitivity to alterations in themodel input/parameter.

85

DISCUSSION

The most accurate FE model predictions were obtained when position-dependent

cortical thickness and elastic modulus were used. When constant cortical bone thickness

and trabecular bone elastic modulus were used, the model was significantly stiffer than

the subject-specific model, so our second hypothesis was accepted. However, FE

predictions of cortical strains were not statistically different than predictions from the

subject-specific model when an average cortical thickness was used. Cortical shell

thicknesses at the locations of the strain gauges were very close to the average thickness

for the pelvis, but showed less deviation (1.38 ± 0.27 mm (SD)). Since the sensitivity

parameter showed that cortical bone strains were very sensitive to changes in cortical

thickness (Table 3.3), this suggests that the similarity in results was most likely

attributable to comparable thickness estimates (Figure 3.7).

Cortical bone was represented using 3-node shell elements. This choice was

based on compatibility with the tetrahedral elements used for the trabecular bone and

considerations of element accuracy. Tetrahedral elements were used for the trabecular

bone because they allow automatic mesh generation based on Delaunay tesselation.

Thick shells (wedges) and pentahedral (prismatic) solid elements were considered for the

cortex but were later rejected since they produced inaccurate predictions of tip deflection

when modeling cantilever beam bending.

Since the geometry of the model was based on the outer cortical surface, with a

shell reference surface positioned to align with the top of the cortical surface, there was

an overlap between the shell and tetrahedral solid elements. In theory, this overlap could

86

produce inaccurate estimations of cortical surface strain. If this were the case then the

sensitivity model that assigned the maximum trabecular elastic modulus to all surface

tetrahedral nodes would have been stiffer than the subject-specific model. However, the

results showed that this was not the case. To remove the overlap, a layer of thin shells

could be placed at the interface between cortical and trabecular bone with thickness

defined towards the outer cortex of the pelvis. However, this approach would not

represent the surface topology of the pelvis as accurately as meshing the outer surface

with tetrahedral elements. FE studies that aim to investigate the mechanics at the

interface between cortical bone and trabecular bone should consider modeling the cortex

without overlap.

Differences in boundary conditions, material properties and applied loading make

it impossible to compare FE predictions of stresses and strains in this study with previous

investigations. The peak values of Von-Mises stress in this study appear to be unrealistic

since bone would degenerate under such high, repetitive stresses [44]. However, high

stresses were confined to a very small area that represented the location of contact

between the head of the prosthetic femur and acetabulum and were still well below

published values for ultimate stress [44].

It is likely that a more physiological loading condition would generate better

femoral head coverage and thus reduce the peak stresses at the contact interface. On

average, the Von Mises stresses for cortical bone in the region of contact changed by

29% and 38% when cartilage thickness was reduced to 0 mm or increased to 4 mm,

respectively. However, the slopes of the regression lines for these sensitivity models

87

were very similar to the subject-specific model (Table 3.3). Although cortical surface

strains were not sensitive to cartilage thickness, the local stresses and strains could be

highly dependent on cartilage material properties and thickness. Nevertheless, the

average stresses for areas of strain gauge attachment, away from the applied load, were

very similar to those reported by Dalstra et al [26]. The value for peak Von-Mises stress

was also consistent with Schuller and co-workers who conducted a FE investigation to

model single-leg stance in which peak values of Von-Mises stresses were as high as 50

MPa [45].

Early models of the pelvis were either simplified 2-D [46-48] or axisymmetric

models [49,50]. Most three-dimensional FE models [26,45,51-56] used simplified pelvic

geometry, average material properties and/or did not validate FE predictions of stress and

strain. The work of Dalstra et al. was the first and only attempt to develop and validate a

three-dimensional FE model of the pelvis using subject-specific geometry and material

properties [26]. The FE model was validated using experimental measures of strain in

the peri-acetabular region of a cadaveric pelvis, but subject-specific experimental

measurements were not performed. Different cadaveric specimens were used for FE

mesh generation and experimental tests. In fact, it was reported that the acetabulum of

the experimental test sample was 45 mm whereas that of the specimen used for FE

geometry and material properties was 62 mm [26]. Subject-specific FE strains were

compared to models that assumed constant cortical thickness and elastic modulus. FE

model accuracy was more dependent on cortical bone thickness than trabecular elastic

modulus, although statistical tests were not performed to support this conclusion. The

88

effect of using average estimates was not investigated. Moreover, the effects of

alterations in other bone and cartilage material properties were not investigated.

FE model predictions of cortical strain were relatively insensitive to most model

inputs (except cortical thickness and modulus), but it is likely that FE strain predictions

would change substantially if an idealized geometry was used rather than a faithful

representation of the external geometry. Previously developed FE models of the pelvis

have been based on coarse geometric representations. For example, Dalstra et al. hand-

digitized 6 mm thick CT slices, which was ten times the thickness used in this study [26].

In this study, the small slice thickness and robust surface reconstruction techniques

yielded a very accurate representation of the original geometry (Figure 3.6). The present

approach allowed cortical bone thickness to be estimated without laborious hand

digitization [26]. While it may be acceptable to model the pelvis with idealized geometry

for some applications, it is absolutely crucial to use accurate pelvic morphology if the

research objective is to study diseases in which geometry is abnormal such as pelvic

dysplasia.

The relative importance of model input parameters will depend heavily on the FE

model predictions that are of interest. For this study deviations to the trabecular elastic

modulus only had a significant effect on cortical surface strains when the upper inter-

quartile range of trabecular bone elastic modulus was assessed. However, one should

refrain from concluding that a position-dependent trabecular modulus is not important

since it was shown that the model that assumed average cortical thickness and trabecular

modulus was not as accurate as the baseline model. In addition, results for position-

89

dependent thickness and constant trabecular modulus were stiffer than the subject-

specific model, although the slopes were not significantly different over the entire inter-

quartile range. Finally, FE predictions of overall model displacement were altered

considerably when a constant trabecular modulus was used (data not shown). This

change in model displacement did not result in significant deviations of strain for the

cortex beneath the gauges but could have altered the surface strain at other locations.

Therefore, it is recommended that a position-dependent trabecular bone modulus be

included to improve overall FE model accuracy.

Although the results of the sensitivity studies suggest that changes in material

properties (except for under/over-estimation of cortical bone elastic modulus) were not

likely to produce significant changes in cortical bone surface strains, it is likely that

strains would be more sensitive to changes in the boundary conditions and applied

loading conditions. For this reason, it was not the intent of this proof of concept study to

replicate physiological loading conditions. The use of a well-defined experimental

loading configuration allowed accurate replication of the loading conditions in the FE

model. Future studies will investigate pelvic mechanics under physiological loading

conditions using additional experimental data.

A limitation to this study was the fact that the contralateral hemipelvis was not

incorporated in the FE model. Nodes along the pubis joint were constrained, but some

deflection may have occurred at the pubis joint in the experiment. If this were the case,

the strains near the pubis joint and along the ischium should have been much lower than

other areas around the acetabular rim. However, strains were found to be greatest at the

90

pubis joint and ischium during the experimental study, which was then confirmed by the

FE results. If compression did occur at the pubis joint, it was probably minimal since

deflection to this joint would act as an immediate strain relief to the pubis and ischium.

Palpation of the pubic cartilage demonstrated that the joint appeared to be an extension of

the trabecular bone, which suggests that the joint was relatively stiff.

CT is notorious for overestimating the thickness of cortical bone. Measurement

accuracy depends largely on the axial and longitudinal resolution of the acquisition

matrix and CT scanner collimation. The accuracy also depends on the energy settings,

pitch, and reconstruction algorithm. Prevrhal et al. determined that cortical bone

thickness could be estimated within 10% for cortices that were equal to or greater than

the minimum collimation of the CT scanner, which was approximately 0.7 mm for their

scanner. Errors increased progressively for cortices that were less than the minimum

collimation [37]. In the present study, a cortical bone phantom was used to assess the

measurement limits of the CT scanner and segmentation procedure simultaneously.

Results demonstrated that cortical thickness could be measured down to approximately

0.7 mm thick with less than 10% error.

In conclusion, our approach for subject-specific FE modeling of the pelvis has the

ability to predict cortical bone strains accurately during acetabular loading. Cortical bone

strains were most sensitive to changes in cortical thickness and cortical bone elastic

modulus. Deviations in other assumed and estimated input parameters had little effect

on the predicted cortical strains. Our approach has the potential for application to

individual patients based on volumetric CT scans. This will provide a means to examine

91

the biomechanics of the pelvis for cases when subject-specific geometry is important,

such as in the case of pelvic dysplasia.

92

REFERENCES

[1] Bergmann, G., Graichen, F., and Rohlmann, A., 1993, "Hip Joint Loading During

Walking and Running, Measured in Two Patients," J Biomech, 26, pp. 969-90. [2] Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A.,

Strauss, J., and Duda, G. N., 2001, "Hip Contact Forces and Gait Patterns from Routine Activities," J Biomech, 34, pp. 859-71.

[3] Michaeli, D. A., Murphy, S. B., and Hipp, J. A., 1997, "Comparison of Predicted

and Measured Contact Pressures in Normal and Dysplastic Hips," Med Eng Phys, 19, pp. 180-6.

[4] Ochsner, M. G., Jr., Hoffman, A. P., DiPasquale, D., Cole, F. J., Jr., Rozycki, G.

S., Webster, D. W., and Champion, H. R., 1992, "Associated Aortic Rupture-Pelvic Fracture: An Alert for Orthopedic and General Surgeons," J Trauma, 33, pp. 429-34.

[5] Rothenberger, D. A., Fischer, R. P., Strate, R. G., Velasco, R., and Perry, J. F., Jr.,

1978, "The Mortality Associated with Pelvic Fractures," Surgery, 84, pp. 356-61. [6] Adams, P., Davies, G. T., and Sweetnam, P., 1971, "Cortical Bone-Loss with

Age," Lancet, 2, pp. 1201-2. [7] Bombelli, R., 1983, Osteoarthritis of the Hip. Springer-Verlag, Berlin, Germany. [8] Croft, P., Cooper, C., Wickham, C., and Coggon, D., 1991, "Osteoarthritis of the

Hip and Acetabular Dysplasia," Ann Rheum Dis, 50, pp. 308-10. [9] Parfitt, A. M., 1984, "Age-Related Structural Changes in Trabecular and Cortical

Bone: Cellular Mechanisms and Biomechanical Consequences," Calcif Tissue Int, 36, pp. S123-8.

[10] Solomon, L., 1976, "Patterns of Osteoarthritis of the Hip," J Bone Joint Surg Br,

58, pp. 176-83. [11] Stulberg, S. D. and Harris, W. H., "Acetabular Dysplasia and Development of

Osteoarthritis of the Hip," presented at Proceedings of the second open scientific meeting of the Hip Society, St Louis, MO, 1974.

[12] Harris, W. H., 1986, "Etiology of Osteoarthritis of the Hip," Clin Orthop, pp. 20-

33. [13] Murray, R. O., 1965, "The Aetiology of Primary Osteoarthritis of the Hip," Br J

Radiol, 38, pp. 810-24.

93

[14] Afoke, N. Y., Byers, P. D., and Hutton, W. C., 1987, "Contact Pressures in the Human Hip Joint," J Bone Joint Surg Br, 69, pp. 536-41.

[15] Brown, T. D. and Shaw, D. T., 1983, "In Vitro Contact Stress Distributions in the

Natural Human Hip," J Biomech, 16, pp. 373-84. [16] Day, W. H., Swanson, S. A., and Freeman, M. A., 1975, "Contact Pressures in the

Loaded Human Cadaver Hip," J Bone Joint Surg Br, 57, pp. 302-13. [17] Hodge, W. A., Fijan, R. S., Carlson, K. L., Burgess, R. G., Harris, W. H., and

Mann, R. W., 1986, "Contact Pressures in the Human Hip Joint Measured in Vivo," Proc Natl Acad Sci U S A, 83, pp. 2879-83.

[18] Ipavec, M., Brand, R. A., Pedersen, D. R., Mavcic, B., Kralj-Iglic, V., and Iglic,

A., 1999, "Mathematical Modeling of Stress in the Hip During Gait," J Biomech, 32, pp. 1229-35.

[19] Ipavec, M., Iglic, A., Iglic, V. K., and Srakar, F., 1996, "Stress Distribution on the

Hip Joint Articular Surface During Gait," Pflugers Arch, 431, pp. R275-6. [20] Mavcic, B., Antolic, V., Brand, R., Iglic, A., Kralj-Iglic, V., and Pedersen, D. R.,

2000, "Peak Contact Stress in Human Hip During Gait," Pflugers Arch, 440, pp. R177-8.

[21] Mavcic, B., Pompe, B., Antolic, V., Daniel, M., Iglic, A., and Kralj-Iglic, V.,

2002, "Mathematical Estimation of Stress Distribution in Normal and Dysplastic Hips," Journal of Orthopaedic Research, 20, pp 1025-30.

[22] Calvo, E., Palacios, I., Delgado, E., Ruiz-Cabello, J., Hernandez, P., Sanchez-

Pernaute, O., Egido, J., and Herrero-Beaumont, G., 2001, "High-Resolution Mri Detects Cartilage Swelling at the Early Stages of Experimental Osteoarthritis," Osteoarthritis Cartilage, 9, pp. 463-72.

[23] Gupta, K. B., Duryea, J., and Weissman, B. N., 2004, "Radiographic Evaluation

of Osteoarthritis," Radiol Clin North Am, 42, pp. 11-41, v. [24] Fazzalari, N. L., Moore, R. J., Manthey, B. A., and Vernon-Roberts, B., 1992,

"Comparative Study of Iliac Crest and Subchondral Femoral Bone in Osteoarthritic Patients," Bone, 13, pp. 331-5.

[25] Fischer, K. J., Manson, T. T., Pfaeffle, H. J., Tomaino, M. M., and Woo, S. L.,

2001, "A Method for Measuring Joint Kinematics Designed for Accurate Registration of Kinematic Data to Models Constructed from Ct Data," J Biomech, 34, pp. 377-83.

94

[26] Dalstra, M., Huiskes, R., and van Erning, L., 1995, "Development and Validation of a Three-Dimensional Finite Element Model of the Pelvic Bone," J Biomech Eng, 117, pp. 272-8.

[27] Pytel, A. and Kiusalaas, J., 2003, Mechanics of Materials, vol. 14. Thomson,

Pacific Grove, CA. [28] Boissonnat, J.-D., 1988, "Shape Reconstruction from Planar Cross-Sections,"

Comp Vis Graph Img Proc, 44, pp. 1-29. [29] Schroeder, W. J., Zarge, J., and Lorensen, W. E., 1992, "Decimation of Triangle

Meshes," Computer Graphics (Proceedings of SIGGRAPH), 25. [30] Taubin, G., Zhang, T., and Golub, G., "Optimal Surface Smoothing as Filter

Design," Stanford University IBM RC-20404, 1996. [31] Schroeder, W. J., Avila, L. S., and Hoffman, W., 2002, The Visualization Toolkit:

An Object Orientated Approach to Computer Graphics, 3 ed. Kitware Inc. [32] Pawlak, T. P. and Yunus, S. M., 1991, "Solid Elements with Rotational Degrees

of Freedom: Part Ii Tetrahedron Elements," International Journal for Numerical Methods in Engineering, 31, pp. 593-610.

[33] Ahmad, S., 1970, "Analysis of Thick and Thin Shell Structures," International

Journal for Numerical Methods in Engineering, 2, pp. 419-451. [34] Hughes, T. J. and Liu, W. K., 1981, "Nonlinear Finite Element Analysis of Shells:

Part I. Two Dimensional Shells.," Computational Methods in Applied Mechanics, 27, pp. 167-181.

[35] Hughes, T. J. and Liu, W. K., 1981, "Nonlinear Finite Element Analysis of Shells:

Part Ii. Three Dimensional Shells.," Computational Methods in Applied Mechanics, 27, pp. 331-362.

[36] Hughes, T. J., 1980, "Generalization of Selective Integration Procedures to

Anisotropic and Nonlinear Media," International Journal for Numerical Methods in Engineering, 15, pp. 9.

[37] Prevrhal, S., Engelke, K., and Kalender, W. A., 1999, "Accuracy Limits for the

Determination of Cortical Width and Density: The Influence of Object Size and Ct Imaging Parameters," Phys Med Biol, 44, pp. 751-64.

95

[38] Nickoloff, E. L., Dutta, A. K., and Lu, Z. F., 2003, "Influence of Phantom Diameter, Kvp and Scan Mode Upon Computed Tomography Dose Index," Med Phys, 30, pp. 395-402.

[39] Suzuki, S., Yamamuro, T., Okumura, H., and Yamamoto, I., 1991, "Quantitative

Computed Tomography: Comparative Study Using Different Scanners with Two Calibration Phantoms," Br J Radiol, 64, pp. 1001-6.

[40] Dalstra, M., Huiskes, R., Odgaard, A., and van Erning, L., 1993, "Mechanical and

Textural Properties of Pelvic Trabecular Bone," J Biomech, 26, pp. 523-35. [41] Mooney, M., 1940, "A Theory of Large Elastic Deformation," J. Appl. Phys., 11,

pp. 582-92. [42] Little, R. B., Wevers, H. W., Siu, D., and Cooke, T. D., 1986, "A Three-

Dimensional Finite Element Analysis of the Upper Tibia," J Biomech Eng, 108, pp. 111-9.

[43] Cohen, J., Cohen, P., West, S. G., and Aiken, L. S., 2003, Applied Multiple

Regression Analysis for the Behavioral Sciences, 3rd ed. Lawrence Erlhaum Associates, Publishers, Mahwah, NJ.

[44] Evans, F. G., 1973, Mechanical Properties of Bone. Thomas, Springfield, IL. [45] Schuller, H. M., Dalstra, M., Huiskes, R., and Marti, R. K., 1993, "Total Hip

Reconstruction in Acetabular Dysplasia. A Finite Element Study," J Bone Joint Surg Br, 75, pp. 468-74.

[46] Vasu, R., Carter, D. R., and Harris, W. H., 1982, "Stress Distributions in the

Acetabular Region--I. Before and after Total Joint Replacement," J Biomech, 15, pp. 155-64.

[47] Carter, D. R., Vasu, R., and Harris, W. H., 1982, "Stress Distributions in the

Acetabular Region--Ii. Effects of Cement Thickness and Metal Backing of the Total Hip Acetabular Component," J Biomech, 15, pp. 165-70.

[48] Rapperport, D. J., Carter, D. R., and Schurman, D. J., 1985, "Contact Finite

Element Stress Analysis of the Hip Joint," J Orthop Res, 3, pp. 435-46. [49] Pedersen, D. R., Crowninshield, R. D., Brand, R. A., and Johnston, R. C., 1982,

"An Axisymmetric Model of Acetabular Components in Total Hip Arthroplasty," J Biomech, 15, pp. 305-15.

96

[50] Huiskes, R., 1987, "Finite Element Analysis of Acetabular Reconstruction. Noncemented Threaded Cups," Acta Orthop Scand, 58, pp. 620-5.

[51] Dalstra, M. and Huiskes, R., 1995, "Load Transfer across the Pelvic Bone," J

Biomech, 28, pp. 715-24. [52] Spears, I. R., Pfleiderer, M., Schneider, E., Hille, E., and Morlock, M. M., 2001,

"The Effect of Interfacial Parameters on Cup-Bone Relative Micromotions. A Finite Element Investigation," J Biomech, 34, pp. 113-20.

[53] Garcia, J. M., Doblare, M., Seral, B., Seral, F., Palanca, D., and Gracia, L., 2000,

"Three-Dimensional Finite Element Analysis of Several Internal and External Pelvis Fixations," J Biomech Eng, 122, pp. 516-22.

[54] Konosu, A., "Development of a Biofidelic Human Pelvic Fe-Model with Several

Modifications onto a Commercial Use Model for Lateral Loading Conditions," presented at SAE International, 2003.

[55] Oonishi, H., Isha, H., and Hasegawa, T., 1983, "Mechanical Analysis of the

Human Pelvis and Its Application to the Artificial Hip Joint--by Means of the Three Dimensional Finite Element Method," J Biomech, 16, pp. 427-44.

[56] Dawson, J. M., Khmelniker, B. V., and McAndrew, M. P., 1999, "Analysis of the

Structural Behavior of the Pelvis During Lateral Impact Using the Finite Element Method," Accid Anal Prev, 31, pp. 109-19.

[57] Lappi, V. G., King, M. S., and Lemay, I., 1979, "Determination of Elastic

Constants for Human Femurs," J Biomech Eng, 101, pp. 193-97. [58] Snyder, S. M. and Schneider, E., 1991, "Estimation of Mechanical Properties of

Cortical Bone by Computed Tomography," J Orthop Res, 9, pp. 422-31. [59] Armstrong, C. G., Bahrani, A. S., and Gardner, D. L., 1979, "In Vitro

Measurement of Articular Cartilage Deformations in the Intact Human Hip Joint under Load," J Bone Joint Surg Am, 61, pp. 744-55.

CHAPTER 4

FACTORS INFLUENCING CARTILAGE THICKNESS MEASUREMENTS

WITH MULTI-DETECTOR CT: A PHANTOM STUDY1

ABSTRACT

The purpose of this study was to prospectively assess in a phantom the accuracy and

detection limits of cartilage thickness measurements from MDCT arthrography as a function

of contrast agent concentration, imaging plane, spatial resolution, joint space and tube

current, using known measurements as the reference standard. A phantom with nine

chambers was manufactured. Each chamber had a nylon cylinder encased by sleeves of

aluminum and polycarbonate to simulate trabecular bone, cortical bone, and cartilage.

Variations in simulated cartilage thickness and joint space were assessed. The phantom was

scanned with and without contrast agent on three separate days, with chamber axes both

perpendicular and parallel to the scanner axis. Images were reconstructed at intervals of both

1.0 and 0.5 mm. Contrast agent concentration and tube current were varied. Simulated

cartilage thickness was determined from image segmentation. Root mean squared and mean

1 Reprint of article In Press: “Factors Influencing Cartilage Thickness Measurements with Multi-Detector CT: A Phantom Study”, Radiology. Anderson, A.E., Ellis, B.J., Peters, C.L., Weiss, J.A. Accepted February 16th 2007.

98

residual errors were used to characterize the measurements. CT scanner and image

segmentation reproducibility were determined. Simulated cartilage was accurately

reconstructed (<10% error) for thicknesses >1.0 mm when no contrast agent or a low

concentration of contrast agent (25%) was used. Errors grew as concentration of contrast

agent increased. Decreasing the simulated joint space to 0.5 mm caused slight increases

in error; below 0.5 mm errors grew exponentially. Measurements from anisotropic image

data were less accurate than those for isotropic data. Altering tube current did not affect

accuracy. This study establishes lower bounds for accuracy and repeatability of cartilage

thickness measurement using MDCT arthrography, and provides data pertinent to

choosing contrast agent concentration, joint spacing, scanning plane, and spatial

resolution to optimize accuracy.

99

INTRODUCTION

Three-dimensional reconstruction of volumes and surfaces from medical image

data has become increasingly common, both for the diagnosis and treatment of patients

with joint pathologies and to define patient-specific geometry for computational models

and computer-assisted surgery. Of particular interest is the ability to visualize the

spatially varying thickness of articular cartilage in diarthrodial joints, which may be

useful for preoperative surgical planning (e.g. cartilage transfer procedures), precise

quantification of cartilage loss due to osteoarthritis (epidemiological studies), tracking of

cartilage degeneration over time, and providing guidelines for interpreting the results of

biomechanical models which aim to investigate joint contact mechanics. With a-priori

knowledge of the reconstruction error the clinician or researcher can make informed

interpretations regarding cartilage thickness.

The advent and availability of multi-detector CT has yielded substantial advances

over single detector CT by providing shorter data acquisition times, thinner beam

collimation, multi-planar scanning and higher temporal and spatial resolution. Recent

evidence suggests that multi-detector CT (MDCT) arthrography may be more sensitive

than MRI for detecting cartilaginous lesions [1-5] and quantifying cartilage thickness [6],

although fat-suppressed spoiled gradient-echo in the steady state (FS-SPGR) is still

considered the best imaging protocol for imaging articular cartilage [7-16]. While a

substantial body of research has examined MRI cartilage reconstruction errors (e.g. [17-

22]), less attention has been given to CT arthrography [6, 18, 23]. Nevertheless,

estimates of cartilage thickness determined via MRI image data are often validated by

100

direct comparison with CT arthrography results [18, 19], which may erroneously imply

that CT arthrography is the “reference standard” for such estimations.

Studies that have compared cartilage thickness measurements estimated from CT

arthrography data to those obtained from physical measurements of anatomical sections

have generally been qualitative assessments [18, 23]. To our knowledge only one study

compared quantitative measurements of cartilage thickness between reconstructed MDCT

arthrography images to excised tissue samples [6]. However, the use of harvested

cartilage plugs in this study limited the range of cartilage thickness that could be analyzed

[6].

CT imaging and subsequent three-dimensional reconstruction of articular cartilage

has a variety of clinical and basic science applications. Although CT arthrography is

most often performed in an effort to diagnose articular cartilage damage rather than to

quantify cartilage thickness, an understanding of the spatial variation in thickness of

articular cartilage in joints without visible damage could prove to be a valuable clinical

tool. For example, recent evidence suggests that cartilage may actually swell in the early

stages of OA [24]. It would be useful, therefore, to quantify cartilage thickness using CT

arthrography in patients who complain of pain that may be related to OA but do not have

direct evidence of radiographic thinning or localized defects. From the point of view of

experimental investigations of cartilage contact mechanics using cadaveric tissues,

quantification of differences in reconstruction accuracy between standard CT and CT

arthrography would clarify whether cadaveric joints should be completely dissected and

imaged with air or if the joint capsule should be left intact to obtain the highest accuracy.

101

The bounds of cartilage thickness detection and hence the ultimate reconstruction error

remains unknown for MDCT arthrography. In addition, the influence of imaging parameters

on the ability to detect and reconstruct articular cartilage from MDCT arthrography image

data has not been assessed. Thus, the purpose of our study was To prospectively assess in a

phantom the accuracy and detection limits of cartilage thickness measurements from

MDCT arthrography as a function of contrast agent concentration, imaging plane, spatial

resolution, joint space and tube current, using known measurements as the reference

standard.

102

MATERIALS AND METHODS

Phantom Description

An imaging phantom was designed and manufactured to quantify the error in

reconstructing cartilage thickness (CNA Precision Machine, Ogden, UT) (Figure 4.1).

The phantom body was constructed using nylon (Natural Cast Nylon, Professional

Plastics Inc., Fullerton, CA). Nine chambers were drilled into the phantom body (Figure

4.1). Each chamber was composed of a central nylon cylinder encased by cylindrical

sleeves of aluminum and polycarbonate (Standard Polycarbonate, Professional Plastics

Inc., Fullerton, CA). The central nylon cylinder simulated trabecular bone, the

cylindrical sleeve of aluminum represented cortical bone, and the outer cylindrical sleeve

simulated cartilage (Figure 4.1 B). All aluminum cylinders were machined to a wall

thickness of 1.00 mm to represent cortical bone with constant thickness. The

polycarbonate cylindrical sleeves were machined to wall thickness values of 0.25, 0.50,

0.75, 1.00, 2.00, and 4.00 mm (Phantom Chambers 1-6, Figure 4.1 A). An outer

polycarbonate four-prong spacer was press-fit into each of the chambers between the

outer layer of simulated cartilage and adjacent nylon phantom body (Figure 4.1 B). The

spacer held the central cylinders securely in place and provided a “joint space” that could

be filled with contrast agent. The joint space in phantom chambers 1-6 (Figure 4.1 A)

was held constant at 2.0 mm. A varying joint space (0.25, 0.50, and 1.00 mm) with

constant simulated cartilage thickness of 2.00 mm was used in the remaining three

compartments (Phantom Chambers 7-9, Figure 4.1 A). Finally, nylon threaded caps were

used to seal the fluid in the chambers. A micrometer with accuracy of ±0.01 mm was

103

used by the manufacturer to determine the wall thickness tolerance of the aluminum and

polycarbonate cylindrical sleeves, representing cortical bone and cartilage, respectively.

The tolerance was reported to be within ± 0.07 mm.

Nylon, polycarbonate and aluminum were chosen because their x-ray attenuation

values are similar to trabecular bone, cartilage and cortical bone, respectively [25-28].

The size of the phantom (250 x 250 mm) was representative of a typical field of view

(FOV) for imaging human diarthrodial joints. The outer diameter of each compartment

(outer boundary of simulated cartilage) was kept constant at 52 mm while the diameter of

the aluminum sleeve and central nylon cylinder were adjusted between 38–46 mm to

accommodate differences in cartilage thickness and joint spacing. This range of cylinder

diameters is similar to that reported in the literature for human femoral and humeral

heads [29-31]. The range of cartilage thickness (0.25–4.00 mm) was chosen to represent

the range reported in the literature for human articular cartilage [32, 33].

104

Figure 4.1. A) schematic of phantom used to assess accuracy and detection limits of MDCT in the transverse plane. The longitudinal (L) imaging plane is also shown. Simulated cartilage thicknesses of 4.0, 2.0, 1.0, 0.75, 0.5, and 0.25 mm with constant joint space of 2.0 mm were used in chambers 1-6, respectively. A constant thickness of 2.0 mm with joint spaces of 1.0, 0.5, and 0.25 mm were used in chambers 7-9, respectively. B) exploded view of chamber #1 detailing: (1) nylon center cylinder to represent trabecular bone, (2) 1 mm thick aluminum sleeve to represent cortical bone, (3) polycarbonate sleeve to represent cartilage, (4) joint space, (5) polycarbonate four-pronged spacer for creating the joint space, and (6) bulk of the phantom body made using nylon. C) CT scan of the phantom with contrast agent and inset showing image details of chamber #1. Number call-outs correspond to the same details provided above.

L

L

1 2 3

4 5 6

7 8 9

1

23

4

56

4

3

1

2

56

A)

B)

C)

105

CT Imaging Protocol

All phantom scans were performed with a Siemens SOMATOM® Sensation 64

CT Scanner (Siemens Medical Solutions USA, Malvern, PA). This scanner makes use of

a periodic motion of the focal spot in the longitudinal direction to double the number of

simultaneously acquired slices with the goal of attaining improved spatial resolution and

elimination of spiral artifacts regardless of spiral pitch. Constant scanning parameters for

this study were: 120 kVp, 512 x 512 matrix, 300 mm FOV, and 1 mm slice thickness. A

total of 6 fluid scans and 4 non-enhanced scans were performed. The imaging protocol

detailed below was performed on three separate days to assess the reproducibility of the

CT scanner and segmentation procedure.

Contrast Enhanced Scans

Contrast agent (Omnipaque 350 mgI/ML, GE Healthcare, Princeton, NJ) was

mixed with 1% lidocaine HCL (Hospira Inc., Lake Forest, IL) in separate concentrations

of 25, 50, and 75%. The phantom was scanned using a tube current of 200 mAs for each

of the three concentrations (n = 3 scans) in the “transverse” or frontal plane (Figure 4.1

A). The laser guide was used to align the CT slice axis perpendicular to the phantom

chambers longitudinal axes, thereby minimizing volumetric averaging between slices.

Additional transverse scans were conducted with tube currents of 150 and 250 mAs using

the phantom filled with 50% contrast agent (n = 2 scans). A scan with tube current of

200 mAs was performed on the phantom filled with 50% contrast agent parallel to the

phantom chambers “longitudinal” axes (Figure 4.1 A) to intentionally introduce

volumetric averaging.

106

Non-Enhanced Scans

The phantom was scanned without fluid to estimate the error in cartilage thickness

reconstruction for disarticulated, dissected cadaveric joints. Non-enhanced scans were

performed in the transverse plane using tube currents of 150, 200, and 250 mAs (n = 3

scans). A final non-enhanced scan was performed with a tube current of 200 mAs

parallel to the phantom chambers longitudinal axes to intentionally introduce volumetric

averaging between successive slices.

Image Segmentation, Surface Reconstruction, and Measurement of Thickness

Phantom image data were transferred to a Linux workstation for post-processing.

Image data were re-sampled post-CT using 0.5 mm slice intervals for the contrast

enhanced and non-enhanced longitudinal scans to assess changes in accuracy between an

anisotropic spatial resolution (0.586 x 1.0 x 0.586 mm) and near isotropic resolution

(0.586 x 0.5 x 0.586 mm). Thinner post-scan reconstructions in the transverse plane

would have been ambiguous since the curvature of the phantom chambers did not change

as slices were taken through this direction.

Separate splines for the outer surface of the aluminum cylinder, representing

cortical bone, and the boundary between the polycarbonate cylinder and air (non-

enhanced scan) or contrast agent (enhanced scan), representing the outer layer of

simulated cartilage, were extracted from the image data. Both automatic and semi-

automatic thresholding techniques were employed using commercial segmentation

software (Amira 4.1, Mercury Computer Systems, Chelmsford, MA).

107

Each dataset was automatically thresholded using a masking technique available

in Amira 4.1, which allows the user to highlight pixels over a range of defined intensities.

For datasets with contrast agent included, the mask was adjusted incrementally until all of

the pixels representing nylon (the bulk of the phantom body) were excluded. Thus, pixels

with intensities greater than this value were masked as contrast agent and simulated

cortical bone whereas values less were defined as simulated cartilage. The same masking

procedure was used for the non-enhanced scan datasets to define the simulated cortical

bone boundary; however, the boundary between simulated cartilage and air was defined

by reversing the mask such that all pixels representing the nylon body of the phantom

were included. As mentioned above, the masking procedure was performed for each CT

dataset separately to ensure that the appropriate threshold range was chosen

independently of alterations in tube current, contrast agent concentration, spatial

resolution or scanner direction. Following masking of all of the datasets it was later

determined that inter-scan threshold values varied by less than 5%.

Due to CT volumetric averaging it was necessary to utilize a semi-automatic

thresholding technique for datasets where contrast agent was included. However, this

procedure was only required for phantom chambers with simulated cartilage thickness of

0.5 and 0.25 mm (chambers 5 and 6, Figure 4.1 A); simulated cartilage thicker than this

was effectively segmented by the automatic method, regardless of contrast agent

concentration, tube current, spatial resolution or scanner direction. For the 0.5 and 0.25

mm chambers the baseline automatic threshold value was first used to define a general

segmentation spline. Next, regions where pixels blended together were separated using a

108

paintbrush tool available in Amira 4.1 such that the resulting spline followed the general

boundary between simulated cartilage and contrast agent. Although volumetric

averaging was present, the intensity gradient between contrast agent and simulated

cartilage was strong enough to allow for easy visual separation. To ensure uniformity, all

of the semi-automatic segmentations were performed by the senior author, A.E.A.

Splines were stacked upon one another and triangulated using the Marching

Cubes algorithm [34] to form surfaces that represented the outer surfaces of simulated

cortical bone and cartilage. To preserve the native splines of the CT image data, the

resulting polygonal surfaces were not altered via decimation or smoothing. A published

algorithm was used to assign thickness to each of the nodes defining the simulated

cartilage surface [35]. The algorithm has been tested for accuracy using concentric

cylinders with known thickness. Reported errors were less than 2% [35].

109

Error Analysis

Thickness values were analyzed to determine the accuracy and detection limit of

MDCT and to investigate the influence of tube current, joint spacing, contrast agent

concentration, and imaging plane. The overall thickness accuracy for each phantom

chamber was assessed using the root mean squared (RMS) error criteria:

RMS = ( )1 2

2

1

nCT Phantom

ii

t t n=

⎡ ⎤−⎢ ⎥⎣ ⎦∑ , (4.1)

where the summation is over the number of surface nodes n and tPhantom is a constant

thickness that was assessed by direct manufacturer measurement of the phantom. The

mean residual error was calculated to determine the directionality of the error:

Mean Residual = ( )1

nCT Phantom

ii

t t n=

−∑ . (4.2)

Statistical Analysis

Descriptive statistics (i.e., quantification of means and standard deviations that

cannot ascertain statistical significance) were calculated using statistical software (SPSS

11.5 for Windows 2002, SPSS Inc. Chicago, IL). Specifically, RMS and mean residual

errors were averaged for the three days that CT scans were conducted. The resulting

means were plotted (SigmaPlot 8.0, Systat Software Inc., San Jose, CA) with standard

deviation error bars to indicate the inter-scan variation in reconstruction accuracy.

110

RESULTS

Contrast Enhanced Scans

There were notable differences in the average RMS and mean residual error due

to alterations in contrast agent concentration (Figure 4.2). The simulated cartilage of the

phantom was accurately reconstructed (less than 10% RMS and mean residual error) for

thickness greater than 1.0 mm when the lowest concentration of contrast agent (25%) was

used and the direction of the CT scan was transverse to the phantom (Figure 4.2).

Transverse scan RMS errors grew progressively as the concentration was increased from

25% – 75% for values of thickness greater than 0.75 mm (Figure 4.2 A). An increase in

contrast agent concentration resulted in a greater tendency for simulated cartilage to be

underestimated for values between 1.0 and 4.0 mm thick (Figure 4.2 B). However, a shift

in error from under to overestimation occurred as the thickness approached the spatial

resolution of the image data (0.586 x 0.586 mm) (Figure 4.2 B).

Substantial differences in average reconstruction errors were also noted when the

scanner direction and spatial resolution were altered (Figure 4.3). The anisotropic

longitudinal reconstructions at 50% concentration produced RMS and mean residual

errors greater than the corresponding transverse and near-isotropic longitudinal dataset at

50% concentration for simulated cartilage thicker than 1.0 mm (Figure 4.3). Finally,

altering the tube current resulted in negligible differences over the range of simulated

cartilage thickness analyzed (data not shown).

111

True Thickness (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Mea

n R

esid

ual E

rror

(% o

f tru

e th

ickn

ess)

-20

-10

0

10

20

30

40

50

80

100

12025%50%75%

Figure 4.2. Simulated cartilage RMS (A) and mean residual (B) reconstruction errors for the transverse contrast enhanced scan datasets as a function of contrast agentconcentration. RMS errors grew progressively as the contrast agent concentrationincreased (for thickness > 0.75 mm). The directionality of the error was dependent on the contrast agent concentration and simulated cartilage thickness.

True Thickness (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Roo

t Mea

n Sq

uare

d Er

ror (

% o

f tru

e th

ickn

ess)

0

10

20

30

40

50

60100

120

140 25%50%75%

A)

B)

112

True Thickness (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Mea

n R

esid

ual E

rror

(% o

f tru

e th

ickn

ess)

-30-20-10

0102030405060708090

100 50%Longitudinal 50%Longitudinal Isotropic 50%

Figure 4.3. Simulated cartilage RMS (A) and mean residual (B) reconstruction errors for the transverse contrast enhanced scan datasets at 50% concentration as a function ofimaging plane direction and spatial resolution. Errors were greatest for the anisotropic longitudinal data reconstructions. The longitudinal isotropic reconstructions yieldederrors more consistent with the transverse scan results.

True Thickness (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Roo

t Mea

n Sq

uare

d Er

ror (

% o

f tru

e th

ickn

ess)

0

10

20

30

40

50

60

70

80

90

100

110

120 Transverse 50%Longitudinal 50%Longitdinal Isotropic 50%

B)

113

There were differences in RMS errors over the range of joint spaces studied due

to changes in contrast agent concentration and scanner direction (Figure 4.4) but not due

to alterations in tube current (data not shown). Errors increased as the concentration of

contrast agent was increased (Figure 4.4). RMS errors for each individual transverse

scan increased slightly when the joint space was decreased from 2.0 – 0.5 mm; however,

below 0.5 mm errors grew exponentially (Figure 4.4). The anisotropic longitudinal

dataset (1.0 mm reconstruction) produced greater RMS errors than the corresponding

transverse and near-isotropic longitudinal scan datasets (0.5 mm reconstruction) over the

full range of joint spaces analyzed (Figure 4.4). Mean residual error analysis indicated

that simulated cartilage thickness was underestimated for all datasets and that these errors

were the smallest for the transverse 25% scan (data not shown).

Examination of the standard deviation error bars in Figures 4.2 – 4.4 indicated a

high level of reproducibility for simulated cartilage between 0.78 – 4.0 mm thick. The

standard deviation error bars also did not overlap adjacent results within this range.

Standard deviations were much larger for simulated cartilage 0.25 – 0.5 mm thick and

error bars overlapped adjacent data points.

114

Figure 4.4. Simulated cartilage RMS errors as a function of joint space thickness, contrastagent concentration, imaging plane direction, and spatial resolution. Errors increased as contrast agent concentration increased. Reconstructions from the isotropic longitudinaldataset were more accurate than the anisotropic dataset in the same imaging plane.

True Joint Space(mm)0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Roo

t Mea

n Sq

uare

d Er

ror (

% o

f tru

e th

ickn

ess)

0

5

10

15

20

25

30

35 Transverse 25%Transverse 50%Transverse 75%Longitudinal 50%Longitudinal Isotropic 50%

115

Non-Enhanced Scans

Reconstructions of the non-enhanced transverse scan at 200 mAs resulted in RMS

errors less than 10% for thickness values greater than 1.0 mm (Figure 4.5 A). RMS

errors for the non-enhanced scans were within 2% of those reported for the contrast

enhanced transverse scans at 25% contrast agent concentration for simulated cartilage

0.78 – 4.0 mm thick. RMS errors grew exponentially for simulated cartilage less than 1.0

mm thick; however, the RMS error leveled out between 0.5 – 0.25 mm (Figure 4.5 A).

The leveling point in the RMS plot aligned well with corresponding points of inflection

on the mean residual error plot (Figure 4.5 B). Therefore, the lack of increase in RMS

error at 0.25 mm was due to a shift from an underestimation to overestimation of

cartilage thickness. RMS errors for the longitudinal and near-isotropic longitudinal scan

datasets were similar to the transverse scan for 2.0 and 4.0 mm thick simulated cartilage;

however errors grew exponentially below 2.0 mm (Figure 4.5 A). Errors for the

longitudinal anisotropic scan were substantially greater than the transverse and near-

isotropic longitudinal scans for simulated cartilage less than 2.0 mm thick (Figure 4.5 A).

Altering the tube current from 150 – 250 mAs did not have an appreciable effect on the

RMS or mean residual errors in the transverse plane (data not shown).

As with the contrast enhanced scans, standard deviation error bars of the non-

enhanced scans were negligible for thicker simulated cartilage (0.78 – 4.0 mm thick) but

increased when thickness was decreased below this range. Standard deviation error bars

also did not overlap at adjacent data points within this range but did for thicknesses less

than 0.78 mm.

116

True Thickness (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Mea

n R

esid

ual E

rror

(% o

f tru

e th

ickn

ess)

-20

-10

0

10

20

30

40

50

100

120

140TransverseLongitudinalLongitudinal Isotropic

Figure 4.5. Simulated cartilage RMS (A) and mean residual (B) reconstruction errors forthe non-enhanced scan datasets at 200 mAs as a function of imaging plane direction andspatial resolution. RMS errors for the longitudinal isotropic datasets were consistentlyless than the anisotropic dataset for simulated cartilage less than 2.0 mm thick.

True Thickness (mm)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Roo

t Mea

n Sq

uare

d Er

ror (

% o

f tru

e th

ickn

ess)

0

10

20

30

40

50

60

120

140

160TransverseLongitudinalLongitudinal Isotropic

A)

B)

117

DISCUSSION

To our knowledge our study is the first quantify the detection limits and accuracy

of MDCT using a phantom. The simulated cartilage of the phantom was accurately

reconstructed (less than 10% RMS and mean residual error) for thicknesses greater than

1.0 mm when either no contrast agent or a low concentration of contrast agent (25%) was

used. The results of our study also demonstrated that the accuracy of CT cartilage

reconstructions were dependent on the concentration of contrast agent, imaging plane

direction, spatial resolution and to a lesser extent, joint spacing. Alterations in the

scanner tube current did not affect the accuracy of simulated cartilage thickness

reconstructions in the range tested for both contrast enhanced and non-enhanced scans.

Care was taken to control confounding factors in our study. The physical

thickness of the phantom was measured to a tolerance of ± 0.07 mm, thus variations in

the true thickness of the phantom would not have a substantial influence on the perceived

values of phantom thickness as assessed by CT. In addition, separate scans were done

whenever a new intervention (e.g. scan direction, tube voltage, and contrast agent

concentration) was performed in an effort to isolate these effects. The entire protocol

was repeated on separate days and only minor inter-scan variation was noted for

simulated cartilage between 0.78 – 4.0 mm for both contrast enhanced and non-enhanced

scans. Therefore, any differences noted in reconstruction error within this range were

due to the intervention studied rather than from confounding factors such as thresholding

procedure or CT scanner variability.

118

The results of the contrast enhanced scan reconstructions showed a direct

relationship between contrast agent concentration and reconstruction error. An

explanation for this finding is as follows: as the concentration was increased larger pixel

intensity gradients were established at the boundary between cartilage and contrast agent.

This initiated more intense volumetric averaging at this boundary and resulted in a

greater tendency for cartilage thickness to be underestimated. However, a shift in error

from under to overestimation occurred as the thickness approached the spatial resolution

of the image data (0.586 x 0.586 mm). This was due to the fact that thickness could not

drop much below the width of a single pixel without extensive surface decimation and

smoothing. Therefore, although CT has been shown to overestimate the thickness of thin

structures [25, 26], the results of our study demonstrate that the direction of the error is

dependent on the concentration of the joint fluid and spatial resolution of the image data

when CT arthrography is used.

El-Khoury et al. [6] compared ankle cartilage measurements obtained from

MDCT double-contrast arthrography and three-dimensional FS-SPGR MRI to physical

measurements of excised plugs from cadaveric ankles (ranging from 1 – 2 mm thick) and

found that CT was more accurate than MRI. Differences in segmentation methodology,

joint geometry, and arthrography technique (double contrast) between this study and our

work make exact comparisons impossible. Nevertheless, El-Khoury’s best-fit line of

physical plug measurements plotted against MDCT estimates indicated that CT

underestimated cartilage thickness by approximately 5% [6], which has the same

119

direction and similar magnitude of error as the 25% concentration agent results of our

study over the same range of thickness.

Study Limitations

The results of our study must be interpreted in light of the inherent differences

between measurements obtained from a phantom to those taken from experimental

studies that use real cartilage specimens. It is well known that articular cartilage exhibits

depth and location dependent inhomogeneities in material structure [36-38], and these

factors were not part of our study design. In addition, although similar [25-28], small

differences will exist between x-ray attenuation values of real tissue to that of the

materials used in our phantom. Finally, diarthrodial joints such as the shoulder and hip

have spherical geometry but the phantom chambers were cylindrical. Nevertheless, our

approach allowed us to eliminate potential confounding factors such as geometry, tissue

homogeneity, and measurement technique. In addition, a total of three scans were

performed and descriptive statistics utilized to assess reproducibility, which was a

statistical methodology consistent with a phantom study related to MRI slice thickness

[39].

For chambers with simulated thicknesses of 0.25 and 0.5 mm it was necessary to

use a semi-automatic method to segment simulated cartilage from the contrast enhanced

scan datasets. Reconstruction errors from these chambers could have been influenced by

user technique. However, the magnitude of the standard deviation error bars for

thicknesses within this range were very similar to the non-enhanced scan deviation bars,

and a purely automatic segmentation technique was used for the latter datasets. The

120

standard deviations for simulated cartilage less than 0.78 thick were substantial for both

contrast enhanced and non-enhanced scans, with bars overlapping adjacent data points;

therefore, it appears that there is little difference between contrast enhanced and non-

enhanced scans for the thinnest phantom chambers.

The phantom was designed to simulate the interface between cartilage and

cortical bone. There was likely some image thinning of polycarbonate due to volumetric

averaging between the polycarbonate and adjacent aluminum cylindrical sleeve; however

the wall thickness of aluminum was held constant for each phantom cylinder and the

thresholding protocol was not biased to changes between phantom chambers or whole

datasets. Thus, any errors introduced would be consistent over all datasets, which would

eliminate simulated cortical bone as a confounding factor to our study.

Practical Applications

The results of our study provide minimum bounds for the errors in cartilage

thickness measurement using MDCT and provide guidelines for practical use. It must be

emphasized that the phantom reconstruction errors are likely a best case result since

confounding factors were controlled. A lower concentration of contrast agent is likely to

reduce the amount of volumetric averaging between cartilage and contrast agent since it

was shown that higher concentrations caused the simulated cartilage to appear thinner

than its true thickness. In addition, joint spacing should be maximized prior to scanning,

which can be done by completely filling the joint capsule with the diluted contrast

solution and/or applying traction to the joint. Failure to do so will result in increased

errors when the joint space reaches a critical threshold (occurring at 0.5 mm in our

121

phantom study). Finally, CT image reconstructions should be chosen such that isotropic

or near-isotropic spatial resolutions are achieved. Fortunately, MDCT (unlike its

predecessors) offers the ability to do this without increased radiation dosage to the patient

[40].

From a basic science point of the view the following conclusion can be made:

assuming that sufficient joint space is maintained and a low contrast agent concentration

is used, one could expect similar cartilage reconstruction accuracies when cadaveric

tissues are CT scanned with or without contrast agent since reconstruction errors were

similar between non-enhanced and contrast enhanced scan (25% concentration) datasets.

However, given the additional technical challenges of keeping joint fluid within the

capsule of a dissected joint, it seems more appropriate to scan the specimen without

contrast agent.

In conclusion, the accuracy of MDCT with and without arthrography is dependent

on several factors including the contrast agent concentration, joint spacing, imaging

plane, and spatial resolution. An improved understanding of the detection limits and

accuracy of MDCT cartilage reconstructions will assist in the diagnosis of joint

pathologies, interpretation of biomechanical models, and design of epidemiological

studies aimed to investigate changes in cartilage thickness.

122

REFERENCES

[1] Vande Berg, B. C., Lecouvet, F. E., Poilvache, P., Jamart, J., Materne, R., Lengele, B., Maldague, B., and Malghem, J., 2002, "Assessment of knee cartilage in cadavers with dual-detector spiral CT arthrography and MR imaging," Radiology, 222(2), pp. 430-436.

[2] Waldt, S., Bruegel, M., Ganter, K., Kuhn, V., Link, T. M., Rummeny, E. J., and

Woertler, K., 2005, "Comparison of multislice CT arthrography and MR arthrography for the detection of articular cartilage lesions of the elbow," Eur Radiol, 15(4), pp. 784-791.

[3] Schmid, M. R., Pfirrmann, C. W., Hodler, J., Vienne, P., and Zanetti, M., 2003,

"Cartilage lesions in the ankle joint: comparison of MR arthrography and CT arthrography," Skeletal Radiol, 32(5), pp. 259-265.

[4] Nishii, T., Tanaka, H., Nakanishi, K., Sugano, N., Miki, H., and Yoshikawa, H.,

2005, "Fat-suppressed 3D spoiled gradient-echo MRI and MDCT arthrography of articular cartilage in patients with hip dysplasia," AJR Am J Roentgenol, 185(2), pp. 379-385.

[5] Daenen, B. R., Ferrara, M. A., Marcelis, S., and Dondelinger, R. F., 1998,

"Evaluation of patellar cartilage surface lesions: comparison of CT arthrography and fat-suppressed FLASH 3D MR imaging," Eur Radiol, 8(6), pp. 981-985.

[6] El-Khoury, G. Y., Alliman, K. J., Lundberg, H. J., Rudert, M. J., Brown, T. D.,

and Saltzman, C. L., 2004, "Cartilage thickness in cadaveric ankles: measurement with double-contrast multi-detector row CT arthrography versus MR imaging," Radiology, 233(3), pp. 768-773.

[7] Eckstein, F., Stammberger, T., Priebsch, J., Englmeier, K. H., and Reiser, M.,

2000, "Effect of gradient and section orientation on quantitative analysis of knee joint cartilage," J Magn Reson Imaging, 11(4), pp. 469-470.

[8] Eckstein, F., Westhoff, J., Sittek, H., Maag, K. P., Haubner, M., Faber, S.,

Englmeier, K. H., and Reiser, M., 1998, "In vivo reproducibility of three-dimensional cartilage volume and thickness measurements with MR imaging," AJR Am J Roentgenol, 170(3), pp. 593-597.

[9] Sittek, H., Eckstein, F., Gavazzeni, A., Milz, S., Kiefer, B., Schulte, E., and

Reiser, M., 1996, "Assessment of normal patellar cartilage volume and thickness using MRI: an analysis of currently available pulse sequences," Skeletal Radiol, 25(1), pp. 55-62.

123

[10] Recht, M. P., Piraino, D. W., Paletta, G. A., Schils, J. P., and Belhobek, G. H., 1996, "Accuracy of fat-suppressed three-dimensional spoiled gradient-echo FLASH MR imaging in the detection of patellofemoral articular cartilage abnormalities," Radiology, 198(1), pp. 209-212.

[11] Recht, M. P., Kramer, J., Marcelis, S., Pathria, M. N., Trudell, D., Haghighi, P.,

Sartoris, D. J., and Resnick, D., 1993, "Abnormalities of articular cartilage in the knee: analysis of available MR techniques," Radiology, 187(2), pp. 473-478.

[12] Disler, D. G., McCauley, T. R., Kelman, C. G., Fuchs, M. D., Ratner, L. M.,

Wirth, C. R., and Hospodar, P. P., 1996, "Fat-suppressed three-dimensional spoiled gradient-echo MR imaging of hyaline cartilage defects in the knee: comparison with standard MR imaging and arthroscopy," AJR Am J Roentgenol, 167(1), pp. 127-132.

[13] Disler, D. G., McCauley, T. R., Wirth, C. R., and Fuchs, M. D., 1995, "Detection

of knee hyaline cartilage defects using fat-suppressed three-dimensional spoiled gradient-echo MR imaging: comparison with standard MR imaging and correlation with arthroscopy," AJR Am J Roentgenol, 165(2), pp. 377-382.

[14] Gold, G. E., Reeder, S. B., Yu, H., Kornaat, P., Shimakawa, A. S., Johnson, J. W.,

Pelc, N. J., Beaulieu, C. F., and Brittain, J. H., 2006, "Articular cartilage of the knee: rapid three-dimensional MR imaging at 3.0 T with IDEAL balanced steady-state free precession--initial experience," Radiology, 240(2), pp. 546-551.

[15] Gold, G. E., Hargreaves, B. A., Vasanawala, S. S., Webb, J. D., Shimakawa, A.

S., Brittain, J. H., and Beaulieu, C. F., 2006, "Articular cartilage of the knee: evaluation with fluctuating equilibrium MR imaging--initial experience in healthy volunteers," Radiology, 238(2), pp. 712-718.

[16] Eckstein, F., Cicuttini, F., Raynauld, J. P., Waterton, J. C., and Peterfy, C., 2006,

"Magnetic resonance imaging (MRI) of articular cartilage in knee osteoarthritis (OA): morphological assessment," Osteoarthritis Cartilage, 14 Suppl A, pp. A46-75.

[17] Cohen, Z. A., McCarthy, D. M., Kwak, S. D., Legrand, P., Fogarasi, F., Ciaccio,

E. J., and Ateshian, G. A., 1999, "Knee cartilage topography, thickness, and contact areas from MRI: in-vitro calibration and in-vivo measurements," Osteoarthritis Cartilage, 7(1), pp. 95-109.

[18] Eckstein, F., Adam, C., Sittek, H., Becker, C., Milz, S., Schulte, E., Reiser, M.,

and Putz, R., 1997, "Non-invasive determination of cartilage thickness throughout joint surfaces using magnetic resonance imaging," J Biomech, 30(3), pp. 285-289.

124

[19] Haubner, M., Eckstein, F., Schnier, M., Losch, A., Sittek, H., Becker, C., Kolem, H., Reiser, M., and Englmeier, K. H., 1997, "A non-invasive technique for 3-dimensional assessment of articular cartilage thickness based on MRI. Part 2: Validation using CT arthrography," Magn Reson Imaging, 15(7), pp. 805-813.

[20] Losch, A., Eckstein, F., Haubner, M., and Englmeier, K. H., 1997, "A non-

invasive technique for 3-dimensional assessment of articular cartilage thickness based on MRI. Part 1: Development of a computational method," Magn Reson Imaging, 15(7), pp. 795-804.

[21] McGibbon, C. A., Bencardino, J., Yeh, E. D., and Palmer, W. E., 2003,

"Accuracy of cartilage and subchondral bone spatial thickness distribution from MRI," J Magn Reson Imaging, 17(6), pp. 703-715.

[22] Hardy, P. A., Nammalwar, P., and Kuo, S., 2001, "Measuring the thickness of

articular cartilage from MR images," J Magn Reson Imaging, 13(1), pp. 120-126. [23] Eckstein, F., Schnier, M., Haubner, M., Priebsch, J., Glaser, C., Englmeier, K. H.,

and Reiser, M., 1998, "Accuracy of cartilage volume and thickness measurements with magnetic resonance imaging," Clin Orthop Relat Res(352), pp. 137-148.

[24] Wu, J. Z., Herzog, W., and Epstein, M., 2000, "Joint contact mechanics in the

early stages of osteoarthritis," Med Eng Phys, 22(1), pp. 1-12. [25] Prevrhal, S., Engelke, K., and Kalender, W. A., 1999, "Accuracy limits for the

determination of cortical width and density: the influence of object size and CT imaging parameters," Phys Med Biol, 44(3), pp. 751-764.

[26] Prevrhal, S., Fox, J. C., Shepherd, J. A., and Genant, H. K., 2003, "Accuracy of

CT-based thickness measurement of thin structures: modeling of limited spatial resolution in all three dimensions," Med Phys, 30(1), pp. 1-8.

[27] Nickoloff, E. L., Dutta, A. K., and Lu, Z. F., 2003, "Influence of phantom

diameter, kVp and scan mode upon computed tomography dose index," Med Phys, 30(3), pp. 395-402.

[28] Suzuki, S., Yamamuro, T., Okumura, H., and Yamamoto, I., 1991, "Quantitative

computed tomography: comparative study using different scanners with two calibration phantoms," Br J Radiol, 64(767), pp. 1001-1006.

[29] McPherson, E. J., Friedman, R. J., An, Y. H., Chokesi, R., and Dooley, R. L.,

1997, "Anthropometric study of normal glenohumeral relationships," J Shoulder Elbow Surg, 6(2), pp. 105-112.

125

[30] Mavcic, B., Pompe, B., Antolic, V., Daniel, M., Iglic, A., and Kralj-Iglic, V., 2002, "Mathematical estimation of stress distribution in normal and dysplastic hips," Journal of Orthopaedic Research, 20(5), pp. 1025-1030.

[31] Takase, K., Yamamoto, K., Imakiire, A., and Burkhead, W. Z., Jr., 2004, "The

radiographic study in the relationship of the glenohumeral joint," J Orthop Res, 22(2), pp. 298-305.

[32] Ateshian, G. A., Soslowsky, L. J., and Mow, V. C., 1991, "Quantitation of

articular surface topography and cartilage thickness in knee joints using stereophotogrammetry," J Biomech, 24(8), pp. 761-776.

[33] Shepherd, D. E., and Seedhom, B. B., 1999, "Thickness of human articular

cartilage in joints of the lower limb," Ann Rheum Dis, 58(1), pp. 27-34. [34] Lorenson, W. E., and Cline, H. E., 1987, "Marching Cubes: a high resolution 3D

surface reconstruction algorithm," Computer Graphics, 21, pp. 163-169. [35] Anderson, A., Peters, C. L., Tuttle, B. D., and Weiss, J. A., 2005, "Subject-

Specific Finite Element Model of the Pelvis: Development, Validation and Sensitivity Studies," Journal of Biomech Eng, 127, pp. 364-373.

[36] Chen, S. S., Falcovitz, Y. H., Schneiderman, R., Maroudas, A., and Sah, R. L.,

2001, "Depth-dependent compressive properties of normal aged human femoral head articular cartilage: relationship to fixed charge density," Osteoarthritis Cartilage, 9(6), pp. 561-569.

[37] Huang, C. Y., Stankiewicz, A., Ateshian, G. A., and Mow, V. C., 2005,

"Anisotropy, inhomogeneity, and tension-compression nonlinearity of human glenohumeral cartilage in finite deformation," J Biomech, 38(4), pp. 799-809.

[38] Shepherd, D. E., and Seedhom, B. B., 1999, "The 'instantaneous' compressive

modulus of human articular cartilage in joints of the lower limb," Rheumatology (Oxford), 38(2), pp. 124-132.

[39] Lemke, A. J., Kazi, I., de Bary, P., Bernhardt, U., Foerster, P. I., Foerster, M., and

Felix, R., 2006, "Development and evaluation of phantom for verification of section thickness at thin-section MR imaging," Radiology, 240(2), pp. 552-558.

[40] Hsieh, J., 2003, "Image artifacts: appearances, causes and corrections.,"

Computed Tomography: principles, design, artifacts, and recent advances, SPIE Press, Bellingham, WA, pp. 167-240.

CHAPTER 5

VALIDATION OF FINITE ELEMENT PREDICTIONS

OF CARTILAGE CONTACT PRESSURE

IN THE HUMAN HIP JOINT

ABSTRACT

Methods to predict contact stresses can provide an improved understanding of

load distribution in the normal and pathologic hip. The objectives of this study were to

develop and validate a three-dimensional finite element (FE) model for predicting

cartilage contact stresses in the human hip using subject-specific geometry from

computed tomography image data, and to assess the sensitivity of model predictions to

boundary conditions, cartilage geometry, and cartilage material properties. Loads based

on in vivo data were applied to a cadaveric hip joint to simulate walking, descending

stairs, and stair-climbing. Contact pressures and areas were measured using pressure

sensitive film. CT image data were segmented and discretized into FE meshes of bone

and cartilage. FE boundary and loading conditions mimicked the experimental testing.

Fair to good qualitative correspondence was obtained between FE predictions and

experimental measurements for simulated walking and descending stairs, while excellent

agreement was obtained for stair-climbing. Experimental peak pressures, average

pressures, and contact areas were 10.0 MPa (limit of film detection), 4.4-5.0 MPa and

127

321.9-425.1 mm2, respectively, while FE predicted peak pressures, average pressures and

contact areas were 10.8-12.7 MPa, 5.1-6.2 MPa and 304.2-366.1 mm2, respectively.

Misalignment errors, determined as the difference in root mean squared error before and

after alignment of FE results, were less than 10%. Magnitude errors, determined as the

residual error following alignment, were approximately 30% but decreased to 10-15%

when the regions of highest pressure were compared. Alterations to the cartilage shear

modulus, bulk modulus, or thickness resulted in ±25% change in peak pressures, while

changes in average pressures and contact areas were minor (±10%). When the pelvis and

proximal femur were represented as rigid, there were large changes, but the effect

depended on the particular loading scenario. Overall, the subject-specific FE predictions

compared favorably with pressure film measurements and were in good agreement with

published experimental data. The validated modeling framework provides a foundation

for development of patient-specific FE models to investigate the mechanics of normal

and pathological hips.

128

INTRODUCTION

It is estimated that 3 percent of all adults over the age of 30 in the United States

have osteoarthritis (OA) of the hip [1], causing pain, loss of mobility and often leading to

the need for total hip arthroplasty. Considerable clinical, epidemiological, and

experimental evidence supports the concept that mechanical factors play a major role in

the development and progression of OA [2-5]. For example, it has been demonstrated

that a combination of duration and magnitude of contact pressures and shear stresses on

the acetabular and femoral cartilage of hips with acetabular dysplasia can predict the

onset of OA [6,7].

The ability to evaluate hip joint contact mechanics on a patient-specific basis

could lead to improvements in the diagnosis and treatment of hip OA. To this end, both

experimental and computational approaches have been developed to measure and predict

hip contact mechanics (e.g. [6,8-14]). Experimental studies have been based on either in

vitro loading of cadaveric specimens [8,10,13,14] or in vivo loading using instrumented

femoral prostheses implanted into live patients [11,15-17]. While in vitro experimental

studies have provided baseline values of hip joint contact pressure, testing protocols are

inherently invasive, mechanical data are limited to the measurement area, and specific

joint pathologies cannot be readily studied. The use of instrumented prostheses

represents the current state of the art for experimental study of in vivo hip mechanics

[11,15-17]. However, the method is highly invasive and existing data are from older

patients who have already been treated for advanced OA. There are no experimental

methods available to assess hip contact mechanics noninvasively on a patient-specific

basis.

129

Computational modeling is an attractive alternative to experimental testing since

it is currently the only method that has the potential to predict joint contact mechanics

noninvasively. Prior computational approaches have included the discrete element

analysis (DEA) technique [18-20] and the finite element (FE) method [9,12,21]. These

models have proven useful in the context of parametric or phenomenological

investigations. However, their ability to accurately predict patient-specific contact

mechanics is questionable due to over-simplification of joint geometry and an absence of

model validation.

Before computational models can be applied to the study of patient-specific hip

joint contact mechanics, it is necessary to demonstrate that the chosen modeling strategy

can produce accurate predictions and to quantify the sensitivity of model predictions to

variations in known and unknown model inputs [22]. The objectives of this study were:

1) to develop and validate a finite element (FE) model of hip joint contact mechanics

using experimental measurements of cartilage contact pressure under physiological

loading, and 2) to assess model sensitivity to several measured and assumed model

inputs.

130

METHODS

A combined experimental and computational protocol was used to develop and

validate a subject-specific FE model of a 25 y/o male cadaveric hip joint (body weight =

82 kg). The joint was screened for osteoarthritis and the cartilage was determined to be

in excellent condition (Tonnis Grade 0) [23].

Experimental Protocol

All soft tissue with the exception of articular cartilage was removed. The

acetabular labrum was dissected free from cartilage. Kinematic blocks were attached to

the femur and pelvis for spatial registration between FE and experimental coordinate

systems [24]. The blocks were used to define anatomical axes for referencing joint

loading angles using Bergmann’s coordinate system definition [15,16]. A volumetric CT

scan of the hip was obtained (512 x 512 acquisition matrix, 320 mm field of view, in

plane resolution = 0.625 X 0.625 mm, 0.6 mm slice thickness) using a Marconi MX8000

CT scanner (Phillips Medical Systems, Bothell, WA). The femur was dislocated from the

acetabulum to ensure separation between the acetabular and femoral cartilage in the

image data. A solid bone mineral density phantom (BMD-UHA, Kyoto Kagaku Co.,

Kyoto, Japan) was included to correlate CT voxel intensities with calcium equivalent

bone density [25,26]. The aforementioned scanner settings produce thickness errors of

less than 10% for simulated cartilage [27,28] and bone [25] when geometry is at least 1.0

and 0.75 mm thick, respectively.

Experimental loading was based on published data for in vivo hip loads [15,16].

Bergmann et al. reported hip joint anatomical orientations (flexion, abduction, rotation)

and equivalent hip joint forces (magnitude and direction) during routine daily activities

131

for 4 patients with instrumented femoral prostheses [15,16]. Data for the average patient

were used in the present study to simulate walking, stair-climbing and descending stairs.

A custom loading apparatus was developed to apply the kinematics that corresponded to

these loading conditions (Figure 5.1).

The iliac crests of the pelvis were cemented into a mounting pan in neutral

anatomical orientation (anterior iliac spine in plane with plane of pubis symphysis,

[15,16]) and attached to a lockable rotation frame (Figure 5.1 A). The frame was flexed

and abducted relative to the vertical axis of the actuator to simulate the orientation of the

equivalent hip joint force vector for each loading scenario. The femur was potted and

attached to a lockable ball joint (Figure 5.1 B). Three-dimensional orientation of the joint

was achieved by flexing, abducting and rotating the femur relative to the pelvis.

Equivalent joint reaction force angle and anatomical orientation were confirmed by

digitizing the loading fixture surfaces (joint force) and planes of the kinematic blocks

(anatomical orientation) using a Microscribe-3DX digitizer (Immersion Corp., San Jose,

CA) with a measured positional accuracy of ±0.085 mm [29]. The digitized points were

fit to planes, and angles between the planes were calculated. The orientation of the pelvis

and femur fixtures were adjusted until the direction of the joint reaction force vector and

anatomical orientation angles were within ± 1° of those reported by Bergmann’s average

subject.

Pressure sensitive film (Sensor Products Inc., Madison, NJ) was used to measure

joint contact pressures. Pilot testing demonstrated that low sensitivity range film (1.7-10

MPa) was best suited for measuring pressures produced during applied loading. Prior to

dissection, different film sizes were cut into a rosette pattern using a knife plotter. The

132

rosette that maximized contact area and minimized overlap was chosen (Figure 5.1 C).

Small notches were cut in the anterior, posterior, and medial aspects of the rosette to

reference the location of contact pressures relative to the hip joint.

Load Cell

Ball Joint

Femur Pot

Pelvis Mounting

Pan

Locks

Figure 5.1. Experimental setup for loading of hip joint. A) schematic of lockable rotation frame and cement pan used to constrain and orient the pelvis relative to the actuatorplane. B) femur pot attached to a lockable ball and socket joint. C) pressure sensitive film, cut into a rosette pattern, on the surface of the femoral cartilage. Polyethylenesheets were used to keep the pressure film dry.

A) B) C)

133

Peak loads for each activity were simulated by displacing the femur into the

acetabulum at a constant rate. For each activity, the rate of actuator displacement was

adjusted until peak loads were achieved within 0.33 sec, representative of the time

required by the average subject reported by Bergmann et al [15,16]. Three to four cycles

of preconditioning were necessary to obtain the correct displacement rate. The pressure

film was then attached to the head of femur between sheets of polyethylene. Planes of

the kinematic blocks were digitized to establish an experimental coordinate system in

neutral orientation. The femur was then displaced into the acetabulum until the target

load was achieved. The actuator was returned to its starting position at the same

displacement. The three notches on the film were digitized. The specimen was allowed

to recover between trials for over 100 times the interval that was needed to reach peak

load. The entire protocol was repeated 3 times for each loading scenario. The films were

stored in a dark location for 48 hours following testing [30] and then scanned and

converted to digital grayscale images. An independent calibration curve was established

to relate pixel intensity to pressure [31].

Computational Protocol

Commercial software was used to segment surfaces of the cortical bone,

trabecular bone, cartilage and kinematic blocks in the CT image data (Amira 4.1,

Mercury Computer Systems, Boston, MA). Splines representing the outer surface of

cortical bone were obtained from automatically thresholded images [25]. Cartilage was

segmented from air using a threshold value that was found to achieve the greatest

accuracy for reconstructing simulated cartilage in a phantom based imaging study

[27,28]. The boundary between trabecular and cortical bone was segmented both

134

automatically and semi-automatically. When cortical and trabecular bone blended

together in the image data they were manually separated.

Triangular surfaces were generated for each structure using the Marching Cubes

algorithm [32]. The outer cortical surface facets were decimated to a density consistent

with our previous study [25]. Cartilage surfaces were decimated and smoothed slightly to

remove visible triangular irregularities and segmentation artifact. The triangular surface

mesh for cortical bone was converted to a quadratic 3-node shell element mesh [25,33-

35]. Position dependent shell thickness was assigned to each node, based on the distance

between adjacent trabecular bone boundary nodes [25]. The resulting pelvis and femur

cortical meshes consisted of 13,562, and 4,196 elements, respectively (Figure 5.2),

representative of the mesh density that has been shown to produce accurate predictions of

cortical bone strains in prior pelvic FE modeling [25]. The interiors of the cortical shell

meshes were filled with tetrahedral elements to represent trabecular bone of the femur

and pelvis [25]. The final pelvis and femur trabecular bone tetrahedral meshes consisted

of 227,108 and 82,176 elements, respectively, which were densities consistent with prior

pelvic FE modeling [25].

Acetabular and femoral cartilage surfaces were imported into FE preprocessing

software (TrueGrid, XYZ Scientific, Livermore, CA) and hexahedral element meshes

were created. Convergence studies were performed by increasing the number of

elements through the thickness incrementally while the overall aspect ratios were held

constant by adjusting the in-plane mesh resolution. The meshes for acetabular and

femoral cartilage were considered converged if there was less than a 5% change in

contact area, peak pressure and average pressure between subsequent meshes.

135

Cartilage was represented as an incompressible, neo-Hookean hyperelastic

material [36] with shear modulus G=6.8 MPa [37]. Incompressibility was enforced using

the augmented Lagrangian method [38]. Cortical bone was represented as hypoelastic,

homogenous, and isotropic with elastic modulus E=17 GPa and Poisson’s ratio ν=0.29

[39]. Trabecular bone was represented as isotropic hypoelastic with ν=0.20 [26]. An

average elastic modulus was calculated for each tetrahedral element using empirical

relationships from the literature [25,26] and the BoneMat software [40]. Overlap

between the shell and tetrahedral solid elements [25] was accounted for by assigning an

elastic modulus of 0 MPa to all tetrahedral elements that shared nodes with shell

elements.

To establish the neutral kinematic position of each loading scenario, the FE model

was transformed from the CT coordinate system to the appropriate experimental

Figure 5.2. A) finite element mesh of the entire hip joint in the walking kinematic position. B) close-up at the acetabulum. Triangular shell elements indicate cortical bone.Cartilage was represented with a hexahedral element mesh, with three elements throughthe thickness.

A) B)

136

reference system [24]. Nodes superior to the pelvis cement line, those residing within the

sacroiliac (SI) and pubis joint, and those inferior to the cement line of the potted femur

were defined rigid according to anatomical boundaries determined experimentally. The

rigid femur nodes were constrained to move only in the direction of applied load, while

the nodes at the pubis, SI and cement line were fully constrained. The Mortar method

was used to tie acetabular and femoral cartilage to the acetabulum and femoral head,

respectively [41,42]. Contact between the femoral and acetabular cartilage was enforced

using the penalty method [43]. All analyses were performed using NIKE3D [43].

Sensitivity Studies

Sensitivity studies were performed to investigate how changes in assumed

cartilage material properties, thickness and FE model boundary conditions affected

predictions of cartilage contact mechanics. The baseline cartilage shear modulus was

altered by ± 1 SD (G=10.45 and 2.68 MPa) using standard deviations for human cartilage

[44]. To ascertain the effects of the assumption of cartilage incompressibility, bulk to

shear modulus ratios of 100:1 (ν=0.495) and 10:1 (ν=0.452) were analyzed. To account

for differences in segmentation threshold intensity between real and simulated cartilage

[27,28], the baseline threshold value used to segment cartilage was adjusted by ± 50%.

Updated cartilage FE hexahedral meshes were generated based on these surfaces. To

quantify the affects of model boundary conditions, three separate cases were analyzed: 1)

bones were assumed rigid, 2) the rigid constraint at the pubis joint was removed, and 3)

trabecular bone was removed so that deformation of only the cortical bone was

considered. Separate models were generated for each loading activity, yielding a total of

27 models.

137

Data Analysis

A program was developed to compare FE predicted cartilage contact pressures

with results from pressure sensitive film. The program allowed for the investigation of

two types of error: 1) misalignment between FE and experimental results, and 2)

differences in the magnitude of contact. First, the program converted the grayscale

images of pressure to fringed color using the calibration curve. Next, FE pressure

predictions were transformed into a synthetic film image with the same dimensions,

including rosette cuts, as the pressure films. Surface nodes of the femur cartilage FE

mesh were fit to a sphere and then flattened by a spherical-to-rectilinear coordinate

transformation. The synthetic image was aligned with the pressure film image using the

experimentally digitized notches on the pressure film. The rosette cuts on the

experimental film were duplicated in the synthetic FE pressure film image by moving the

FE pressure results circumferentially, according to the wedge angle of the rosette.

Separate synthetic FE images were created and aligned for each experimental image since

the pressure films were not placed in the exact same anatomical position between loading

trials. Finally, a difference image between each synthetic and experimental image was

created.

A root mean squared (RMS) error criterion was used to assess the degree of

similarity by comparing pixel intensity values between FE and experimental images.

Only those pixel intensities within a user specified range were compared. This range was

taken as the full sensing range of the film (1.7-10 MPa) but was also determined for

smaller 2 MPa bins of pressure to assess the ability of the FE models to predict pressures

within specific ranges. Further constraints were made in the calculation of RMS error

138

because, in this study, the experimental film data were considered the “truth”.

Specifically, if a pixel in the synthetic FE image indicated a pressure within the specified

range but the corresponding experimental film pixel did not, then the pixel was not

included in the calculation. However, if an experimental pixel was within the range but

its corresponding FE pixel was not, then the pixel was included.

Misalignment error was also distinguished from magnitude error. Misalignment

error could occur due to fitting the FE mesh to a sphere, from inaccurate digitization of

the notches used to align the results, or from FE model inaccuracies. Misalignment error

was quantified independently by calculating the RMS error real time while the synthetic

FE image was rigidly rotated about a spherical coordinate system. The rotations required

to minimize RMS error, along with the re-calculated anterior, posterior, and lateral

positions of the notches were recorded. Misalignment error was then expressed as the

difference in pre and post alignment RMS error whereas magnitude error was taken as the

post alignment error.

Peak pressure, average pressure, contact area, and center of pressure were

calculated for each experimental film and synthetic FE image after the synthetic FE films

were aligned with experimental images to minimize RMS error. FE peak pressure was

determined by recording the maximum FE pressure value within the region of

experimentally measured contact. Experimental peak pressures were calculated as the

maximum experimental film pixel intensity. Pixel intensities that indicated pressures

within the film range (1.7-10 MPa) were used to determine FE and experimental average

pressures. Contact area was calculated by multiplying the number of pixels within the

detectable pressure range of the film by the area of each pixel (0.0154 mm2). The center

139

of pressure (COP) was found by determining the center of the image, which was

weighted according to pixel intensity. The difference in the centers of pressure between

images (FE synthetic film COP - experimental film COP) was expressed as the

anatomical difference in anterior/posterior and medial/lateral positions over the

detectable range of the film.

Similar analyses were performed for the sensitivity studies. First, a baseline

image was created for each baseline FE model from which subsequent sensitivity study

predictions were compared. RMS errors were calculated per above. Changes in peak and

average pressure, and contact areas were calculated per the methodology discussed

above, but a larger pressure range was used (0.5 - 10 MPa) since the pressure range was

no longer limited by the film. For the cartilage sensitivity studies, percent changes in

peak pressure, average pressure and contact area were reported as combined results from

the three loading scenarios analyzed. For the boundary condition sensitivity studies,

results were reported as percent changes with respect to each loading scenario.

140

RESULTS

FE Mesh Characteristics

Cortical bone thickness in the pelvis and femur averaged 1.8±0.8 and 2.9±2.3

mm, respectively. The resulting trabecular bone modulus in the pelvis and femur

averaged 270±188 and 295±198 MPa, respectively. Three elements through the cartilage

thickness were necessary to yield converged FE predictions. The final mesh for

acetabular and femoral cartilage consisted of 15,000 and 23,415 elements, respectively

(Figure 5.2). Cartilage thickness in the acetabular and femoral cartilage meshes was

1.6±0.4 and 1.5±0.5 mm, respectively as estimated using the cortical bone thickness

algorithm [25] (Figure 5.3). The final FE model was composed of ~400k elements

(Figure 5.2), and each analysis took on the order of 2 hours of wall clock time.

0.8 mm

2.0 mm

Figure 5.3. Contours of cartilage thickness. Femoral and acetabular cartilage wasthickest in the anterormedial and superior regions, respectively.

141

Peak Pressure, Average Pressure, Contact Area

Experimental pressures ranged from 1.7-10.0 MPa (range of film detection). All

pressure films recorded pressures at the upper limit of film detection (10 MPa).

However, less than 5% of the total pixels fell into this category. FE predictions of peak

pressure were 10.78, 12.73 and 11.61 MPa for walking, descending stairs and stair-

climbing, respectively. Experimental average pressure and contact area ranged from 4.4-

5.0 MPa and 321.9-425.1 mm2, respectively, while FE predicted average pressure and

contact area ranged from 5.1-6.2 MPa and 304.2-366.1 mm2, respectively (Figure 5.4).

Ave

rage

Pre

ssur

e (M

Pa)

0

1

2

3

4

5

6

7

8

Average C

ontact Area (m

m2)

0

50

100

150

200

250

300

350

400

450

500Average FE PressureAverage Exp. PressureAverage FE Contact AreaAverage Exp. Contact Area

Walking Descending Stairs Stair-Climbing

Figure 5.4. FE predicted and experimentally measured average pressure (left y-axis) and contact area (right y-axis). FE models tended to overestimate average pressure and to underestimate contact area during simulated walking and descending stairs. There wasexcellent agreement between FE predictions and experimental measurements for stair-climbing. Error bars indicate standard deviation.

142

Contact Patterns

The experimental pressure recordings revealed bi-centric patterns of contact

during simulated walking and descending stairs and a more or less mono-centric pattern

during simulated stair-climbing (Figure 5.5 top row). Experimental pressure distributions

were similar during simulated walking and descending stairs, with a horseshoe shaped bi-

centric contact pattern directed anterorlaterally to posterormedially. As the femur was

rotated internally during simulated stair-climbing the contact pattern was oriented in a

lateral to medial direction (Figure 5.5 top row). Overall, the magnitude and location of

FE predicted contact pressures corresponded well with experimental measures. However,

experimental bi-centric contact patterns during simulated walking and descending stairs

were not predicted by the FE models (Figure 5.5 middle row).

Patterns of FE-predicted contact varied with the loading activity (Figure 5.6 B).

The majority of contact occurred along the lateral aspect of the acetabulum for all three

loading activities (Figure 5.6 bottom row). The contact area moved from anterior to

posterior as the resultant load vector changed from shallow extension during descending

stairs to more moderate flexion angles during walking and stair-climbing (Figure 5.6

bottom row).

143

Walking Descending Stairs Stair-Climbing Posterior

Anterior

Late

ral M

edial

Exp

erim

enta

l FE

D

iffer

ence

0 MPa

10 MPa

Figure 5.5. Top row - experimental film contact pressures (representative results areshown). Bi-centric patterns of contact were observed during simulated walking anddescending stairs, while a mono-centric pattern was observed during stair-climbing. Middle row - FE synthetic films. Models predicted mono-centric, irregularly shaped patterns of contact. Bottom row - difference images, indicating locations where contactwas not predicted by the models. The best qualitative correspondence was during stair-climbing. Note: FE synthetic films and difference images are shown prior to manualalignment with experimental results.

144

Figure 5.6. FE predicted contact pressures on the femur (top) and acetabulum (bottom). Acetabular cartilage contact pressures moved from anterior to posterior as the equivalentjoint reaction force vector changed from shallow extension during descending stairs todeep flexion during stair-climbing. The highest contact pressures primarily occurred near the lateral region of the acetabulum.

0 MPa

8 MPa

Walking Descending Stairs Stair-Climbing

Oblique Lateral View

Superior-Anterior View

145

Misalignment and Magnitude Errors

Difference images, calculated prior to manual alignment between FE synthetic

and experimental films, further clarified the degree of qualitative agreement between FE

synthetic and experimental films (Figure 5.5 bottom row). Differences in contact

pressure were greatest for descending stairs and were least during stair-climbing (Figure

5.5 bottom row). Overall, misalignment errors were less than 7% (Table 5.1). The

rotations and resulting translations of the experimental film fiducials required to

minimize RMS errors were less than 3° and 5 mm for walking and stair-climbing but

were substantially higher for the descending stairs case (22° and 9 mm) (Table 5.1).

Following manual alignment, residual RMS errors were on the order of 30%. As

suggested by the difference images, errors were greatest for descending stairs and least

for stair-climbing (Figure 5.5 bottom row). When RMS error was plotted in 2 MPa

pressure bins, RMS errors decreased to around 10-15% at the maximum bound of

pressure analyzed (8-10 MPa). This finding indicates that FE models were best suited for

predicting the higher stressed regions of cartilage, corroborating the good qualitative

correspondence between FE synthetic and experimental films in these locations (Figure

5.5).

Differences in center of pressure locations, as calculated over the entire film

detection range, were less than 10 mm (Table 5.2). The smallest difference in the COP

occurred for stair-climbing, while the largest difference occurred during descending

stairs. In general, COPs for the FE models were directed more lateral (-) and anterior (+)

to experimentally measured COPs.

146

Center of Pressure Difference (mm) Medial/Lateral (±SD) Anterior/Posterior (±SD)

Walking -6.88 (1.34) 7.22 (1.39) Descending Stairs -7.92 (0.32) 8.09 (0.86)

Stair-Climbing 0.14 (0.196) 3.08 (0.93)

Misalignment RMS

Error (%) (±SD) Magnitude RMS Error (%) (±SD)

Rot X (°) (±SD)

Rot Z (°) (±SD)

∆ Position mm (±SD)

Walking 0.24 (0.11) 32.03 (0.26) 2.37 (1.00) -0.77 (0.38) 2.26 (2.22) Descending Stairs 6.59 (2.58) 33.75 (2.90) 1.60 (1.13) -22.55 (1.06) 9.31 (0.34)

Stair-Climbing 2.49 (2.51) 26.74 (0.14) 3.05 (6.86) 2.65 (7.70) 4.73 (0.00)

Table 5.1. FE misalignment and magnitude errors. Misalignment error was calculated as the reduction in total RMS error after the synthetic films were manually rotated to minimize RMS error between FE and experimental films. Magnitude error was the residual error following alignment. The rotations required to align results and associated changes in the positions of the film fiducials are shown.

Table 5.2. Differences in centers of pressure between synthetic FE and experimentalfilms (negative = lateral/posterior, positive = medial/anterior).

147

Sensitivity Studies - Cartilage Material Properties and Thickness

Changes of ±50% to the shear modulus resulted in approximately a ±30% change

in FE predictions of peak pressures, while changes in average pressure and contact area

were around ±10% (Figure 5.7 A). Lowering the cartilage Poisson’s ratio from ν=0.5 to

ν=0.495 did not have an appreciable effect (Figure 5.7 B). However, a further decrease

in the Poisson’s ratio to 0.452 resulted in a 25% decrease in peak pressures, while

changes in average pressure and contact area were less than 10% (Figure 5.7 B). Altering

the thickness of femoral and acetabular cartilage (~ 10% change average cartilage

thickness) resulted in less than a ±10% change in FE predictions (Figure 5.7 C). RMS

differences between baseline and all cartilage sensitivity study results were

approximately 6.5%, indicating that the spatial distributions and magnitudes of contact

pressure did not change substantially.

148

Figure 5.7. Percent changes in peak pressure, average pressure and contact area due toalterations in cartilage material properties and geometry. A) effects of changes to theshear modulus by ±1 SD. B) effects of changes to cartilage compressibility (100:1, 10:1bulk to shear ratios). C) effects of altering the cartilage thickness. Error bars indicate standard deviations over the three loading activities analyzed.

Perc

ent C

hang

e

-10

-8

-6

-4

-2

0

2

4

6

8

10

Peak PressureAverage PressureContact Area

+50%

-50%

Cartilage Thickness

Perc

ent C

hang

e

-35

-30

-25

-20

-15

-10

-5

0

Peak PressureAverage PressureContact Area

100:1

10:1

Bulk:Shear

Perc

ent C

hang

e

-40

-30

-20

-10

0

10

20

30

40

Peak PressureAverage PressureContact Area

+1S -1SD

Shear Modulus

A) B)

C)

149

Sensitivity Studies - FE Boundary Conditions

Rigid bone models decreased computation times from ~2 hours to <10 minutes.

Representing the bones as rigid structures affected both the magnitude (Figure 5.8 A) and

spatial distribution (Figure 5.9) of cartilage contact pressure, but the degree of effect

depended on the loading activity. RMS differences in synthetic films between baseline

and rigid bone models averaged 29.2±5.5%. FE predictions of peak pressure, average

pressure and contact area were altered but also varied according to the loading scenario

analyzed (Figure 5.8 A). When the rigid constraint on the pubis joint was removed, FE

predictions changed on the order of -15 to +5% (Figure 5.8 B). Finally, when the

trabecular bone was removed, i.e. only the cortical shells supported the cartilage, changes

in FE predictions ranged from -25 to +5% (Figure 5.8 C). Average RMS differences

between baseline results and the latter boundary condition sensitivity studies were only

3.1%.

150

Figure 5.8. Percent changes in peak pressure, average pressure and contact area due toalterations in boundary conditions. A) effects of a rigid bone material assumption. B) effects of removing the pubis joint constraint. C) effects of removing the trabecular bonefrom the FE analysis. W, DS, SC indicate walking, descending stairs, and stair-climbing, respectively.

Perc

ent C

hang

e

-30

-25

-20

-15

-10

-5

0

5

10

Peak PressureAverage PressureContact Area

W DS SC

Trabecular Bone Removed

Perc

ent C

hang

e

-15

-10

-5

0

5

Peak PressureAverage PressureContact Area

W DS SC

Pubis Joint Free

Perc

ent C

hang

e

-60

-40

-20

0

20

40

60

80

100

120Peak PressureAverage PressureContact Area

W DS SC

Rigid Bones

A) B)

C)

151

Figure 5.9. Contours of cartilage contact pressure predicted by the baseline (top row) andrigid bone FE models (bottom row) for the three loading activities. The largest effect ofthe rigid bone assumption occurred for simulated walking and descending stairs.

Walking Descending Stairs Stair-Climbing Posterior

Anterior

Late

ral Medial

Bas

elin

e FE

R

igid

0 MPa

10 MPa

152

DISCUSSION

To our knowledge this is the first study to validate FE predictions of cartilage

contact pressure with experimental measurements in the human hip joint. The FE model

provided very reasonable predictions of both the spatial distribution and magnitude of

cartilage contact pressure under the simulated loading conditions. Excellent predictions

were obtained for simulated stair-climbing. The posterior aspect of the bi-centric

experimental contact pattern was not predicted by the FE model for walking and

descending stairs. Nevertheless, the magnitude of pressure in these locations was low in

comparison to the anterior region where the FE models provided more reasonable

correspondence.

Small manual rotations of the pressure film were necessary to minimize RMS

errors for simulated walking and stair-climbing. In contrast, the descending stairs case

required a substantial amount of manual rotation (Table 1). It is likely that the majority

of misalignment error was due to the method of digitizing the film fiducials during the

experiment. It was necessary to move the linear actuator up by ~20 mm to access the

film markers. It was assumed that this displacement resulted in a perfect vertical

translation for purposes of defining the marker coordinates, but when the coordinates

were plotted relative to the translated model they did not reside on the surface of the

cartilage. This offset was minor during walking and stair-climbing but was greater

during descending stairs. The femur was in extension for this loading activity and when

the translation was applied, the femoral neck would have contacted the edge of the

acetabulum, resulting in an offset of the film marker coordinates. Contact in this location

153

would not have occurred with the hip in moderate and deep flexion during walking and

stair-climbing.

The finding that RMS magnitude errors decreased when the bounds of pressure

were increased suggest that the models were best suited for predicting localized “hot

spots”. Therefore, the modeling strategies developed herein may be well suited for

predicting the primary region of contact, which may be sufficient for many patient-

specific modeling applications.

FE predictions of average pressure and contact area were not overly sensitive to

changes in the cartilage shear modulus, bulk modulus or thickness (±10%). However,

greater changes in peak pressure were noted (up to ~25%). This finding demonstrates

that peak pressure prediction requires more accurate model inputs for cartilage geometry

and material properties than for average pressure prediction.

Computational models of the hip have often represented bones as rigid structures

[12,45], which is an attractive simplification because solution times are greatly reduced.

The present study demonstrated that the assumption of rigid bones can alter predictions

of cartilage contact stresses in the hip. The effect is modulated by the specific boundary

and loading conditions in the model. Because the consequence of the rigid bone

assumption cannot be assessed without a direct comparison to the case of deformable

bones, investigators should use caution when representing the bones as rigid for modeling

cartilage contact mechanics in the human hip.

Although the contralateral pelvis was left intact in the experimental study, the FE

models assumed that the pubis joint was rigid. The results of the sensitivity study that

removed the pubis constraint demonstrated only minor differences in FE predicted

154

cartilage contact mechanics, thereby giving credence to this model assumption. While

this simplification was warranted for the current study, it may not be appropriate for

models where load is directed more medially (e.g. simulations of side-impact loading

[46]).

Since the reported elastic modulus of trabecular bone is orders of magnitude less

than cortical bone, we investigated whether or not trabecular bone needed to be

represented in the models. The results of the sensitivity study suggest that it plays little

mechanical role with regard to cartilage contact stresses. Therefore, for patient-specific

modeling applications it may be appropriate to exclude trabecular bone assuming that

similar boundary and loading conditions are assigned.

Experimental studies have used pressure sensitive film to measure hip joint

contact pressures under similar loading conditions [8,13,14]. Peak pressures measured by

von Eisenhart-Rothe et al. [13] ranged from 7 MPa at 50% body weight to 9 MPa at

300% body weight, in fair agreement with the results of the current study. Bi-centric,

horseshoe shaped patterns extended from the anterior to posterior aspect of the femur

were noted [13]. Afoke et al. [8] measured peak pressures on the order of 10 MPa at

350% body weight and the anterorsuperior surface of the cartilage was identified as an

area of high pressure [8]. It is worth mentioning that all of the aforementioned studies

predicted irregular, non-symmetric pressure distributions [8,13,14].

Large differences in material properties, geometry and boundary conditions make

it impossible to directly compare the FE predictions from this study with prior modeling

studies, but some general trends can be identified. Nearly all FE hip joint modeling

studies to date have used two-dimensional, plane strain models [9,12,21,45] with either

155

rigid [12,45] or deformable bones [9,21]. To our knowledge, the earliest FE contact

model was reported by Brown and DiGioia [9]. In this study, FE predicted pressures

were irregularly distributed over the surface of the femoral head. Values of peak pressure

were on the order of 4 MPa at loads representative of those applied in the current study.

Rapperport et al. [21] developed a similar model that predicted peak pressures on the

order of 5 MPa at 1000 N of load. Using rigid bone models resulted in predictions only

slightly different than the deformable bone model.

Macirowski et al. [12] used a combined experimental/analytical approach to

model fluid flow and matrix stresses in a biphasic contact model of a cadaveric

acetabulum. This is the only previous FE study to explicitly model the acetabular

cartilage thickness. The acetabulum was step loaded to 900 N using an instrumented

femoral prosthesis, yielding peak contact pressures on the order of 5 MPa. When the

experimentally measured total surface stress was applied to the FE model, average

predicted pressures (solid stress + fluid pressures) were approximately 1.75 MPa. The

lower range of pressure used to determine average pressures was not specified, making it

impossible to directly compare average results. However, scaling the applied load of our

model to 900 N and assuming a lower bound of 0.3 MPa to calculate average pressure

(lowest pressure isobar indicated by Macirowski et al.) yields average pressures of

2.47±0.29 MPa over the three loading scenarios analyzed, which is in good agreement

with Macirowski et al’s predictions.

Yoshida et al. [20] developed a dynamic DEA model to investigate the

distribution of hip joint contact pressures using the Bergmann gait data. The model

assumed spherical geometry and concentric articulation. Qualitatively our predictions of

156

primary contact during simulated walking, descending stairs, and stair-climbing are in

good agreement with the results of this study, but the spatial distributions of contact were

markedly different. Peak pressures during walking, descending stairs, and stair-climbing

were substantially less than those predicted in the current study (3.26, 3.77, 5.71 MPa,

respectively).

With the exception of the study by Macirowski et al., the FE models developed

herein predicted higher contact pressures than previous FE and DEA studies. This

discrepancy is most likely due to the assumptions of spherical geometry and concentric

articulation in the prior computational studies. Although the literature suggests that

normal hips may be modeled as spherical structures with concentric articulation [19,47],

the hip joint is not spherical and cartilage thickness is nonuniform [12,48,49]. The

aforementioned computational models assumed a cartilage modulus ranging from 10-15

MPa [9,21] yet cartilage was given a baseline modulus of ~40 MPa (G=6.8 MPa) in the

current study. While one might expect that a higher modulus would result in higher

contact pressures, the results of our sensitivity studies demonstrate that this is not the

case, as changes in the cartilage shear modulus of ±50% resulted in only a ±25% and

±10% change in peak and average contact pressures, respectively. Even with a 25%

reduction, peak pressures predicted in this study were still nearly double those reported

previously [9,18-20].

Several limitations of the current study must be mentioned. First, experimental

loads were based on average in vivo data from older patients who had already undergone

treatment for advanced hip OA. Given the large inter-patient variation in joint kinematics

observed by Bergmann et al. [15,16] the use of average data loading data likely did not

157

accurately represent the actual kinematics for the specimen in this study. Our approach is

justified since the objective of the experimental protocol was to apply realistic loading

and boundary conditions that could be reproduced in the FE simulations for model

validation. A limitation of film pressure measurement is that the technique records a

“high watermark” rather than measurements of time-loading history [50,51]. However,

film measurements have been shown to be equivalent to the contact stresses resulting

from an incompressible elastic analysis [52], making the use of pressure film appropriate

in the current study. Results from the pressure measurements indicate that contact

occurred beyond the perimeter of the film during simulated walking and descending

stairs. While it would be desirable to capture the entire region of contact, it was not

feasible to do so using larger rosettes as they caused excessive overlap and crinkle artifact

during pilot testing.

The acetabular labrum was removed in this study, yet it has been suggested that

the labrum helps to maintain fluid pressurization in the hip [45,53]. The labrum was

removed because its material properties are unknown, making its inclusion a potential

confounding factor. It is possible that leaving the labrum intact would have altered the

experimentally measured and computationally predicted contact pressures [45,53].

Although actions of individual muscles were not considered, the equivalent joint reaction

force was based on in vivo data [15,16]. The primary focus of the present research was

to quantify cartilage contact pressures in the peri-acetabular region rather than bone

stresses in areas where muscles were attached. Therefore, we could justifiably model the

action of all muscles as a single equivalent force vector acting through the hip joint.

158

Although cartilage exhibits biphasic material behavior [54], it was represented as

incompressible hyperelastic in this study. In vitro studies suggest that fluid flow is

minimal during fast loading [12,53], making our assumption of incompressibility

warranted given the loading rates used in the experiments. We recently demonstrated the

equivalence between biphasic and incompressible hyperelastic FE predictions during

instantaneous loading [55]. Cartilage also exhibits depth dependent material properties

[56], variation in stiffness over its surface [44,57] and tension-compression nonlinearity

[58]. Incorporating these aspects might have resulted in different, perhaps better,

predictions of contact stress magnitude and distribution. Future modeling efforts should

investigate the importance of these effects via sensitivity studies.

In conclusion, our approach for subject-specific FE modeling of the hip joint

produced very reasonable predictions of cartilage contact pressures and areas when

compared directly to pressure film measurements. Predictions were in good agreement

with other experimental studies that used pressure film, piezoelectric sensors and

instrumented prostheses [8,12-14,59,60]. The sensitivity studies established the

modeling inputs and assumptions that are important for predicting contact pressures. The

validated FE modeling procedures developed in this study provide the basis for the future

analysis of patient-specific FE models of hip cartilage mechanics.

159

REFERENCES

[1] Felson, D. T., Lawrence, R. C., Dieppe, P. A., Hirsch, R., Helmick, C. G., Jordan,

J. M., Kington, R. S., Lane, N. E., Nevitt, M. C., Zhang, Y., Sowers, M., McAlindon, T., Spector, T. D., Poole, A. R., Yanovski, S. Z., Ateshian, G., Sharma, L., Buckwalter, J. A., Brandt, K. D., and Fries, J. F., 2000, "Osteoarthritis: New Insights. Part 1: The Disease and Its Risk Factors," Ann Intern Med, 133, pp. 635-46.

[2] Mankin, H. J., 1974, "The Reaction of Articular Cartilage to Injury and

Osteoarthritis (Second of Two Parts)," N Engl J Med, 291, pp. 1335-40. [3] Mankin, H. J., 1974, "The Reaction of Articular Cartilage to Injury and

Osteoarthritis (First of Two Parts)," N Engl J Med, 291, pp. 1285-92. [4] Mow, V. C., Setton, L. A., Guilak, F., and Ratcliffe, A., 1995, "Mechanical

Factors in Articular Cartilage and Their Role in Osteoarthritis," in Osteoarthritic Disorders. American Academy of Orthopaedic Surgeons.

[5] Poole, A. R., 1995, "Imbalances of Anabolism and Catabolism of Cartilage

Matrix Components in Osteoarthritis," in Osteoarthritic Disorders. American Academy of Orthopaedic Surgeons.

[6] Maxian, T. A., Brown, T. D., and Weinstein, S. L., 1995, "Chronic Stress

Tolerance Levels for Human Articular Cartilage: Two Nonuniform Contact Models Applied to Long-Term Follow-up of Cdh," J Biomech, 28, pp. 159-66.

[7] Hadley, N. A., Brown, T.D., Weinstein, S.L., 1990, "The Effect of Contact

Pressure Elevations and Aseptic Necrosis on Long Term Outcome of Congenital Hip Dislocation," J Orthop Res, 8, pp. 504-510.

[8] Afoke, N. Y., Byers, P. D., and Hutton, W. C., 1987, "Contact Pressures in the

Human Hip Joint," J Bone Joint Surg Br, 69, pp. 536-41. [9] Brown, T. D. and DiGioia, A. M., 3rd, 1984, "A Contact-Coupled Finite Element

Analysis of the Natural Adult Hip," J Biomech, 17, pp. 437-48. [10] Brown, T. D. and Shaw, D. T., 1983, "In Vitro Contact Stress Distributions in the

Natural Human Hip," J Biomech, 16, pp. 373-84. [11] Hodge, W. A., Fijan, R. S., Carlson, K. L., Burgess, R. G., Harris, W. H., and

Mann, R. W., 1986, "Contact Pressures in the Human Hip Joint Measured in Vivo," Proc Natl Acad Sci U S A, 83, pp. 2879-83.

160

[12] Macirowski, T., Tepic, S., and Mann, R. W., 1994, "Cartilage Stresses in the Human Hip Joint," J Biomech Eng, 116, pp. 10-8.

[13] von Eisenhart-Rothe, R., Eckstein, F., Muller-Gerbl, M., Landgraf, J., Rock, C.,

and Putz, R., 1997, "Direct Comparison of Contact Areas, Contact Stress and Subchondral Mineralization in Human Hip Joint Specimens," Anat Embryol (Berl), 195, pp. 279-88.

[14] von Eisenhart-Rothe R, A. C., Steinlechner M, Muller-Gerbl M and Eckstein F,

1999, "Quantitative Determination of Joint Incongruity and Pressure Distribution During Simulated Gait and Cartilage Thickness in the Human Hip Joint," Journal of Orthopaedic Research, 7, pp. 532-539.

[15] Bergmann, G., 1998, Hip98: Data Collection of Hip Joint Loading on Cd-Rom.

Free University and Humboldt University, Berlin. [16] Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A.,

Strauss, J., and Duda, G. N., 2001, "Hip Contact Forces and Gait Patterns from Routine Activities," J Biomech, 34, pp. 859-71.

[17] Carlson, C. E., Mann, R. W., and Harris, W. H., 1974, "A Radio Telemetry

Device for Monitoring Cartilage Surface Pressures in the Human Hip," IEEE Trans Biomed Eng, 21, pp. 257-64.

[18] Genda, E., Iwasaki, N., Li, G., MacWilliams, B. A., Barrance, P. J., and Chao, E.

Y., 2001, "Normal Hip Joint Contact Pressure Distribution in Single-Leg Standing--Effect of Gender and Anatomic Parameters," J Biomech, 34, pp. 895-905.

[19] Genda, E., Konishi, N., Hasegawa, Y., and Miura, T., 1995, "A Computer

Simulation Study of Normal and Abnormal Hip Joint Contact Pressure," Arch Orthop Trauma Surg, 114, pp. 202-6.

[20] Yoshida, H., Faust, A., Wilckens, J., Kitagawa, M., Fetto, J., and Chao, E. Y.,

2006, "Three-Dimensional Dynamic Hip Contact Area and Pressure Distribution During Activities of Daily Living," J Biomech, 39, pp. 1996-2004.

[21] Rapperport, D. J., Carter, D. R., and Schurman, D. J., 1985, "Contact Finite

Element Stress Analysis of the Hip Joint," J Orthop Res, 3, pp. 435-46. [22] Anderson, A., Ellis, B. J., and Weiss, J. A., 2006, "Verification, Validation and

Sensitivity Studies in Computational Biomechanics," Computer Methods in Biomechanics and Biomedical Engineering, In Press Dec 2006.

[23] Tönnis, D., 1987, Congenital Dysplasia and Dislocation of the Hip in Children

and Adults. Springer-Verlag, Berlin.

161

[24] Fischer, K. J., Manson, T. T., Pfaeffle, H. J., Tomaino, M. M., and Woo, S. L., 2001, "A Method for Measuring Joint Kinematics Designed for Accurate Registration of Kinematic Data to Models Constructed from Ct Data," J Biomech, 34, pp. 377-83.

[25] Anderson, A. E., Peters, C. L., Tuttle, B. D., and Weiss, J. A., 2005, "Subject-

Specific Finite Element Model of the Pelvis: Development, Validation and Sensitivity Studies," J Biomech Eng, 127, pp. 364-73.

[26] Dalstra, M., Huiskes, R., Odgaard, A., and van Erning, L., 1993, "Mechanical and

Textural Properties of Pelvic Trabecular Bone," J Biomech, 26, pp. 523-35. [27] Anderson, A., Ellis, B. J., Peters, C. L., and Weiss, J. A., 2007, "Factors

Influencing Cartilage Thickness Measurements with Multi-Detector Ct: A Phantom Study," Radiology, In Press, Feb 2007.

[28] Anderson, A., Ellis, B. J., Peters, C. L., and Weiss, J. A., "Factors Influence

Cartilage Thickness Measurements Using Multi-Detector Ct: A Phantom Study," presented at Transactions of the 53rd Annual Meeting of the Orthopaedic Research Society, San Diego, CA, 2007.

[29] Lujan, T. J., Lake, S. P., Plaizier, T. A., Ellis, B. J., and Weiss, J. A., 2005,

"Simultaneous Measurement of Three-Dimensional Joint Kinematics and Ligament Strains with Optical Methods," J Biomech Eng, 127, pp. 193-7.

[30] Liggins, A. B., 1997, "The Practical Application of Fuji Prescale Pressure-

Sensitive Film," in Optical Measurement Methods in Biomechanics. Chapman and Hall, London.

[31] Sparks, D. R., Beason, D. P., Etheridge, B. S., Alonso, J. E., and Eberhardt, A.

W., 2005, "Contact Pressures in the Flexed Hip Joint During Lateral Trochanteric Loading," J Orthop Res, 23, pp. 359-66.

[32] Lorensen, W. E. and Cline, H. E., 1987, "Marching Cubes: A High Resolution 3d

Surface Construction Algorithm," Comput. Graph., 21, pp. 163-169. [33] Hughes, T. J., 1980, "Generalization of Selective Integration Procedures to

Anisotopic and Nonlinear Media," Interational Journal for Numerical Methods in Engineering, 15, pp. 9.

[34] Hughes, T. J. and Liu, W. K., 1981, "Nonliner Finite Element Analysis of Shells:

Part I. Two Dimensional Shells.," Compuational Methods in Applied Mechanics, 27, pp. 167-181.

162

[35] Hughes, T. J. and Liu, W. K., 1981, "Nonlinear Finite Element Analysis of Shells: Part Ii. Three Dimensional Shells.," Computational Methods in Applied Mechanics, 27, pp. 331-362.

[36] Buchler, P., Ramaniraka, N. A., Rakotomanana, L. R., Iannotti, J. P., and Farron,

A., 2002, "A Finite Element Model of the Shoulder: Application to the Comparison of Normal and Osteoarthritic Joints," Clin Biomech (Bristol, Avon), 17, pp. 630-9.

[37] Park, S., Hung, C. T., and Ateshian, G. A., 2004, "Mechanical Response of

Bovine Articular Cartilage under Dynamic Unconfined Compression Loading at Physiological Stress Levels," Osteoarthritis Cartilage, 12, pp. 65-73.

[38] Hestenes, M. R., 1969, "Multiplier and Gradient Methods," Journal of

Optimization Theory and Applications, 4, pp. 303-320. [39] Dalstra, M., Huiskes, R., and van Erning, L., 1995, "Development and Validation

of a Three-Dimensional Finite Element Model of the Pelvic Bone," J Biomech Eng, 117, pp. 272-8.

[40] Zannoni, C., Mantovani, R., and Viceconti, M., 1998, "Material Properties

Assignment to Finite Element Models of Bone Structures: A New Method," Med Eng Phys, 20, pp. 735-40.

[41] Puso, M. A., 2004, "A 3d Mortar Method for Solid Mechanics," International

Journal for Numerical Methods in Engineering, 59, pp. 315-36. [42] Puso, M. A. and Laursen, T. A., 2004, "A Mortar Segment-to-Segment Contact

Method for Large Deformation Solid Mechanics," Computer Methods in Applied Mechanics and Engineering, 193, pp. 601-29.

[43] Maker, B. N., Ferencz, R. M., and J.O., H., 1990, "Nike3d: A Nonlinear, Implicit,

Three-Dimensional Finite Element Code for Solid and Structural Mechanics," Lawrence Livermore National Laboratory Technical Report, UCRL-MA.

[44] Athanasiou, K. A., Agarwal, A., and Dzida, F. J., 1994, "Comparative Study of

the Intrinsic Mechanical Properties of the Human Acetabular and Femoral Head Cartilage," J Orthop Res, 12, pp. 340-9.

[45] Ferguson, S. J., Bryant, J. T., Ganz, R., and Ito, K., 2000, "The Influence of the

Acetabular Labrum on Hip Joint Cartilage Consolidation: A Poroelastic Finite Element Model," J Biomech, 33, pp. 953-60.

[46] Ruan, J. S., El-Jawahri, R., Rouhana, S. W., Barbat, S., and Prasad, P., 2006,

"Analysis and Evaluation of the Biofidelity of the Human Body Finite Element

163

Model in Lateral Impact Simulations According to Iso-Tr9790 Procedures," Stapp Car Crash J, 50, pp. 491-507.

[47] Konishi, N. and Mieno, T., 1993, "Determination of Acetabular Coverage of the

Femoral Head with Use of a Single Anteroposterior Radiograph. A New Computerized Technique," J Bone Joint Surg Am, 75, pp. 1318-33.

[48] Rushfeldt, P. D., Mann, R. W., and Harris, W. H., 1981, "Improved Techniques

for Measuring in Vitro the Geometry and Pressure Distribution in the Human Acetabulum--I. Ultrasonic Measurement of Acetabular Surfaces, Sphericity and Cartilage Thickness," J Biomech, 14, pp. 253-60.

[49] Shepherd, D. E. and Seedhom, B. B., 1999, "Thickness of Human Articular

Cartilage in Joints of the Lower Limb," Ann Rheum Dis, 58, pp. 27-34. [50] Hale, J. E. and Brown, T. D., 1992, "Contact Stress Gradient Detection Limits of

Pressensor Film," J Biomech Eng, 114, pp. 352-7. [51] Brown, T. D., Rudert, M. J., and Grosland, N. M., 2004, "New Methods for

Assessing Cartilage Contact Stress after Articular Fracture," Clin Orthop Relat Res, pp. 52-8.

[52] Ateshian, G. A., Lai, W. M., Zhu, W. B., and Mow, V. C., 1994, "An Asymptotic

Solution for the Contact of Two Biphasic Cartilage Layers," J Biomech, 27, pp. 1347-60.

[53] Ferguson, S. J., Bryant, J. T., Ganz, R., and Ito, K., 2003, "An in Vitro

Investigation of the Acetabular Labral Seal in Hip Joint Mechanics," J Biomech, 36, pp. 171-8.

[54] Mow, V. C., Kuei, S. C., Lai, W. M., and Armstrong, C. G., 1980, "Biphasic

Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments," J Biomech Eng, 102, pp. 73-84.

[55] Ateshian, G. A., Ellis, B. J., and Weiss, J. A., 2006, "Equivalence between Short-

Time Biphasic and Incompressible Elastic Material Response," Journal of Biomechanical Engineering, In Press Nov 2006.

[56] Chen, S. S., Falcovitz, Y. H., Schneiderman, R., Maroudas, A., and Sah, R. L.,

2001, "Depth-Dependent Compressive Properties of Normal Aged Human Femoral Head Articular Cartilage: Relationship to Fixed Charge Density," Osteoarthritis Cartilage, 9, pp. 561-9.

[57] Shepherd, D. E. and Seedhom, B. B., 1999, "The 'Instantaneous' Compressive

Modulus of Human Articular Cartilage in Joints of the Lower Limb," Rheumatology (Oxford), 38, pp. 124-32.

164

[58] Chahine, N. O., Wang, C. C., Hung, C. T., and Ateshian, G. A., 2004, "Anisotropic Strain-Dependent Material Properties of Bovine Articular Cartilage in the Transitional Range from Tension to Compression," J Biomech, 37, pp. 1251-61.

[59] Rushfeldt, P. D., Mann, R. W., and Harris, W. H., 1981, "Improved Techniques

for Measuring in Vitro the Geometry and Pressure Distribution in the Human Acetabulum. Ii Instrumented Endoprosthesis Measurement of Articular Surface Pressure Distribution," J Biomech, 14, pp. 315-23.

[60] Adams, D. and Swanson, S. A., 1985, "Direct Measurement of Local Pressures in

the Cadaveric Human Hip Joint During Simulated Level Walking," Ann Rheum Dis, 44, pp. 658-66.

CHAPTER 6

PATIENT-SPECIFIC FINITE ELEMENT MODELING:

PROOF OF CONCEPT

ABSTRACT

Acetabular dysplasia may be the leading cause of premature osteoarthritis (OA) of

the hip [1-6]. However, the relationship between geometric alterations to the acetabular

geometry [7,8] and cartilage [9,10] associated with dysplasia and the resulting cartilage

biomechanics are poorly understood. The objectives of this study were to demonstrate

the feasibility of patient-specific finite element (FE) modeling by investigating

differences in cartilage biomechanics between a normal and dysplastic hip joint and to

assess the sensitivity of model predictions to changes in joint loading. Institutional

review board approval was obtained to perform CT arthrography under fluoroscopic

control. Computed tomography (CT) image data were segmented and meshed using a

previously validated protocol [11-13]. Model loading was based on in-vivo data from the

literature and simulated conditions of walking, stair-climbing, and descending stairs

[14,15]. Cartilage stresses were substantially elevated in the dysplastic joint. Mean

cartilage peak pressures, average pressures, and shear stresses in the dysplastic joint were

28.4, 6.7, and 6.6 MPa, respectively whereas the normal model predicted values of 18.6,

166

3.6, and 3.8 MPa, respectively. Surprisingly, contact areas in the dysplastic hip

joint (976.1 - 1143.3mm2) were greater than those predicted in the normal joint (512.3 -

579.6 mm2). The results from this proof of concept study suggest that patients with

dysplasia may have altered cartilage biomechanics, providing the motivation for efforts to

analyze a population of subjects.

167

INTRODUCTION

Several studies have shown that mild developmental dysplasia may indeed be the

leading cause of osteoarthritis in the hip [2-6,16]. Wilson and Poss [6] found deformity

of the acetabulum in 25-35% of adult cases of hip OA. Harris et al. [2] estimated that

40% of patients with hip OA have some type of untreated hip dysplasia. Aronson [1] and

Bombelli et al. [17,18] estimate that as many as 76% of patients with hip OA have some

type of untreated acetabular dysplasia. In contrast to these reports, other studies have

failed to find a statistically significant relationship between acetabular dysplasia and the

risk of hip OA [19-24]. The discrepancies in the literature motivate the need for an

improved understanding of the biomechanics of the dysplastic hip.

It is believed that the biomechanics of the hip plays an important role in the

development of osteoarthritis in the dysplastic joint [2,16,25-27]. Subluxation

(incomplete dislocation) caused by dysplasia of the hip joint is a primary cause of

degenerative joint disease and clinical disability [25]. It is believed that subluxation leads

to increased stresses across the articulating surface each time the hip is loaded during gait

[17,18]. Consequently, it is thought that altered biomechanics causes cartilage and bone

of the hip to degenerate prematurely, leading to early hip osteoarthritis. Differences in

joint biomechanics between normal and dysplastic hips may have important implications

for predicting the development and progression of hip OA and for developing treatment

strategies, but few attempts have been made to quantify these differences.

Mathematical and computational models are an attractive methodology for

studying hip dysplasia since they may have the ability to non-invasively predict joint

168

mechanics on a patient-specific basis. A handful of analytical and computational studies

have inferred cartilage contact pressures in dysplastic hips as a means to differentiate

their mechanical environment [27-29]. Analytical studies use simplified mathematical

statics calculations based on 2-D geometry, bodyweight, and estimated muscles forces to

solve for equivalent joint reaction forces, contact pressures, and contact area [27-29].

Although analytical studies further support the notion of pathological biomechanics and

in particular increased contact stresses in the dysplastic hip, they neglect several

important aspects. These studies used idealized geometry to represent all or part of the

hip articulation, neglecting the issues of regional and patient-specific congruency

between the femoral and acetabular cartilage layers.

Unlike analytical approaches, computational models have the ability to predict

joint mechanics using calculations that are based on three-dimensional geometry. This is

a significant advantage since hip dysplasia is a three-dimensional pathology [30,31].

Rigid body spring models (RBSM) and the finite element (FE) method have been applied

to illustrate mechanical differences between normal and dysplastic joints [32,33]. Most

models have made simplifying assumptions regarding model geometry and have utilized

modeling protocols that have not been validated. However, prior to patient-specific

modeling it is necessary to demonstrate that the chosen computational protocol produces

accurate models [34].

The objectives of this study were to demonstrate the feasibility of patient-specific

finite element (FE) modeling by investigating differences in cartilage biomechanics

between a normal and dysplastic hip joint and to assess the sensitivity of model

169

predictions to changes in joint loading. Patient-specific FE models were constructed and

analyzed using a protocol that has been subjected to extensive validation [11-13].

170

METHODS

Subject Selection

Approval to recruit and image subjects for CT arthrography was obtained from

the University of Utah Institutional Review Board. Informed consent was obtained from

a patient with dysplasia and a normal control subject. The pathological hip was from a

35 y/o female patient (body weight = 149 lbs.) who had been diagnosed with an

excessively anteverted hip. The normal control was a 27 y/o male (BW = 147 lbs) with

no history of dysplasia or hip pain. The traditionally dysplastic patient had a center edge

angle [25] of 0°, acetabular angle of Sharp [25] of 47°, and pre-operative Harris Hip

Score [2,25] of 57. A Tonnis grade of 1 was assigned to this patient (increased sclerosis

of the head and acetabulum and slight lipping at the joint margins [35]). There was no

evidence of visible joint narrowing in the pre-operative radiograph.

CT Arthrography

CT arthrography was performed to enable detection of cartilage layers in the

image data. The pathologic joint (left hip) was injected for the subject with dysplasia

whereas a random assignment was made for the normal control subject (left hip). An 18-

gauge needle was inserted into the hip joint capsule under fluoroscopic control. A

solution consisting of equal parts of contrast agent (Omnipaque, Nycomed Amersham,

Princeton, NJ) and 1% Lidocaine (Hospira Inc., Lake Forest, IL) was injected into each

hip joint capsule. A small amount of epinephrine (0.1 ml) was included to keep the fluid

within the capsule. Approximately 20 ml of solution was injected into each subject’s hip

171

capsule. Following injection the subject was transferred to the CT scanner via a

wheelchair to limit joint loading and associated fluid loss.

Immediately prior to scanning the joint was passively flexed, abducted, and

rotated to ensure that the articulating surfaces of cartilage were coated with contrast agent

[36]. A Siemans Somatom 64 CT (Siemens Medical Solutions USA, Malvern, PA)

scanner was used to acquire volumetric CT data of each subject’s pelvis and proximal

femur in a supine position (120 kVp, 250 mAs, 512 x 512 matrix, FOV = 300 mm, 1 mm

slices, 0.586 x 0.586 x 1.0 mm voxel resolution, ~400 slices). The scan started at the

superior iliac crest on the pelvis and ended at the superior third of the femur.

Image Data Analysis and Segmentation

DICOM images were transferred to a Linux workstation for post-processing. The

data were re-sampled at 0.5 mm slice thicknesses to achieve a near isotropic voxel

resolution (0.586 x 0.585 x 0.5 mm), which has been shown to produce more accurate

reconstructions of cartilage thickness than anisotropic resolutions [12]. Separate splines

representing the outer layer of cartilage, outer cortex, and boundary between cortical and

trabecular bone were automatically and semi-automatically segmented using commercial

software (Amira 4.1, Mercury Computer Systems, Chelmsford, MA.) Pixel threshold

values assigned to bone were based on our previous modeling efforts [34]. Cartilage

boundaries were delineated using a threshold value from a phantom-based imaging study

of cartilage [12]. In most regions bone and cartilage could be segmented automatically.

However, some regions demonstrated volumetric averaging, requiring semi-automatic

segmentation. Manual segmentation tools available in Amira were used to further define

172

boundaries in these regions. Although volumetric averaging was present, the boundaries

between tissue structures could be easily discerned by visual inspection.

Triangular surfaces were generated for each structure using the Marching Cubes

algorithm [37]. The outer cortical bone surface facets were decimated to a density

consistent with our previous study [11,34]. Cartilage surfaces were decimated and

smoothed slightly to remove visible triangular irregularities and segmentation artifact

[11].

FE Mesh Generation, Cartilage Thickness, Material Properties

The triangular surface mesh for cortical bone was converted to a quadratic 3-node

shell element mesh [11,34,38,39]. Position dependent shell thickness was assigned to

each node, based on the distance between adjacent trabecular bone boundary nodes [34].

Acetabular and femoral cartilage surfaces were imported into FE preprocessing software

(TrueGrid, XYZ Scientific, Livermore, CA) and hexahedral element meshes were created

[11]. Cartilage thickness for the acetabular and femoral cartilage mesh geometries was

also assessed using the cortical bone thickness algorithm [34]. The final normal and

dysplastic hip joint FE meshes (Figure 6.1) had densities consistent with our prior hip

joint FE modeling studies [11,34].

Trabecular bone was neglected in this study as we previously demonstrated that it

has little effect on the prediction of cartilage contact pressures and cortical bone strains

[11,34]. Cartilage was represented as an incompressible, neo-Hookean hyperelastic

material [40] with shear modulus G=6.8 MPa [41]. Incompressibility was enforced using

the augmented Lagrangian method [42]. Cortical bone was represented as hypoelastic,

173

homogenous, and isotropic with elastic modulus E=17 GPa and Poisson’s ratio ν=0.29

[43].

Figure 6.1. Patient-specific FE meshes of normal (top) and dysplastic (bottom) hip joints. Insets show details of FE discretization. Note lack of anterior femoral head coverage andincongruence in the dysplastic hip.

174

FE Boundary and Loading Conditions

Stair-climbing, walking, and descending stairs were simulated using average in-

vivo instrumented prostheses gait data [14,15]. These data describe both the anatomical

orientation of the hip as well as the magnitude and direction of the equivalent joint

reaction force vector throughout the gait cycle. Data at peak loading for each scenario

(~2.5 times bodyweight) were used to drive the FE simulations.

The CT coordinate axes of each subject’s FE mesh were transformed into an

embedded joint coordinate system that used the convention described by Bergmann

[14,15]. Specifically, the Xp axis originates at the center of a vector passing through the

center of the left and right femoral heads and is aligned along that vector, while the Zp

axis is aligned upwards, passing through the center of the L5-S1 vertebral body. The Yp

axis is perpendicular to Xp and Zp and points in the ventral direction.

The femur was flexed, abducted, and rotated relative to the pelvis so that 3D

kinematic alignment was identical to that for Bergmann’s average subject. Next, the

entire hip joint was flexed and abducted so that a vertically directed force in the Z-axis

would result in the correct equivalent joint reaction force vector for Bergmann’s average

subject [11,14,15]. Reaction force data were scaled based on patient body weight.

Nodes residing within the sacroiliac (SI) and pubis joint and those at the base of

the proximal femur diaphysis were defined as rigid [11,34]. The rigid nodes at the base

of the proximal femur were constrained to move only in the direction of applied load,

while the nodes at the pubis and SI joints were fully constrained [11,34]. The Mortar

method was used to tie acetabular and femoral cartilage to the acetabulum and femoral

175

head, respectively [44,45]. Contact between the femoral and acetabular cartilage was

enforced using the penalty method [46]. All analyses were performed using the non-

linear, implicit FE code NIKE3D [46].

Sensitivity Studies

Sensitivity studies were performed for each model to assess the effects of altering

joint kinematic angles and direction of equivalent joint reaction force using the standard

deviations reported by Bergmann [14,15]. 15 cases were analyzed per subject, yielding a

total of 30 FE analyses. For each loading scenario there were 5 models: 1 baseline, 2 to

assess the effects of variations in joint reaction force (± 1 SD) and 2 to assess variations

in joint kinematics (± 1 SD of flexion, abduction, rotation). One standard deviation in the

kinematic and reaction force data represented nearly 50% of the baseline values.

Data Analysis

If damage due to habitual mechanical overload is the instigating factor in the

onset of OA, this implies that mechanical measures of stress are the critical factors

defining the overload conditions. Therefore, peak contact pressure, average pressure and

maximum shear stress for cartilage were determined from each FE model. Contact area

was also calculated using a method described in our prior work [11] since this measure

may provide indirect insight into material stresses and studies have suggested that contact

area is reduced in the dysplastic joint [28,29,33]. Qualitative anatomical differences in

the location of cartilage contact were also interpreted. All quantitative results were

176

reported as means and standard deviations based on combined data for the baseline model

and all sensitivity models for each loading scenario.

177

RESULTS

Computational measurements of cartilage thickness demonstrated that cartilage in

the dysplastic hip was slightly thicker than that of the normal hip. Acetabular and

femoral cartilage thickness was 1.22±0.47 and 1.36±0.31 mm for the dysplastic hip, and

1.14±0.36 and 1.01±0.35 mm for the normal hip (Figure 6.2). Both the dysplastic and

normal subject had thicker cartilage in the medial aspect of the femur (Figure 6.2 left

column). A small region of thick cartilage was also noted along the lateral aspect of both

femurs (Figure 6.2 left column). The normal subject had thicker cartilage in the

superorlateral region of the aceteabulum whereas cartilage was thicker in the posterior

aspect in the dysplastic acetabulum (Figure 6.2 right column).

1.75 mm

0.0 mm

AcetabulumFemur

NO

RM

AL

D

YSP

LA

SI

Inferior

Superior

Posterior

Anterior

Posterior

Med

ial

Figure 6.2. Fringe plots of femoral (left column) and acetabular (right column) cartilagethickness in the normal (top row) and dysplastic (bottom row) hip joints.

178

Peak cartilage contact pressure, average pressure and maximum shear stress for the

dysplastic patient were consistently higher than those for the normal subject during all

three activities (Table 6.1). Surprisingly, contact areas were larger for the dysplastic hip

joint (Table 6.1).

179

Fringe plots of cartilage contact pressures elucidated the origins of altered loading

in the dysplastic hip (Figure 6.3 top). Anterior wall cartilage pressures were nearly non-

existent in the normal model where most of the load was distributed along the superior

aspect of the acetabulum (Figure 6.3 bottom). The pattern of contact demonstrated was

more or less mono-centric over the three loading scenarios analyzed (Figure 6.3 bottom).

In contrast, for the dysplastic hip, the distal anterior horn of the acetabular cartilage was

consistently in contact during all three loading scenarios (Figure 6.3 top).

Max. Press. (MPa) (±SD)

Average Press. (MPa) (±SD)

Max Shear (MPa) (±SD)

Contact Area (mm2) (±SD)

DYSPLASIA Walking 30.3 (2.9) 6.8 (0.5) 8.6 (1.5) 1143.3 (99.42) Stair Climbing 29.3 (6.1) 7.1 (0.9) 5.5 (1.8) 976.1 (141.5) Descending Stairs 25.6 (2.2) 6.1 (0.6) 5.8 (1.3) 1084.0 (249.9) NORMAL Walking 16.1 (0.9) 3.3 (0.4) 3.8 (0.6) 569.3 (89.0) Stair Climbing 20.0 (1.3) 3.7 (0.5) 4.0 (0.6) 512.3 (62.4) Descending Stairs 19.7 (1.7) 3.9 (0.3) 3.6 (1.1) 579.6 (86.0)

Table 6.1. Average FE model results (± SD) for the dysplastic and normal hip. A total of15 models were analyzed for each subject- 3 baseline (walking, stair-climbing, descending stairs) and 12 sensitivity models (4 for each loading scenario).

180

Figure 6.3. Lateral inferior oblique view of FE predicted contact pressures for the threeloading scenarios simulated. Top row) dysplastic hip. Bottom row) normal hip. Note that the results shown are for the best case (lowest peak and average pressures) for eachof the subjects. Dysplastic contact pressures were higher and the location of contact wasaltered when compared to the normal hip joint model.

Walking Stair-Climbing Descending-Stairs

DY

SPLA

SIA

20 MPa

NO

RM

AL

0 MPa

181

When compared to the baseline model, the location of contact did not change

substantially when the joint kinematics and kinetics were altered in all of the sensitivity

models for each subject. As shown in the fringe plots of cartilage contact pressure for the

normal and dysplastic joints for 10 of the 30 cases (Figure 6.4), the general location and

magnitude of contact did not change substantially intra-subject following alteration of

both the joint angles and angles of the equivalent force vector. Fringe plots of the

additional 20 analyses are not shown due, but those analyses also demonstrated little

variation as indicated by the small standard deviations in Table 6.1.

Avg. Kinematics Avg. Kinetics

+1 SD Flexion, Abduction, Rotation,

Avg. Kinetics

-1 SD Flexion, Abduction, Rotation,

Avg. Kinetics

+1 SD Angles of Joint Reaction Force

Avg. Kinematics

-1 SD Angles of Joint Reaction Force

Avg. Kinematics20 MPa

0 MPa

NO

RM

AL

DY

SPLA

SIA

Figure 6.4. Lateral inferior oblique view of FE predicted contact pressures for 10 of the 30 sensitivity studies analyzed (walking loading scenario only). Top row) normalsubject. Bottom row) dysplastic patient. The location of contact did not change substantially following alteration of the joint angles and angles of the equivalent forcevector (separated by columns).

182

DISCUSSION

This study developed realistic three-dimensional FE models of the hip joint to

compare joint biomechanics between a normal and dysplastic hip. This is the first

patient-specific modeling study to our knowledge to utilize a computational protocol that

had been previously validated by comparing subject-specific FE model predictions

directly with experimental measurements [11-13]. Model predictions suggested that

cartilage stresses were elevated in the dysplastic hip joint, which may provide a

mechanical explanation as to why persons with hip dysplasia frequently develop hip joint

OA.

The predicted patterns of contact pressure and bone stress can be interpreted

directly in terms of the type of acetabular dysplasia. Anteversion of the acetabulum

creates poor anterior support of the femur, which causes the anterior wall to be loaded

more than normal. The fringe plots of cartilage stress indicated that this was the case for

the anteverted joint where a localized “hot spot” of cartilage stress was noted. The

posterior aspect of the acetabulum was also contacted resulting in a distinct bi-centric

contact pattern which was likely due to incongruent mating between the femur and

acetabulum (Figure 6.1). The normal acetabulum was not excessively tilted anteriorly

and was more spherical in shape when qualitatively compared to the dyplastic joint.

Therefore, most of the cartilage contact occurred on the superior wall of the joint,

resulting in a mono-centric pattern of contact.

The dysplastic FE model predicted contact areas that were larger than the normal

control, which was contradictory to several studies reported in the literature [28,29,33].

183

A possible explanation for this was that the location of contact in the dysplastic joint was

predominately confined to areas that were nearly parallel to the principal direction of

loading, whereas the normal joint had substantial support perpendicular to the load.

Therefore, greater compressive and shear strains were required to carry the applied load

in the dysplastic joint, resulting in larger contact areas. Although limited by the small

sample size, the results of this study suggest that the location of contact may be more

important than the absolute value of contact area when assessing joint mechanics in the

dysplastic hip. This conclusion augments recent data reported by Armand et al. [47].

They developed pre and post-operative computational models to analyze changes in peak

pressures and contact areas following peri-acetabular osteotomy and found that while 9 of

12 cases showed decreased peak pressure after surgery, the mean changes in contact area

were not statistically significant.

Several attempts have been made to quantify the biomechanics associated with

dysplasia. Mavcic et al. [27] used a mathematical model of static, single-leg stance based

on AP radiographs of normal and dysplastic subjects. Dysplastic hips had significantly

larger peak contact stresses than healthy hips (7.1 kPa/N and 3.5 kPa/N, respectively).

Michaeli and co-workers combined experiments and computer modeling to predict the

contact stress in the human hip joint and to investigate differences in location and

magnitude of contact stresses between normal cadaveric pelvi and plastic pelvi with

simulated dysplasia [29]. Their computational model was based on 3-D reconstructions

from CT image data that was fit to spheres to represent femoral and acetabular geometry.

The surface of each sphere was discretized into 0.5 mm2 patches. At each surface patch

184

the dot product between the applied load and a vector normal to the patch was calculated

and the total load was divided among the patches. Computational predictions of contact

pressure, as calculated by dividing the force magnitude by the surface area of each patch,

were nearly 7 times less than those measured by the pressure film in the cadaveric and

plastic pelvi. They concluded that the technique was not proven to yield accurate

predictions of contact stress in dysplastic joints [29]. Nevertheless, Hipp et al. [28]

applied this computational model to analyze joint contact pressures for 70 dysplastic and

12 normal hips. Contact areas were 26% smaller and contact pressures were 23% higher

in dysplastic hips. Peak pressures for dysplastic hips were on the order of 7 MPa.

Genda et al. [32] used a three-dimensional rigid body spring model (RBSM) to

compare hip joint mechanics between 112 normal and 66 dysplastic hip joints.

Geometric models were made from conventional anteroposterior radiographs with the

assumption that the acetabular surface was spherical. At 4.5 times bodyweight the mean

peak pressures for normal hips was around 3 MPa. Mean contact pressures for the

dysplastic hips were not reported, however the model with the largest peak pressure

predicted a value of 16 MPa.

Peak pressures reported in the aforementioned studies consistently underestimated

those measured in vitro [7,8,48-52] and in vivo [15,53] and were substantially less than

those predicted in the current study. This discrepancy is likely attributed to the

assumption of spherical joints and uniform cartilage thickness. Anthropometric studies

have demonstrated that the hip joint is neither concentric nor has uniform cartilage

thickness [54-56] and that even normal joints demonstrate irregular patterns of cartilage

185

contact with steep pressure gradients [7,8,49-52]. Therefore, an accurate representation

of the three-dimensional geometry of the hip joint may be a necessary precursor to

predicting accurate biomechanics.

Recently, Russell et al. [33] generated realistic three-dimensional FE models of

six dysplastic, five asymptomatic and one normal subject using CT arthrogram data.

They reported significant differences between the normal control and the asymptomatic

hips and trend towards significance between the asymptomatic hips and the symptomatic

hips of patients afflicted with DDH, suggesting that the contralateral hip in DDH is also

affected. Peak contact pressures for the symptomatic and asymptomatic hips ranged from

3.56 – 9.88 MPa whereas normal hip peak pressures ranged from 1.75 – 1.89 MPa. The

peak pressures in the current study were substantially elevated in comparison to these

results despite very similar boundary and loading conditions. One of the reasons for this

discrepancy could be that Russell et al. applied a substantial amount of smoothing to the

articulating surface of femoral and acetabular cartilage. In addition, they assumed a

cartilage elastic modulus of 10 MPa, which is roughly 4 times less than the modulus used

in the current study.

Several limitations of the current study must be mentioned. First, only one

patient-specific FE model was analyzed for each subject group, eliminating the ability to

perform statistical tests. However, the primary objective of this paper was to demonstrate

the feasibility of the FE method for modeling hip dysplasia. Future modeling efforts

could use this patient-specific modeling protocol to investigate a more reasonable sample

size. In addition, both patient-specific FE models were loaded using identical kinetics

186

and kinematics based on average in-vivo data. While inaccurate kinematics could be a

source of modeling error, our sensitivity studies demonstrate that the spatial distribution

of contact pressures are clearly more dependent on joint geometry than variations in

kinematics or loading vector direction. Nevertheless, it is possible that some intermediate

kinematic position would place the joint in an optimal position that could result in

reduced peak bone and cartilage stresses. This in fact may be the reason why our patient-

specific models predicted peak cartilage pressures that were higher than those predicted

by previous models [27-29,33,51,57] and measured in-vitro [7,8,48-52]. This will be

investigated in future studies.

Our prior work [12] has demonstrated that cartilage thickness reconstruction

errors based on CT arthrogram image data increase exponentially when cartilage

thickness reaches a critical value (around 1 mm). This could present a challenge while

studying OA since the disease is predominately associated with a loss of cartilage

[58,59]. Nevertheless, studies have shown that cartilage in patients with dysplasia is

actually thicker than normal joints during the early onset of symptoms [9,10,60].

Average cartilage thicknesses for the models analyzed in our study demonstrated that

cartilage was thicker in the dysplastic joint and was above the critical threshold for

obtaining accurate reconstructions for both models analyzed. Model accuracy would

likely degrade if patients with thinner cartilage were studied, and thus it is presently

recommended that our modeling technique should not be applied to patients who have

cartilage thicknesses that are predominantly less than 1 mm.

187

Trabecular bone was not modeled in this study since we demonstrated that it has

little effect on the prediction of cartilage stresses in the hip [11]. However, it is well

known that trabecular bone architecture and density are sensitive to localized stresses (i.e.

Wolff’s Law [61]). Therefore, a better understanding of trabecular bone orientation,

density and mechanics may provide valuable insight into the biomechanics of hip

dysplasia. Because we did not explicitly validate trabecular bone stresses and strains

[13], we are hesitant to predict trabecular bone mechanics on a patient-specific basis. In

addition, the acetabular labrum was removed in this study, yet it has been suggested that

the labrum helps to maintain fluid pressurization in the hip [62,63]. It is possible that

leaving the labrum intact would have altered the predicted contact patterns and

magnitudes. Although actions of individual muscles were not considered, the equivalent

joint reaction force was based on in vivo data [14,15], which justifies our method of

modeling the action of all muscles as a single equivalent force vector. Finally, cartilage

exhibits depth dependent material properties [64], variation in stiffness over its surface

[65,66] and tension-compression nonlinearity [67] yet was modeled as an isotropic,

homogenous material. Future patient-specific modeling efforts should investigate the

importance of these effects via sensitivity studies.

It is unlikely that mathematical or computational models that use simplified or

idealized representations of the articular surface geometry (e.g., [27-29]) provide accurate

insight into differences between normal and dysplastic hips. Our protocol allows for

realistic three-dimensional models to be developed and analyzed non-invasively using

patient-specific CT arthrogram image data. The modeling protocol could be improved by

188

including patient-specific kinematics, more sophisticated cartilage constitutive equations

and by incorporating the acetabular labrum. In conclusion, the results from this proof of

concept study suggest that patients with dysplasia may have altered joint biomechanics

and motivates future modeling efforts to analyze a greater number of subjects.

189

REFERENCES

[1] Aronson, J., 1986, "Osteoarthritis of the Young Adult Hip: Etiology and

Treatment," in Instructional Course Lectures, vol. 35, I. D. Anderson, Ed. ICV Mosby, St. Louis, MO.

[2] Harris, W. H., 1986, "Etiology of Osteoarthritis of the Hip," Clin Orthop, pp. 20-

33. [3] Murray, R. O., 1965, "The Aetiology of Primary Osteoarthritis of the Hip," Br J

Radiol, 38, pp. 810-24. [4] Solomon, L., 1976, "Patterns of Osteoarthritis of the Hip," J Bone Joint Surg Br,

58, pp. 176-83. [5] Stulberg, S. D. and Harris, W. H., "Acetabular Dysplasia and Development of

Osteoarthritis of the Hip," presented at Proceedings of the second open scientific meeting of the Hip Society, St Louis, MO, 1974.

[6] Wilson, M. G. and Poss, R., 1992, "Osteoarthritis: Diagnosis and

Medical/Surgical Treatment," R. W. Moskowitz, D. S. Howell, V. M. Goldberg, and H. J. Mankin, Eds. WB Saunders, Philadelphia, pp. 621-50.

[7] von Eisenhart-Rothe, R., Eckstein, F., Muller-Gerbl, M., Landgraf, J., Rock, C.,

and Putz, R., 1997, "Direct Comparison of Contact Areas, Contact Stress and Subchondral Mineralization in Human Hip Joint Specimens," Anat Embryol (Berl), 195, pp. 279-88.

[8] von Eisenhart-Rothe R, A. C., Steinlechner M, Muller-Gerbl M and Eckstein F,

1999, "Quantitative Determination of Joint Incongruity and Pressure Distribution During Simulated Gait and Cartilage Thickness in the Human Hip Joint," Journal of Orthopaedic Research, 7, pp. 532-539.

[9] Nishii, T., Sugano, N., Sato, Y., Tanaka, H., Miki, H., and Yoshikawa, H., 2004,

"Three-Dimensional Distribution of Acetabular Cartilage Thickness in Patients with Hip Dysplasia: A Fully Automated Computational Analysis of Mr Imaging," Osteoarthritis Cartilage, 12, pp. 650-7.

[10] Soboleski, D. A. and Babyn, P., 1993, "Sonographic Diagnosis of Developmental

Dysplasia of the Hip: Importance of Increased Thickness of Acetabular Cartilage," AJR Am J Roentgenol, 161, pp. 839-42.

190

[11] Anderson, A. E., Ellis, B. J., Maas, S. A., Peters, C. L., and Weiss, J. A., 2007, "Validation of Finite Element Predictions of Cartilage Contact Pressure in the Human Hip Joint," Journal of Biomechanical Engineering.

[12] Anderson, A. E., Ellis, B. J., Peters, C. L., and Weiss, J. A., 2007, "Factors

Influencing Cartilage Thickness Measurements with Multi-Detector Ct: A Phantom Study," Radiology, In Press, Feb 2007.

[13] Anderson, A. E., Peters, C. L., Tuttle, B. D., and Weiss, J. A., 2005, "Subject-

Specific Finite Element Model of the Pelvis: Development, Validation and Sensitivity Studies," J Biomech Eng, 127, pp. 364-73.

[14] Bergmann, G., 1998, Hip98: Data Collection of Hip Joint Loading on Cd-Rom.

Free University and Humboldt University, Berlin. [15] Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A.,

Strauss, J., and Duda, G. N., 2001, "Hip Contact Forces and Gait Patterns from Routine Activities," J Biomech, 34, pp. 859-71.

[16] Kim, W. Y., Hutchinson, C. E., Andrew, J. G., and Allen, P. D., 2006, "The

Relationship between Acetabular Retroversion and Osteoarthritis of the Hip," J Bone Joint Surg Br, 88, pp. 727-9.

[17] Bombelli, R., 1983, Osteoarthritis of the Hip. Springer-Verlag, Berlin, Germany. [18] Bombelli, R., Santore, R. F., and Poss, R., 1984, "Mechanics of the Normal and

Osteoarthritic Hip. A New Perspective," Clin Orthop, pp. 69-78. [19] Ali-Gombe, A., Croft, P. R., and Silman, A. J., 1996, "Osteoarthritis of the Hip

and Acetabular Dysplasia in Nigerian Men," J Rheumatol, 23, pp. 512-5. [20] Croft, P., Cooper, C., Wickham, C., and Coggon, D., 1990, "Defining

Osteoarthritis of the Hip for Epidemiologic Studies," Am J Epidemiol, 132, pp. 514-22.

[21] Croft, P., Cooper, C., Wickham, C., and Coggon, D., 1991, "Osteoarthritis of the

Hip and Acetabular Dysplasia," Ann Rheum Dis, 50, pp. 308-10. [22] Croft, P., Cooper, C., Wickham, C., and Coggon, D., 1992, "Is the Hip Involved

in Generalized Osteoarthritis?," Br J Rheumatol, 31, pp. 325-8. [23] Inoue, K., Shichikawa, K., and Ota, H., 1999, "Prevalence of Hip Osteoarthritis

and Acetabular Dysplasia in Kamitonda: From a Longitudinal Population-Based

191

Epidemiological Study of Rheumatic Diseases in Japan," Rheumatology (Oxford), 38, pp. 793-4.

[24] Inoue, K., Wicart, P., Kawasaki, T., Huang, J., Ushiyama, T., Hukuda, S., and

Courpied, J., 2000, "Prevalence of Hip Osteoarthritis and Acetabular Dysplasia in French and Japanese Adults," Rheumatology (Oxford), 39, pp. 745-8.

[25] Cooperman, D. R., Wallensten, R., and Stulberg, S. D., 1983, "Acetabular

Dysplasia in the Adult," Clin Orthop, pp. 79-85. [26] Malvitz, T. A. and Weinstein, S. L., 1994, "Closed Reduction for Congenital

Dysplasia of the Hip. Functional and Radiographic Results after an Average of Thirty Years," J Bone Joint Surg Am, 76, pp. 1777-92.

[27] Mavcic, B., Pompe, B., Antolic, V., Daniel, M., Iglic, A., and Kralj-Iglic, V.,

2002, "Mathematical Estimation of Stress Distribution in Normal and Dysplastic Hips," Journal of Orthopaedic Research, 20, pp. 1025-1030.

[28] Hipp, J. A., Sugano, N., Millis, M. B., and Murphy, S. B., 1999, "Planning

Acetabular Redirection Osteotomies Based on Joint Contact Pressures," Clin Orthop, pp. 134-43.

[29] Michaeli, D. A., Murphy, S. B., and Hipp, J. A., 1997, "Comparison of Predicted

and Measured Contact Pressures in Normal and Dysplastic Hips," Med Eng Phys, 19, pp. 180-6.

[30] Reynolds, D., Lucas, J., and Klaue, K., 1999, "Retroversion of the Acetabulum. A

Cause of Hip Pain," J Bone Joint Surg Br, 81, pp. 281-8. [31] Siebenrock, K. A., Leunig, M., and Ganz, R., 2001, "Periacetabular Osteotomy:

The Bernese Experience," Instr Course Lect, 50, pp. 239-45. [32] Genda, E., Konishi, N., Hasegawa, Y., and Miura, T., 1995, "A Computer

Simulation Study of Normal and Abnormal Hip Joint Contact Pressure," Arch Orthop Trauma Surg, 114, pp. 202-6.

[33] Russell, M. E., Shivanna, K. H., Grosland, N. M., and Pedersen, D. R., 2006,

"Cartilage Contact Pressure Elevations in Dysplastic Hips: A Chronic Overload Model," J Orthop Surg, 1, pp. 6.

[34] Anderson, A., Ellis, B. J., and Weiss, J. A., 2006, "Verification, Validation and

Sensitivity Studies in Computational Biomechanics," Computer Methods in Biomechanics and Biomedical Engineering, In Press Dec 2006.

192

[35] Tönnis, D., 1987, Congenital Dysplasia and Dislocation of the Hip in Children and Adults. Springer-Verlag, Berlin.

[36] Nishii, T., Tanaka, H., Nakanishi, K., Sugano, N., Miki, H., and Yoshikawa, H.,

2005, "Fat-Suppressed 3d Spoiled Gradient-Echo Mri and Mdct Arthrography of Articular Cartilage in Patients with Hip Dysplasia," AJR Am J Roentgenol, 185, pp. 379-85.

[37] Lorensen, W. E. and Cline, H. E., 1987, "Marching Cubes: A High Resolution 3d

Surface Construction Algorithm," Comput. Graph., 21, pp. 163-169. [38] Hughes, T. J., 1980, "Generalization of Selective Integration Procedures to

Anisotopic and Nonlinear Media," Interational Journal for Numerical Methods in Engineering, 15, pp. 9.

[39] Hughes, T. J. and Liu, W. K., 1981, "Nonliner Finite Element Analysis of Shells:

Part I. Two Dimensional Shells.," Compuational Methods in Applied Mechanics, 27, pp. 167-181.

[40] Buchler, P., Ramaniraka, N. A., Rakotomanana, L. R., Iannotti, J. P., and Farron,

A., 2002, "A Finite Element Model of the Shoulder: Application to the Comparison of Normal and Osteoarthritic Joints," Clin Biomech (Bristol, Avon), 17, pp. 630-9.

[41] Park, S., Hung, C. T., and Ateshian, G. A., 2004, "Mechanical Response of

Bovine Articular Cartilage under Dynamic Unconfined Compression Loading at Physiological Stress Levels," Osteoarthritis Cartilage, 12, pp. 65-73.

[42] Hestenes, M. R., 1969, "Multiplier and Gradient Methods," Journal of

Optimization Theory and Applications, 4, pp. 303-320. [43] Dalstra, M., Huiskes, R., and van Erning, L., 1995, "Development and Validation

of a Three-Dimensional Finite Element Model of the Pelvic Bone," J Biomech Eng, 117, pp. 272-8.

[44] Puso, M. A., 2004, "A 3d Mortar Method for Solid Mechanics," International

Journal for Numerical Methods in Engineering, 59, pp. 315-36. [45] Puso, M. A. and Laursen, T. A., 2004, "A Mortar Segment-to-Segment Contact

Method for Large Deformation Solid Mechanics," Computer Methods in Applied Mechanics and Engineering, 193, pp. 601-29.

193

[46] Maker, B. N., Ferencz, R. M., and J.O., H., 1990, "Nike3d: A Nonlinear, Implicit, Three-Dimensional Finite Element Code for Solid and Structural Mechanics," Lawrence Livermore National Laboratory Technical Report, UCRL-MA.

[47] Armand, M., Lepisto, J., Tallroth, K., Elias, J., and Chao, E., 2005, "Outcome of

Periacetabular Osteotomy: Joint Contact Pressure Calculation Using Standing Ap Radiographs, 12 Patients Followed for Average 2 Years," Acta Orthop, 76, pp. 303-13.

[48] Adams, D. and Swanson, S. A., 1985, "Direct Measurement of Local Pressures in

the Cadaveric Human Hip Joint During Simulated Level Walking," Ann Rheum Dis, 44, pp. 658-66.

[49] Afoke, N. Y., Byers, P. D., and Hutton, W. C., 1987, "Contact Pressures in the

Human Hip Joint," J Bone Joint Surg Br, 69, pp. 536-41. [50] Brown, T. D. and Shaw, D. T., 1983, "In Vitro Contact Stress Distributions in the

Natural Human Hip," J Biomech, 16, pp. 373-84. [51] Macirowski, T., Tepic, S., and Mann, R. W., 1994, "Cartilage Stresses in the

Human Hip Joint," J Biomech Eng, 116, pp. 10-8. [52] Rushfeldt, P. D., Mann, R. W., and Harris, W. H., 1981, "Improved Techniques

for Measuring in Vitro the Geometry and Pressure Distribution in the Human Acetabulum. Ii Instrumented Endoprosthesis Measurement of Articular Surface Pressure Distribution," J Biomech, 14, pp. 315-23.

[53] Hodge, W. A., Fijan, R. S., Carlson, K. L., Burgess, R. G., Harris, W. H., and

Mann, R. W., 1986, "Contact Pressures in the Human Hip Joint Measured in Vivo," Proc Natl Acad Sci U S A, 83, pp. 2879-83.

[54] Bullough, P., Goodfellow, J., Greenwald, A. S., and O'Connor, J., 1968,

"Incongruent Surfaces in the Human Hip Joint," Nature, 217, pp. 1290. [55] Rushfeldt, P. D., Mann, R. W., and Harris, W. H., 1981, "Improved Techniques

for Measuring in Vitro the Geometry and Pressure Distribution in the Human Acetabulum--I. Ultrasonic Measurement of Acetabular Surfaces, Sphericity and Cartilage Thickness," J Biomech, 14, pp. 253-60.

[56] Shepherd, D. E. and Seedhom, B. B., 1999, "Thickness of Human Articular

Cartilage in Joints of the Lower Limb," Ann Rheum Dis, 58, pp. 27-34. [57] Brown, T. D. and DiGioia, A. M., 3rd, 1984, "A Contact-Coupled Finite Element

Analysis of the Natural Adult Hip," J Biomech, 17, pp. 437-48.

194

[58] Radin, E. L., 1995, "Osteoarthrosis--the Orthopedic Surgeon's Perspective," Acta Orthop Scand Suppl, 266, pp. 6-9.

[59] Radin, E. L., Burr, D. B., Caterson, B., Fyhrie, D., Brown, T. D., and Boyd, R. D.,

1991, "Mechanical Determinants of Osteoarthrosis," Semin Arthritis Rheum, 21, pp. 12-21.

[60] Nishii, T., Sugano, N., Tanaka, H., Nakanishi, K., Ohzono, K., and Yoshikawa,

H., 2001, "Articular Cartilage Abnormalities in Dysplastic Hips without Joint Space Narrowing," Clin Orthop Relat Res, pp. 183-90.

[61] Wolff, J., 1892, Das Gesetz Der Transformation Der Knochen. Hirschwald,

Berlin. [62] Ferguson, S. J., Bryant, J. T., Ganz, R., and Ito, K., 2000, "The Influence of the

Acetabular Labrum on Hip Joint Cartilage Consolidation: A Poroelastic Finite Element Model," J Biomech, 33, pp. 953-60.

[63] Ferguson, S. J., Bryant, J. T., Ganz, R., and Ito, K., 2003, "An in Vitro

Investigation of the Acetabular Labral Seal in Hip Joint Mechanics," J Biomech, 36, pp. 171-8.

[64] Chen, S. S., Falcovitz, Y. H., Schneiderman, R., Maroudas, A., and Sah, R. L.,

2001, "Depth-Dependent Compressive Properties of Normal Aged Human Femoral Head Articular Cartilage: Relationship to Fixed Charge Density," Osteoarthritis Cartilage, 9, pp. 561-9.

[65] Athanasiou, K. A., Agarwal, A., and Dzida, F. J., 1994, "Comparative Study of

the Intrinsic Mechanical Properties of the Human Acetabular and Femoral Head Cartilage," J Orthop Res, 12, pp. 340-9.

[66] Shepherd, D. E. and Seedhom, B. B., 1999, "The 'Instantaneous' Compressive

Modulus of Human Articular Cartilage in Joints of the Lower Limb," Rheumatology (Oxford), 38, pp. 124-32.

[67] Chahine, N. O., Wang, C. C., Hung, C. T., and Ateshian, G. A., 2004,

"Anisotropic Strain-Dependent Material Properties of Bovine Articular Cartilage in the Transitional Range from Tension to Compression," J Biomech, 37, pp. 1251-61.

CHAPTER 7

DISCUSSION

SUMMARY

The research described in this dissertation investigated the mechanics of

the human hip joint and developed novel experimental and computational tools

that will facilitate future studies of the hip. Further, the results of this dissertation

may be applied to the study of other joints such as the knee and shoulder.

Experimental hip joint tests were conducted to measure pelvic cortical bone

strains and cartilage contact stresses in separate studies. Detailed computational

protocols were developed and validated by comparing finite element (FE)

predictions directly with bone strains and cartilage contact stresses measured

experimentally. Model sensitivity studies were performed to analyze the effects

of altering assumed and measured inputs including material properties, geometry,

and boundary conditions. The ability of computed tomography (CT) to accurately

reconstruct cortical bone and cartilage thickness was also determined using

phantoms. Finally, the feasibility of patient-specific FE modeling was

demonstrated by developing and analyzing FE models of a normal and dyplastic

hip joint. The results of this proof of concept study indicated altered

biomechanics in the dysplastic hip, motivating further study of this patient

population.

196

The results of the bone modeling study demonstrated the accuracy of the

FE method for quantifying bone strains and has direct relevance to the study of

hip dysplasia and OA as it is believed that bone mechanics play an important role

in the progression of these pathologies [1,2]. Although previous models of the

pelvis have been described [3,4], direct validation between computational

predictions and experimental measurements was not performed. The accuracy of

CT reconstructions of cortical bone was also quantified in this study and it was

determined that cortical bone should be at least 0.7 mm thick to obtain accurate

geometrical reconstructions. The pelvis analyzed in this study rarely had

thickness below this critical threshold. Thus, our approach for modeling the

cortex as a layer of thin shells has direct applicability to the analysis of patient-

specific models, assuming that subjects have cortical bone with sufficient

thickness. The results of the parameter studies demonstrated that predictions of

cortical bone strains were most sensitive to changes in cortical bone thickness.

Therefore, the cortical bone thickness algorithm developed herein will be useful

for constructing accurate FE models in the future. Finally, the model detailed in

this study may have the ability to serve as a template for studying general

biomechanics of the pelvis or to investigate changes in bone stresses and strains

due to surgical procedures such as peri-acetabular osteotomy (PAO) or total hip

arthroplasty (THA).

Prior to developing subject and patient-specific joint contact stress models

it was important to demonstrate that cartilage thickness could be accurately

reconstructed from CT image data. The results from the phantom imaging study

197

suggested that cartilage should be at least 1.0 mm thick to ensure accurate (<10%

error) reconstructions. Additionally, it was shown that cadaveric hips could be

imaged without contrast agent as errors in the “dry” scans were nearly identical to

those when using a low concentration of contrast agent. It is generally assumed

that CT underestimates the thickness of thin tissues due to volumetric averaging

[5,6], but the results of this study demonstrate that the direction of the error during

CT arthrography is dependent on several parameters such as contrast agent

concentration, scanner direction, and spatial resolution. From our recent

experience working alongside radiologists, we have found that the choice of

contrast agent concentration generally depends on the particular radiologist who is

performing the injection. It is hoped that the results of this study will circulate to

a larger audience of clinicians and scientists who may be unaware of the

consequences of using higher concentrations.

The FE modeling study of cartilage contact was the first to validate

predictions directly with experimental pressures measurements. Overall, the FE

model demonstrated good qualitative and quantitative correspondence between

computational predictions and experimental data. Prior hip joint contact models

assumed spherical geometry and concentric articulation between opposing layers

of cartilage [7-11]. Therefore, most models have predicted pressures that are

substantially less than those measured experimentally. In addition, many studies

have made the assumption of rigid bones [12,13] yet the results of this study

demonstrated that this model simplification may lead to erroneous estimates of

contact stress and area. Modeling errors decreased when larger bounds of

198

pressure were compared, and thus the protocol discussed herein may be more

suitable for generating models that can predict highly stressed regions of cartilage

as opposed to the entire pattern of contact.

Hip dysplasia may be the primary etiology of OA in the hip joint

[2,14,15]. Because the geometric pathologies associated with hip dysplasia are

three-dimensional [16-19], it was important to develop techniques to analyze joint

mechanics without simplifying assumptions regarding bone and cartilage

geometry. Although mathematical and computational models have been

developed to study hip dysplasia [8,9,14,20-22], the patient-specific models

presented in Chapter 6 represent one of the first three-dimensional modeling

efforts. Recent three-dimensional models [22] represent significant

improvements over 2-D techniques however this particular protocol was not

validated. The patient-specific models described in this dissertation demonstrated

differences in joint biomechanics between normal and dysplastic hips. Changing

the direction of loading and the anatomical orientation using standard deviations

reported in the literature did not alter the pattern of cartilage contact substantially.

Therefore, it is likely that the topology of the joint surfaces primarily drives the

patterns of hip joint contact rather than the underlying boundary and loading

conditions. Nevertheless it is possible that some intermediate kinematic position

would provide a “path of least resistance” that would likely reduce pressures from

the values that were predicted in this study. It will be important to analyze several

additional patient-specific FE models to learn more about the pathological

mechanics of hip dysplasia.

199

The primary purpose of this dissertation was to develop and validate

protocols to generate patient-specific models of the hip joint. After review of the

joint modeling literature, it is clear that substantial effort has been directed

towared model “development” yet the notion of model “validation” has been

largely neglected. Model credibility must be established before clinicians and

scientists can be expected to extrapolate information and decisions based on

model predictions [23]. Although it has been argued that absolute model

validation is impossible [24,25] it is hoped that the protocol developed herein has

been subject to enough scrutiny that it will be accepted as an appropriate

methodology for generating patient-specific hip joint models. If a similar

combined experimental and computational approach is adopted by analysts who

wish to study other joints such as the knee and shoulder, peer acceptance will

ultimately be improved.

200

LIMITATIONS AND FUTURE WORK

One of the primary critiques of using the FE method for studying joint

biomechanics is that it is very time consuming to segment surface geometry from

medical image data [9], potentially limiting the amount of subjects that could be

analyzed in a given study. The surface used to create the pelvic mesh in Chapter

3 took nearly one month to manually segment from the CT image data. However,

recent commercial segmentation programs have made the process of data

segmentation nearly automated. By using a commercial program (Amira 4.1,

where) we were able to reduce the time to segment the pelvic surface from one

month to less than three hours.

Is it believed that the architecture of trabecular bone is primarily dictated

by the stress history [26]. Therefore, it would be beneficial to predict trabecular

bone stresses and strains in both normal and pathological hips since this could

provide insight into why diseases such as OA develop. It was not possible to

experimentally measure trabecular bone strains in the pelvic FE modeling study

(Chapter 3). Therefore, caution should be exercised when interpreting patient-

specific trabecular bone mechanics using models formulated from the protocol

discussed in Chapter 3. Nevertheless, predictions of cortical bone stresses

corresponded well with experimental measures despite changes in the trabecular

bone modulus and Poisson’s ratio. Therefore, this modeling approach for the

analysis of patient-specific cortical bone mechanics does not require one to

stipulate a preferred material direction for trabecular bone.

201

The labrum was removed in the cartilage contact stress study (Chapter 5)

and was not segmented and meshed in the patient specific FE study (Chapter 6).

The locations of contact stresses in the subject-specific model were primarily on

the lateral aspect of the acetabulum during each loading scenario studied.

Therefore it is possible that the labrum may also serve some (albeit limited) load

bearing function in the intact joint. To model the labrum it would first be

necessary to perform material testing to ascertain its material properties as these

have not been reported in the literature. Given its preferred circumferential

alignment of collagen is it quite possible that the transversely isotropic model

described by Quapp and Weiss [27] would work well and this will be investigated

in future experimental and computational studies.

During loading of both normal and pathological joints it is likely that the

hip joint follows a path of least resistance in an effort to minimize energy [28].

To obtain FE model convergence it is often necessary to limit the degrees of

freedom of the model, thus eliminating rigid body modes. This assumption is

appropriate when the same boundary conditions have been applied

experimentally. However, this could result in substantial elevations in patient-

specific models since the exact boundary conditions are not known a-priori.

Although the parameteric studies detailed in Chapter 6 indicated that cartilage

contact pressures were not sensitive to changes in the kinetics and kinematics,

only extreme positions were analyzed. Therefore, it is likely that these models

overestimated cartilage contact pressures in both the normal and dysplastic joint.

202

Several possible approaches could be adopted to resolve the possible need

for patient-specific kinematics. First, using the basis of minimization of energy,

an algorithm could be developed to incrementally rotate and translate the femur

relative to the acetabulum, prior to model loading, until the distance between

opposing layers of cartilage was minimized. Then the model could be constrained

to move only in the direction of applied load. This technique would require an

analyst to assume it is the differences in joint congruence rather than deformation

that dictates the preferred kinematics of the hip joint. A second approach, which

could also be used in conjunction with the former, is related to patient-specific

gait analysis. The kinematic position at any point in the gait cycle could be

quantified using surface markers and standard motion capture technology. The

peak reaction force at the hip measured in-vivo corresponds very well with peaks

of force plate readings [29,30]. Therefore, an estimate of the joint reaction force

could be based on a linear scaling of the force plate data.

Based largely on the work described in this dissertation, our laboratory

has recently obtained federal funding to continue the study of hip dysplasia. This

ongoing work will more thoroughly characterize the biomechanics of hip

dysplasia by developing additional patient-specific FE models. Several subject-

specific FE hips will also be tested experimentally and subsequent FE models will

be validated using methodologies very similar to those described in this

dissertation. Dynamic measurements of cartilage contact pressures will be

recording using a novel tactile pressure sensor. More realistic constitutive

equations will be used to model the tension-compression behavior of cartilage.

203

Finally, patient-specific models will be developed for two different manifestations

of dysplasia (i.e. “traditional” dysplasia and acetabular retroversion). It is hoped

that this study will elucidate the mechanics of dysplasia and result in better

diagnosis and treatment of young adults who are afflicted with this disease.

The long-term goals of this research are to improve the diagnosis and

treatment of acetabular dysplasia and to extend the applicability of hip joint FE

modeling. Treatment decisions for patients with acetabular dysplasia currently

follow a simplified procedure with surgical decision making primarily based on

empiric recommendations and past outcomes. Patients are roughly divided into

those who manifest instability due to acetabular undercoverage (usually classic

dysplasia) and those with acetabular overcoverage (retroversion [16-18]) or

impingement [19,31]. In reality there is likely a spectrum of abnormal hip

morphology in terms of severity and location of stress transmission [16-19].

Using patient-specific modeling techniques could delineate the true spectrum of

this disease process by quantifying the degree of stress transfer from the

acetabulum to the femoral head and primary location of contact, which could

fundamentally change the way that acetabular dysplasia is diagnosed and treated.

Many orthopaedic surgeons are unaware of multiple facets of the dysplasia

diagnosis and their potential implications for joint degeneration. Improved

diagnostic ability translates into more appropriate surgical treatment [31].

Recognizing the mechanical consequences of different forms of dysplasia allows

earlier identification of “at risk” hips so that earlier treatment can be initiated,

hopefully delaying the need for THA.

204

Patient-specific FE models of the hip joint have a number of potential

longer-term uses and benefits, including improved diagnosis of pathology,

patient-specific approaches to treatment, and prediction of the long-term success

rate of corrective surgeries based on pre- and post-operative mechanics. Patient

models could potentially be applied to quantify changes in mechanical loading

due to surgical intervention, allowing one to assess the efficacy of different

approaches to osteotomy. In addition, these techniques could be utilized in

longer-term prospective studies in an effort to correlate surgical correction with

changes in mechanical loading and outcome. Currently, success is measured by

avoidance of a total hip arthroplasty and is not correlated with any preoperative

variable other than the relatively crude radiographic measurements [31].

Hip joint FE modeling may also assist the development of other treatment

methods, such as osteochondral autografting of defective cartilage in patients with

dysplasia. Allograft techniques require mapping of the articular cartilage

anatomy, including cartilage thickness and underlying bone geometry, to

understand how geometric and mechanical abnormalities affect cartilage

mechanics. As tissue engineering techniques continue to improve, autologous

cartilage cell tissue engineering could offer the same type of treatment potential.

205

REFERENCES

[1] Bombelli, R., 1983, Osteoarthritis of the Hip. Springer-Verlag, Berlin,

Germany. [2] Harris, W. H., 1986, "Etiology of Osteoarthritis of the Hip," Clin Orthop,

pp. 20-33. [3] Dalstra, M., Huiskes, R., and van Erning, L., 1995, "Development and

Validation of a Three-Dimensional Finite Element Model of the Pelvic Bone," J Biomech Eng, 117, pp. 272-8.

[4] Oonishi, H., Isha, H., and Hasegawa, T., 1983, "Mechanical Analysis of

the Human Pelvis and Its Application to the Artificial Hip Joint--by Means of the Three Dimensional Finite Element Method," J Biomech, 16, pp. 427-44.

[5] Prevrhal, S., Engelke, K., and Kalender, W. A., 1999, "Accuracy Limits

for the Determination of Cortical Width and Density: The Influence of Object Size and Ct Imaging Parameters," Phys Med Biol, 44, pp. 751-64.

[6] Prevrhal, S., Fox, J. C., Shepherd, J. A., and Genant, H. K., 2003,

"Accuracy of Ct-Based Thickness Measurement of Thin Structures: Modeling of Limited Spatial Resolution in All Three Dimensions," Med Phys, 30, pp. 1-8.

[7] Brown, T. D. and DiGioia, A. M., 3rd, 1984, "A Contact-Coupled Finite

Element Analysis of the Natural Adult Hip," J Biomech, 17, pp. 437-48. [8] Genda, E., Iwasaki, N., Li, G., MacWilliams, B. A., Barrance, P. J., and

Chao, E. Y., 2001, "Normal Hip Joint Contact Pressure Distribution in Single-Leg Standing--Effect of Gender and Anatomic Parameters," J Biomech, 34, pp. 895-905.

[9] Genda, E., Konishi, N., Hasegawa, Y., and Miura, T., 1995, "A Computer

Simulation Study of Normal and Abnormal Hip Joint Contact Pressure," Arch Orthop Trauma Surg, 114, pp. 202-6.

[10] Rapperport, D. J., Carter, D. R., and Schurman, D. J., 1985, "Contact

Finite Element Stress Analysis of the Hip Joint," J Orthop Res, 3, pp. 435-46.

[11] Yoshida, H., Faust, A., Wilckens, J., Kitagawa, M., Fetto, J., and Chao, E.

Y., 2006, "Three-Dimensional Dynamic Hip Contact Area and Pressure

206

Distribution During Activities of Daily Living," J Biomech, 39, pp. 1996-2004.

[12] Ferguson, S. J., Bryant, J. T., Ganz, R., and Ito, K., 2000, "The Influence

of the Acetabular Labrum on Hip Joint Cartilage Consolidation: A Poroelastic Finite Element Model," J Biomech, 33, pp. 953-60.

[13] Macirowski, T., Tepic, S., and Mann, R. W., 1994, "Cartilage Stresses in

the Human Hip Joint," J Biomech Eng, 116, pp. 10-8. [14] Mavcic, B., Pompe, B., Antolic, V., Daniel, M., Iglic, A., and Kralj-Iglic,

V., 2002, "Mathematical Estimation of Stress Distribution in Normal and Dysplastic Hips," Journal of Orthopaedic Research, 20, pp. 1025-1030.

[15] Solomon, L., 1976, "Patterns of Osteoarthritis of the Hip," J Bone Joint

Surg Br, 58, pp. 176-83. [16] Bircher, M. D., 1999, "Retroversion of the Acetabulum," J Bone Joint

Surg Br, 81, pp. 743-4. [17] Kim, W. Y., Hutchinson, C. E., Andrew, J. G., and Allen, P. D., 2006,

"The Relationship between Acetabular Retroversion and Osteoarthritis of the Hip," J Bone Joint Surg Br, 88, pp. 727-9.

[18] Reynolds, D., Lucas, J., and Klaue, K., 1999, "Retroversion of the

Acetabulum. A Cause of Hip Pain," J Bone Joint Surg Br, 81, pp. 281-8. [19] Siebenrock, K. A., Schoeniger, R., and Ganz, R., 2003, "Anterior Femoro-

Acetabular Impingement Due to Acetabular Retroversion. Treatment with Periacetabular Osteotomy," J Bone Joint Surg Am, 85-A, pp. 278-86.

[20] Hipp, J. A., Sugano, N., Millis, M. B., and Murphy, S. B., 1999, "Planning

Acetabular Redirection Osteotomies Based on Joint Contact Pressures," Clin Orthop, pp. 134-43.

[21] Michaeli, D. A., Murphy, S. B., and Hipp, J. A., 1997, "Comparison of

Predicted and Measured Contact Pressures in Normal and Dysplastic Hips," Med Eng Phys, 19, pp. 180-6.

[22] Russell, M. E., Shivanna, K. H., Grosland, N. M., and Pedersen, D. R.,

2006, "Cartilage Contact Pressure Elevations in Dysplastic Hips: A Chronic Overload Model," J Orthop Surg, 1, pp. 6.

[23] Anderson, A., Ellis, B. J., and Weiss, J. A., 2006, "Verification, Validation

and Sensitivity Studies in Computational Biomechanics," Computer

207

Methods in Biomechanics and Biomedical Engineering, In Press Dec 2006.

[24] Oreskes, N., Shrader-Frechette, K., and Belitz, K., 1994, "Verification,

Validation, and Confirmation of Numerical Models in the Earth Sciences," Science, 263, pp. 641-646.

[25] Popper, K. A., 1992, The Logic of Scientific Discovery. Routledge

(originally published 1959 by Hutchinson Education), London. [26] Wolff, J., 1892, Das Gesetz Der Transformation Der Knochen.

Hirschwald, Berlin. [27] Quapp, K. M. and Weiss, J. A., 1998, "Material Characterization of

Human Medial Collateral Ligament," J Biomech Eng, 120, pp. 757-63. [28] Sahrmann, S. A., 1998, "The Twenty-Ninth Mary Mcmillan Lecture:

Moving Precisely? Or Taking the Path of Least Resistance?," Phys Ther, 78, pp. 1208-18.

[29] Bergmann, G., 1998, Hip98: Data Collection of Hip Joint Loading on

Cd-Rom. Free University and Humboldt University, Berlin. [30] Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A.,

Strauss, J., and Duda, G. N., 2001, "Hip Contact Forces and Gait Patterns from Routine Activities," J Biomech, 34, pp. 859-71.

[31] Peters, C. L. and Erickson, J., 2006, "The Etiology and Treatment of Hip

Pain in the Young Adult," J Bone Joint Surg Am, 88 Suppl 4, pp. 20-6.