Angle estimation of human femora in a three-dimensional virtual

environment

Mariano E. Casciaro, Lucas E. Ritacco, Federico Milano, Marcelo Risk and Damian Craiem

Abstract—The estimation of human femur morphology andangulation provide useful information for assisted surgery,follow-up evaluation and prosthesis design, cerebral palsymanagement, congenital dislocation of the hip and fractures ofthe femur. Conventional methods that estimate femoral neckanteversion employ planar projections because accurate 3Destimations require complex reconstruction routines. In a recentwork, we proposed a cylinder fitting method to estimate bifurca-tion angles in coronary arteries and we thought to test it in theestimation of femoral neck anteversion, valgus and shaft-neckangles. Femora from 10 patients were scanned using multislicedcomputed tomography. Virtual cylinders were fitted to 3 regionsof the bone painted by the user to automatically estimate thefemoral angles. Comparisons were made with a conventionalmanual method. Inter- and intra-reading measurements wereevaluated for each method. We found femoral angles fromboth methods strongly correlated. Average anteversion, neck-shaft and valgus angles were 17.5◦, 139.5◦, 99.1◦, respectively.The repeatability and reproducibility of the automated methodshowed a 5-fold reduction in inter- and intra-reading variability.Accordingly, the coefficients of variation for the manual methodwere below 25% whereas for the automated method werebelow 6%. The valgus angle assessment was globally themost accurate with differences below 1◦. Maximum distancesfrom true surface bone points and fitting cylinders attained 6mm. The employment of virtual cylinders fitted to differentregions of human femora consistently helped to assess true 3Dangulations.

I. INTRODUCTION

The estimation of human femur morphology provides

useful information for assisted surgery, follow-up evaluation

and prosthesis design, cerebral palsy management, congenital

dislocation of the hip and fractures of the femur [1]-[4].

Computed tomography ensures the most accurate measure-

ment of femoral anteversion, despite its cost and the exposure

of the patient to potentially harmful radiation [5]. Traditional

X-rays and straightforward angles measures in CT images

were used to quantify angles in orthopedics [6]-[9]. For

instance, methods that estimate femoral neck anteversion

employ planar projections because accurate 3D estimations

require complex reconstruction routines [2], [4], [10]. Our

intention is to provide an alternative to those complicated

routines.

In a recent work, we proposed a cylinder fitting method

to estimate bifurcation angles in coronary arteries [11].

Assuming a cylindrical shape for the arteries in the vicinity

M.E. Casciaro and D.Craiem are with Favaloro Univer-sity, Av. Belgrano 1723 (1093), Buenos Aires, Argentinadcraiem@favaloro.edu.ar

L. Ritacco and M. Risk are with Hospital Italiano, ArgentinaF. Milano is with Universidad Tecnolgica Nacional, FRBA, ArgentinaD. Craiem and M. Risk are with CONICET

of the bifurcations, the algorithm automatically adjusts a

cylinder to a group of candidate points belonging to the artery

and informs a directrix vector in a 3D hyperspace.

In this work, we propose to apply the cylinder fitting

method to estimate femoral neck anteversion, valgus and

neck-shaft angles. Femora from 10 patients were scanned

using multisliced computed tomography. Virtual cylinders

were fitted to 3 regions of the bone to automatically esti-

mate the femoral angles. Comparisons were made with a

conventional method. Inter- and intra-reading measurements

were also evaluated for automated and manual methods.

II. METHODS

A total of twenty fresh-frozen whole femora were selected

from the bone bank for this IRB-approved study, 10 right

and 10 left (age range: 16-58, 35.9 ± 12.0; 6 males and

4 females). We only analyzed 10 left bones in this study.

They were scanned on a Toshiba Aquilion CT scanner, with

a resolution of 0.877 pixels/mm and slice increments of 0.5

mm. In the next sections we describe the complete process

to obtain 3D geometrical models from DICOM images to es-

timate relevant femur angles. The bone surface was obtained

from raw gray scale images applying a Laplacian filter and a

subsequent binarization [11][12]. The spatial coordinates of

each pixel belonging to the surface were stored in a file. A

custom software developed in the Favaloro University (using

Borland C++ Builder 6.0 running in a PC, 2.60GHz, 2GB

RAM) was designed to help the user to manually segment 3

femoral regions and then automatically determine the desired

angles. The automated process includes a cylinder fitting to

each region. In the next 2 sections, femur segmentation and

automatic cylinder fitting are described in detail.

A. Femur segmentation

First, the software opens the file and performs a 3D ren-

dering process. It allows the user to rotate the volume in any

direction in order to determine some particular anatomical

landmarks. Three anatomical axes must be calculated in 3D

to measure the desired angles. Briefly, the femur must be

divided into 3 regions: condylar, diaphyseal and proximal

epiphyseal as sketched in 1A. Then, a virtual cylinder is

automatically fitted to each region and the centerlines of

these cylinders are adopted as the 3 required anatomical axes

(See Fig. 2(A)). Regions are manually painted following a

protocol:

Step 1 Condylar region segmentation: The user must rotate

the bone with the condylar region down and prox-

imal epiphysis up as in Fig. 1(B). Then, the femur

32nd Annual International Conference of the IEEE EMBSBuenos Aires, Argentina, August 31 - September 4, 2010

978-1-4244-4124-2/10/$25.00 ©2010 IEEE 3946

Fig. 1. Three femur regions are manually painted. (A) Neck (yellow),

dyaphisis (blue) and condyle (red) regions. Arrows are showing the endof the dyaphiseal region. (B) and (C) describe neck and condyle regions

fot he segmentation protocol.

must be rotated to superpose the lateral and medial

condyles. Below the epicondylar region and tracing an

imaginary line orthogonal to the diaphysis, the user

paints a preliminary region using a custom brush tool.

Finally, the bone is returned to its original position and

the user ends the region segmentation painting below

a final imaginary line above the lateral and medial

epicondyles (See arrows in Fig. 1(A).

Step 2 Proximal epiphyseal region segmentation: The bone

must be slightly rotated in order to get a complete

superposition of the anterior and posterior parts of

the greater trochanter (see 1C). Then, the user is

asked to paint the femoral neck using the anterior

intertrochantereal line as a reference.

Step 3 Diaphyseal region segmentation: This region is painted

from the final imaginary line that was traced in Step 2

(see arrows in Fig. 1(A)) to an imaginary line below

the lesser trochanter and orthogonal to the diaphysis.

B. Automatic cylinder fitting

The points painted for each region are automatically

adjusted to a 3D virtual cylinder by performing a numerical

minimization of the sum of orthogonal distances of every

pixel belonging to the bone surface and the virtual cylinder

surface. A more detailed explanation of the method can be

found in [11]. Briefly, this virtual cylinder is represented by

5 parameters: νx, νy, Px, Py and R, where ~ν = (νx,νy,1) is

the directrix vector of the cylinder, P = (Px,Py,0) is the point

where the directrix line crosses the xy plane, and R, the radius

Fig. 2. (A) Cylinders adjusted to neck, dyaphisis and condyle regions.Centerlines are showed with vectors ,νe , νd and νc , respectively. (B) Neck-shaft angle, (C) Valgus angle (D) Anteversion angle definition.

of the cylinder. The initial conditions for the Nelder-Meads

minimization algorithm to estimate the cylinder directrix

vector in 3D are automatically set using a 3D Hotteling

transform [12] of the region surface. This transform returns a

vector that describes the main direction of the region surface

and is used as the initial value for ~ν . The initial value for P

is calculated as the intersection point between a line passing

through the center of gravity of the region surface and the

xy plane. Initial value for R was always 20 mm. This value

was adopted as a good average dimension between condyles,

dyaphisis and femoral neck radius.

C. Angle calculation

Three angles were automatically calculated using the 3

cylinders (see Fig. 2(A)). The following definitions were

used:

~νc : directrix of the condylar cylinder

~νd : directrix of the dyaphiseal cylinder

~νe : directrix of the neck cylinder

~νN =~νc ×~νd : vector normal to νc and νd

Πc/d = α.~νc +β .~νd : plane formed by νc and νd

ΠP = α.~νc +β .~νN : ~νeprojection plane

The angle φ formed by a pair of vectors ~ν1 and ~ν2 is :

cos(φ ) =~ν1 ·~ν2

||~ν1|| · ||~ν2||(1)

Accordingly, valgus and inclination angles were automati-

cally determined between vectors (νc,νd) and (νe,νd), re-

spectively (Fig. 2(B) and Fig. 2C, respectively).

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We calculated the anteversion angle as the angle between

the vector resulting from the projection of νe over ΠP , and

the condylar νc vector. In other words, this is equivalent

to an observer standing over the plane crossing the femur

through its condylar and dyaphiseal region, Πc/d , observing

perpendicular to ΠP, measuring the angle between the floor

and the resultant projection of νe on his plane of view,

ΠP (see Fig.2(D)). This is exactly the angle that follows

the definition of the femoral anteversion as it is the angle

between the neck axis and the condylar line projected onto

a plane perpendicular to the shaft axis.

D. Inter- and intra-reading variability

The proposed method to estimate anteversion angle was

compared with the conventional method of Reikeras in

which the neck axis is determined from a superimposed

image of the femoral head and neck [13]. Valgus and neck-

shaft angles were manually measured using a custom 3D

software incorporated into the CT equipment (Mimics v 12,

Materialise, Leuven, Belgium). Briefly, the user manually

rotated the bone in a 3D hyperspace to find a proper planar

projection and measured the angles with caliper tools [7],

[9].

Intra (same observer twice) and inter-observer (two differ-

ent observers) angles were calculated and compared between

the automated and the manual method. Pearson correlations

and Bland-Altman plots were calculated. Also, coefficients of

variation (CV%) were calculated for inter and intra readings.

To quantify the cylinder fitting accuracy, absolute mean

distances from femur points to each cylinder were calculated.

III. RESULTS

Measured angles for manual and automated methods are

presented in table I. Mean values for neck-shaft and valgus

angles were similar between methods although anteversion

angle was larger for the automated case. Scatter in valgus

angle was small in both methods. Differences between

manual and automated methods for inter and intra-observer

readings are shown in table II. Coefficients of variation for

the manual method attended 22% when the same observer

made a second measurement and 25% for a second observer.

Conversely, less important CV of 3% and 6% were found in

the automated case respectively. Again, the valgus angle was

correctly estimated with both methods with differences below

1◦. Finally, a high correlation was found between methods as

shown in Fig. 3 (r2 = 0.98, p < 0.001). Bland-Altman plot

in Fig. 3 shows an overestimation of the anteversion angle

for the automated with respect to the manual method. This

systematic mean difference was 12◦. Standard deviations

for all angles was 10.2◦. Distances from femur points to

cylinders after the fitting algorithm resulted 5.45±0.4 mm,

3.3±0.5 mm and 2.7±0.4 mm for condyle, dyaphisis and

neck regions, respectively.

IV. DISCUSSION

In this work we proposed a semiautomated method to as-

sess relevant angles of human femora. We compared it with a

TABLE I

MEASURED ANGLES WITH BOTH METHODS. VALUES ARE EXPRESSED

AS MEAN±SD. CV%=COEFFICIENT OF VARIATION.

Angle Manual method Automated method

Anteversion 17.5◦±8.6◦ 29.4◦±7.4◦

Neck-shaft 139.5◦±8.9◦ 135.0◦±7.2◦

Valgus 99.1◦±2.1◦ 100.1◦±4.5◦

TABLE II

INTRA AND INTER READING DIFFERENCES WITH BOTH METHODS.

VALUES ARE EXPRESSED AS MEAN±SD

Intra-observer Manual angles CV% Automated angles CV%

Anteversion 3.3◦±7.4◦ 22.0 0.5◦±1.6◦ 3.5Neck-shaft 4.5◦±6.2◦ 2.5 -0.3◦±1.3◦ 0.6

Valgus -0.8◦±0.9◦ 0.7 0.1◦±0.4◦ 0.2

Inter-observer Manual angles CV% Automated angles CV%

Anteversion 2.7◦±7.6◦ 25.4 -0.9◦±2.9◦ 6.2Neck-shaft -5.5◦±9.6◦ 4.9 -0.5◦±1.6◦ 0.6

Valgus -0.7◦±1.2◦ 0.7 -0.0◦±0.6◦ 0.3

conventional manual method. A strong correlation was found

between methods. The automated method improved inter-

and intra-reading variability attaining a 5-fold reduction in

the coefficients of variation. In the proposed method, the

user paints 3 different regions of the femur and the fitting

algorithm automatically finds the corresponding axis and

geometrically calculates the angles in 3D. The software is

easy to use and the whole process took an average time of

4 minutes per bone.

Manual methods cannot accurately estimate femoral an-

gles, mostly due to limitations in the neck axis assessment

[14]. There are some complex 3D reconstruction routines

that can be employed for angle estimations [3], [5], [15].

Our approach is simple. The user must identify 3 regions

and then the algorithms fits 3 cylinders and uses centerlines

to geometrically estimate the angles in a true 3D hyperspace.

No planar projections are required, avoiding user subjectivity.

Neck-shaft angles measured in this work did not differed

from others [3], [7], [16]. From table I, both methods

agreed in valgus and neck-shaft angle estimation, whereas

anteversion has a systematic difference. These evidences

were confirmed in inter- and intra-reading analysis in table

II. Whereas valgus and neck-shaft angles were assessed with

coefficients of variations below 1% for repeated measures

and using 2 different observers, the anteversion attained

errors of 6%. This can be mostly due to the complicated

definition of anteversion angle. Femoral neck anteversion

depends on 2 structures that are distant and must be measured

in a specific plane orthogonal to the long axis. In the manual

method, the user has the difficulty of finding this specific

plane. In the automated case, medial and lateral femoral

condyles can be unbalanced, probably biasing the cylindrical

fit. Dyaphisis and neck are almost cylindrical structures

and errors were consistent with this affirmation attaining

average distances between cylinders and bone surfaces below

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Fig. 3. Manual vs automated methods measurements. Left: Linear correlation. Right: Bland-Altman plot.

4 mm. In fact, the cylindrical fit was previously employed.

Kim et al. used it to fit the dyaphisis [17] and Sugano et

al. to adjust the femoral neck [13]. The cylindrical fit of

the condyles resulted systematically biased with respect to

manual measurements. Actually, this error is clearly visible

for small angles in Fig. 3, corresponding to anteversion

angles. These angles were wider for the automated with

respect to the manual method in ≈12◦. However, cylinders

fitted condyles relatively well. In fact, maximum distances

from cylinders to condylar surfaces were 6 mm. In future

works, modifications of the condylar axis assessment must

be proposed to reduce these discrepancies, correcting this

systematic bias.

V. CONCLUSION

Femoral angles can be used as preoperative planning

tool in orthopedics deformities and implemented into a

navigation system. Our study presented an automated method

to measure femoral angles in a 3D virtual environment

using cylinders that improved repeatability with respect to

conventional methods. Long and neck axis were found with

less variability than condylar axis. Acordingly, further studies

with more specimens will be needed to improve the femoral

neck anteversion estimation.

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