Transformation of muscle architecture at the fiber bundle - T-Space

Transformation of muscle architecture at the fiber bundle level to fit parametric b-spline volumes: extensor carpi

radialis brevis and longus

by

Mayoorendra Ravichandiran

A thesis submitted in conformity with the requirementsfor the degree of Masters of Science

Institute of Medical ScienceUniversity of Toronto

© Copyright by Mayoorendra Ravichandiran 2010

Transformation of muscle architecture at the fiber bundle level to fit parametric b-spline volumes: extensor carpi radialis brevis and

longus

Mayoorendra Ravichandiran

Masters of Science

Institute of Medical ScienceUniversity of Toronto

2010

Abstract

Most models of the musculoskeletal system incorporate individual or groups of muscles as a

series of line segments, assuming all fiber bundles within a muscle have the same length and

moment arm, and do not account for architectural differences throughout the muscle volume.

The purpose was to develop an algorithm to fit digitized fiber bundle data from one specimen

into muscle volume and intramuscular nerve distribution data from seven other specimens of

extensor carpi radialis longus (ECRL) and brevis (ECRB). Coherent Point Drift (CPD)

algorithm was successfully adapted for this purpose. The intramuscular nerve distribution and

fiber bundle architecture was modeled in all the muscle volumes. ECRL was found to have two

neuromuscular compartments, superficial and deep, while ECRB was found to have two, three or

four, in a proximal to distal direction depending on the number of primary nerve branches.

ii

Acknowledgments

With the help of many people in my life, both at the lab and my family, I accomplished

many things over the past year that I did not think was possible. Without their help, I would not

be where I am today.

I would like to start by thanking my research supervisors Dr. Anne Agur and Dr. Nancy

McKee, who have guided and supported me for many years. From the day I met her as a first

year student, Dr. Agur has encouraged me to think outside the box and has spent countless hours

to support my learning and encourage my interests. Dr. McKee has always been source of

motivation for me, asking the difficult questions, challenging me to push the limits and prodding

me “onward!”. For these reasons, and many more, I will always be grateful.

I also extend a heartfelt thank you to my Program Advisory Committee, Dr. Bernie

Liebgott and Dr. Denyse Richardson for their commitment and support throughout my project. I

would also like to thank my examination committee Dr. Kathy Amara, Dr. Paulo Koeberle and

Dr. Doug Gould.

In addition, I would like to thank fellow graduate students Kate Sauks and Alex Rosatelli

for their support and advice; the Autodesk crew, Azam Khan, Jacky Schuster, Dongwoon Lee and

Michael Glueck for all of their technical expertise; Anton Semechko, University of Guelph, for

his timely assistance at a critical point in my project; and Christopher Yuen who has been a good

friend and mentor during my undergraduate and graduate journey.

Most importantly, I would like to thank my family. Firstly, my brother, Kajeandra, and

sister, Nisha, whose help proved invaluable in the late, critical stages of my thesis. Also a special

iii

thank you to Nisha for her help in digitizing during my project. Finally, I would like to thank my

mom and dad, who have been there for me and supported me in all of my endeavors. Their

perseverance, hard work and sacrifices will continue to be a source of motivation in my life.

I would also like to acknowledge the work of past summer and thesis students who

provided the digitized fiber bundle data that was used in the current study: Tiu Hess, Lembi Hess

and Yajur Shukla.

iv

Table of Contents

...........................................................................................................List of Tables ix

...........................................................................................................List of Figures x

.............................................................................................List of Abbreviations xiii

1. .................................................................................................Introduction 1

1.1. ..................................................................................Contents of Thesis 2

2. ...................................................................................Review of Literature 4

2.1. ............................................................Muscle architectural parameters 4

2.2. .............................Methods used to obtain architectural parameter data 7

2.2.1. ...............................................................Cadaveric specimens 7

2.2.1.1. .........................................................Manual methods 7

2.2.1.2. .........................................................Photogrammetry 9

2.2.1.3. ................................................................Digitization 11

2.2.2. .......................................................................In vivo methods 13

2.2.2.1. .......................................................Ultrasonography 13

2.2.2.2. ...................................Magnetic resonance imaging 14

2.3. ...................................................................................Muscle modeling 16

2.3.1. ......................................................................Linear modeling 16

2.3.2. .Volumetric muscle modeling from MRI reconstruction 17

2.3.3. ......................................Volumetric 3D fiber bundle modeling 17

2.4. ....................................................................................Nerve modeling 18

2.5. ............................................................................Computer algorithms 19

2.6.Point set registration 19

2.6.1. ..............................................Iterative closest point algorithm 20

v

2.6.2. .................................................Coherent point drift algorithm 21

2.6.2.1. ...........................................Gaussian Mixture Model 21

2.6.2.2. .........................Expectation-maximization algorithm 23

2.6.2.3. ........................................................Bayesʼ Theorem 24

2.7.Extensor carpi radialis longus and brevis 25

2.8.Summary 30

3. ......................................................................Hypothesis and Objectives 31

3.1. ............................................................................................Hypothesis 31

3.2. .............................................................................................Objectives 31

4. .............................................................................Materials and Methods 32

4.1. ...........................................................Digitization of ECRL and ECRB 32

4.1.1. ..............................................................................Specimens 32

4.1.2. .....................................Dissection, Digitization and Modeling 32

4.1.2.1. ..........................................................Muscle volume 34

4.1.2.2. ......................................................Nerve distribution 35

4.1.2.3. ......................................................Bone and tendon 39

4.1.2.4. ......................................................Fiber bundle data 39

4.2.Exploring methods for fitting architectural data to generic muscle ......................................................................................................volumes 40

4.2.1. ..............................................Iterative closest point algorithm 40

4.2.2. ...........Sectioning muscle volume and fiber bundle data sets 43

4.2.3. .................................................................Coherent point drift 45

4.2.3.1. ......................................Validation of CPD algorithm 54

4.3.Volume fitting of fiber bundle architecture and intramuscular innervation of ................................................ECRL and ECRB using the CPD algorithm 56

5. .......................................................................................................Results 57

vi

5.1. .................................Three-dimensional reconstruction and modeling 57

5.2. ..................................................................................Nerve distribution 59

5.2.1. .................................................Extensor carpi radialis longus 59

5.2.1.1. .........................Extramuscular innervation of ECRL 59

5.2.1.2. ..........................Intramuscular innervation of ECRL 60

5.2.2. ..................................................Extensor carpi radialis brevis 62

5.2.2.1. .........................Extramuscular innervation of ECRB 62

5.2.3. ........................................Intramuscular innervation of ECRB 67

5.3.Fitting fiber bundle data to muscle volume and innervation obtained from ....................................................................................different specimens 73

5.3.1. ..................................Fitting muscle fiber bundle architecture 73

5.3.2. .........Quantification of architectural parameters of fitted data 75

5.3.3.Distribution of intramuscular nerves within the muscle volume at ........................................................................the fiber bundle level 77

5.4. .............................................................................Summary of findings 83

5.4.1. .................Fitting fiber bundle architecture to muscle volume 83

5.4.2.Modeling the intramuscular innervation of ECRL and ECRB at the ..............................................................................fiber bundle level 83

6. .................................................................................................Discussion 84

6.1. .................Fitting fiber bundle architecture to generic muscle volumes 85

6.1.1. .............................................Exploration of different methods 85

6.1.2.Using Coherent Point Drift (CPD) to fit ECRL and ECRB fiber .............................................bundle architecture to muscle volume 87

6.2.Modeling the intramuscular innervation of ECRL and ECRB at the fiber .................................................................................................bundle level 87

6.3.Previous studies of radial nerve distribution in ECRL and ECRB have ......................................................................................................relied on 87

6.3.1. .......................................Extramuscular innervation of ECRB 90

vii

6.3.2.Relation of ECRB innervation pattern to muscle architecture 90

6.4. ........................Functional relevance of neuromuscular compartments 91

6.5. .................................................................................Clinical relevance 92

7. ..............................................................................................Conclusions 94

7.1.Fitting fiber bundle architecture to muscle volume from different ..................................................................................................specimens 94

7.2. .............................Neuromuscular compartments in ECRL and ECRB 94

8. ......................................................................................Future Directions 96

..............................................................................................................References 97

viii

List of Tables

Table 2.1. Fiber bundle length (FBL) and pennation angle (PA) of extensor carpi

radialis longus (ECRL) and brevis (ECRB): summary of previous studies.

26

Table 2.2. Fiber bundle length (FBL) and pennation angle (PA) of proximal and distal

regions of extensor carpi radialis longus (ECRL) and brevis (ECRB) as reported

by Ravichandiran et al. (2009).

27

Table 2.3. Summary of the source of extra-muscular nerve supply to ECRB 27

Table 5.1. Number and source of primary nerve branches to ECRB. Five innervation (I to

V) patterns based on the source and number of primary branches.

62

Table 5.2. Intramuscular nerve distribution for each of the five types of innervation

patterns in ECRB.

67

Table 5.3. ECRL: architectural parameters of the original fiber bundle data set (S0) and

the seven specimens to which the data sat was fit (S1-S7).

75

Table 5.4. ECRB: architectural parameters of the original fiber bundle data set (S0) and

the seven specimens to which the data sat was fit (S1-S7).

76

ix

List of Figures

Figure 2.1. Elements of skeletal muscles (Adapted from Lippincott, Williams & Wilkins,

Essential Clinical Anatomy (2007), Figure 1.10).

4

Figure 2.2. Arrangement of fiber bundles in skeletal muscles. A. Parallel fiber bundle

arrangement. B. Pennated fiber bundle arrangement.

6

Figure 2.3. Arrangement of cameras for photogrammetry (Reproduced with permission

from Agur 2001).

9

Figure 2.4. Pinned fiber bundles of soleus. A. Superficial. B. Intermediate. C. Deep.

Posterior views. (Reproduced with permission from Agur 2001).

10

Figure 2.5. Schematic illustration of the measurement of angle of pennation using the

B-spline muscle model. (Reproduced with permission from Agur 2001).

11

Figure 2.6. Volumetric representation of fiber bundles of pectoralis major with

architecturally distinct regions indicated in different colors.

12

Figure 2.7. A. Rigid point set registration and B. Non-rigid point set registration. 19

Figure 2.8. Unimodal Gaussian distribution. 21

Figure 2.9. Gaussian mixture. 22

Figure 2.10. Summary of extramuscular nerve supply to ECRL relative to the nerve to

brachioradialis (Branovacki et al. 1998).

27

Figure 4.1. Microscribe 3DX digitizer. 33

Figure 4.2. Reconstruction of muscle volume from digitized data. A. Digitized volume of

muscle. B. Lofted polygon mesh. C. Surface is rendered with color.

35

Figure 4.3. Figure 4.3. Reconstruction of nerve distribution from digitized data. 37

Figure 4.4. Modeling some of the nerve branches from digitized data of one ECRL. A.

Digitized nerve data imported as curves. B. Tubes extruded from curves. C. Nerve

branches color coded.

38

Figure 4.5. Iterative closest point algorithm. A. Two data sets X and P. B. Iteration of

translation, rotation and scaling to register points in P with points in X.

42

Figure 4.6. Sectioned data sets. A. Muscle volume data set. B. Fiber bundle data set. 43

x

Figure 4.7. A. Centroid of one section of the muscle volume data set. B. Centroid of the

corresponding section of the fiber bundle data. C. Alignment of centroids.

44

Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian

Gram Matrix of the data set

47

Figure 4.9. Outline of CPD algorithm. 50

Figure 4.10. Iterations of the CPD algorithm for ECRL fiber bundle data set.

A. Prealignment step with fiber bundles. B. Prealignment step with data points

(Iteration 0). C. Iteration 1.

51

Figure 4.10. Iterations of the CPD algorithm for ECRL fiber bundle data set (continued).

D. Iteration 2. E. Iteration 6. F. Iteration 10.

52

Figure 4.10. Iterations of the CPD algorithm for ECRL fiber bundle data set (continued).

G. Iteration 15. H. Iteration 20. I. Iteration 50. J. Fiber bundle data set of iteration

50.

53

Figure 4.11. Validation of the CPD algorithm. A. Data set A and data set B. B. Data set B

registered to data set A using the CPD algorithm.

55

Figure 5.1. Anterior view of a cadaveric specimen of the ECRL, ECRB, supinator and

radial nerve.

57

Figure 5.2. Comparison of 3D model and cadaveric specimen, lateral views. A.

Cadaveric specimen with color coded muscles, tendons and nerves.

B. Three-dimensional model of ECRL and ECRB reconstructed from digitized

data. C. Three-dimensional model of ECRB reconstructed from digitized data.

58

Figure 5.3. Extramuscular bifurcation of branch to ECRL into anterior and posterior

branches, anterior view.

59

Figure 5.4. Extramuscular innervation of ECRL. 60

Figure 5.5. Intramuscular innervation of the ECRL. A. Posterolateral view. B.

Lateral view.

61

Figure 5.6. Type I: Extramuscular distribution pattern of ECRB. 63

Figure 5.7. Type II: Extramuscular distribution pattern of ECRB. 64

xi

Figure 5.8. Type III: Extramuscular distribution pattern of ECRB. 65

Figure 5.9. Type IV: Extramuscular distribution pattern of ECRB. 65

Figure 5.10. Type V: Extramuscular distribution pattern of ECRB. 66

Figure 5.11. Type I: Intramuscular innervation pattern of ECRB. A. Posterolateral view.

B. Lateral view.

68

Figure 5.12. Type II: Intramuscular innervation pattern of ECRB. A. Posteroateral view.

B. Lateral view

69

Figure 5.13. Type III: Intramuscular innervation pattern of ECRB. A. Posterolateral

view. B. Lateral view.

70

Figure 5.14. Type IV: Intramuscular innervation pattern of ECRB. A. Posterolateral

view. B. Lateral view.

71

Figure 5.15. Type V: Intramuscular innervation pattern of ECRB. A. Posterolateral view.

B. Lateral view.

72

Figure 5.16. Specimen S3 volume and nerve data fitted with fiber bundle data set. 73

Figure 5.17. Specimen S2 volume and nerve data fitted with fiber bundle data set. 74

Figure 5.18. ECRL: Pennation angles of fiber bundle data set and specimens (S1-S7). A.

Proximal pennation angle. B. Distal pennation angle.

77

Figure 5.19. ECRL: Pennation angles of fiber bundle data set and specimens (S1-S7). A.

Proximal pennation angle. B. Distal pennation angle.

77

Figure 5.20. Regional nerve supply of ECRL. A. Posterior branch of radial nerve in

posterior region of muscle belly. B. Anterior branch of radial nerve in anterior

region of muscle belly. C. Anterior and posterior regions combined.

79

Figure 5.21. Fiber bundle regions of ECRB specimen with three motor points. A.

Proximal region. B. Distal region.

80

Figure 5.22. Fiber bundle regions of ECRB specimen with three motor points. A.

Proximal region. B. Middle region. C. Deep region.

81

Figure 5.23. Regions of ECRB specimen with four motor points. A. Proximal

region. B. Deep middle region. C. Superficial middle region. D. Distal region.

82

xii

List of Abbreviations

CPD Coherent Point Drift

GMM Gaussian Mixture Model

ECRL Extensor carpi radialis longus

ECRB Extensor carpi radialis brevis

FBL Fiber bundle length

ICP Iterative Closest Point

PA Pennation angle

PA1 Proximal pennation angle

PA2 Distal pennation angle

R3 Three-dimensional coordinate system of rational numbers

xiii

Chapter 1Introduction

1 Introduction

Bio-mechanical modeling of the musculoskeletal system has been the focus of many

studies. The interest in modeling muscles of the human body comes from a variety of fields,

including computer animation, biomechanics, prosthetic design, rehabilitation science, surgery

(Blemker et al. 2007; Teran et al. 2005) and athletics. The computer animation industry often

uses reverse kinematics to model muscle function, where the movement of the skeleton produces

the resulting visual deformations of muscle architecture. Bio-mechanical studies, which focus

more on function than appearance, have modeled muscles by simplifying the musculoskeletal

system by grouping muscles with similar function and by reducing complex muscle geometries

to simpler ones (Delp et al. 1990; Hoy et al. 1990). Knowledge of accurate muscle architecture

can provide insight into how individual muscles function, as well as how groups of muscles

function to produce movement in the musculoskeletal system. Furthermore, it has been found

that even within individual muscles there are sub-volumes with distinct architecture and

innervation, that are differentially activated to produce muscle function (English et al. 1993;

Segal et al. 2002; Segal et al. 1991). Therefore, in order to accurately represent muscle function

and architecture, knowledge of both fiber bundle architecture and innervation of the

musculoskeletal system is essential.

Many different methods have been used to obtain muscle architectural parameters

including cadaveric and in vivo methods. The data collected using these methods have been

used to model muscles and estimates of fiber bundle architecture. However, only a few studies

1

have modeled the actual fiber bundle architecture within the muscle volume (Agur et al. 2003;

Fung et al. 2009; Kim et al. 2007; Rosatelli et al. 2008). Since it has been found that the

architecture of muscles is consistent between individuals of the same species (R. L. Lieber &

Friden 2000), the architectural data obtained from one individual can be used to explore muscle

function in other individuals.

In this thesis, extensor carpi radialis longus (ECRL) and brevis (ECRB) muscles were

studied. These muscles were chosen due to their functional importance in wrist extension and

abduction and due to the availability of densely digitized data sets of muscle architecture from a

pervious study (Ravichandiran et al. 2009). The intramuscular innervation of ECRL and ECRB

was digitized and characterized throughout the volume of seven specimens. The patterns of

innervation have not been previously investigated throughout the muscle volume, although it is

an important functional consideration. To develop a comprehensive volumetric model that

includes fiber bundle architecture and intramuscular innervation, a computer algorithm was

developed to fit nerve and muscle volume data generated in the current study with fiber bundle

architecture data from Ravichandiran et al. (2009). The fitted data were used to determine if

neuromuscular compartments exist within the ECRL and ECRB.

1.1 Contents of Thesis

This thesis is divided into eight chapters:

• Chapter 1 is an introduction to this thesis.

2

• Chapter 2 is review of the literature concerning the modeling of muscle architecture, a

brief overview of point set registration algorithms, and innervation of the extensor carpi

radialis longus and brevis muscles.

• Chapter 3 is a statement of the hypothesis and objectives of this thesis.

• Chapter 4 covers the materials and methods used in this study, including the steps involved

in the Coherent Point Drift algorithm.

• Chapter 5 is a summary of the results of this study.

• Chapter 6 is a discussion of the results and their significance.

• Chapter 7 summarizes the conclusions of the current study.

• Chapter 8 examines possible future directions and applications of the methods and results

in this study.

3

Chapter 2Review of Literature

2 Review of Literature

2.1 Muscle architectural parameters

Muscle architecture is the arrangement of contractile and connective tissue elements

within the muscle. The contractile elements have a hierarchical arrangement. Fiber bundles

(fascicles) of skeletal muscle consist of muscle fibers (muscle cells) containing myofibrils

arranged into sarcomeres. Each sarcomere is composed of actin and myosin filaments (Figure

2.1). The connective tissue elements include epimysium, perimysium and endomysium.

Epimysium surrounds the entire muscle, perimysium surrounds fascicles and endomysium

individual muscle fibers.

Tendon

Muscle

Fiber bundle

Muscle !ber

Myo!bril

Sarcomere

Epimysium

Perimysium

Cell membrane

Nucleus

Endomysium

Figure 2.1. Elements of skeletal muscles (Adapted from Lippincott, Williams & Wilkins, Essential Clinical Anatomy (2007), Figure 1.10)

4

Architectural parameters that describe the shape and dimensions of a muscle as a whole

are muscle length and volume. Intramuscular architectural parameters that define fiber bundle

arrangement include fiber bundle length and pennation angle (Ward, Kim et al. 2009). Muscle

length is defined as the distance from the most proximal to the most distal part of the muscle,

whereas muscle fiber bundle length is defined as the length of the fiber bundle from its origin to

its insertion (Ward, et al. 2009). The angle between the fiber bundle and the muscle’s line of

action, the curve that intersects the centroids of cross-sections through the muscle volume, is the

pennation angle (Jensen & Davy 1975).

The geometric arrangement of fiber bundles within muscles can take a number of forms

and can vary from simple parallel arrangement to more complex pennate arrangements. Muscles

with fiber bundles arranged parallel to the line of action can be subdivided into strap and

fusiform types (Figure 2.2A). Strap muscles have longitudinally oriented fiber bundles, whereas

fusiform muscles have similarly oriented fiber bundles with tapering ends. Fiber bundles can

also be arranged at an angle relative to the line of action, referred to as pennate muscles, and can

be described as unipennate, bipennate or multipennate (Figure 2.2B). Muscle fiber bundles

attaching to one side of a central tendon are unipennate, where as a muscle with fiber bundles

attaching to both sides of a central tendon are bipennate. Multipennate muscles have fiber

bundles attaching to multiple central tendons.

5

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Figure 2.2. Arrangement of fiber bundles in skeletal muscles. A. Parallel fiber bundle arrangement. B. Pennated fiber bundle arrangement.

Lieber and Friden (2000) suggested that the architecture of a muscle, the arrangement of

fiber bundles, is consistent within species. The arrangement of fiber bundles and their

architectural parameters are important factors in determining the muscle’s lines of action and the

force a muscle is capable of producing (Enoka 1988; Zajac 1989). Muscles with similar external

morphology may differ in function due to differences in internal muscle architecture (R. L.

Lieber & Friden 2000).

6

2.2 Methods used to obtain architectural parameter data

Descriptive and quantitative methods have been used to study muscle architecture in

cadaveric specimens and in vivo. Muscle models depend on detailed quantitative data to define

skeletal muscle biomechanical properties. Therefore “accurate descriptions of muscle geometry

are needed to characterize muscle function.” (Blemker et. al, 2005). Muscle architecture/

geometry has been quantified using digital/dial calipers, protractors/goniometers,

photogrammetry, digitization, CT and/or MRI measurements. Each of these methods will be

discussed in this section of this thesis.

2.2.1 Cadaveric specimens

2.2.1.1Manual methods

Earlier studies used manual methods to quantify muscle length, fiber bundle length,

pennation angle and muscle volume of cadaveric specimens.

Muscle length has been defined using various points of reference. For example,

Wickiewicz et al. (1983) and Ward et al. (2006) recorded muscle length as the distance between

the most proximal and the most distal fiber bundles, whereas Friederich and Brand (1990)

measured the distance between the centroid of insertion and the centroid of origin.

In previous studies, fiber bundle length has been measured in-situ between attachment

sites (Agur et al. 2003) or from excised fiber bundles (R.L. Lieber et al. 1992). Due to the elastic

properties of fiber bundles, Cutts et al. (1991) have shown that fiber bundle length changes upon

excision from the muscle belly. In addition, mean fiber bundle length of a muscle has often been

obtained from a limited number of fiber bundles sampled from unspecified location within the

muscle volume. For example, Wickerwicz et al. (1983) randomly sampled ten to twenty fiber

7

bundles per muscle whereas Friederich and Brand (1990) sampled only two to five fiber bundles.

Several investigators have also normalized the measured fiber length to an optimum sarcomere

length (2.2-2.8 µm) to allow for intermuscular comparisons (Langenderfer et al. 2004; R. L.

Lieber & Friden 2000; Mutungi & Ranatunga 2000).

Pennation angle of the fiber bundle was measured relative to the attachment sites to bone,

tendon or aponeurosis using a protractor or goniometer (Wickerwicz et al. 1983; Lieber 1999;

Ward et al. 2009). With manual measurement techniques, pennation angles were measured

within a single 2D plane and usually only fiber bundles from the superficial surface of the

muscle were sampled to determine mean pennation angle of fiber bundles within a muscle

(Ward, Eng et al. 2009).

Muscle volume has been measured using: water displacement (Wickiewicz, et al. 1983),

three-dimensional reconstruction of MRI images (Holzbaur et al. 2007) and the division of

muscle mass by muscle density. Muscle density used for the volume calculation has been

obtained from rabbit, canine, or from fixed or fresh human cadaveric tissues (Mendez & Keys

1960; Ward & Lieber 2005). Water displacement method can only give an approximate measure

of muscle volume as it includes intramuscular connective and tendinous tissue. However, Ward

and Lieber (2005) found that formaldehyde concentration also changes muscle density and

therefore calculated volume. A 4% formaldehyde concentration resulted in a muscle density of

1.112±0.006 g/cm3 whereas a 37% formaldehyde concentration resulted in a density of

1.055±0.006 g/cm3.

8

2.2.1.2 Photogrammetry Photogrammetry is a technique that uses photographs from different perspectives to

determine geometric properties of objects, i.e. spacial location. Stereo-photogrammetry expands

on this technique by using two or more cameras to determine the three dimensional coordinates

of points on objects of interest. Linear and angular measurements of each point are made on

photographs obtained from at least two cameras to triangulate the position of the point in R3

space (Figure 2.3). Series of points on the object surface can be used to reconstruct the 3D

geometry of an object.

Figure 2.3. Arrangement of cameras for photogrammetry (Reproduced with permission from Agur 2001).

Agur et al. (2003) used stereo-photogrammetry to model the fiber bundle architecture in

soleus. In the study, the muscle was serially dissected layer by layer to expose the fiber bundles

9

throughout the volume. At each layer, colored pin markers were used to delineate the path of

each fiber bundle from origin to insertion; about 50-100 fiber bundles were delineated (Figure

2.4).

Figure 2.4. Pinned fiber bundles of soleus. A. Superficial. B. Intermediate. C. Deep. Posterior views. (Reproduced with permission from Agur 2001).

The specimen was then photographed using three spatially calibrated cameras to capture and

spatially orient the markers in a R3 Cartesian coordinate system. The layer of fiber bundles was

removed and the subsequent layers were marked with pins and photographed in the same

manner. The markers and calibration points were digitized on a computer and using direct linear

transformation, the 3D spatial positioning was obtained. The 3D coordinates were fitted into a b-

spline solids model using DANCE, a three-dimensional computer modeling software (Ng-Thow-

Hing et al. 2003). Fiber bundle length and pennation angle were computed from the three-

dimensional model of the muscle. Fiber bundle length was measured as the sum of the line

segments joining each point in the b-spline curve, while angle of pennation was measured as the

10

angle between the tangent of the fiber bundle and the tangent of the surface of the aponeurosis at

the site of attachment (Figure 2.5).

Figure 2.5. Schematic illustration of the measurement of angle of pennation using the B-spline muscle model. (Reproduced with permission from Agur 2001).

2.2.1.3 Digitization For muscle digitization, a Microscribe 3DX digitizer was used to trace the path of fiber

bundles in situ throughout the volume of supraspinatus (Kim et al. 2007), lumbar multifidus

(Rosatelli et al. 2008), pectoralis major (Fung et al. 2009), and extensor carpi radialis longus and

brevis (Ravichandiran et al. 2009). For each muscle, fiber bundles were serially dissected,

digitized and removed. The coordinate data was imported into Autodesk® Maya® and used to

construct a three-dimensional model of fiber bundle architecture as b-spline curves. Using the

model and software developed in the laboratory (Ravichandiran et al. 2009), the length of each

11

fiber bundle was computed as the length of the b-spline curve used to represent each fiber

bundle, pennation angle was measured as the angle between the tangent of the fiber bundle and a

mathematically defined line of action of the muscle. To add volumetric dimension to the

digitized fiber bundle curves, Ravichandiran et al. (2009) represented each digitized fiber

bundles as a set of serially arranged cylinders (Figure 2.6). The radius of each cylindrical

segment was computationally determined as half the distance to the nearest fiber bundle. Muscle

volume was computed as the sum of the volume of all cylinders used to represent the muscle.

Lateral Medial

Inferior

Superior

Clavicular head

Sternocostal head

Figure 2.6. Volumetric representation of fiber bundles of pectoralis major with architecturally distinct regions indicated in different colors.

12

2.2.2 In vivo methods

In vivo muscle architecture has been studied using ultrasonography and magnetic

resonance imaging (MRI). Both techniques allow collection of data in realtime.

Ultrasonography has been proven to be a versatile method that can be used in most clinical

settings due to the portability of the equipment.

2.2.2.1 Ultrasonography

Musculoskeletal ultrasonography can be used to visualize normal and pathological joints,

muscles, tendons and other soft tissue structures. Ultrasonography is based on high frequency

sound waves that are emitted toward the structure of interest and based on the material

characteristics, the waves are absorbed and/or reflected. A receiver unit detects the reflected

sound waves and creates a white output when all sound waves are reflected and dark output

when the sound waves are absorbed, with intermediate amounts of reflections/absorptions

represented as a gradient of grey tones. Ultrasound waves are reflected from collagen rich

structures, i.e. fiber bundles, and absorbed in the facial septa between fiber bundles, resulting in a

striped pattern in muscle. This striped pattern enables measurement of architectural parameters.

Ultrasound has been used to study muscle architecture by exploiting the variation in the

tissue density of muscle fiber bundles and the surrounding connective tissue in normal

(Fukunaga et al. 1997) and pathological states. Chow et al. (2000) studied intramuscular

architecture of soleus and gastrocnemius in normal male and female subjects and found that

females have longer mean fiber bundle lengths and males thicker muscles and larger angles of

pennation. Martin et al. (2001) compared the architectural parameters of soleus and

gastrocnemius in cadavers with that of in vivo architecture in relaxed and contracted states.

13

Architectural parameters, eg. fiber bundle length, lay between that of relaxed and contracted in

vivo muscle. It was suggested that architectural differences between live and cadaveric tissues

should be taken into consideration when developing muscle models.

However, when using ultrasound, the fiber bundles must be visible in their entirety, which

at times may be difficult. Furthermore, it is difficult to determine the plane at which the

ultrasound needs to be taken in order to visualize the curvature of the fiber bundles.

2.2.2.2 Magnetic resonance imaging

Magnetic resonance imaging (MRI) is useful in differentiating between different soft

tissue structures due to its ability to provide greater contrast than computed tomography (CT)

scans. MRI works by detecting changes in the alignment of magnetic moments in protons when

magnetic fields are turned on or off. Structures can be visualized because protons in different

tissues change alignments at different rates. High-resolution MRI was used by Engstrom et al.

(1991) and Scott et al. (1993) to reconstruct fiber bundle architecture in three-dimensions of the

muscles of the thigh from cadaveric specimens. The visible striation patterns in high resolution

MRI scans were used to mathematically determine the direction of the muscle fiber bundles.

Using the model, the fiber bundle length was measured using two methods: by following the path

of the fascicle through the scans and by assuming a straight line path of the fiber bundle.

Pennation angle was measured as the angle between the fiber bundle and the line of action of the

muscle, which was determined from the position of the tendon or aponeurosis. The

measurements were also made directly from excised muscles using a ruler and goniometer for

comparison. However, the authors noted a number of limitations in the technique, primarily in

the measurement of the architectural parameters and the application of the technique to other

14

muscles. Measurement of fiber bundle length was subjective and required considerable

knowledge of gross muscle anatomy and muscle representation in MRI sections, and fiber bundle

length of muscles with more complex architecture could not be measured using this technique.

Furthermore, it is difficult to apply this method to other specimens and muscles because striation

patterns integral to the technique are not visible in all muscles. Finally, fascicle orientation

needed to be coplanar to the images for the highest resolution, which was difficult to achieve for

all muscles.

Three-dimensional reconstruction from diffusion tensor MRI (DT-MRI) was later

introduced as a more accurate method of tracking muscle architecture (Lansdown et al. 2007;

Sinha et al. 2006; van Donkelaar et al. 1999). DT-MRI can be used to study the structure of both

skeletal and cardiac muscles in vivo (Sinha, et al. 2006) using the “correspondence between

water diffusion and local cellular geometry in the tissues” (Rutherford & Jones 1992). Diffusion

tensor MRI was used to track architectural properties of fiber bundles, including fiber direction

and pennation angle of the tibialis anterior muscle (Lansdown, et al. 2007), and only fiber

direction of the lateral gastrocnemius and medial soleus (Sinha, et al. 2006). Lansdown et al.

(2007) concluded that pennation angle measurements of human muscle could be made using DT-

MRI muscle fiber tracking. However, despite its value as a non-invasive method to study in vivo

muscle architecture, Sinha et al. noted errors in fiber length measurements due to noise in

diffusion tensor images that often causes fiber termination before the aponeurosis. Furthermore,

the process of collecting data using DT-MRI was found to be very time consuming.

15

2.3 Muscle modeling

2.3.1 Linear modeling

Most models of the musculoskeletal system incorporate individual or groups of muscles

as a series of line segments without representing the overall muscle volume (Hoy, et al. 1990).

These line segments represent the line of action of the muscle which was used to define muscle

function. The line of action has been represented as the centroidal line of the muscle (Chao et al.

1993), as single line vectors that traveled from the site of origin to insertion (Brand et al. 1982;

Hoy, et al. 1990) or as a series of vectors that included via points to represent muscles that

wrapped around bones and other muscles (Delp, et al. 1990).

In the cases of large muscles with broad attachment sites, the muscles were separated into

compartments where each compartment was represented as a line segment (van der Helm &

Veenbaas 1991). However, the number and locations of the line segments needed to accurately

define a muscle were unclear (Blemker & Delp 2005). Furthermore, these “lumped parameter”

models assume all fiber bundles within a muscle have the same length and moment arm, and do

not account for architectural differences throughout the muscle volume. Therefore, simplifying

muscle architecture to single lines or even sets of lines does not accurately represent the complex

geometry within the muscles and “assumes that moment arms are equivalent for all fibers within

a muscle” (Blemker & Delp 2005).

16

2.3.2 Volumetric muscle modeling from MRI reconstruction

MRI scans can be three-dimensionally reconstructed and used for direct volume

rendering. In this technique, the structures of interest are outlined on each scan and used to loft a

3D surface model of the structure. Anastasi et al. (2007) used this technique to model the human

knee joint including muscle, tendon, ligaments and bone.

Allison S. Arnold et al. (2000) first created a three-dimensional model of the medial

hamstrings and the psoas muscles by using direct volume rendering of MRI scans, and then

assigned motion constraints to the model. Moment arm measurements made from this model

were then compared with moment arms measured from the cadaveric specimens used to create

the model, using a custom-designed apparatus that provided control of hip and knee movement.

The differences in moment arms were found to be within 10%. However, this model

lacksnarchitectural specificity such fiber bundle length and pennation angle.

2.3.3 Volumetric 3D fiber bundle modeling

Blemker and Delp (2005) first reconstructed psoas, gluteus maximus, gluteus medius and

iliacus volumetrically from MRI scans and filled the volume with fiber bundles based on four

“template fiber geometries.” The templates included parallel, pennate, curved and fanned fiber

bundle arrangements interpolated into the muscle volume meshes as b-spline curves. The goal

was to create a muscle model that characterized a range fiber bundle lengths and moment arms.

In a similar study, Teran et al. (2005) modeled thirty muscles of the upper limb from the

Visible Human Project Data Set. Bones, muscles and tendons were reconstructed as triangular

meshes and the volume of the muscle was filled with a body-centred cubic (BCC) tetrahedral

lattice. B-spline solids were then used to represent fiber bundles as determined from descriptions

17

in anatomy textbooks; however, “working with anatomy experts or using fiber information from

scanning technologies would improve accuracy” (Teran, et al. 2005).

Fiber bundle architecture has been captured throughout the volume of in situ cadaveric

muscles using digitization and modeled in 3D using the digitized cartesian coordinates, thereby

reconstructing the entire muscle (see section 2.2.1.3). In these studies, digitized data was

imported into Autodesk® Maya® to rebuild the fiber bundle architecture throughout the volume

of the muscle as b-spline curves with control vertices as the digitized coordinates (Fung et al.

2009, Ravichandiran et al. 2009, Rosatelli et al. 2008 and Kim et al. 2007, Agur et al. 2003).

The fiber bundles were then volumetrically represented as a set of serially arranged cylinders

(Ravichandiran et al. 2009). Volumetric fiber bundle modeling provides the most detailed

architectural information to date. However, the process of data collection is time consuming and

could be made more efficient by the capability to transfer architectural data between muscle

volumes.

2.4 Nerve modeling Loh et al. (2002) constructed a three-dimensional model of the intramuscular distribution

of the tibial nerve within the soleus muscle using digitized data. This method is based on the

principles described above for modeling in situ fiber bundle architecture from digitized data.

The entry points of the tibial nerve were identified and each branch was sequentially exposed

and digitized within the muscle volume using a Microscribe 3DX digitizer. The digitized data

was modeled in DANCE (Ng-Thow-Hing et al. 1998), a 3D modeling software. The distribution

of the nerve within the muscle volume, as in situ, was reconstructed.

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2.5 Computer algorithms

2.5.1 Point set registration Registration of point sets has been used extensively in many computer vision tasks, such

as the reconstruction of a complete three-dimensional model using scans from various planes of

view of an object. In addition, this technique has also been used in facial recognition algorithms,

as well as in reconstruction of models from computer tomography (CT) data and endoscopic

images (Burschka et al. 2005). The goal of the point set registration algorithm is to find a

correspondence between two sets of points and to determine the transformation that maps one

point set to the second (Myronenko et al. 2007). The point set registration process involves

manipulation of a set of two or three-dimensional points that represents the surface topography

of a model shape, including translation, rotation and scaling (Besl & Mckay 1992; Myronenko,

et al. 2007).

The methods that have been used to solve the point set registration problem can be

classified into two main categories: rigid and non-rigid point set registration. Rigid point set

registration involves uniform translation, rotation or scaling of the points in one data set in order

to map each point in the model to the template data set. Non-rigid point set registration involves

non-uniform manipulation or warping of the points in the data set in order to map the data, and

allows for matching of features and topographical structures (Figure 2.7).

19

!" #"

Figure 2.7. A. Rigid point set registration and B. Non-rigid point set registration.

2.5.2 Iterative closest point algorithm

The iterative closest point algorithm (ICP), introduced by Besl and McKay (1992) is the

most popular method for rigid point set registration due to its simplicity and low need for

computational power. The method was initially developed as a way to match a set of points from

a source data set to its corresponding points in the target data set, where the two point sets were

scans of the same object from different views. The source data is usually a digitized point cloud

representing the surface topography of a rigid object.

The algorithm works by finding the nearest point in the target data set to each point in the

source data set and iteratively transforming the source data set until the sum of square errors is

minimized. The original implementation of the ICP algorithm was used to stitch together

different views of the same point set by matching points in overlapping regions (Besl & Mckay

1992).

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2.5.3 Coherent point drift algorithm

Myronenko et al. (2007) described a statistical method for registering one set of points to

another set, in both rigid and non-rigid point set registrations, called the Coherent Point Drift

(CPD) algorithm. This algorithm approached point set registration as a probability density

estimation problem and made use of the Motion Coherence Theory, which states that points close

to one another tend to move coherently (Yuille & Grzywacz 1988). Therefore, the coherent

movement of the Gaussian Mixture Model (GMM) centroids allowed the topological structure,

or features, of the objects to be preserved after registration and transformation of point sets. This

section of the thesis will discuss the theory behind the CPD algorithm.

2.5.3.1 Gaussian Mixture Model

A Gaussian mixture model (GMM) is a statistical model that allows for the representation

of data sets that cannot be modeled by normal parametric distributions, such as multimodal

Gaussian (normal) distributions or normal distributions with abnormal tails. GMM is able to

represent a complex data set by incorporating multiple normal distributions with different means

and variance. Parametric mixture models can be used in situations where the distribution of one

point set, A, is known and samples of data can be obtained from the second point set, B. The

mixture model is then used to determine the parameters that relate A to B (McLachlan & Basford

1988).

The Gaussian distribution is also referred to as normal distribution in statistics (Figure

2.8).

21

where µ is equal to mean and σ is the standard deviation.

Figure 2.8. Unimodal Gaussian distribution.

For a single gaussian curve the parameter θ describes µ and σ. Multi-modal data sets are

better modeled as a mixture of gaussians (Figure 2.9), in which case θ is ω (weight), µ and σ.

Figure 2.9. Gaussian mixture.

22

In a given data set, if it is known which data point belongs with which Gaussian, the

points in the data set can be assigned such that they influence the parameters of their respective

unimodal gaussians. However, when this information is not known, a mixture model is used and

a more complex method called the Expectation-Maximization algorithm needs to be used to

assign the data points to the appropriate gaussians.

2.5.3.2 Expectation-maximization algorithm

Mixture models, and many other statistical models, make use of the expectation-

maximization (EM) algorithm in maximum likelihood estimates of parameters that depend on

unobserved latent variables. Latent variables are variables that cannot be directly measured or

observed, but are instead inferred from other variables that can be observed or directly measured

(Dempster 1977).

Maximum likelihood estimation is a method that attempts to estimate parameters for a

data set that maximize the probability, or likelihood, of that data set (Dinov 2008). For

example, in pattern recognition, training data is often available and is used to tune the parameters

of a model data set to explain the training data. This is done by maximizing p(x|θ), the

probability of a feature value, x, given the model parameters, θ. p(x|θ) is maximized by

maximizing L(θ|X), the likelihood of the model parameters given the training data (Gurrapu

2004).

Maximum likelihood estimations are usually solved using the EM algorithm, which is an

iterative algorithm that alternates between two steps (Bilmes 1998):

23

•Expectation (E) step - the missing parameters are estimated given the observed data and

current estimate of the distribution using Bayes’ Theorem. In the first iteration of the

algorithm, the parameters are assigned a random value.

•Maximization (M) step - the likelihood function is maximized under the assumption that

the missing parameters are now known

The parameters computed in the M-step are then used in the expectation step of the next

iteration of the algorithm (Myronenko, et al. 2007).

2.5.3.3 Bayes’ Theorem

The Expectation Step of the EM algorithm uses Bayes’ Theorem to determine the

parameters using knowledge about a population prior to making observations (a priori). The

Bayesian inference states that as evidence, E, for or against a hypothesis, H, accumulates, the

probability of the hypothesis being true changes (Schmitt 1969). The Bayes' theorem can also be

written as:

Where,

•H represents a specific hypothesis.

•P(H) is the probability of H occurring inferred before the new evidence, E, was

presented.

•P(E|H) is the conditional probability of seeing the evidence E, under the condition that

hypothesis H is true. P(E|H) is also referred to as the likelihood function when it is

considered as a function of H for constant E.

24

•P(E) is defined as the marginal probability of E, which is the probability of witnessing

the new evidence E under all possible hypotheses, a priori. It can be calculated as the

sum of the product of all probabilities of any complete set of mutually exclusive

hypotheses and corresponding conditional probabilities:

•P(H|E) is called the posterior probability of H, or the probability of an occurrence given

evidence E.

Applied to the Coherent Point Drift algorithm, Bayes’ theorem states that as the points in one

data set are registered to the GMM centroids in the second data set, evidence accumulates. The

result of this accumulating evidence is either evidence supporting the newly calculated

parameters or against the parameters. The new parameters obtained via this method are then

used in the Maximization step of the EM algorithm.

2.6 Extensor carpi radialis longus and brevis

Extensor carpi radialis longus (ECRL) and brevis (ECRB) muscles, found on the

dorsolateral aspect of the forearm, are responsible for extension and abduction of the wrist.

ECRL and ECRB originate on the lateral supra-epicondylar ridge of the humerus and insert on

the bases of the second and third metacarpals, respectively. Studies investigating the muscle

architecture and innervation of ECRL and ECRB are discussed below.

25

The fiber bundle length and pennation angle of ECRL and ECRB as a whole have been studied

by various investigators and are summarized in Table 2.1.

Table 2.1. Fiber bundle length (FBL) and pennation angle (PA) of extensor carpi radialis longus (ECRL) and brevis (ECRB): summary of previous studies.Table 2.1. Fiber bundle length (FBL) and pennation angle (PA) of extensor carpi radialis longus (ECRL) and brevis (ECRB): summary of previous studies.Table 2.1. Fiber bundle length (FBL) and pennation angle (PA) of extensor carpi radialis longus (ECRL) and brevis (ECRB): summary of previous studies.Table 2.1. Fiber bundle length (FBL) and pennation angle (PA) of extensor carpi radialis longus (ECRL) and brevis (ECRB): summary of previous studies.Table 2.1. Fiber bundle length (FBL) and pennation angle (PA) of extensor carpi radialis longus (ECRL) and brevis (ECRB): summary of previous studies.Table 2.1. Fiber bundle length (FBL) and pennation angle (PA) of extensor carpi radialis longus (ECRL) and brevis (ECRB): summary of previous studies.Table 2.1. Fiber bundle length (FBL) and pennation angle (PA) of extensor carpi radialis longus (ECRL) and brevis (ECRB): summary of previous studies.

Author Type of study Muscle N FBL (cm) PA (°) MethodAn et al. (1981) Cadaveric ECRL 4 7.8±0.5 -

Manual (ruler/caliper and protractor)

An et al. (1981) Cadaveric

ECRB 4 5.3±0.6 -


Brand et al. (1981)Cadaveric ECRL 5 9.3 -Manual (ruler/caliper and protractor)

Brand et al. (1981)Cadaveric ECRB 5 6.1 - Manual

(ruler/caliper and protractor)

Lieber et al.

(1990)

Cadaveric ECRL 5 7.63±0.59 2.5±0.7Manual (ruler/caliper and protractor)

Lieber et al.

(1990)

Cadaveric ECRB 5 4.77±0.37 8.9±2.0


Murray et al.

(2000)

Cadaveric ECRL 10 9.2±1.8 1±2


Murray et al.

(2000)

CadavericECRB - - -


Cutts et al. (1991) Fresh

Amputated

ECRL 1 9.0 -


Cutts et al. (1991) Fresh

Amputated ECRB 1 4.9 -


Ravichandiran et al. (2009) described the regional differences in architecture of the

ECRL and ECRB muscles using serial dissection, digitization and computer modeling of

individual fiber bundles. ECRL and ECRB were both found to have proximal (superficial) and

distal (deep) regions but fiber bundle orientation differed within the muscles. Fiber bundles of

the proximal and distal regions of ECRL were parallel in orientation with the distal fiber bundles

being shorter than the proximal. In contrast, the proximal fiber bundles of ECRB were pennated

and the distal fibers parallel in arrangement. This study found proximal fiber bundles of ECRL

(6.90±1.19 cm) were significantly (p≤0.05) longer than in ECRB (5.00±1.05 cm). Mean

pennation angle of the proximal region of ECRL and ECRB tended to be larger than in the distal

region (Table 2.2).

26

Table 2.2. Fiber bundle length (FBL) and pennation angle (PA) of proximal and distal regions of extensor carpi radialis longus (ECRL) and brevis (ECRB) as reported by Ravichandiran et al. (2009).





Muscle Region FBL (cm) *PA1 (°) *PA2 (°)

ECRLProximal 6.90±1.19 7.11±2.62 15.53±2.72ECRL

Distal 5.00±1.05 5.69±1.96 14.74±2.30

ECRBProximal 4.61±0.71 6.44±1.43 8.50±1.88ECRB

Distal 3.83±0.58 5.63±1.05 7.25±1.41* PA1 = pennation angle at superior attachment site* PA1 = pennation angle at superior attachment site* PA1 = pennation angle at superior attachment site* PA1 = pennation angle at superior attachment site* PA1 = pennation angle at superior attachment site* PA2 = pennaiton angle at inferior attachment site* PA2 = pennaiton angle at inferior attachment site* PA2 = pennaiton angle at inferior attachment site* PA2 = pennaiton angle at inferior attachment site* PA2 = pennaiton angle at inferior attachment site

Based on the architectural differences between the proximal and distal regions, Ravichandiran et

al. (2009) suggested possible neuromuscular compartments in ECRL and ECRB.

Studies that have investigated the extramuscular innervation of ECRL and ECRB will be

summarized first, followed by studies which describe the intramuscular innervation of ECRL and

ECRB. El-Din Safwat et al. (2007) found one branch from the radial nerve entering ECRL

(n=23 embalmed cadaveric specimens) where as Segal et al. (1991) reported two branches, a

proximal and distal (n=8 embalmed cadaveric specimens). Chen et al. (2009) reported that

ECRL had 1.8±0.7 primary extramuscular branches but their points of origin were not

documented. Branovacki et al. (1998) studied the relative position of the branch to

brachioradialis and the branch to ECRL from the radial nerve (n=60 embalmed cadaveric

specimens). In the majority of specimens (70%), the branch to ECRL arose distal to the branch

to brachioradialis (Figure 2.10).

27

Figure 2.10. Summary of extramuscular nerve supply to ECRL relative to the nerve to brachioradialis (Branovacki et al. 1998).

Most previous studies of the innervation of ECRB found one nerve entry point,

originating from either the superficial or deep branch of the radial nerve or from the radial nerve

proper, proximal to its bifurcation (Table 2.3). Two studies (al-Qattan 1996; Salsbury 1938)

found the superficial branch of the radial nerve to most commonly innervate ECRB and three

studies (Abrams et al. 1997; Nayak, Vadgaonkar et al. 2009) found deep branch as the most

common innervation. Only two studies were found that reported 2 or more nerve entry points in

the ECRB: El-Din Safwat & Abdel-Meguid (2007) found one or two primary nerves with two to

five motor points and Chen et al. (2009) found 1.4 ± 0.5.

28

Table 2.3. Summary of the source of extramuscular nerve supply to ECRBTable 2.3. Summary of the source of extramuscular nerve supply to ECRBTable 2.3. Summary of the source of extramuscular nerve supply to ECRBTable 2.3. Summary of the source of extramuscular nerve supply to ECRB

Authors n* # of entry points Source from radial nerve

Salsbury (1938) 50 1Superficial branch (n=28, 56%)Deep branch (n=18, 36%)At bifurcation (n=4, 8%)

al-Qattan (1996) 25 1Superficial branch (n=12, 48%)Deep branch (n=8, 32%)Radial nerve (n=5, 20%)

Cricenti et al. (1994) 30 1Superficial branch (n=2, 7%) Deep branch (n=28, 93%)

Abrams et al. (1997) 20 1Superficial (n=5, 25%)Deep branch (n=9, 45%)Proximal to bifurcation (n=6, 30%)

Nayak et al. (2009) 72 1Superficial branch (n=25, 34.7%)Deep branch** (n=36, 50%)Radial nerve (n=11, 15.2%)

Chen et al. (2009) 10 1.4 ± 0.5 Origin not specified

El-Din Safwat & Abdel-Meguid (2007) 23 3.7 ± 1.3 Origin not specified

* embalmed cadaveric specimens

** authors referred to as poster branch of radial nerve







Intramuscular innervation of ECRL was reported by Segal et al. (1991) as originating

from a proximal and distal branch of the radial nerve. The proximal branch of the radial nerve

innervated the proximal two-thirds of the muscle whereas the distal branch innervated the distal

one-third of the muscle. Chen et al. (2009) reported 2.7±1.2 primary intramuscular branches in

ECRL and classified this muscle as type IIb according to Lym’s method, a muscle with no

central tendon. ECRB was reported to have 2.3±0.7 primary intramuscular branches and was

classified as IIa, a muscle with a central tendon dividing it into two parts.

Clinically, knowledge of the nerve supply to the ECRL and ECRB has great value

because injuries of the radial nerve may involve the nerve to ECRB or ECRL (al-Qattan 1996).

29

Therefore, radial nerve branch anatomy is important during "nerve repair, performing motor

nerve blocks, forecasting location of a compressive lesion and in predicting rate and order of

motor recovery" (Abrams, et al. 1997).

2.7 Summary

In summary, many methods have been discussed for modeling muscles and muscle

architecture to represent muscle function. However, these studies simplified muscles as single

lines or a series of lines estimating fiber bundle architecture. Muscle models can be improved

with the use of real fiber bundle architectural data. Furthermore, studies of muscle innervation

have primarily studied extramuscular innervation and the few studies that examined

intramuscular innervation looked at the innervation in relation to muscle volume (Loh et al.

2003) or only at primary nerve branches within the muscle (Chen, et al. 2009). None of these

studies have examined the relationship between innervation and fiber bundle architecture. The

study of the relationship between fiber bundle architecture and intramuscular innervation in the

muscle volume requires accurate representation of fiber bundle architecture within muscle

volume. Point set registration algorithms introduced in this section of the thesis may provide a

basis for fitting digitized fiber bundle data sets from one specimen to muscle volume data sets

from other specimens.

30

Chapter 3Hypothesis and Objectives

3 Hypothesis and Objectives

3.1 Hypothesis

It is feasible to mathematically fit fiber bundle architecture to muscle volumes, while

maintaining fiber bundle architectural parameters.

There are neuromuscular compartments in the extensor carpi radialis (ECRL) and brevis

(ECRB).

3.2 Objectives

The objectives of this study are as follows:

1.To develop a computer algorithm to transform fiber bundle data from one specimen to fit a

muscle volume obtained from a different specimen.

2.To use this algorithm to transform digitized fiber bundle data of extensor carpi radialis longus

(ECRL) and brevis (ECRB) to fit volumetric data obtained from other specimens.

3.To model, using digitized data, the intramuscular innervation of ECRL and ECRB.

4.To fit fiber bundle and innervation data of ECRL and ECRB to muscle volumes from other

specimens.

5.To document the distribution of the radial nerve throughout the volume of the ECRL and

ECRB, and to relate the innervation pattern to muscle architecture.

6.To determine if there are neuromuscular compartments within ECRL and ECRB.

31

Chapter 4Materials and Methods

4 Materials and Methods This section outlines the process of digitization of extra- and intramuscular nerves and

muscle volume of seven ECRL and ECRB specimens in this current study, and the digitization of

fiber bundle architecture of one specimen of each of ECRL and ECRB that was done in a

previous study (Ravichandiran, et al. 2009). In the previous study, eight specimens were

digitized. The data set chosen for this study was from a specimen of average size with densely

digitized data points. The method of fitting the fiber bundle architecture into the muscle volumes

of a different set of seven specimens is then described.

4.1 Digitization of ECRL and ECRB

4.1.1 Specimens Seven formalin embalmed cadaveric specimens (5M/2F), mean age 75.7±15.2 years were

used for this study. Exclusion criteria included visible evidence of deformities, pathologies,

previous surgeries or trauma. Ethics approval was received from the University of Toronto

Research Ethics Board (Protocol Reference 21966).

4.1.2 Dissection, Digitization and Modeling

Prior to dissection, the elbow joint was stabilized with a metal plate screwed into the

distal humerus and proximal ulna. The specimen was securely mounted in a vice. Three screws,

acting as reference markers for the digitization process, were drilled into the following sites:

anterior surface of the distal humerus, lateral epicondyle and head of the ulna. The centre of the

three screws were repeatedly digitized to assure orientation and alignment of the digitized data.

To expose the ECRL and ECRB, the skin, subcutaneous tissue, fascia and superficial muscles

32

were removed. Next, the radial nerve was exposed as it emerged between the brachialis and

brachioradialis muscles. The process of dissection and digitization of the muscle volume, fiber

bundles and innervation of ECRL and ECRB is outlined in the next sections of the thesis.

All digitization was carried out using a MicroscribeTM 3DX Digitizer (Immersion

Corporation , San Jose, CA, USA). The digitizer consists of a base and digitizing arm with five

degrees of freedom that terminates in a fine tip stylus (Figure 4.1). When the stylus tip is placed

on a surface and a button is pressed, the cartesians coordinates (x,y,z) of the point is recorded and

stored in a computer as a text file. The digitizer records the coordinates of the stylus tip with an

accuracy of 0.23 mm. The digitization protocol followed was similar to that used in earlier

studies in our laboratory (Agur, et al. 2003; Kim, et al. 2007; Loh, et al. 2003; Rosatelli, et al.

2008).

Figure 4.1. Microscribe 3DX digitizer.

33

The digitized data points from the muscle volume and nerve data were imported into

Autodesk® Maya® 2009 (Autodesk Inc., San Jose, CA, USA: http://www.autodesk.com/maya)

and used to reconstruct a three-dimensional model of the surface volume of ECRL and ECRB

muscles in situ along with the bone and extra- and intra-muscular distribution of the radial nerve.

Autodesk® Maya® 2009 is a three-dimensional modeling and animation software with a

programming interface called Maya Embedded Language (MEL) or Python.

4.1.2.1 Muscle volumeThe same method was used to digitize the volume of seven pairs of ECRL and ECRB

muscles from seven specimens, starting with ECRL. Prior to dissection and digitization of the

branches of the radial nerve, the superficial surface of the muscle was digitized at points placed

at 5 mm intervals over the entire surface of the muscle belly. As the nerve was serially exposed

by removing fiber bundles, the remaining parts of the muscle belly were continuously digitized

until all the fiber bundles had been removed.

Using the digitized data, the muscle volume was reconstructed as volumetric rings

(Figure 4.2A). The volumetric rings provided a framework for modeling the volume of each

muscle as a polygon mesh using the “Loft” function in Autodesk® Maya® 2009 (Figure 4.2B).

The surface was then rendered by “Assigning materials” (Maya terminology) to color code the

muscle volumes (Figure 4.2C).

34

http://www.autodesk.com/maya

http://www.autodesk.com/maya

C. Lateral View

A. Lateral View

Proximal

Distal

B. Lateral View

Proximal

Distal

Proximal

Distal

Posterior

Posterior

Posterior

Figure 4.2. Reconstruction of muscle volume from digitized data. A. Digitized volume of muscle. B. Lofted polygon mesh. C. Surface is rendered with color.

4.1.2.2 Nerve distributionNerves were followed throughout the muscle volume of the same seven specimens used

to digitize muscle volume. A x40 dissection microscope was used to follow the nerve branches

35

as far as possible. The radial nerve and its branches were traced distally from where it emerged

between the brachialis and the brachioradialis. Entry point(s) of the radial nerve branches to the

ECRL were identified. Intramuscular segments of the nerve were sequentially exposed and

digitized (Figure 4.3). Serial dissection of the muscle fiber bundles exposed deeper segments of

the nerve branches. This process was repeated until the branches of the nerves could no longer be

followed using a dissection microscope. After the dissection of the ECRL was completed, the

nerve branches to and within ECRB were identified and digitized in a similar manner.

The nerve data were imported into Autodesk® Maya® and reconstructed as curves

(Figure 4.4A). Next, using a Maya Embedded Language (MEL) Script, the curves were extruded

as cylindrical tubes and assigned colors to code the nerve branching to different regions of the

muscle (Figure 4.4B and C). The muscle volume model was combined with the 3D nerve data to

allow documentation of the intramuscular course of the radial nerve in each muscle.

36

Nerve entry point Nerve entry point

Nerve entry pointSt

ylus

Extensor carpi radialis longus

Radial nerveDistal

Anterior

Prox

imal

Radial nerve branch to ECRL

Radial nerve


Figure 4.3. Reconstruction of nerve distribution from digitized data.

37

A.

B.

C.

Nerve entry point

Proximal

Distal

Proximal

Distal

Proximal

Distal

Nerve entry point

Nerve entry point

Figure 4.4. Modeling some of the nerve branches from digitized data of one ECRL. A. Digitized nerve data imported as curves. B. Tubes extruded from curves. C. Nerve branches color coded.

38

4.1.2.3 Bone and tendonOnce dissection and digitization of the muscle volume and nerve was complete, the

surface of the tendon was digitized (n=7 pairs). The bony surfaces were digitized in one

specimen for illustrative purposes only. For this specimen, the tendon and all remaining soft

tissue were removed to expose the humerus and radius, which were then digitized to the edges of

the joint capsule (n=1). The muscle volume and nerve data were combined with the tendon and

bone data to show the location of the muscle volume and innervation in the forearm of this

specimen.

4.1.2.4 Fiber bundle dataA previously digitized fiber bundle data set obtained throughout the volume of ECRL and

ECRB of one of the specimens used in Ravichandiran et al. (2009), was selected for further

study. The same specimen could not be used to trace both intramuscular nerve distribution and

fiber bundles. This fiber bundle data set had been digitized by previous undergraduate research

students. To obtain the data, the following process was used.

Fiber bundles on the superficial surface of the muscle were traced from origin to insertion

using a dissection microscope. Each fiber bundle was digitized by placing points at

approximately 3 mm intervals between attachment sites to capture fiber bundle curvature. The

digitized fiber bundles were removed and deeper fiber bundles exposed and digitized. This

process was repeated until the fiber bundles had been digitized throughout the volume of the

muscle. The number of fiber bundles digitized was: 96 for ECRL and 127 for ECRB.

In this study, the data was used for development of fitting algorithms so that architectural

data could be accurately incorporated into any ECRL and ECRB muscle volume.

39

4.2 Exploring methods for fitting architectural data to generic muscle volumes

Many methods were used in this thesis to attempt to fit digitized fiber bundle data to

muscle volume digitized from any specimen. The iterative closest point (ICP) algorithm, fitting

fiber bundle data as cross-sections to muscle volume and the coherent point drift (CPD)

algorithm were used as a basis for developing these methods.

4.2.1 Iterative closest point algorithm

The ICP algorithm is a rigid point set registration method that registers points in one data

set to another data set using an iterative process. Since the ICP algorithm was implemented to

register points obtained from the same object from different views, it was not possible using the

original algorithm to accurately register two different objects such as digitized fiber bundle data

obtained from one specimen to volumetric data obtained from another specimen. To attempt to

overcome this limitation, a scaling component based on ZinBer (2005) was added to each

iteration of the algorithm. The scale factor was calculated as the sum of the scalar dot products

of each associated point pair divided by the sum of the magnitudes of point vectors in the fiber

bundle data set :

where ai is a point in the volumetric data set, bj is a point in the fiber bundle data set, n is the size

of the data set and s is the scale factor.

40

The fiber bundle and muscle volume data sets were imported into The Mathworks®

MATLAB®, a mathematical programming software and language. The ICP algorithm, along

with the scale factor, was used to register the two point sets as outlined below and in Figure 4.5:

1.Points in fiber bundle data set, B, were associated with points in the muscle volume

data set, A, by finding the closest points in A.

2.The transformation parameters (rotation, translation, scaling) were estimated so that

distances between each associated pair of points is decreased.

3.The points in the fiber bundle data set were transformed using the estimated

transformation parameters.

4.Steps 1 to 3 were iterated until the distances between corresponding points reached a

predefined threshold, t, where t is 2x10-5 < t < 2x10-4.

41

Registered Points after Step 1.Registered Points after Step 1.X P

x1 p5

x2 p2

x3 p3

x4 p4

x5 p1

Registered Points after Step 3.Registered Points after Step 3.A B

x1 p1

x2 p2

x3 p3

x4 p4

Figure 4.5. Iterative closest point algorithm. A. Two data sets X and P. B. Iteration of translation, rotation and scaling to register points in P with points in X.

A.

B.

Limitations of this method include that:

•the initial position of the two point sets must be close in size and rotation

•the difference in scale between the data set and template volume needs to be consistent

throughout the volume of the muscle

42

•an optimal threshold value needs to be determined individually for each fiber bundle

data set when fitting to a muscle volume.

These limitations rendered this rigid method inadequate for accurately fitting fiber bundle

data to volumetric muscle data sets. Therefore, other methods of fitting fiber bundle data to

muscle volume were explored.

4.2.2 Sectioning muscle volume and fiber bundle data sets

Next, a non-rigid fitting method was attempted. The process is outlined below:

1.The fiber bundle data set of an entire muscle was divided into 2 millimetre sections, in

an anteroposterior direction from the proximal end of the muscle belly (Figure 4.6A).

The number of sections, n, was counted and the muscle volume data set was divided into

the same number of sections (Figure 4.6B).

Proximal Distal

Proximal Distal

Figure 4.6. Sectioned data sets. A. Muscle volume data set. B. Fiber bundle data set.

43

2.The size of each section (s) in the muscle volume data set was the length of the muscle

belly (L) in the volume data set divided by the number of sections, n, in fiber bundle data

set:

3.The centroid of each slice of the fiber bundle data set was aligned with the

corresponding centroid in the muscle volume data set (Figure 4.7).

A. B. C.

Figure 4.7. A. Centroid of one section of the muscle volume data set. B. Centroid of the corresponding section of the fiber bundle data. C. Alignment of centroids.

4.The scale factor between the fiber bundle section and muscle volume section was

calculated as the mean of the distances from the centroid to each point in each slice of the

fiber bundle data set divided by the mean of the distances from the centroid to points on

the circumference:

,

44

where µa and µb represent the centroids of a and b, ai is a point on the circumference of

the volume and bj is a point in the fiber bundle data set. This factor was used to scale

each slice independently.

However, it was not possible to algorithmically determine an accurate rotation parameter

for each fiber bundle section independently, that ensured that the overall path of the fiber bundles

was maintained. Therefore, this method was also found to be insufficient for fitting fiber bundle

data sets to muscle volume.

4.2.3 Coherent point drift

Finally the CPD algorithm, another non-rigid fitting method, was implemented in

MATLAB®. Both the digitized fiber bundle and muscle volume data sets were imported into

MATLAB® as two point sets, A and B:

• A - 3 x N muscle volume data set

•B - 3 x M fiber bundle data set

where N and M are the number of data points in A and B, respectively.

Before applying CPD to register data set B with data set A, the approximate alignment of

A and B was determined using the Principal Component Analysis (PCA). PCA is a statistical

technique used for quantifying multivariate correlations. In this context PCA was used to

compute the principal spatial directions of data distribution. Principal directions are collinear

with eigenvectors of the covariance matrix of the data. Points in B were aligned with principal

components of A using Equation 1.

45

Equation 1

where

€

VA = orthogonal transformation matrix of set A, columns are eigenvectors arranged in the

order of decreasing eigenvalues and

€

XA = centroid of set A

The justification for prealignment was based on the assumption that CPD is more likely

to converge on the optimal solution if the initial distance between potentially corresponding

points is small. In most general terms the goal of the CPD algorithm was to parametrize B using

a Gaussian Mixture Model (GMM) and determine parameters which maximize the posterior

probabilities of individual Gaussian components for corresponding points in A. The structure of

the CPD algorithm can be visualized in the flowchart of figure 4.9.

1. Gaussian Mixture Model

The Gaussian Mixture Model (GMM) is a weighted sum of Gaussian probability density

functions (PDFs) commonly used to parametrize distributions that cannot be explained by single

parametric PDF. The points in data set B, were designated as GMM centroids while the points in

data set A, were considered the samples generated by the GMM. GMM is defined as:

Equation 2

where P(m) is the probability of each member of the point set, A. Assuming all components are

equally probable then P(m) = 1/M. p(a|m) is a Gaussian PDF with isotropic covariance, σ2:

46

Equation 3

where bm is a point in data set B and D is the dimensionality of the data (in this case D=3).

2. Gaussian affinity matrix

The Gaussian affinity matrix is an M x M matrix, also known as the Gram matrix (Figure

4.8B). Points in data set B (Figure 4.8A) were used to build a Gaussian affinity matrix, G, which

was used in the calculation of the transformation parameters, W, at the end of each iteration of

the Expectation Maximization (EM) algorithm.

B =

b1 x1 y1 z1

G =

b1 b2 b3 bj bM

B =

b2 x2 y2 z2

G =

b1 g1,1 g2,1 g3,1 ... gM,1

B = b3 x3 y3 z3 G = b2 g1,2 g2,2 g3,2 ... gM,2B =

... … … …

G =

b3 g1,3 g2,3 g3,3 ... gM,3

B =

bM xM yM zM

G =

bi ... ... ... ... ...

A. B. bM g1,1 g2,M g3,M ... gM,M

Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.Figure 4.8. Gaussian affinity matrix. A. A 3 x M data set and B. the M x M Gaussian Gram Matrix of the data set.

Each element of the matrix is calculated as:

Equation 4

47

where bi and bj are points in B, β is transformation smoothness parameter which controls the

coherence of the velocity field which is used to update the GMM centroid positions (CPD was

applied using default setting β=2).

3. Expectation Step

During the expectation step posterior probabilities of GMM components are calculated

for a given set of transformation parameters using Bayes’ theorem. For the very first iteration

these parameters can be estimated or initiated randomly. During subsequent iterations the

parameters from preceding M step are used.

4. Maximization and Transformation

During maximization step the parameters (θ and σ2) which maximize the likelihood

function (Equation 5) are computed. These parameters are used to update the GMM centroid

positions (i.e. move B closer to A) and are passed on to the expectation step which follows

immediately after.

Equation 5

Data set B is transformed according to Equation 6:

Equation 6

48

where T is the transformed data set and v is a displacement field regularized by parameters θ and

σ2.

The EM algorithm is iterated until the change in the transformation parameters falls

bellow a pre-determined threshold value at which point the iterative loop is broken. Sets A and B

are now registered. The steps involved in the algorithm are summarized in Figure 4.9.

Figure 4.9. Outline of CPD algorithm.

49

With each iteration of the algorithm, the GMM centroids, points in the fiber bundle data

set, gradually registered with corresponding points in the muscle volume data set (Figure 4.10J).

Figure 4.10A shows the alignment of the two data sets after the pre-alignment step, where the

translational and rotation along the length of the muscle is estimated to bring the two data sets

close together.

50

Proximal Distal

Proximal Distal

ProximalDistal

A.

B.

C.

Figure 4.10. Iterations of the CPD algorithm for ECRL fiber bundle data set. A.Prealignment step with fiber bundles. Fiber bundle data points are show in red, muscle volume in green. Fiber bundle data starts with a different orientation than muscle volume at the start of the algorithm. B. Prealignment step with data points (Iteration 0). C. Iteration 1.

51

Figure 4.10. Iterations of the CPD algorithm for ECRL fiber bundle data set (continued). D. Iteration 2. E. Iteration 6. F. Iteration 10.

52

Figure 4.10. Iterations of the CPD algorithm for ECRL fiber bundle data set (continued). G. Iteration 15. H. Iteration 20. I. Iteration 50. J. Fiber bundle data set of iteration 50.

53

Once the CPD registration algorithm was complete, the fitted fiber bundle data set was

imported into Autodesk® Maya® 2009 and the fiber bundles were modeled, along with the

muscle volume and nerve branching. The fiber bundle architecture was reconstructed as b-spline

curves and then as polygon tubes to represent the fiber bundle architecture within the muscle

volume. Muscle fiber bundle architecture was fit to the muscle volume for each of the ECRL

and ECRB muscles of the seven digitized specimens.

4.2.3.1 Validation of CPD algorithm In order to test the validity of the CPD algorithm as a fitting tool, two 2D objects (A and

B) were drawn (Figure 4.11A). The points that represented critical features on which the shape

was dependent were marked (a1 to a7 and b1 to b7). These points were imported into MATLAB

and the CPD algorithm was used to fit data set B to data set A. The validation criterion was that

the critical points identified in each shape were matched to make the objects the same shape after

the iterations of the CPD algorithm were complete. The result of the validation test case was

yielded after fifteen iterations of the CPD algorithm. The algorithm matched the features of the

two shapes, A and B (Figure 4.11B).

54

Figure 4.11. Validation of the CPD algorithm. A. Data set A and data set B. B. Data set B registered to data set A using the CPD algorithm.

A.

B.

55

4.3 Volume fitting of fiber bundle architecture and intramuscular innervation of ECRL and ECRB using the CPD algorithm

Digitized data of the intramuscular innervation and muscle volume from seven ECRL and

ECRB specimens digitized in this study and digitized data of the muscle volume and fiber bundle

architecture from one previously digitized specimen were used for modeling. Using the CPD

algorithm, ECRL and ECRB fiber bundle architecture was fit to each of the seven respective

muscle volume and nerve data sets. From these 3D models, the intramuscular innervation in

relation to fiber bundle arrangement was documented to determine if there were regions within

ECRL and ECRB innervated by independent branches, i.e. the presence of neuromuscular

compartments. The regions of muscle architecture that appeared to be differentially innervated

were color coded.

Fiber bundle length (FBL), muscle volume (V) and pennation angle (PA1 and PA2) were

calculated for the fiber bundle data set before and after the fiber bundle data was fit into each

muscle volume. The results were then compared to determine if there was any noticeable

difference in the mean FBL and pennation angles of the fiber bundles before and after the data

had been fit to muscle volume.

56

Chapter 5Results

5 Results

5.1 Three-dimensional reconstruction and modeling

The muscle volume and radial nerve distribution in the extensor carpi radialis longus

(ECRL) and brevis (ECRB) muscles of seven embalmed cadaveric specimens were dissected and

digitized (Figure 5.1).


Extensor carpi radialis brevis

Branch to ECRL

Deep branch ofradial nerve

Proximal

Distal

Supinator

Figure 5.1. Anterior view of a cadaveric specimen of the ECRL (green), ECRB (yellow), supinator and radial nerve (blue). The superficial branch of the radial nerve was removed.

57

The muscle volumes, tendons and innervation of the ECRL and ECRB were modeled

from the digitized data (Figure 5.2). The models enabled 3D visualization of muscle, tendon

Figure 5.2. Comparison of 3D model and cadaveric specimen, lateral views. A. Cadaveric specimen with color coded muscles, tendons and nerves. B. Three-dimensional model of ECRL and ECRB reconstructed from digitized data. C. Three-dimensional model of ECRB reconstructed from digitized data. Note: Humerus was digitized with the joint capsule intact and is therefore lacking anatomical detail distally.

58

and nerve. The muscle bellies of ECRL and ECRB are shown in situ in the specimen and in the

model. Also shown is the course of the superficial and deep branches of the radial nerve, the

articular branch to the elbow joint and the branch to ECRL. The model can be reconstructed to

show any of the above components in isolation or in combination.

5.2 Nerve distribution

In all seven specimens, the superficial branch of the radial nerve travelled superficially

along the length of the ECRL towards the wrist. The deep branch pierced the supinator muscle

(Figure 5.1). An articular branch to the joint capsule of the elbow joint was given off proximal to

the bifurcation of the radial nerve into the deep and superficial branches (Figure 5.2A).

5.2.1 Extensor carpi radialis longus

5.2.1.1 Extramuscular innervation of ECRL

One primary branch from the radial nerve provided innervation to the ECRL. In all

seven specimens, this branch was given off the radial nerve distal to the elbow joint but proximal

59

Figure 5.3. Extramuscular bifurcation of branch to ECRL into anterior and posterior branches, anterior view.

to the articular branch and the bifurcation of the radial nerve into deep and superficial branches

(Figure 5.3). The primary branch divided, in all specimens, into anterior and posterior branches

at the proximal third of the muscle belly. This branching occurred extramuscularly very close to

the muscle belly in three specimens and intramuscularly in four specimens.

Figure 5.4. Extramuscular innervation of ECRL.

5.2.1.2 Intramuscular innervation of ECRL

The anterior branch of the nerve to ECRL lay at deeper plane within the muscle belly

than the posterior branch, whether nerve bifurcated intramuscularly (Figure 5.1) or

extramuscularly (Figure 5.4).

Once entering the muscle belly, the posterior branch innervated approximately the

superficial one-third of the muscle belly, while the anterior branch innervated approximately the

deep two-thirds (Figure 5.5). Both the anterior and posterior branches were distributed

proximally and distally in the muscle belly. The proximally distributed branches ascended

60

towards the origin of ECRL and the longer distally distributed fiber bundles coursed through the

muscle belly towards the musculotendinous junction.

Figure 5.5. Intramuscular innervation of the ECRL. A. Posterolateral view. B. Lateral view.

61

5.2.2 Extensor carpi radialis brevis

5.2.2.1 Extramuscular innervation of ECRB

Two to four primary nerve branches were found to innervate ECRB. In five specimens

one primary branch divided extramuscularly, whereas in the remaining two specimens, the

primary branches divided intramuscularly. Five distinct innervation patterns were observed in

the seven specimens based on the source of the primary nerve branches. The primary nerve

branches in six specimens were given off the radial nerve and/or its superficial and deep

branches but in one specimen, one branch arose from the median nerve (Table 5.1).

Table 5.1. Number and source of primary nerve branches to ECRB. Five innervation (I to V) patterns based on the source and number of primary branches.Table 5.1. Number and source of primary nerve branches to ECRB. Five innervation (I to V) patterns based on the source and number of primary branches.Table 5.1. Number and source of primary nerve branches to ECRB. Five innervation (I to V) patterns based on the source and number of primary branches.Table 5.1. Number and source of primary nerve branches to ECRB. Five innervation (I to V) patterns based on the source and number of primary branches.Table 5.1. Number and source of primary nerve branches to ECRB. Five innervation (I to V) patterns based on the source and number of primary branches.Table 5.1. Number and source of primary nerve branches to ECRB. Five innervation (I to V) patterns based on the source and number of primary branches.Table 5.1. Number and source of primary nerve branches to ECRB. Five innervation (I to V) patterns based on the source and number of primary branches.Table 5.1. Number and source of primary nerve branches to ECRB. Five innervation (I to V) patterns based on the source and number of primary branches.

Innervation

pattern

n Number of primary

nerve branches

Number of entry points

Source of primary nerve branchesSource of primary nerve branchesSource of primary nerve branchesSource of primary nerve branchesInnervation

pattern

n Number of primary

nerve branches

Number of entry points

Prox. Mid. Dist. Other

I 2 2 3* RN N/A DRN -

II 2 3 4* SRN SRN SRN -

III 1 3 4* RN DRN DRN -

IV 1 3 3 RN SRN SRN -

V 1 4 4 RN DRN SRN MN

RN = radial nerve, SRN = superficial branch of radial nerve, DRN = deep branch of radial nerve, MN = median nerve, n = number of specimens, * = division of primary branch extramuscularly.








Each of the five innervation patterns will be described below.

Type I: Two primary nerve branches, proximal and distal, entered the medial aspect of the

muscle belly. The proximal branch originated from the radial nerve prior to its bifurcation into

62

superficial and deep branches and divided extramuscularly before entering the proximal part of

the muscle belly. The distal branch originated from the deep branch of the radial nerve and

entered the muscle at about the mid-point of the muscle belly without extramuscular bifurcation

(Figure 5.6).

Figure 5.6. Type I: Extramuscular distribution pattern of ECRB. Contractile elements are yellow, the tendon is gray.

Type II: Three primary nerve branches, proximal, middle and distal, all originating from the

superficial branch of the radial nerve (Figure 5.7). The proximal branch divided

extramuscularly, and entered the proximal quarter of the muscle belly. The middle and distal

branches entered the mid-point and distal quarter of the muscle belly, respectively, without

dividing extramuscularly.

63

Figure 5.7. Type II: Extramuscular distribution pattern of ECRB. Contractile elements are yellow, the tendon is gray.

Type III: Three primary nerve branches, proximal, middle and distal (Figure 5.8). The

proximal branch originated from the radial nerve and entered the muscle belly near its proximal

end. The middle and distal branches originated in close proximity from the deep branch of the

radial nerve and entered the half way along the length of the muscle belly. Only the proximal

branch divided extramuscularly.

Figure 5.8. Type III: Extramuscular distribution pattern of ECRB. Contractile elements are yellow, the tendon is gray.

64

Type IV: Three primary branches, proximal, middle and distal (Figure 5.9). The proximal

branch originated from the radial nerve, however the middle and distal originated from the

superficial branch of the radial nerve. None of the branches divided extramuscularly. The

proximal branch entered the proximal quarter of the muscle belly. The middle and distal

branches entered the mid-point and distal quarter of the muscle belly, respectively.

Figure 5.9. Type IV: Extramuscular distribution pattern of ECRB. Contractile elements are yellow, the tendon is gray.

Type V: Four primary nerve branches (Figure 5.10). Three branches originated from the radial nerve: the proximal branch, from the radial nerve proper, just proximal to its bifurcation, the middle branch from the deep branch of the radial nerve and the distal branch, from the superficial branch of the radial nerve. The fourth and most distal branch originated from the median nerve. Each branch supplied about one-quarter of the muscle belly.

65

Figure 5.10. Type V: Extramuscular distribution pattern of ECRB. Contractile elements are yellow, the tendon is gray.

There was no one predominant innervation pattern. Two specimens had Type I

innervation pattern, two had Type II and Types III, IV and V were seen in one specimen each.

66

5.2.3 Intramuscular innervation of ECRB

The intramuscular nerve distribution depended on the innervation pattern (Type I-V).

The portion of the muscle volume innervated by the branches in each innervation pattern is

summarized in Table 5.2 and Figures 5.11-5.15.

Table 5.2. Intramuscular nerve distribution for each of the five types of innervation patterns in ECRB.Table 5.2. Intramuscular nerve distribution for each of the five types of innervation patterns in ECRB.Table 5.2. Intramuscular nerve distribution for each of the five types of innervation patterns in ECRB.Table 5.2. Intramuscular nerve distribution for each of the five types of innervation patterns in ECRB.Table 5.2. Intramuscular nerve distribution for each of the five types of innervation patterns in ECRB.

Innervation pattern

Primary nerve branchesPrimary nerve branchesPrimary nerve branchesPrimary nerve branchesInnervation pattern

Proximal Middle Distal MN

I Proximal quarter of belly

- Distal three-quarters of belly

-

II Proximal third of belly

Middle third of belly

Distal third of belly

-

III Proximal quarter of belly

Second quarter of belly

Distal half of belly

-

IV Proximal third of belly

Middle third of belly

Distal third of belly

-

V Proximal quarter of belly

Second quarter of belly

Third quarter of belly

Distal quarter of belly

MN - primary branch from median nerveMN - primary branch from median nerveMN - primary branch from median nerveMN - primary branch from median nerveMN - primary branch from median nerve

67

Figure 5.11. Type I: Intramuscular innervation pattern of ECRB. A. Posterolateral view. B. Lateral view.

68

Figure 5.12. Type II: Intramuscular innervation pattern of ECRB. A. Posteroateral view. B. Lateral view.

69

Figure 5.13. Type III: Intramuscular innervation pattern of ECRB. A. Posterolateral view. B. Lateral view.

70

Figure 5.14. Type IV: Intramuscular innervation pattern of ECRB. A. Posterolateral view. B. Lateral view.

71

Figure 5.15. Type V: Intramuscular innervation pattern of ECRB. A. Posterolateral view. B. Lateral view.

72

5.3 Fitting fiber bundle data to muscle volume and innervation obtained from different specimens

5.3.1 Fitting muscle fiber bundle architecture

Previously digitized fiber bundle data sets of each of ECRL and ECRB were fitted into

the volume and nerve data of each of the seven specimens digitized for this thesis. In the

coherent point drift (CPD) algorithm, the fiber bundle and volume/nerve data sets converged in

less than 50 iterations for all seven specimens of ECRL and ECRB. Examples of the fitted data

are shown in Figures 5.16 and 5.17.

Figure 5.16. Specimen S3 volume and nerve data fitted with fiber bundle data set. The fitted data for specimen S3 is quantified in Tables 5.2 and 5.3.

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Figure 5.17. Specimen S2 volume and nerve data fitted with fiber bundle data set. The fitted data for specimen S2 is quantified in Tables 5.2 and 5.3.

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5.3.2 Quantification of architectural parameters of fitted data

The fiber bundle length (FBL), distal pennation angle (PA1), proximal pennation angle

(PA2) and volume of the fiber bundle data set after it had been fit to muscle volume data, were

summarized with the original fiber bundle data set, referred to as S0 data (Table 5.3 and Table

5.4).

For both ECRL and ECRB fiber bundle length varied as a result of being fit to different muscle

volumes. The pennation angles of each of the fitted data sets (S1-S7) falls within the standard

deviation of S0 (Figures 5.18 and 5.19). The standard deviations of the pennation angles are

large because the data is amalgamated for the entire specimen, i.e. includes architecturally

distinct regions with considerable variation in pennation angles.

Table 5.3. ECRL: architectural parameters of the original fiber bundle data set (S0) and the seven specimens to which the data sat was fit (S1-S7).Table 5.3. ECRL: architectural parameters of the original fiber bundle data set (S0) and the seven specimens to which the data sat was fit (S1-S7).Table 5.3. ECRL: architectural parameters of the original fiber bundle data set (S0) and the seven specimens to which the data sat was fit (S1-S7).Table 5.3. ECRL: architectural parameters of the original fiber bundle data set (S0) and the seven specimens to which the data sat was fit (S1-S7).Table 5.3. ECRL: architectural parameters of the original fiber bundle data set (S0) and the seven specimens to which the data sat was fit (S1-S7).

Specimen FBL (cm) PA1 (°) PA2 (°) Volume (cm3)

S0 6.32 ± 1.62 10.35 ± 4.16 13.39 ± 8.11 30.57

S1 8.53 ± 2.28 8.39 ± 3.07 6.93 ± 5.21 25.78

S2 7.50 ± 2.04 6.62 ± 2.53 12.07 ± 6.56 31.01

S3 10.43 ± 1.32 7.85 ± 4.18 15.38 ± 7.43 51.16

S4 7.15 ± 3.12 14.46 ± 11.40 19.72 ± 9.53 21.23

S5 6.17 ± 1.76 10.91 ± 4.55 14.93 ± 11.11 23.88

S6 8.84 ± 2.86 11.74 ± 6.34 12.10 ± 7.32 36.01

S7 6.36 ± 1.55 11.49 ± 4.50 11.83 ± 6.58 16.61

V = volume, FBL = mean fiber bundle length ± standard deviation (SD), PA1 = mean distal pennation angle ± SD, PA2 = mean proximal pennation angle ± SD.V = volume, FBL = mean fiber bundle length ± standard deviation (SD), PA1 = mean distal pennation angle ± SD, PA2 = mean proximal pennation angle ± SD.V = volume, FBL = mean fiber bundle length ± standard deviation (SD), PA1 = mean distal pennation angle ± SD, PA2 = mean proximal pennation angle ± SD.V = volume, FBL = mean fiber bundle length ± standard deviation (SD), PA1 = mean distal pennation angle ± SD, PA2 = mean proximal pennation angle ± SD.V = volume, FBL = mean fiber bundle length ± standard deviation (SD), PA1 = mean distal pennation angle ± SD, PA2 = mean proximal pennation angle ± SD.

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Table 5.4. ECRB: architectural parameters of the original fiber bundle data set (S0) and the seven specimens to which the data set was fit (S1-S7).Table 5.4. ECRB: architectural parameters of the original fiber bundle data set (S0) and the seven specimens to which the data set was fit (S1-S7).Table 5.4. ECRB: architectural parameters of the original fiber bundle data set (S0) and the seven specimens to which the data set was fit (S1-S7).Table 5.4. ECRB: architectural parameters of the original fiber bundle data set (S0) and the seven specimens to which the data set was fit (S1-S7).Table 5.4. ECRB: architectural parameters of the original fiber bundle data set (S0) and the seven specimens to which the data set was fit (S1-S7).

Specimen FBL (cm) PA1 (°) PA2 (°) Volume (cm3)

S0 4.97 ± 0.68 7.66 ± 5.42 7.86 ± 5.26 27.14

S1 5.80 ± 0.87 6.16 ± 4.01 8.11 ± 6.36 23.63

S2 5.95 ± 1.21 6.97 ± 4.56 7.75 ± 4.62 28.99

S3 8.49 ± 1.41 7.29 ± 4.68 7.40 ± 4.71 41.87

S4 6.44 ± 1.05 6.42 ± 3.59 6.79 ± 4.41 37.14

S5 4.25 ± 0.91 7.37 ± 4.15 6.94 ± 4.52 24.45

S6 5.07 ± 1.72 8.39 ± 7.04 6.76 ± 4.33 21.16

S7 4.73 ± 0.90 8.19 ± 7.62 9.78 ± 6.38 12.77

V = volume, FBL = mean fiber bundle length ± standard deviation (SD), PA1 = mean distal pennation angle ± SD, PA2 = mean proximal pennation angle ± SD.V = volume, FBL = mean fiber bundle length ± standard deviation (SD), PA1 = mean distal pennation angle ± SD, PA2 = mean proximal pennation angle ± SD.V = volume, FBL = mean fiber bundle length ± standard deviation (SD), PA1 = mean distal pennation angle ± SD, PA2 = mean proximal pennation angle ± SD.V = volume, FBL = mean fiber bundle length ± standard deviation (SD), PA1 = mean distal pennation angle ± SD, PA2 = mean proximal pennation angle ± SD.V = volume, FBL = mean fiber bundle length ± standard deviation (SD), PA1 = mean distal pennation angle ± SD, PA2 = mean proximal pennation angle ± SD.

Figure 5.18. ECRL: Pennation angles of fiber bundle data set and specimens (S1-S7). A. Proximal pennation angle. B. Distal pennation angle.

Figure 5.19. ECRB: Pennation angles of fiber bundle data set and specimens (S1-S7). A. Proximal pennation angle. B. Distal pennation angle.

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5.3.3 Distribution of intramuscular nerves within the muscle volume at the fiber bundle level

The intramuscular distribution of the radial nerve within the ECRL and ECRB was

defined relative to fiber bundle architecture.

The anterior and posterior branches of the radial nerve had specific distribution in the

ECRL muscle belly. The anterior branch supplied the fiber bundles of the deep region of the

muscle belly and the posterior branch supplied the superficial region of the muscle belly (Figure

5.20). This was found in all seven specimens. The regional distribution pattern was distinct,

although there was some overlap of innervation at the margins of adjacent regions.

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Figure 5.20. Regional nerve supply of ECRL. A. Posterior branch of radial nerve in posterior region of muscle belly. B. Anterior branch of radial nerve in anterior region of muscle belly. C. Anterior and posterior regions combined.

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The intramuscular innervation of ECRB is dependent on the number of primary nerve

branches entering the muscle belly. In a specimen with two primary branches the muscle belly

was found to be divided into two regions, proximal and distal (Figure 5.21). Where three

primary branches were present, the muscle belly was divided into proximal, middle and distal

regions (Figure 5.22). In the case where the median nerve also innervated the muscle belly, four

regions were present (Figure 5.23). In this specimen, the middle region was found to be further

divided by innervation into superficial and deep regions. The proximal region was innervated by

a branch from the radial nerve proper, the superficial middle region by a branch from the deep

branch of the radial nerve and the deep middle region by a branch from the superficial branch of

the radial nerve. The distal region of the muscle belly was innervated by a branch from the

median nerve.

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Figure 5.21. Fiber bundle regions of ECRB specimen with two motor points. A. Proximal region (green). B. Distal region (red).

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Figure 5.22. Fiber bundle regions of ECRB specimen with three motor points. A. Proximal region (green). B. Middle region (blue). C. Deep region (red).

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Figure 5.23. Regions of ECRB specimen with four motor points. A. Proximal region (green). B. Superficial middle region (red). C. Deep middle region (blue). D. Distal region (black).

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5.4 Summary of findings

Fitting fiber bundle architecture to muscle volume

•The coherent point drift (CPD) algorithm was adapted for a novel application to fit digitized

fiber bundle data to muscle volume and nerve data from other specimens.

•The fitting algorithm enabled representation of fiber bundle architecture in the muscle volume

and quantification of fiber bundle length and pennation angles.

Modeling the intramuscular innervation of ECRL and ECRB at the fiber bundle level

•Extra- and intramuscular radial nerve distribution was modeled in the muscle volumes of ECRL

and ECRB, and at the fiber bundle level using the fitting algorithm.

•One primary branch from the radial nerve proper was found to innervate ECRL. This primary

branch divided into anterior and posterior branches that supplied the fiber bundles in the

superficial and deep regions of the muscle belly, respectively.

•Five innervation patterns were identified in ECRB using the source and number of primary

nerves supplying the muscle belly. The number of regions within the muscle belly depended on

the number of primary nerves supplying it.

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Chapter 6Discussion

6 Discussion Bio-mechanical models of muscle function and models of muscle architecture have

simplified muscles and groups of muscles to single lines or series of lines (Delp, et al. 1990;

Hoy, et al. 1990). Models that attempted to account for more complex muscle geometries did

this by defining a single fiber bundle arrangement pattern for the whole muscle to estimate the

fiber bundle geometry (Blemker & Delp 2005). These models could not account for regional

differences in fiber bundle architecture within the volume. However, three dimensional

modeling studies have used digitization to capture the complexity of a muscle’s architecture and

to model the fiber bundles throughout the muscle volume (Agur, et al. 2003; Fung, et al. 2009;

Kim, et al. 2007; Rosatelli, et al. 2008). These models of the entire muscle volume were used to

quantify fiber bundle architecture (Ravichandiran, et al. 2009). Each fiber bundle arrangement

was modeled as it is in situ in a cadaveric specimen, making it a representation of the actual fiber

bundles, not a generalized pattern. Intramuscular innervation has also been modeled using this

technique (Loh, et al. 2003).

The current study provided a novel application for the coherent point drift (CPD)

algorithm to fit digitized fiber bundle data to muscle volumes obtained from other specimens.

Since actual fiber bundle data are fit to muscle volumes, rather than estimates of fiber bundle

architecture, the model is able to represent the complexity and regional variation in fiber bundle

architecture within muscles. Another unique application of this fitting method was that it can be

used to relate fiber bundle architecture to nerve distribution in the muscle volume. This has not

been done previously.

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6.1 Fitting fiber bundle architecture to generic muscle volumes

6.1.1 Exploration of different methods

An algorithm used to fit fiber bundle architecture to muscle volume must:

•be able to scale different regions of the fiber bundle data by different scale factors in

order to account for variation within the muscle volume.

•maintain the overall fiber bundle arrangement, i.e. functional alignment of the fiber

bundles, while preserving the pennation angles of the fiber bundle data set.

The iterative closest point (ICP) algorithm and the cross-sectional fitting algorithm, which did

not meet the above criteria, will be discussed first, followed by the new application of the CPD

algorithm which was successful in fitting fiber bundle data to muscle volume data from a

different specimen.

The ICP algorithm, a rigid point set registration technique, assumes that the volume of the

two objects are the same. Therefore, the nature of the original implementation of the algorithm

made it impossible to use for fitting fiber bundle architecture to muscle volume from two

different specimens, which would have different sizes. The addition of the iterative scaling

component to the algorithm was intended to allow for fitting of data sets of different sizes and

geometry. However, two muscles from different specimens are very rarely the same geometry

throughout the volume of the muscle. Therefore, the rigid nature of the scaling meant that

natural variation in muscle shape between specimens could not be accounted for by the

algorithm.

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In an attempt to overcome the difficulties posed by the rigid fitting algorithm, fiber

bundle architecture was fit to muscle volume as cross-sections. However, fitting fiber bundle

architecture by sections provided new challenges. Of these, the primary challenge was the

rotational alignment of individual sections while maintaining the overall path of each fiber

bundle. Manual alignment by the investigator was a possibility that was considered, but the

subjectivity of this method resulted in too many errors and this technique would heavily depend

on the skill of the investigator. Therefore, this method was also not feasible.

Simply adding fiber bundles to the surface of the muscle, for fitting data into a larger

volume, or by removing fiber bundles, for fitting into a smaller volume is not a solution because

it changes the fiber bundle distribution within the volume of the muscle.

Finally, the coherent point drift algorithm was explored due to its non-rigid approach to

fitting data. This algorithm was designed to calculate the relationship of each point to every

other point in the data set, which resulted in a coherent movement of points. When adapted in

the current study to fit fiber bundle data to muscle volume, the architectural features of the

muscle were maintained. Since the algorithm used a non-rigid point set registration algorithm,

rather than a rigid scale factor, different regions of the muscle could be scaled using an

independent set of parameters.

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6.1.2 Using Coherent Point Drift (CPD) to fit ECRL and ECRB fiber bundle architecture to muscle volume

Coherent Point Drift was used to fit one fiber bundle data set into seven different muscle

volumes for each of ECRL and ECRB. After being fit to the muscle volume, the mean fiber

bundle length varied from that observed in the original data set, this difference was seen in both

ECRL and ECRB. One reason for this variation is the variation in overall muscle size, including

muscle volume.

Fitting the digitized fiber bundle data to a different muscle volume resulted in an increase

or decrease in the fiber bundle length. However, the pennation angle remained within the

standard deviations of the original specimen. The consistency seen in the pennation angle

supported integrity of this algorithm because it demonstrated that the fiber bundle arrangement

within the muscle volume was maintained after being fit into a new muscle volume. This is

important because fiber bundle arrangement determines the direction of muscle action and is one

of the determinants of muscle force generating capacity (R. L. Lieber & Friden 2000). The fiber

bundle arrangement pattern, and hence the direction of muscle action does not vary greatly from

specimen to specimen (R. L. Lieber & Friden 2000).

6.2 Modeling the intramuscular innervation of ECRL and ECRB at the fiber bundle level

Previous studies of radial nerve distribution in ECRL and ECRB have relied on

dissection, two-dimensional drawings and written documentation, and have mainly focused on

the extramuscular distribution of the radial nerve (Branovacki,etal.1998;El‐DinSafwat&Abdel‐

Meguid2007). A method of modeling the 3D intramuscular distribution of nerves within the

muscle volume using digitization was introduced in a study by Loh et al. (2003). In this current

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study, the method of Loh et al. (2003) was used to reconstruct the distribution of the radial nerve

and its branches within the muscle volume. The main innovation of the current study is the

development of a method of fitting fiber bundle data from one specimen to the same muscle of

any other specimen. Therefore, along with studying the distribution of nerves in muscle volume,

fiber bundles could be fit to these muscle volumes to study the relationship between fiber bundle

architecture and nerve distribution. The model could be manipulated to view nerve branching

from various perspectives. Color-coding enabled visualization of nerve branches, and the

regions of the muscle innervated by these branches.

6.3Neuromuscular compartments in ECRL

6.3.1 Extramuscular innervation of ECRL

The extramuscular innervation of ECRL has been found to consist of one or more

primary branches. Branovacki et al. (1998) and El-Din Safwat and Abdel-Meguid (2007) have

reported ECRL to be supplied by a single nerve, while Segal et al. (1991) found two nerves,

proximal and distal, and Chen et al. (2009), 1.8±0.7 primary extramuscular branches. In the

current study, all seven ECRL specimens were found to be innervated by a single nerve, which

originated from the radial nerve, proximal to its bifurcation into superficial and deep branches.

The nerve to ECRL was found to bifurcate into posterior and anterior branches, extramuscularly

in three specimens and intramuscularly in four specimens. Therefore, although each specimen

had only one primary nerve supplying ECRL, there could be one or two motor points.

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6.3.2 Relation of ECRL innervation pattern to muscle architecture

Most previous studies reported 2 to 3 intramuscluar branches in ECRL: Chen et al. (2009)

2.7±1.2 branches and Segal et al. (1991) one proximal and one distal branch. In the current study,

two intramuscular branches, anterior and posterior were found in all specimens. By fitting fiber

bundles into the muscle volumes with detailed intramuscular innervation, the current study

enabled the investigation of the presence of neuromuscular compartments in all seven specimens.

Muscle fiber bundles and intramuscular innervation cannot be concurrently digitized as portions

of fiber bundles must be removed to expose nerve segments. Using the fitted models, fiber

bundles innervated by individual nerve branches could be identified. Superficial and deep

regions, innervated by posterior and anterior, respectively, were found in all seven specimens.

The posterior branch was found to innervate the superficial one-third of ECRL, while the

anterior branch supplied the deep two-thirds, with some overlap in the margins of adjacent

regions. This corresponds to the architecturally distinct regions, superficial and deep, defined by

fibre bundle length and pennation angle by Ravichandiran et al. (2009).

Although Segal et al. (1991) also found superficial and deep regions based on

architecture, it was reported that the proximal branch supplied the superficial region of the

proximal part and deep regions of the muscle belly and the distal branch supplied the deep region

of the proximal part of the muscle belly. Segal’s study was descriptive and illustrated with line

drawings that lacked fiber bundle architectural detail. The findings of both Ravichandiran et al.

(2009) and Segal et al. (1991) suggest the presence of neuromuscular compartments.

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6.4 Neuromuscular compartments in ECRB

6.4.1 Extramuscular innervation of ECRB

Variation was observed in the number of primary nerves supplying the ECRB: 2 of 7 had

two primary nerves (Type I), 4 of 7 specimens had three primary nerves (Type II, III and IV),

while one ECRB specimen was found to be supplied by four primary nerves (Type V). Many

researchers (al-Qattan 1996; Branovacki et al. 1998; Colborn et al. 1993; Salsbury 1938) have

reported a single primary nerve but El-Din Safwat & Abdel-Meguid (2007) found one or two

primary nerves with two to five motor points.

In the current study, the origin of the primary nerves was variable. The proximal branch

was found to originate from the radial nerve or the superficial branch of the radial nerve, while

the middle and distal branches generally arose from the superficial or deep branch of the radial

nerve. In the specimen with four distinct nerves innervating the muscle (Type V), the most distal

nerve arose from the median nerve - this finding has not been previously documented. Previous

studies have found similar origins of the extramuscular nerves to ECRB (al-Qattan, 1996;

Branovacki, et al. 1998; Colborn, et al. 1993; Salsbury 1938).

6.4.2 Relation of ECRB innervation pattern to muscle architecture

In the current study, although the origin and number of primary nerves to ECRB varied,

all specimens showed a proximal to distal partitioning pattern, e.g. nerves which entered more

proximally supplied more proximal regions of the muscle. The number of partitions depended

on the number of primary branches. In a previous study, Ravichandiran et al. (2009)

reconstructed ECRB muscle architecture by using digitized fiber bundle data and found

proximal/superficial and distal/deep compartments. The use of fitted fiber bundle data in the

current study, suggests that there can be further partitioning of these architectural regions based

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on innervation. For example, if four primary branches were present, they innervated the

proximal region, superficial middle region, deep middle region and distal region independently

with some overlap between adjacent regions.

Only one previous study was identified which investigated the intramuscular innervation

of ECRB: Chen et al. (2009) reported 2.3±0.7 primary intramuscular branches; however, the

region of the muscle volume supplied by each of these branches was not discussed.

6.5 Functional relevance of neuromuscular compartments

Neuromuscular compartments have functional relevance since axons in a muscle nerve

branch supply isolated regions of muscle fibers, compartments within a muscle may be

differentially activated (Segal, et al. 2002). According to the partitioning hypothesis, a muscle

may be differentially activated depending on the required function of the muscle, thus allowing

multifunctional muscles to contribute to a variety of movement actions (Segal, et al. 2002).

This hypothesis is supported by a previous MRI study by Livingston et al. (2001),

exploring the spatial activation of ECRL and ECRB during extension and radial deviation. Non-

homogeneous activation of the muscle bellies was observed, with proximal and distal regions of

ECRL and ECRB showing differential activation. Significant differences in activation were also

observed during extension versus radial deviation. Livingston et al. (2001) analyzed the extensor

carpi radialis muscles as a unit, rather than separating the activation of ECRL and ECRB. The

proximal-distal functional partitioning of the ECRL-ECRB muscle complex found by

Linvingston et al. (2001) is congruent with the finding of proximal-distal neuromuscular

partitioning of ECRB in the current study, but is different from the finding of superficial-deep

neuromuscular partitioning of ECRL.

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Understanding the mechanism by which neuromuscular partitioning affects muscle

function remains limited. It is known that muscle architecture is a primary determinant of force

generation (R. L. Lieber & Friden 2000). Studies in mammalian muscles have suggested that

differential activation of neuromuscular compartments may translate to differences in the

magnitude, direction and distribution of force in the corresponding tendon (English, et al. 1993).

This is a potential mechanism by which differential activation of neuromuscular compartments

may contribute to the diverse force generation required for multifunctional muscles. Further

studies are needed to confirm this functional role for neuromuscular compartments in general, as

well as specifically in the human ECRL and ECRB muscles.

6.6 Clinical relevance

Investigating the innervation of ECRL and ECRB can contribute to the understanding of

injury and pathology of these muscles. Unlike previous studies, the methods used in the current

study allow the three-dimensional reconstruction of nerve distribution within muscle volume at

the fiber bundle level, and provide highly detailed documentation of extra- and intramuscular

innervation.

Radial nerve branch anatomy is relevant to treating nerve lacerations and compressions,

identifying the location of lesion and repairing damaged nerves (Abrams, et al. 1997). For

instance, selection of the site of botulin toxin injection to treat muscle spasticity, as well as

surgical reconstruction following injury or disease, can be enhanced by detailed knowledge of

innervation pattern (El-Din Safwat & Abdel-Meguid 2007). Similarly, knowledge of nerve

distribution can facilitate the insertion of electrodes for functional electrical stimulation, a

procedure which has been used to restore function to extremities paralyzed by injuries or

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cerebrovascular disorders (El-Din Safwat & Abdel-Meguid 2007). Finally, radial nerve branch

anatomy is relevant to disorders such as lateral epicondylitis, which may result from compression

of the radial nerve or its branches (Nayak, Ramanathan et al. 2009).

Rehabilitation can be enhanced by using knowledge of neuromuscular compartments to

predict the “rate and order of motor recovery” (Abrams, et al. 1997). Procedures such as surgical

partitioned tendon transfer may be enhanced by selecting donor muscles with similar functional

capabilities and partitioning/architecture to the original muscle (R. L. Lieber & Friden 2000). In

particular, because of its central position of insertion on the wrist and its contribution to wrist

extension, the ECRB is often a recipient for tendon transfers following nerve or spinal injury

(Doyle & Botte 2003). Chen et al. (2009) found that both ECRL and ECRB were type II

muscles as classified by Lym’s classification and suggested that these muscles “are easy to split

into independent parts for muscular flap transfer according to morphology and intramsucular

neurovascular distribution.” This emphasizes the importance of understanding neuromuscular

compartments for restoring function following injury.

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Chapter 7Conclusions

7 Conclusions

7.1 Fitting fiber bundle architecture to muscle volume from different specimens

1. The Coherent Point Drift algorithm was adapted to create a novel method of fitting fiber

bundle architecture from digitized cadaveric specimens to volumes of the same muscle

obtained from any other specimen.

2. Fiber bundle architecture from one specimen was fitted to seven digitized extensor carpi

radialis longus (ECRL) and brevis (ECRB) muscle volumes and the architectural parameters

were compared. The overall fiber bundle arrangement was maintained.

7.2 Neuromuscular compartments in ECRL and ECRB

1. The intramuscular nerve distribution in ECRL and ECRB was documented through

digitization and three-dimensional modeling, at greater detail than had been previously done.

2. Using the CPD algorithm, fiber bundle data were fit to the digitized ECRL and ECRB volume

and nerve data of seven specimens. The fitted fiber bundle data were used to study the

relationship between intramuscular nerve distribution and fiber bundle architecture. This has

not been previously possible.

3. ECRL: A single primary branch with two branches, anterior and posterior, innervating the

deep and superficial regions, respectively, were found in all seven specimens. The fiber

bundles were found to have superficial-deep partitioning based on nerve distribution.

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4. ECRB: Two, three or four primary branches were found innervating the muscle volume. The

number of partitions corresponded to the number of primary nerves supplying the muscle

belly. In specimens with two or three primary nerves (n=6), the fiber bundles of the ECRB

were found to be divided in a proximal to distal direction based on this innervation. In one

specimen with four nerve entry points, the middle region was further divided into superficial

and deep regions.

Limitations

2. After fitting fiber bundle data to the muscle volume and nerve data, it is possible to use the

nerve distribution in the fiber bundles to identify possible neuromuscular compartments.

These compartments may have functional implications, however further study is required

using methods such as intra-operative stimulations of nerves, fMRI and EMGs.

3. Only one fiber bundle data set was fit to the seven muscle volume specimens. It was assumed

that the muscle architecture was relatively consistent from one specimen to the next.

However, fitting more than one specimen to each muscle volume would allow for comparison

of the results of different fiber bundle data sets being fit to each muscle volume data set.

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Chapter 8Future Directions

8 Future DirectionsThe ability to fit fiber bundle architecture to muscle volume has numerous applications

beyond the study of neuromuscular compartments. Some of the areas of future exploration

include:

• Obtain magnetic resonance imaging scans of extensor carpi radialis longus (ECRL) and

brevis (ECRB) in vivo to construct a database of external volume data for these muscles.

Use the developed methods of this thesis to fit the architectural data to these models

using the software developed. Implementation of this method would allow for a means of

investigating in vivo muscle architecture using the external muscle volume as a guide.

• Develop a database of the muscle architecture of all skeletal muscles found within the

human body to construct a parametric model of human muscle architecture that can be

applied to any in vivo volumetric muscle data that lack internal architectural data.

• Biomechanical muscle models can be made more robust with the use of actual fiber

bundle architecture to represent muscles. In addition, mechanisms to include physical

properties, i.e. tensile strength, Young’s modules, etc., of the fiber bundles to the

computer model may be explored further to enhance the model’s capabilities.

• In vivo ultrasound protocols could be developed to study the static and dynamic

architecture of each of the neuromuscular compartments in ECRL and ECRB.

• EMG and intra-operative nerve stimulation could be used to study the activation patterns

of the neuromuscular compartments in ECRL and ECRB.

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Transformation of muscle architecture at the fiber bundle - T-Space

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