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THESiS

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LIBRARY

Michigan State
University

 

 

 

This is to certify that the

thesis entitled

Development and Validation of a
C omputer Model of the Equine Tarsal Joint

presented by

Adam Karekin Arabian

has been accepted towards fulfillment
of the requirements for

Masters d . Mechanical Engineering
egree 1n

 

 

 

UMajor professor

Date £61721 Q8, 2000

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

PLACE IN RETURN Box to remove this checkout from your record.
TO AVOID FINE return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE

DATE DUE

DATE DUE

 

W? 9 2062

 

 

 

 

 

 

 

 

 

 

 

 

 

moo chiRC/DfiDmpfiS-p.“

 

 

 

DEVELOPMENT AND VALIDATION OF A COMPUTER MODEL OF THE
EQUINE TARSAL JOINT

By

Adam Karekin Arabian

A THESIS
Submitted To
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Mechanical Engineering

2000

ABSTRACT
DEVELOPMENT AND VALIDATION OF A COMPUTER MODEL OF
THE EQUINE TARSAL JOINT
By

Adam Karekin Arabian

The equine tarsal joint is the site of a high percentage of hindlimb lameness
cases seen in veterinary medicine. In order to better understand the defining
morphology of the tarsal joint, a computer model of the joint was developed.
Computerized tomography (CT) scans were taken of the disarticulated bones
of the joint and edge detection was performed on the resultant images. The
edge data were translated into a format readable by an engineering design
software package, and the three-dimensional points were used in the
definition of solid models of the bones of the tarsal joint. As an example of
the model’s utility, it was used to evaluate the generally held assumption
that all motion of the tarsal joint occurs at the articulation of the tibia and
talus. The motion of the tibia with respect to the metatarsus was determined
based on the curvature and orientation of the talar trochlea, and compared to
the motion determined from experimental kinematic analysis. The results
indicated that the tibia demonstrated motion not fully explainable by the
morphology of the talus, and hence it was determined that some amount of

tarsal joint motion must occur at the intertarsal and tarsometatarsal joints.

Acknowledgments

I would like to thank my supervisors, Professor Hilary M. Clayton of
the Michigan State University Department of Veterinary Medicine, and
Professor Ranjan Mukherjee of the Michigan State University Department of
Mechanical Engineering for their support and guidance during the course of
this research and the writing of this thesis. My sincerest appreciation is also
expressed to Joel Lanovaz, Manager of the McPhail Lab for Equine Sports

Medicine, for his technical assistance and support throughout this research.

I would also like to express my gratitude to my friends and family, without

whose support I could not have completed this research.

This research was supported in part by the Mary Anne McPhail Endowment,

to which I am indebted

iii

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table of Contents

LIST OF TABLES vi
LIST OF FIGURES - vii
GLOSSARY ix
1. INTRODUCTION 1
1.1. HISTORICAL PERSPECTIVE ................................................................ .. ....... 1
1.2. EQUINE BIOMECHANICS .................................................................................................................... 4
1.3. COMPUTER MODELS IN BIOMECHANICS ............................................................................................ 5
1.4. RESEARCH OBJECTIVES ........................................................................................... - - 7

2. ANATOMY OF THE EQUINE HINDLIMB 8
2.1. STRUCTURE AND MORPHOLOGY ...... - 8
2.2. ANATOMY, MOTION, AND PATHOLOGY OF THE TARSAL JOINT 10
2.2.1. Bones of the Tarsal Joint 10
2.2.2. Inter-tarsal Joints ....... - - 12
2.2.3. Pathologies of the Tarsal Joint ............... - - l3

3. METHOD OF INVESTIGATION 15
3.1. COLLECTION AND PREPARATION OF ARTTCULATED SPECIMEN OF THE TARSAL JOINT .................... 15
3.2. COMPUTERIZED TOMOGRAPHY SCAN OP ARTICULATED TARSAL JOINT ......................................... 15
3.3. PREPARATION OF DISARTICULATED TARSAL BONES - 16
3.4. COMPUTERIZED TOMOGRAPHY SCAN OF DISARTICULATED TARSAL BONES .................................. 18
3.5. IMAGE PROCESSING .......................... ............................. 19
3.6. EDGE DETECTION ALGORn'HM ....................................................................................................... 20

iv

3.7. CREATION OF THE SOLID MODEL.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

................ 24

3.8. DEVELOPMENT OF TOOL FOR MODEL VISUALIZATION .............................. 29
3.9. MODEL VALIDATION BY VOLUMETRIC MEASUREMENTS ....................................... 32
3.10. APPLICATION OF MODEL ............................................................................................................ 33

4. RESULTS 42
4.1. COMPUTER MODELS OF THE BONES OF THE TARSAL JOINT ............................................................ 42
4.1.1. Tibia ...................................................................................................................................... 43

4. 1.2. Talus ..................................................................................................................................... 44

4. 1.3. Calcaneus .......................................................... 45

4. I .4. Central and Third Tarsal Bones ........................................................................................... 46
4.1.5. First and Second Tarsal Bone and Fourth Tarsal Bone ....................................................... 48
4.1.6. Metatarsus ................................................................................................. 49

4.2. RESULTS OF VOLUMETRIC MEASUREMENTS. ..................................... 50
4.3. APPLICATION OF MODEL T0 PREDICTION OF MOTION OF THE TARSAL JOINT ..... 51
4.3.1. Stance phase ................................................................................... 54
Swing Phase . - - .- ............................................ 57

5. DISCUSSION 59
5.1. MODELING TECHNIQUES 59
5.2. MODEL VALIDATION BY VOLUMETRIC MEASUREMENTS - 64
5.3. APPLICATION OF MODEL IN THE EVALUATION OP TARSAL JOINT KINEMATICS 65

6. CONCLUSION AND FUTURE STUDIES 70
REFERENCES - 73

 

List of Tables

TABLE 1. NUMBER OF CROSS SECTIONAL CURVES AND SURFACES IN COMPUTER MODEL OF EACH BONE... 43

TABLE 2. COMPARISON OF SPECIMEN VOLUMES AND CAI£ULATED VOLUMES OF COMPUTER MODELS ..... 50

FIGURE I.

FIGURE 2.

FIGURE 3.

FIGURE 4.

FIGURE 5.

FIGURE 6.

FIGURE 7.

FIGURE 8.

FIGURE 9.

FIGURE 10.

FIGURE 11.

FIGURE 12.

FIGURE 13.

FIGURE 14.

FIGURE 15.

FIGURE 16.

FIGURE 17.

FIGURE 18.

FIGURE 19.

FIGURE 20.

FIGURE 21.

FIGURE 22.

FIGURE 23.

List of Figures

COMPARISON OF ANATOMY BETWEEN THE HUMAN LEG AND EQUINE HINDLIMB (EQUINE SPECIFIC

 

 

 

 

NAMES IN PARENTHASEs) .............................................................................. -- 8
RIGHT TARSALIOINT, CRANIAL VIEW ......................................................................................... 10
RIGHT TARSAL JOINT, MEDIAL VIEW ........................................... ....... 10
RIGHT TARSAL JOINT, CRANIAL VIEW ....................................................... 12
RIGHT TARSAL JOINT, MEDIAL VIEW .............................................................. 12
FINAL DESIGN OF COORDINATE APPARATUS ............................... . 18

 

CROSS SECTIONAL IMAGE OF THE TARSUS TRANSECTING THE CALCANEUS AND TIBIO’TARSAL

JOINT ....................... .. ................. -- ...... - ...... 23

 

 

CROSS SECTIONAL OF IMAGE AFTER APPLYING THE CANNY EDGE DETECTION ALGORITHM

 

 

 

 

 

 

(SCHNUCK, 1986) ....................................................................................................................... 23

CROSS SECTION CURVES USED FOR LOFT DEFIN ITION ON THE METATARSUS - 27
RESULTANT SURFACE FROM THE LOFTING TECHNIQUE ON THE METATARSUS ........................ 27
CROSS SECTION AND RAIL CURVES USED FOR SURFACE DEFINrIION ON THE CALCANEUS ...... 28
RESULTANT SURFACE FROM THE MESH OF CURVES TECHNIQUE ON THE CALCANEUS ............ 28
CURVE GRID USED FOR SURFACE DEFINmON ON PROXIMAL SURFACE OF THE METATARSUS. 29
RESULTANT SURFACE FROM THE SURFACE STITCHING TECHNIQUE ON THE METATARSUS ..... 29
DIRECTX ANIMATION VIEWER ..................................... 31
ROTATION AL AXIS DEFINmONS USED IN ANALYSIS OF JOINT ANGLES 34
MARKER LOCATIONS USED ON THE TIBIA FOR KINEMATIC DATA COLLECTION ...................... 35
MARKER LOCATIONS USED ON THE METATARSUS FOR KINEMATIC DATA cou.ECIION .......... 35
EXPERIMENTAL SETUP FOR KINEMATIC DATA COLLECIION 36
METATARSAL. TALAR, AND TIBIAL COORDINATE SYSTEM DEFINmONS FOR MODEL BASED
ANALYSIS ................................................................................................... 38
DISTAL END OF TIBIA ....................................................................... - - 43
COMPUTER MODEL OF DISTAL TIBIA ...................................................................................... 43
TALUS SPECIMEN ................................................................................................................... 44

FIGURE 24.

FIGURE 25.

FIGURE 26.

FIGURE 27.

FIGURE 28.

FIGURE 29.

FIGURE 30.

FIGURE 31.

FIGURE 32.

FIGURE 33.

FIGURE 34.

FIGURE 35.

FIGURE 36.

FIGURE 37.

FIGURE 38.

FIGURE 39.

FIGURE 40.

FIGURE41.

FIGURE 42.

FIGURE 43.

FIGURE 44.

FIGURE 45.

FIGURE 46.

FIGURE 47.

FIGURE 48.

 

COMPUTER MODEL OF TALUS. - ....... - 44

 

 

 

 

 

 

CALCANEUS SPECIMEN .......................................................................................................... 45
COMPUTER MODEL OF CALCANEUS ....................................................................................... 45
CENTRAL TARSAL BONE SPECIMEN ........................................................................................ 46
COMPUTER MODEL OF CENTRAL TARSAL BONE ......................................... - . 46
THIRD TARSAL BONE SPECIMEN 47
COMPUTER MODEL OF THIRD TARSAL BONE .......................................................................... 47
FIRST AND SECOND TARSAL BONE SPECIMEN ......................................................................... 48
COMPUTER MODEL OF FIRST AND SECOND TARSAL BONE ...................................................... 48
FOURTH BONE SPECIMEN- - -- ......................... - . 48
COMPUTER MODEL OF FOURTH TARSAL BONE ....................................................................... 48
PROXIMAL END OF METATARSUS SPECIMEN .......................................................................... 49
COMPUTER MODEL OF PROXIMAL METATARSUS ..... - - ............. 49

 

PREDICTED ABDUCTIONIADDUCTION ANGIE VS. FLEXION/EXTENSION ANGLE BASED ON

ANALYSIS OF MORPHOLOGY OF TALUS AND TIBIA - - 52

 

PREDICTED INTERNAUEXTERNAL ROTATION ANGLE VS. FLEXION/ EXTENSION ANGLE BASED

 

 

 

 

 

 

 

ON ANALYSIS OF MORPHOLOGY 0F TALUS AND TIBIA 53
FLEXION/EXTENSION ANGLE VS. ABDUCTIONIADDUCTION FOR STANCE PHASE ..................... 54
FLEXION/EXTENSION VS. INTERNAIJEXTERNAL ROTATION FOR STANCE PHASE ..................... 55
FLEXION/EXTENSION VS. ABDUCTIONIADDUCTION ANGLE FOR SWING PHASE ....................... 57
FLExION/EXTENSION VS. INTERNAI/EXTERNAL ROTATION FOR SWING PHASE ...................... 58
SECITON OF ORIGINAL IMAGE -- .................................................. 64
ROBERTS EDGE DETECIION OF SELECTED REGION .................................... 64
CANNY EDGE DETECIION OF SELECTED REGION ...... - ....... 64
SECITON OF ORIGINAL IMAGE .......... ..... - - - - 64
SOBEL EDGE DETECTION OF SELECTED REGION ......... . - - - ................................ 64
CANNY EDGE DETECTION OF SELECTED REGION .................................................................... 64

viii

Internal
Rotation

Abduction

Adduction

Biomechanics

Equine
Etiology
Extension
External
Rotation

Flexion

in vitro
in viva
Kinematic

Lameness

Lateral

Medial

Glossary

Positive rotation about the axis defined by the long
axis of the bone

Increase in segment angle with respect to the midline
of the body

Decrease in segment angle with respect to the midline
of the body

The application of engineering principles to the study
of biological systems

Of or pertaining to a horse
A scientific account of the causes of a disease

Increase in saggital plane angle between two
segments

Negative rotation about the axis defined by the long
axis of the bone

Decrease in saggital plane angle between two
segments

Dealing with cadaver specimens
Dealing with live Specimens
The study of the motion of bodies

Abnormal locomotion resulting from an injury or
physiological defect

With respect to the limb, the side which faces away
from the body, perpendicular to a line between the
head and tail

With respect to the limb, the side which faces towards

the centre of the body, perpendicular to a line between
the head and tail

ix

Morphology

Palmar

Proximal

Saggital

Trotting

The science of the forms and structures of organisms
In the digit, this refers to the rear facing side of the
digit

In the limb, the longitudinal direction towards the
body of the horse

A vertical plane through the animal parallel to the
median plane

A gait in which the forelimb and the diagonally
opposite hind limb move as a unit and in opposition to
the other diagonal pair

1. Introduction

1.1. Historical Perspective

Interest in equine locomotion dates as far back as the Shang dynasty (1750 —
1045 BC). In ancient China, the fimdamental importance of the horse in war
and agriculture necessitated the expansion of understanding and treatment
of lameness in the equine limb (Chang, 1980). Similar interest appeared
later in ancient Greece, where in 380 BC Xenophon authored his treatise The
Art of Horsemanship (Xenophon, 380 BC). This and a similar study by
Aristotle at approximately the same time on the equine locomotor system
(Aristotle, 360 BC) remained the definitive works in the western world on the

nature of human and horse interaction throughout the next two millennia.

The importance of the horse, and hence the importance of developing a
fundamental understanding of the pathologies in the horse, cannot be
understated. For centuries, beginning with the nomadic warriors in
Mongolia and the Ukraine and proceeding to the highly effective cavalry of
the late 19‘” century, there have been few sights more intimidating on the
battlefield than the figure of a mounted warrior. During these years, the

1

numerous advances in the technology pertaining to the use of horses as
instruments of war and agriculture revolutionized the military, economic,

and political systems around the world.

The horse continued to play a significant role in both warfare and agriculture
until early in the 20"I century when its utility was eroded by the development
of the internal combustion engine, resulting in a loss of military importance
and the inevitable replacement of the horse in civilian use by automobiles
and tractors. The loss of the practical need did not, however, negate the bond
that had developed between man and horse over the previous centuries. The
overall economic growth seen in the United States and western Europe
through the years following the second world war has resulted in a
resurgence of horse ownership for both equestrian sports and as companion
animals. This is evidenced by the increased popularity of equestrian events
such as the world equestrian games, the Rolex circuit, and the Olympic

competitions.

This increase in ownership coincided with a renewal of interest in the study
of equine sports science. This field, which had been actively pursued in
Germany during the inter-war period by pioneers such as Wiechert (1927),
Moskovits (1930), Kadletz (1937), and Kruger (1937, 1938), was left
languishing in the post-war period in Germany as focus shifted from

scientific pursuits to reconstruction (van Weeren, In Press). Slowly, however,

2

as economies recovered, horses ownership was once again feasible, and hence
research into equine gait and gait pathologies was once again an area of
active pursuit. The Shifi in horse usage from transportation and farm work
to competitive sports required a more strenuous exercise schedule, which
brought a need for a deeper understanding of equine locomotion. The focus
was shifted from functionality to highly efficient performance (van Weeren,

In Press) and treatment of injuries.

By far the most common equine injuries studied and treated in veterinary
medicine are those of the locomotor apparatus (Rossdale et a1, 1985),
collectively referred to as lameness. Throughout the 19708, 19803, and 1990s,
a substantial body of work has been accumulated that has fundamentally
revolutionized the understanding of the equine locomotor apparatus and,
hence, improved the effectiveness and quality of life of the sport horse. In
spite of this, however, the understanding of equine locomotion remains
limited, particularly as compared to the status of similar research into

human locomotion.

1.2. Equine Biomechanics

In order to be an efi'ective rider, it is necessary to have a fundamental
understanding of the motion of the horse. Hence, studies of equine
biomechanics can be tangentially seen in every study on effective
horsemanship, from Xenophon (380 BC) to de Pluvinel (1626) to modern
masters of equitation such Charles de Kunffy and Richard Shrake. As
previously stated, however, scientific studies have been far less numerous
and were limited by the available technology until the advent of
computerized data collection and modeling methods. These tools have
dramatically increased both the quantity and quality of data available to
researchers in the general biomechanics community as well as that dedicated

to the study of equine locomotion.

Some research has been performed in the area of animal gait analysis using
techniques practiced in human medicine. Equine and canine locomotion have
been regularly studied in order to improve athletic performance and to

improve understanding of the causes, symptoms, and treatment of lameness.

Gait analysis typically involves the measurement of temporal, linear, and
angular kinematics, ground reaction forces, joint moments, and/or joint

powers. Through the observation of these parameters, normal gaits can be

4

characterized and pathologies can be detected earlier and treated more

effectively (Whittle, 1991).
1.3. Computer Models in Biomechanics

The use of computer models revolutionized the study of locomotion.
Beginning in 1969 with the first two-dimensional analysis of the human arm
(Chaffin, 1969), to recent advances in surgical techniques utilizing computer
models to prepare for difficult procedures (McGurk et al, 1997), computer
models have allowed the study of the interactions of complex bones, muscles,
and soft tissue. These studies have resulted in improved artificial joints,
advancements in clinical diagnosis of musculo-skeletal disease, and a better

comprehension of the mechanical interactions within joints.

The primary focus of A much of the work performed in human anatomy is the
creation of accurate models of joints. These models, generally of a single joint
such as the hip (Tsumura et a1, 1998) or knee (Sathasivam and Walker,
1997), or occasionally of more complex areas such as the hand (Buford and
Thompson, 1987; Van Sint Jan et a1, 1997 ), or ankle (Delp et al, 1990), are
able to demonstrate the natural motion of the bones within the joint as well
as to provide a basis for more accurate dynamic simulations and analyses. In

spite of the importance and significance of many of these human studies, cost

and technical challenges have limited the use of these techniques in the study

of animal locomotion.

A few notable examples of research utilizing computer models to study the
structure and function of the equine locomotor apparatus Should be
mentioned. These include comprehensive dynamic models (van den Bogert et
al, 1989), limb specific models pertaining to kinematics and joint moments
and powers (Colborne et al, 1998; Lanovaz et al, 1999), and models focusing
on the dynamic or static loading and response of specific segments such as
the sesamoid bones of the metacarpophalangeal joint (Cheung and Thompson
1994), metacarpus (Les, et a1 1997), and hoof (Hogan 1991). These models
have proven invaluable in the general understanding of the nature of equine
locomotion and the process of adaptive development of the equine skeletal

structure.

Although these studies remain the most comprehensive research performed
in this field to date, a great deal of work remains to be done in the
development of accurate and specific joint models, particularly in regions of
high degrees of complexity. In humans, analysis has been performed to
create gross models of gait, and specialized models have been developed to
analyze the interactions of particular joints. Special emphasis has been
placed on the human hip and knee due to the overall importance of

quantifying the effect of medical procedures involving the replacement of

6

these joints. Interest in horses, however, typically focuses on the stifle,
carpus, tarsus, and fetlock, due to the high incidence of lameness originating

at these joints.
1.4. Research Objectives

The focus of this research is to develop a method of creating an accurate and
comprehensive model of the equine tarsal joint and to validate the model for
o
its accuracy and utility. This research, in addition to its benefits as a tool for
understanding the complexities of equine locomotion, has the potential of
being extended into a more comprehensive model of the tarsus that will
include information on the dynamic loading throughout the gait. Theifinal
goal is to develop a sufficiently accurate computer model so as to provide a
basis for future studies that would allow for improved clinical procedures in

cases pertaining to tarsal joint injuries, and limit the necessity of using live

subjects in the study of tarsal joint mechanics.

2. Anatomy of the Equine Hindlimb

2.1. Structure and Morphology

The horse is by its nature a cursorial (running) species. The survival of the
animal was innately dependent on its ability to outrun predators. Because of
this, the evolution of its locomotor apparatus was towards speed and economy

of movement (Figure 1).

  
   
  
 
 

 

Pelvic Girdle

 

Hip joint

 

 

Femur

Knee (Stifle) joint

/ Tibia
‘ " me (Tarsal) joint

_. .1 / Metatarsus
: / phalanges
. r - . _ 1. .

Figure 1. Comparison of anatomy between the human leg and
equine hindlimb (equine specific names in parenthases)

 

 

 

 

 

K

8

To achieve optimal efficiency, the limbs of the horse have adapted for planar
motion. The bones at joints interlock tightly and are constrained by
collateral ligaments to prevent out-of-plane motion. Additionally, the fibula
and tibia have fused; and only a single functional digit exists, both of which

serve to prevent rotation of the distal limb.

In order to increase the efficiency of gait, the heavy muscle mass is confined
to the proximal limb. Joints distal to the tarsus are controlled by long
tendons that cross the tarsus and attach to muscles in the proximal limb.
This results in an overall shifting of the mass moment of inertia closer to the
body, allowing for much faster motion of the limbs than would be possible .

with additional mass in the distal segments.

The metatarsus and phalanges are elongated, and elevate the tarsus from the
ground. The horse moves in an unguligrade stance, which is to say that it
walks on the tips of the phalanges (like a ballerina “on point”). This serves to
increase the effective limb length, hence increasing the overall stride length
and subsequently the top Speed of the animal. This is as opposed to human
stance, referred to as plantigrade, with the metatarsals and phalanges
parallel to ground during weight bearing, or the digitigrade canine stance, in
which the phalanges are parallel to the ground but the metatarsals are

elevated.

2.2. Anatomy, Motion, and Pathology of the Tarsal Joint

2.2.1. Bones of the Tarsal Joint

   
 
 
 

      

Plantar
Lateral
As t
Aspect P9c
Talus
Fourth Tarsal
Fourth Tarsal

Central Tarsal First and second

Third Tarsal ‘ 7 ‘ tarsal (fused)

Metatarsus

Figure 2. Right tarsal joint, Figure 3. Right tarsal joint,
cranial view medial view

The tarsus is a composite joint located distal to the tibia and proximal to the
metatarsus (Figures 2 and 3). The joint capsule itself contains all or parts of
the tibia; calcaneus; talus; central tarsal; the first through fourth tarsal

bones; and the second, third, and fourth metatarsal bones.

10

It is worthwhile to note here the unique morphology of a few of these bones;
the first and second tarsal bones are fused at birth and, hence, move
collectively as a single unit. The second and fourth metatarsals are, in fact,
vestigial remnants of ‘digits’. These bones, attached via ligaments to the
third metatarsal, extend the surface area of the third metatarsal and are of

little importance independently except for cases of inflammation or fracture.

The calcaneal tuberosity serves as a lever arm for the insertion for the
gastrocnemius, biceps femoris, and semitendinous muscles, as well as serving
as an attachment for the superficial digital flexor tendon. The calcaneus also
affords protection for the deep digital flexor tendon as it runs over the
sustentaculum tali (a groove on the talus). The calcaneus is stabilized by the
long plantar ligament that connects to the metatarsus on its plantar aspect.
Accessory ligaments assist in supporting the joint. These ligaments originate

on the talus and calcaneus and insert primarily onto the metatarsals.

11

2.2.2. Intertarsal Joints

     
  
 

  
  
    
 

Tibiotarsal
or
alocrura

joint
(articulation
of Talus and
tibia)

‘ \Proximal Intertarsal

joint
Distal intertarsal
joint
Tarsometatarsal
joint
Figure 4. Right tarsal joint, Figure 5. Right tarsal joint,
cranial view medial view

The tibia interfaces with the talus Via the tibiotarsal or talocrural joint,
constrained by the talar trochlea (ridges) that define the rotation of the joint.
A majority of the motion at the tarsal joint as a whole occurs at the
tibiotarsal articulation (Schamhardt et al, 1984; Badoux, 1987), and occurs in
the sagittal plane, though all horses show a degree of out of plane tarsal
motion due to the oblique orientation of the trochlea of the talus. The
proximal and distal intertarsal joints allow some degree of sliding motion, but

are constrained by collateral ligaménts around the tarsus. Similarly, the

12

motion of the tarsometatarsal joint is restricted by the collateral ligaments,
and it is generally accepted that there is virtually no motion at this joint. As
a whole, the complexities of the articulated surfaces as well as the
surrounding ligaments greatly constrain the motion of the joints distal to the
tibiotarsal, resulting in a limited range of motion as described by Schamhardt

(1984) and Badoux (1987).

2.2.3. Pathologies of the Tarsal Joint

A number of pathological conditions affect the tarsal joint. One of the most
common is bone spavin, an osteoarthritic degenerative joint disease. It
typically affects the medial aspect of the distal intertarsal and
tarsometatarsal joints (Adams, 1977). This condition results in pain during
flexion of the tarsus, which results in a reduced flight arc and a Shortening of
the stride (Adams, 1977 ). Treatment of this condition typically involves anti-
inflammatory medication, sometimes in combination with corrective shoeing
or, in more serious cases, surgical intervention to denervate or fuse the
affected joints. In spite of these treatments, more than half of the horses
diagnosed with spavin do not respond and remain chronically lame (Adams,

1977).

Additional pathologies related to tarsal joint lameness include tendon and

ligament inflammation induced by injury or abnormal abrasion due to poor

13

conformation. One of the most common is curb, in which the plantar
ligament that stabilizes the calcaneus becomes inflamed (Adams, 1977).
Although mild cases are easily treated with anti-inflammatories
(administered orally, topically or by injection), cases due to poor conformation

tend to recur and become chronic.

These and other pathologies of the tarsal joint remain difficult to treat due to
the complexity of the joint. Additional understanding of the kinematics of
normal and pathological locomotion could substantially improve our
understanding of the etiology, diagnosis, and treatment of tarsal joint

lameness.

14

3. Method of Investigation

3.1. Collection and Preparation of Articulated Specimen of the

Tarsal Joint

The specimen used in the development of the computer model was harvested
from a six-year—old thoroughbred euthanized by the Michigan State
University College of Veterinary Medicine, Department of Large Animal
Clinical Sciences. The subject was euthanized for reasons unrelated to
locomotion. The specimen was harvested by transectingthe hindlimb
through the middle of the tibia, and also transecting the middle of the
metatarsus. This was performed within 30 minutes of euthanasia, and the

specimen was subsequently frozen until the data were collected.

3.2. Computerized Tomography Scan of Articulated Tarsal Joint
The first step in the development of the kinematic model of the joint was the
creation of accurate computer models of the bones comprising the joint.

Computerized tomography (CT) scans were taken of the fully articulated

15

joint. The scans were taken on a General Electric 9800 CT machine (General
Electric Medical Systems, Waukesha, WI) at 120 kV and 120 mA. The small
field of view was selected, resulting in a pixel to millimeter ratio of 2.048.
Scans were taken at 3 millimeter increments with an exposure time of 2
seconds. The scan data were recorded to 10.5” reel tape, which was
subsequently downloaded to a Sun UltraSparc 1 workstation (Sun

Microsystems, Palo Alto, CA).

3.3. Preparation of Disarticulated Tarsal Bones

After scanning the fully articulated joint, it was disarticulated. The initial
separation was performed using standard dissection techniques to isolate the
bones and remove the collateral ligaments which support the joint. In order
to separate the central tarsal and third tarsal bones, which have a large
amount of connective tissue deep within the joint capsule, as well as to
remove the remaining connective tissue, the joint was placed in a skeletal
preparation box containing dermestid beetles (genus Dermestes), which are
commonly used in the preparation of anatomical specimens as they consume

soft tissue without degenerating the bone.

To restrict the motion of the loose bones during the process of CT scanning,
they were embedded in silicone in a cylindrical container. Previous research

indicated that the x-ray diffusion of a non-metallic substrate silicone was

16

sufficiently different from that of bone as to allow clear differentiation of the
two (Ocello and Rosenstein, unpublished data). After pouring the silicone
around the separated tarsal bones, the container was placed in a vacuum to
degassify for a period of 30 minutes, then left to cure at room temperature

and ambient pressure for two days.

In order to reconstruct the three-dimensional structure of the bones following
scanning, it was necessary to provide a fixed set of points that were visible in
all scans that would indicate the three-dimensional position of the bones. An
additional concern in the construction of this reference frame was that
metallic substances could not be used, as they have high levels of x-ray

absorptivity which degrades the quality of the CT scan.

The final design for the coordinate axis definition consisted of two nylon
wires, 0.4 mm in diameter, stretched taught above the bone and silicone. The
wires were attached via angle brackets to a wood frame with an angle of
approximately 90 degrees between them. The silicone/bone matrix container

was then secured to the wood frame by epoxy resin.

17

 

Figure 6. Final design of coordinate apparatus

3.4. Computerized Tomography Scan of Disarticulated Tarsal

Bones

CT scans were subsequently taken of the container containing the tarsal
bones embedded in silicone. This assembly was scanned along two axes
approximately 90 degrees from each other. This was necessary due to the
limits on resolution of CT scans. Each scan consists of a cross-sectional
image of the scan region. This results in a high resolution image in the scan
plane, but along the axis of the scan the sequence of images are of much
lower resolution. By conducting two separate scans separated by a 90-degree

rotation, there is high resolution image data in three-dimensions.

18

A sequence of 150 scans was taken using the same CT machine and
parameters as used for the articulated scans, however these scans were taken

at 1.5 mm increments to ensure a high degree of accuracy for the models.

3.5. Image Processing

Data from CT scans are stored in a proprietary format specific to the model
and manufacturer of the machine. This is primarily legacy code due to the
use of CT scans prior to the development of imaging standards but is also
necessary to some degree due to the quantity of data present for each image.
The GE 9800 format consists of a 24-bit, grayscale imagemap of the 512 x 512
image. In order to use these images for any purpose other than viewing on
the GE 9800 CT console, they must be converted to a more commOnly

available image format.

An open source initiative in the medical community has fortunately resulted
in the distribution of a toolkit for this purpose (American College of
Radiology, 1993). This set of programs, referred to as the DICOM toolkit, can
be used to convert the proprietary image format of CT (as well as MRI and
PET) manufacturers into the more accessible Portable Graymap (or PGM)
format. In order to improve the specific resolution for bone, however, it was

necessary to slightly modify the code of the DICOM toolkit such that the

19

grayscale values associated with bone were enhanced and those associated

with the silicone embedding material were reduced.

A batch processing script was developed to convert the GE 9800 format CT
scans into bitmaps en masse. This script utilized public domain code from the
DICOM toolkit to convert the image to a portable graymap (PGM) format,

and subsequently to a bitmap format.

At this point, the data consisted of two sets of 150 independent sequential
bitmap grayscale images. The exact three-dimensional point locations of the
bone edges were determined by application of an edge detection algorithm to
the images. For this purpose, a program was written in MATLAB
(Mathworks, Inc., Natick, MA) that took a user defined region of the image

and analyzed it using edge detection algorithms.
3.6. Edge Detection Algorithm

All edge detection algorithms operate on similar principles, that of seeking
maxima in the derivative or gradient of the given image. Specific techniques
vary however in how this principle is applied. The Sobel (J ahne, 1997) and
Roberts (J ahne, 1997) methods rely on fixed vector differentiation from the
original image. The result of this is that the gradient is accurately calculated

only in a single direction, and the edge data normal to the selected vector are

20

lost. Although each of these methods use Slightly different techniques
(Roberts using a simple finite difference technique, and Sobel using a
weighted average technique), without a priori knowledge of the pertinent
gradients and rotation of the image to align them appropriately to the
direction of gradient calculation, they will not perform well. In the case of
the images being analyzed here, the variability in edge direction effectively

rules out these techniques.

The Canny edge detection technique as described by Canny (1984) and
Schunck (1986) improves on previous algorithms by employing a gaussian
filter to reduce image noise. A two-dimensional gaussian function is used to

filter the image prior to analyzing the gradient (Equation 1).

_(’2+,2)

80% y) = e 2” (1)
This function effectively acts as a low pass filter with a definable gaussian
parameter, 6, that allows for control over the degree of smoothing performed

prior to determining the gradient.
Once the image has been smoothed, the gradient is then calculated using the

partial derivative of the filter in both the x and y directions, and

subsequently adding the results (Equations 2 and 3).

21

 

 

6 F(X.-.p)’,-)—F(x.-,y,-)+F(x.-.p)’,-+1)"F(x,-.yj.l)

__z (2)
ch 2

i: F(xi’yj)_F(xi’yj-I)+F(xi+l’yj)—F(xi+l’yj-l) (3)
5y 2

The magnitude and direction of the gradient were subsequently solved by a
simple magnitude and angle solution as shown by Schnuck (1986) (Equation

4).

 

p(xwyj)=Jl:':_x(xwyj):l +['%(xny1'):l (4)

By defining the threshold value, the allowable minimum gradient magnitude
for defining an edge could be controlled. A sample image demonstrating the

Canny edge detection algorithm is shown figures 7 and 8.

22

 

Figure 7. Cross sectional image Figure 8. Cross sectional of
of the tarsus transecting the image after applying the Canny
calcaneus and tibiotarsal joint edge detection algorithm
(Schnuck, 1986)

Typically, one performs edge thinning and edge connection analysis on the
image after performing the edge detection; however, the results of the edge

detection alone were found to be sufficient for accurate modeling of the bones.

When the bone surface does not lie perpendicular to the plane of the scan, the
edge of the bone appears as a region with a variation of grayscales, none of
which is sufficiently distinct to produce a well defined edge by a differential
gradient method. Consequently, a threshold cutoff was used on these areas
prior to the gradient analysis in order to improve the edge definition. The
threshold was chosen based on user input and could be modified to improve

the edge quality of a specific image.

23

3.7. Creation of the Solid Model

After performing the edge detection in MATLAB, the global coordinates of
points representing the edges of the bones were written to a file in the format
used by the batch scripting method of the I—DEAS solid modeling package
(SDRC, Milford, Ohio). The I-DEAS package was selected due to availability
and the capabilities of the software for medical reconstruction. Previous
studies including finite element analysis of the human skull (Remmler, 1998)
and equine metacarpus (Chung and Thompson, 1993) indicated that it would
be satisfactory not only for this project but for subsequent research into

dynamic loading and simulations.

After the output files from the MATLAB program had been read into I-DEAS,
the result was a ‘point cloud’ representing the outside surface of each bone as
seen by the two orthogonal scan axes. These independent data sets were
oriented with respect to each other by determining the angle of rotation and
translational position of the relative scans based on the reference coordinate
frame defined by the nylon lines on the scan frame. The values were
determined by digitizing the coordinates of the lines in the sequential CT
scan images and conducting a linear regression of the datapoints to recreate

the vectors defined by the nylon lines.

24

After the (relative) point clouds had been aligned in three-dimensions, solid
models were created from these points. Three separate methods were

employed to create the models: lofting, curve mesh, and surface stitching.

Lofting is a process by which surfaces are created from a sequential set of
cross sectional curves. It is used in computer aided-design and modeling
packages for the creation of highly sculpted surfaces with small variations in
curvature, but it performs poorly in regions in which the model has a
substantial variation in curvature or creates a sharp angle with adjoining
surfaces. It uses polynomial interpolation between sequential complete
curves (i.e. curves whose endpoint is coincident with the start point). This
method is highly suitable for the creation of models of bones along their

primary axes.

In order to use this method, it was necessary to create a single continuous
curve in a single plane representing the outside perimeter of the bone being
modeled. The I-DEAS software package uses non-uniform rational basis

splines (NURBS) to create curves through given points.

NURBS are frequently used in computer applications for drafting,
engineering design, or drawing. They are extremely powerful in that they
allow for the definition of ‘smooth’ surfaces (those without sharp bends) with

a relatively small amount of data. A NURBS is mathematically defined by a

25

set of geometrical locations called control points. These control points define
the curve using the weighted local average of their relative locations (the
weighting being based on user defined parameters of the dominance of a
particular point in the curve definition). Hence each control point in theory
affects all parts of the curve, with the closest points having substantially
greater impact than those farther away. By using the three-dimensional
locations of the bone edges derived from the CT scans as the control points,
and heavily weighting them to force the curve to trace the path, an accurate
representation of the bone surfaces was defined. After these continuous
curves had been created, solid models were developed using the lofting
procedure to describe the surfaces defining the primary axes of the bones

(Figures 9 and 10).

26

     

3!.
"v ""IIII
I , n, '

4, 'llll’
i:.',‘ulll%

 
      
     
        

1.1301”,
I'm” , oz...

r ' " “
titre/{Ma‘sfiwh
.vrumaug await!
”W'fi'} =.’*.~"'

\_ .
— -

 
  
    

      
 

 

   

Figure 9. Cross section curves Figure 10. Resultant surface
used for loft definition on the from the lofting technique on the

metatarsus metatarsus

Since the lofting process performs poorly in areas with high degrees of
variability in curvature, it was unsuitable for the majority of the contact

surfaces of the bones. For those surfaces, either curve meshing or surface

stitching was used.

Curve meshes use a grid of intersecting curves to create the surface
representation. The intersecting curves are produced using NURBS, similar
to the technique described for lofting. The highly sculpted surfaces of the

contact areas of bones make the curve mesh ideal for most of these areas.

27

For each surface, a series of non-continuous curves were created describing
the cross section of the surface in a series of parallel planes called ‘profile
curves’. The separation of the curves, typically 1.5 or 3 mm, was dependent
upon the complexity of the surface with more curves being needed to describe
more complex surfaces. A second set of curves, referred to as ‘rail curves’,
were used to define the connection of the profile curves on their edges, and
give additional information on the contours across the surface. The software
then interpolated these curves to create the surface definition (Figures 11

and 12).

        

l
,/

/ I I I), I
inf/i/ I" /i ff/H Aft/l

 

Figure 11. Cross section and rail Figure 12. Resultant surface
curves used for surface definition from the mesh of curves
on the calcaneus technique on the calcaneus
For the metatarsus, however, the proximal surface, which is in contact with
the third and fourth tarsal bones, was too complex even for this technique
due to the concavity at the point of contact between the fourth tarsal bone,
the third tarsal bone, and the metatarsus. The inability for the software to

accurately interpolate the surface definition in these regions necessitated the

28

use of surface stitching. This method uses low weighted control point NURBS
to interpolate a cubic spline between three control points to create a grid of
roughly square surface sections, which were subsequently combined or
‘stitched’ at the edges. This method, although lengthy and tedious, results in
highly accurate surface representations due to the fact that it is a
combination of 1-1.5 mm squares developed directly from the CT scan data,

rather than from interpolated surface information (Figures 13 and 14).

 

Figure 13. Curve grid used for Figure 14. Resultant surface
surface definition on proximal from the surface stitching
surface of the metatarsus technique on the metatarsus

3.8. Development of Tool for Model Visualization

Once the computer representations had been constructed, the next step of the

process was to develop a method of linking the models with spreadsheet data

29

derived from external kinematic measurements. This was important due to
the interest in using the models as visualization tools for the three-
dimensional kinematics of the joint and as a research tool to study the range
of motion between the joints in relation to the effects of degenerative diseases
in the tarsus. It is possible to perform Simple animation based on external
tab delimited data in I-DEAS, the modeling package used to develop the solid
models; but the flexibility of application intended in the original concept of
the project required more powerful animation and rendering software. The
use of a proprietary file format by SDRC in the I-DEAS product precluded

direct use of the solid model data in I-DEAS.

A number of external formats were considered, including Virtual Reality
Markup Language (VRML), Microsoft DirectX, Stereolithogrophy (STL)
definition files, and Initial Graphics Exchange Standard (IGES). An
evaluation of the respective accuracy of the formats indicated that IGES did
not reliably produce models of sufficient surface accuracy for the purposes of
this study. The VRML format appeared ideal initially, but was subsequently
found to have a number of drawbacks relating to code limitations for collision
detection and file size limitations in VRML viewers. Although the STL
format performed reasonably well, it was determined to use the DirectX

format due to the publicly available resources for rendering and animation.

30

DirectX retained mode relies upon binary encoded object data for the creation
of models, so it was necessary to convert the text based VRML format to that
used by DirectX. A Visual Basic program was written to perform this
conversion. Once the binary formatted DirectX files had been created, they
were imported into a second program, which allowed the user to define the
specific relations between geometric models and kinematic data. This
program used the input data to animate the models, allowing the animation

to be viewed from any position or angle (Figure 15).

5t SHEENAMQBI "A

 

 

 

Figure 15. DirectX Animation Viewer

31

3.9. Model Validation by Volumetric Measurements

The objective of this research was to develop a highly accurate model of the
bones of the equine tarsal joint. In order to validate the quality of the models
a comparison was made between the volumes of the original bones and their
respective computer models. The volumetric measurement was performed by
observing the volume of displaced fluid when the specimen was placed in a
container of liquid. Due to the natural porosity of bone, the specimens were

sealed with a thin layer of petroleum jelly to prevent absorption of the liquid.

Due to the large difference in apparent relative volumes between the largest
and smallest bones, two displacement techniques were used. The first and
second tarsal bones were placed in a graduated cylinder containing the
measurement fluid, and the increased volume was measured. For this

technique, water was a satisfactory fluid.

Cylinders wide enough to accommodate the larger bones of the tarsal joint
have a large surface area and this decreases the sensitivity of the technique.
Therefore, instead of performing a direct volumetric measurement of the
larger bones, an indirect measurement based on the mass and density of the

displaced fluid was used.

32

A nonionic wetting agent and detergent was added to water to reduce its
surface tension. The mass of known volumes of this fluid was measured five
times using an electronic rate calculating balance (Pelouze, Chicago, IL) and
the resulting calculated densities were averaged to reduce the effect of
erroneous measurements. Approximately 1 litre of fluid was placed in a large
cylinder that had a hole and spout near the top. Any change in the height of
the liquid would result in an overflow through the spout into a beaker. Each
bone was slowly lowered into the water and the overflowing liquid was
collected and weighed. The volume of the bone was calculated from the
experimentally determined density of the displaced fluid. For each of the
tarsal bones, the volume measured by one of the displacement techniques

was compared with the volumes calculated by the I-DEAS software package.

3.10. Application of Model

In order to indicate the practical research aspects of the model, a pilot study
was conducted to evaluate the hypothetical motion of the tarsal joint as
projected by the computer model with experimentally measured kinematic
motion. According to the cadaver study performed by Schamhardt et al
(1984), almost all motion observable using in vivo techniques should occur at
the tibiotarsal joint. The model was used to validate this assumption by

observing the correlation between flexion and extension of the tarsal joint

33

and the abduction/adduction and internal/external rotation of the joint

(Figure 16).

Abduction i
Adduction

Flexion I Extension

 

 

‘1. )
Internal i External
Rotation

Figure 16. Rotational axis definitions used in analysis of joint angles

The motions of the tibia and metatarsus were recorded by the placement of
reflective markers on the skin overlaying palpable bony landmarks (Soutas-
Little, 1996, Lanovaz et al., Submitted). Marker locations were chosen that
had minimal Skin displacement during locomotion and such that an axis
vector was established along the lateral Side of the diaphysis of the bone, and
a second vector was oriented in the mediolateral direction at the joint

(Figures 17 and 18).

34

5’ a?
f;
is
qr

. ' Tibia Y Metatarsus Y

  

\Q . . r \ii \3
\ \. . A .
.w \\\\\ I -5.“ K\\\ 3‘:
2‘}. \ 3% _ \\t a \ 5\-.\_.\ '\\‘\\‘ \\\ B“
. . . \ ..’ -‘ N.“ .S
Tibia Z 4% I“; ‘ i\\\\ . . -
23% )r I K;\\\\ ‘I .i :‘F
3 "Si?" ‘3‘ \ \ \
g 1 . . . \\ “ .~'
i le13 x i ,.

’4‘,» Metatarsus Z (.3 b ‘5 Meta X

. r. .. in i
H ~." I ..
Ti i .393“? -. '19 .4; I;
‘- I a? ‘ 3‘3““:
‘ iii l

ii.
1:.
i .

Figure 17. Marker locations used Figure 18. Marker locations used
on the tibia for kinematic data on the metatarsus for kinematic
collection data collection

An 11 year old Thoroughbred of approximately the same size and weight as
the horse used for the computer model of the tarsal joint was filmed using
two Panasonic AG 450 video cameras (Matsushita Electric Corp., Secaucus,
NJ ) while moving on a Mustang equine treadmill (Kagra, A.G., Fahrwangen,

Switzerland) (Figure 19).

35

MW ngion on had-Ii

 

 

 

 

 

 

 

 

 

 

 

 

 

392.7 cm Jul——
2
400 on 415.5 cm
8 cm
J_ H J-
§ .11,
(anon 1 (arm: 2

Figure 19. Experimental Setup for Kinematic Data Collection

The horse had been previously trained on the treadmill and its motion was
typical for a healthy horse moving at the studied gaits. Recordings were made

of the horse trotting at 4.2 m/s.

The resulting kinematic data was analyzed using the Ariel Performance
Analysis System (Ariel Dynamics, Trabuco Canyon, California). The results
of this analysis described the three-dimensional translation and rotation of

the tibia and metatarsus in the segmental coordinate system.

36

The resulting experimental data were then compared to the model based
motion of the tarsal joint based on the assumption that all motion occurred at
the talocrural joint. This projected motion was determined from the
computer model of the talus. The curvature of the talus at its articulation
with the tibia was analyzed to derive the estimated three-dimensional path

curve for the tarsus for a given flexion angle.

In order to determine the model based three-dimensional location and
orientation of the tibia, the curvature of the talar trochlea was determined
using the minima of the groove on the talus along which the tibia moves. This
curve was found by intersecting a plane with the computer model of the talus

and taking the minimum point on the resulting curve.

The three-dimensional points were used to define the curve of the groove

between the talar trochlea, and hence define the motion of the tibia (Figure

20).

37

  
  

"f {'1 ibial CS
'. Qt”.

   

:39 Metatarsal cs
i] : "I

9. Si

Figure 20. Metatarsal, talar, and tibial coordinate system definitions
for model based analysis

Using a global coordinate system coincident with the kinematic metatarsal

coordinate system, the talar X vector at a point p was determined using an

approximation of the instantaneous tangency calculated as shown in

equation 5.
Xhluop =pn+I—pn-l (5)

38

where
3,, is the vector from the global coordinate system to the nth three-

dimensional point defining the groove between the talar trochlea.

The talar Z vector was found by determining the normal of the instantaneous
plane formed by three successive points defining the talar trochlear groove

(Equation 6).

2min”: = (p:_ 1):] ) x (Ian—:- pn:) (6)

The final coordinate vector for the tibia was found by taking the cross product

of the instantaneous talar X and Z vectors (Equation 7).

Ytalnul = Ztaluut x Xuluut (7)

The unit vectors defining these coordinate axes (Equations 8-10) were used to
create the transformation matrix between the metatarsal coordinate system

and the instantaneous talar coordinate system (Equation 11).

f = 71,, i + 3”} + 71,213 (8)
j = 2,, i ””1" My}; (9)
I; =xiz‘xi+/iz,lfl +1221? (10)

39

ALX Ax] 23.2
[R] = ’l'y.x ’l'yx ’l'yz (11)
2:.X ’12! 12.2

A vector A relating the each of the tibial coordinate system points to the talar
point was defined using the grounded coordinate system, and this vector was
transformed into the tibial coordinate system using the rotation matrix

(Equation 12).
52—. [R]; (12)

This vector and the rotation matrix R were used to resolve the location of

each of the tibial markers in terms of the grounded coordinate system

(Equation 13).

T‘ = p: + [R T ('13 (13)

where

F is the resultant vector from the metatarsal coordinate system
to the tibial coordinate system marker and

13‘ is the vector from the metatarsal coordinate system to the talar point

location.

40

This calculation was performed for each talar point location corresponding to
0 to 180 degrees of tibiotarsal flexion using a program written in MATLAB,
and the tibial positions and orientations were compared to the results of the

kinematic analysis.

41

4. Results

4.1. Computer Models of the Bones of the Tarsal Joint

The focus of this research was the development of a comprehensive and
accurate model of the bones and joints of the equine tarsal joint. Since this
was the primary goal, the results of the research were the computer models
themselves, and most of the research consisted of the development of the

modeling technique to ensure accuracy and repeatability in the process.

The relative complexity of each model may be evaluated qualitatively by

examination of the total number of cross sectional curves and surfaces

required to construct the model (Table 1).

42

Table 1. Number of cross sectional curves and surfaces in computer

Bone Number of cross section Number

 

4.1.1. Tibia

 

Figure 21. Distal end of tibia Figure 22. Computer model of
distal tibia
The complexity of the distal surface of the tibia which contacts the talus, and
the need for a high degree of accuracy at this location due to the interest in
the motion at the junction of the tibia and talus, required that special
emphasis be placed on the data obtained for this surface. By examining the

43

two point clouds and judiciously using the points from the image processing
of the two scans, the surface was created with a high degree of accuracy,
which is evident both by a visual comparison of the computer model to the
bone (Figures 21 and 22), and by comparison of the surface to surface contact

at the talocrural joint throughout its range of motion.

4.1.2. Talus

   

Figure 23. Talus specimen Figure 24. Computer model of
talus
An exceptional degree of accuracy was demanded in the model of the talus,
for the same reasons as specified for the tibia. Additional challenges were
posed by the fact that this bone made surface to surface contact with a total
of five bones (tibia, calcaneus, central tarsal, first and second tarsal, and
fourth tarsal bones). Surface interaction analysis via the interference

analysis tools in I-DEAS indicated that the surfaces coincided very well

44

between the models. As each model was developed independently, this was
assumed to indicate a high degree of accuracy in the models themselves

(Figures 23 and 24).

4.1.3. Calcaneus

 

Figure 25. Calcaneus specimen Figure 26. Computer model of
calcaneus

The calcaneus acts as a lever arm and as a support surface for the tendons
transferring forces to the segments of the distal limb. As such, it is necessary

that the surface tolerance between it and the talus be extremely tight to

45

ensure stability and optimal transfer of the force through the tarsal joint. A
comparison of the respective surfaces between the calcaneus and talus
indicated that the model would lock the calcaneus in place accurately and
prevent rotation, in the same way as seen in the joint itself (Figures 25 and

26).

4.1.4. Central and Third Tarsal Bones

   

Figure 27. Central tarsal bone Figure 28. Computer model of
specimen central tarsal bone

46

   

Figure 29. Third tarsal bone Figure 30. Computer model of
specimen third tarsal bone

The structures of the central and third tarsal bones are quite similar. They
are both roughly elliptical bones that lock tightly to each other, supported by
connective tissue deep within the joint. The surfaces of these bones
presented excellent opportunities to evaluate the modeling process, as they
should be smooth and have very similar reciprocating curvatures (Figures 27-
30). The bone surfaces interface tightly, both with each other and with the
surrounding structures (talus, metatarsus, first and second tarsal bone, and
fourth tarsal bone). The computer models, however, fail to represent the
roughness on the dorsal aspect of the interfacing surfaces to a high degree of

accuracy, due to the limitations of resolution in the CT image data.

47

4.1.5. First and Second Tarsal Bone and Fourth Tarsal Bone

-0

Figure 31. First and second Figure 32. Computer model of
tarsal bone specimen first and second tarsal bone

Figure 33. Fourth bone specimen Figure 34. Computer model of
fourth tarsal bone

Examination of the models of these bones indicate that they satisfactorily

represent the general shape and areas of surface to surface contact (Figures

48

31-34). However, it is also evident that some of the surface intricacies have
been lost in the modeling process due to their sizes with respect to the CT

image resolution.

4.1.6. Metatarsus

   

Figure 35. Proximal end of Figure 36. Computer model of
metatarsus specimen proximal metatarsus

The proximal surface of the metatarsus is by far the most geometrically
intricate and complex of the bones of the tarsal joint due to the discontinuity
between the contact with the third tarsal bone cranially and, the first and
second and fourth tarsal bones caudally. The surface stitching technique
however resulted in an accurate representation of the surface when compared
both visually with the original model (Figures 35 and 36), and by use of the

interference checking techniques for the bone surface interaction.

49

4.2. Results of Volumetric Measurements

Few methods are available for validation of the geometry of the computer

models, due to the fact that the best geometric data, derived from the CT

scans, were used in the development of the model. By comparing gross

volumetric differences between the computer model and the bone models,

some indication of general accuracy may be determined (Table 2).

Table 2. Comparison of specimen volumes and calculated volumes of

 

 

 

 

 

 

 

 

 

computer models
Specimen Experimental Theoretical Percent
Volume from volume from Difference
specimen (cmz) computer model
(cmz)
Tibia 214.33 201.81 5.8
Calcaneus 158.66 164.29 3.5
Metatarsus 136.39 144.15 5.7
Talus 172.58 166.19 3.7
First and second 7.93 7.58 4.4
tarsal bone
Fourth tarsal 34.87 35.92 3.0
bone
Central tarsal 27.90 28.38 1.7
bone
Third tarsal 27.00 27.92 3.4
bone

 

 

 

 

 

The volumes of all models correlated reasonably well with the measured

volumes of the original bones, with the tibia and metatarsus having higher

discrepancies than the other bones of the model.

 

4.3. Application of Model to Prediction of Motion of the Tarsal

Joint

The assumption for the model prediction was that all observable kinematic
motion occurred at the tibiotarsal joint and only along the path defined by the
talar ridges. Regression equations correlating flexion/extension with
internal/external rotation and abduction/adduction were created using a

statistical analysis software package (SPSS Inc., Chicago, IL) (Equations 14

and 15).

AA = — 0.025217*FE + 0.208808*FE’ — 0.03981*FE’— 0.014949 (R’ = 0.985) (14)
IE —.— 0.360453*FE — 0.02316*FE‘— 0.034005*FE’ - .118174 (R2 = 0.991) (15)
Where

AA = Abduction/Adduction angle (radians)
IE = Internal/External rotation angle (radians)

FE = Flexion/Extension angle (radians)

The predicted correlation curves indicate a quadratic relationship between

flexion/extension and abduction/adduction (Figure 37), as well as between

flexion/extension and internal/external rotation (Figure 38).

51

 

0.40

 

 

0.20 “r— fl‘

 

Abduction/Adduction Angle (Radians)
O
8

 

 

 

-0.20 . T . , . . , ‘
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

FiexlonlExtension Anglo (Radiant)

Figure 37. Predicted abduction/adduction angle vs. flexionlextension
angle based on analysis of morphology of talus and tibia

52

Internal/External Rotation Angle (Radians)

 

 

 

 

 

 

 

0.40
0.20 ~~———— —~—— ——~——— /-
0.00
-0.20 . r . fl . . . 1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

FlexloniExtension Ange (Radars)

Figure 38. Predicted internal/external rotation angle vs.
flexionlextension angle based on analysis of morphology of talus and
tibia

These predicted results were compared to the average of five sets of
kinematic data which were normalized to stance and swing phases. It should
be noted that the resultant regression equation allows for only one solution
for internal/external rotation and abduction/adduction for a given

flexion/extension angle, due to the fact that the talar trochlea form planar

curves.

53

4.3.1. Stance phase

AbductionIAdductlon Angle (Radians)

 

 

 

 

 

 

 

 

 

 

 

0. l0
0% of stance phase
I 25% of stance phase
0 50% of stance phase
A 75% of stance phase
0 100% of stance phase
0.05
0.00
— Kinematic results
- - - Motion predicted from
computer model
-0.05 . . . .
0.20 0.30 0.40 0.50 0.60 0.70

FlexlonIExtenslon Angle medians)

Figure 39. Flexionlextension angle vs. abduction/adduction for
stance phase

The abduction/adduction of the stance phase shows a general trend of
adduction throughout the stance phase (Figure 39). The range and rate of
increase of adduction shown by the limb during the stance phase is similar to
that predicted by the computer model. The variability in magnitudes are
explained by Slight variability in marker placement between the computer
model and the kinematic results, or by differences in conformation between

the subject used for the kinematic data collection and the development of the

54

computer model. Of particular importance, however, is the range of possible
solutions of abduction and adduction and internal/external rotation for a
given flexion extension angle. The solution derived from the computer model
allows for only a single possible value of abduction/adduction or internal and ‘
external rotation for a given flexion/extension angle. Results from the
experimental kinematic data analysis show a lack of a unique orientation for
a given flexion/extension angle, which indicates a coupling between the
solutions not taken into account by the cubic regression equations derived

from the computer model.

 

0.30
B 0% of stance phase

I 25% of stance phase
9 50% of stance phase
A 75% of stance phase
0 100% of stance phase

 

0.20

 

0.10

 

 

lnternaliExternal Rotation Angle (Radians)

 

 

 

 

 

 

0.00 ’ , ,—
- . r ’ ' — Kinemdic Rum
. - - Motion predated from
computer model
'0.1 0 T I I I
0.20 0.30 0.40 0.50 0.60 0.70
FlexloNExtension Angle (Radans)

Figure 40. Flexion/extension vs. internal/external rotation for stance
phase

55

The internal/external rotation of the limb during stance phase shows a
substantial deviation from the projected results (Figure 40). The limb follows
an are that has endpoints close to those predicted by the model, but showing
much greater-external rotation through the duration of the weight bearing
phase of the stride. The substantially greater internal rotation seen in the
kinematic results suggest that the tarsal joint is twisting more under loading

than would be allowed by planar rotation about the talar trochlea.

56

4.3.2. Swing Phase

 

0.30
E 0% of swing phase

I 25% of swing phase
0 50% of swing phase
A 75% of swing phase

0 . A
0.20 O 100 A of swrng phase

 

 

 

 

 

AbducflonIAdductlon Angle (Radians)

 

 

 

 

 

 

0.1 0
0.00
— Kinematic results
' --- Motion predicted from
computer model
-0.1 0 . . .
0.30 0.50 0.70 0.90 1.10

FlexionIExtenslon Angle (Radians)

Figure 41. Flexion/extension vs. abduction/adduction angle for swing
phase
The swing phase abduction/adduction angle of the limb shows a relatively
close correlation to the trend of the motion predicted using the computer
model (Figure 41). There is some amount of deviation, however, in that the
model predicts a single possible abduction/adduction angle for a given
flexion/extension angle, and the kinematics indicate that there is a consistent
0.1 radian (6°) difference between the first half and second half of swing
phase.

57

 

0.30
B 0% of swing phase

I 25% of swing phase
0 50% of swing phase
A 75% of swing phase
0 100% of swing phase
’ f

’

 

 

0.20

 

0.10

 

 

 

lntemallExtemal Rotation Angle (Radians)

 

 

 

 

 

 

0.00
—— Kinematic results
---- Motion predicted from
computer model
-0.10 . . Y .
0.20 0.40 0.60 0.80 1 .00 1.20

FlexionlExtension Angle (Radians)

Figure 42. Flexion/extension vs. internal/external rotation for swing
phase

Similarly, the internal external rotation of the limb follows the same general
trends as those predicted by the morphology of the joint, but it as well
demonstrates a noticeable deviation between the initial and final 50% of
swing phase, whereas the predicted results state that there should be a single
possible internal/external rotation angle for a given flexion/extension angle
(Figure 42). The difference in this case somewhat greater, being on the order
of 0.15 radians (9°).

58

5. Discussion

5.1. Modeling Techniques

Although no previous computer models of the tarsal joint have been
developed, the techniques presented here may be compared with human and
equine models of other joints. Although some unique difficulties are
associated with each Specific region of interest, similar issues must be

addressed in almost all research into joint structure.

A number of extremely complex models have been developed focusing on the
interaction of the joints in the human. The studies into the kinematics of the
hand are of particular interest, as their complexity is quite similar to that of
the equine tarsus. Of particular note are the studies by van Sint Jan et al.
(1997 ) and Buford and Thompson (1987 ). Both of these focused on three-
dimensional simulation of hand biomechanics based on models derived from

medical imaging data.

One of the most evident and pertinent challenges seen in almost any
computer model of a physiological structure is that of raw image data

59

resolution. The inherent limitations on image resolution from any medical
imaging technique, be it CT, MRI, or ultrasound, results in the loss of surface
contour that is close to the noise amplitude of the system. This was a far
more profound problem in the development of the hand models, and was
addressed in the case of van Sint Jan et a1 (1997 ) by substantially reducing
the CT scan field of view to obtain a resolution of 0.14 mm/pixel. This
compares to the resolution of 0.5 mm/pixel used in this study. The lower
resolution used for this study was more than compensated by the general

increase in the Sizes of the features of interest.

Another technique, employed by Buford and Thompson (1987 ), used digitized
curves from radiographs performed at 10° increments. This difficult and
labor intensive process was much more prone to error, and was most likely
utilized simply due to the limitations on computational power and available

software at that time.

This limitation in raw data is seen also in equine studies, though most
structures in the horse are proportionally larger than their counterparts in
the human, allowing for somewhat greater definition of ‘acceptable’ image
resolution. The lower forelimb model (fetlock, pastern, and coffin joints)
performed by Cheung and Thompson (1993) did not report a resolution, and
the three-dimensional metacarpus model developed by Les et al (1997) had a

1 pixel/mm resolution. Needless to say, the definition of acceptable image

60

resolution is wholly dependent on the objective of the work. In the case of the
study performed by Les et al (1997 ), the goal was the development of a finite
element model of the carpus with the target being 8 node square elements of
3 mm per side. As the image data were to be ‘filtered’ into the finite element
model, the 1 mm resolution was quite satisfactory. In the study described
here, however, the objective was the development of a morphologically highly
accurate model of an extremely complex joint, which necessitated a higher

degree of accuracy in the image data.

A second issue pertaining to resolution for all of these studies was that of
image thickness. A CT scan results in an image that is an approximation of
the grayscales seen over a particular distance. This approximation ”means
that the image, although highly accurate perhaps in the plane of the scan,
may be of significantly lower accuracy normal to this plane. The study
performed by Les et al (1997) used 3 mm slice thickness, Cheung and
Thompson (1993) used 2 mm, and no image thickness was reported by van
Sint Jan et a1 (1997 ). The study reported here used the smallest image
thickness available on the CT scanner being used (1.5 mm), but it also used
two semi-orthogonal scans, which resulted in high resolution images in all
three-dimensions. It should be noted, however, where data describing a
single plane are of primary interest, such as the axis of the bone as studied
by Les et a1 (1997 ), or the evaluation of hoof stresses performed by Hogan et

al (1991), it is quite satisfactory to conduct scans in a single direction. This is

61

particularly relevant when the data will be applied in the development of a
finite element model, which will eliminate most of the smaller surface

variations anyway.

One final issue pertaining to raw image resolution that must be of concern in
all cases is the effects of radiation on live subjects. CT scans are the products
of relatively high dosages of radiation due to the fact that the cross sectional
images are the outcome of a series of relatively long duration and high dosage
X-rays. Should a technique such as this be used on live specimens,
recommended limitations on radiation exposure must be taken into account,

which will inherently limit the number of scans that can reasonably be taken.

Image processing presents a far more unique challenge. This is particularly
interesting, as none of the previously discussed papers (van Sint Jan et al,
1997; Les et al, 1997 ; Buford and Thompson, 1987 ; Hogan et al, 1991; Cheung
and Thompson, 1993) address this issue directly. Some studies, such as
Buford and Thompson (1987) and Delp et al. (1990), circumvented this issue
somewhat by constructing their models as hand digitized points from
radiographs. This technique is extremely labor intensive and would be
nearly impossible on models constructed from the inherently more accurate

(due to the previously discussed issues of image resolution) CT scan images.

62

The use of CT scan images, however, requires some technique for edge
detection and model reconstruction be employed. The lack of information on
the techniques employed in the other studies prevents comparison, but the
use of the Canny edge detection algorithm provided excellent data. The
decision to use this technique was the product of both the common belief that
it is ideal (J ahne, 1997) and a comparison with other commonly used
techniques. It was evident following an analysis of techniques that the
Canny algorithm (Canny, 1984) resulted in far superior edge definition than

provided by other commonly used algorithms (Figures 41-46).

63

   

Figure 43. Section of Figure 44. Roberts Figure 45. Canny
original image edge detection of edge detection of
selected region selected region

 

Figure 46. Section of Figure 47. Sobel edge Figure 48. Canny
original image detection of selected edge detection of
region selected region

5.2. Model Validation by Volumetric Measurements

Model validation was addressed in this case by comparison of the volumetric
measurements of the original specimens and reported by I-DEAS. Although
this is not comprehensive in that it does not address the accuracy of the fine

structure, it does serve as a gross comparison and validation of the technique.

64

The high degree of correlation seen between the volumetric measurements in
this study indicates that the computer models do in fact, at least to the extent
measurable by this technique, represent the original specimens. In actuality,
however, the capacity of the software to accurately model the volume of the
computer model is probably significantly higher than the resolution of the
volumetric technique would allow, so the deviation between the model and its
original specimen is almost certainly due to this. Increased errors seen in the
case of the metatarsus and tibia are due at least to some degree to the coarse
modeling technique applied to the non-articular regions of these bones. Since
these regions were of lesser interest in this study, little emphasis was placed
on the accuracy of the computer model outside the tarsal joint. This

undoubtedly introduced additional error into the volumetric measurement.

5.3. Application of Model in the Evaluation of Tarsal Joint

Kinematics

The use of the model for a kinematic examination of the statement that all
tarsal joint motion occurs at the tibiotarsal joint (Schamhardt et al, 1984)
was primarily to indicate the usefulness of the model in the examination of
kinematic results. Kinematic analysis is used in the study of both human and
animal locomotion (Soutas-Little, 1996). Although the technique is
mathematically accurate, a number of assumptions are necessary for its
computation.

65

The method is fundamentally based on the solutions of rigid body kinematics
as described by Soutas-Little (1996). Although this assumption is quite
accurate for the bones of the equine limb, the technique employed in this
study uses retroreflective markers applied to the skin overlying bony
landmarks. This introduces the possibility of the motion of the skin over the
bone, which can introduce errors in the kinematic results. According to a
study conducted by van Weeren (1989), skin displacement with respect to the
bone on the distal end of the tibia during stance phase is negligible, and
during swing phase peaks to approximately 1 cm. Skin displacement over
the proximal end of the metatarsus was found to be very small throughout

stance and swing.

An additional difficulty of this technique pertains to the capacity to
accurately determine the three-dimensional locations of the tracked points.
The tracking is performed by digitizing 60 Hz videographic image data. This
technique introduces errors fiom the relatively low resolution of the video, as
well as the possibilities of distortions introduced by lens irregularities. By
averaging five strides, however, the effect of random errors was reduced,
hence it may be assumed that the averaged results are generally

representative of the actual motion of the limb.

66

The general trend of the stance phase of the abduction and adduction of the
limb appears to be relatively well explained by the morphology of the
tibiotarsal joint. The kinematic results in general see limited variation from
the predicted motion of the joint, and what variability is seen is at least
partially explained by errors introduced by the kinematic data collection
process. The internal/external rotation of the limb during stance phase,
however, shows much greater deviation based on the general trend of the

motion of the respective segments.

For both relative rotations (internal/external and abduction/adduction), the
swing phase of the limb shows variability in motion that appears to not be
fully explainable simply by the motion predicted by analysis of the
morphology of the talocrural/tibiotarsal joint. There is consistently a
variation not only between the measured kinematic results and the results
predicted using the computer model, but also in the kinematic results during
swing phase for the first 50% of the stride and the return path of the final
50% of the stride. The structure of the tibiotarsal joint fails to explain this
variability, and hence it is implied that there is additional motion occurring

within the joint not fully explained simply by the shape of the talar ridges.

The results presented here for the motion of the metatarsus with respect to
the tibia should not be taken as representative of a wide range of the equine

population; they are the product of a single data collection session on a single

67

horse. They do, however, demonstrate that the horse is capable of a great
deal of motion at the tarsal joint during its normal locomotion, and there is
almost certainly some coupling of motion that results in the deviation from

the model based predictions.

The discrepancy between this and the results reported by Schamhardt et a1
(1984) could be explained in a number of ways. Small variations in
internal/external rotation and abduction/adduction between the predicted
and actual results can be explained by the natural morphological variation
between horses, as the experimental data were taken from a different horse
than the computer model was developed from. Additionally, the study
performed by Schamhardt et al (1984) focused on stance phase loading and
hence, although possibly accurate for the stance phase, would not accurately
demonstrate the motion of the swing phase. The stance phase results could
also be the product of non-axial loading not simulated in the technique
described by Schamhardt et a1 (1984). The curvatures of the sliding
intertarsal joints would explain this motion, and the technique employed by
Schamhardt et al. (1984) could have inaccurately simulated the stance phase

loading and hence misrepresented the amount of motion at these joints.

Another possibility that does not invalidate the conclusions drawn by
Schamhardt et al (1984) is that the majority of the tarsal motion occurs at

the tibiotarsal joint, but the joint between the tibia and the talus is far less

68

rigid structure than the bone morphology would indicate. Should the bones
be free to rotate slightly with respect to each other during stance, and the
collateral ligaments be sufficiently dynamic as to allow for a small amount of
separation during swing, it is conceivable that the out-of-plane rotations
could be explained by motion occurring at the tibiotarsal joint. This is in
contrast to the assertion made by Badoux (1987) that the motion of the tarsal
joint is a single degree of freedom, with the talar ridges being tightly fitted
into the tibial groove, preventing motion out of the plane defined by the talar
trochlea. This is an unlikely explanation, however, as the additional freedom
of motion between the tibia and talus would result in increased loading on
limb impact and would subsequently increase the chances of degenerative

joint diseases at the tarsus.

69

6. Conclusion and Future Studies

It is evident, based on both the visual inspection of the computer models, as
well as the validation procedure conducted, that the technique described is
viable for the development of computer models of equine joints for both
observation of the motion, as well as for subsequent morphological studies.
The models developed accurately represent the structures of the joint, and

will certainly be of use for educational and research purposes.

The code developed for viewing the results of kinematic analysis in three-
dimensions has proven useful in the demonstration of the research being
conducted in the McPhail Lab, as well as in enhancing the general
understanding of the more complex three-dimensional motions seen in
certain breeds of horses by more comprehensively demonstrating their

motion.

The model has also proven to be a valuable tool in the evaluation of joint
kinematics. Additional analysis of tarsal joint kinematics should be

conducted in order to determine the extent of variation between individuals.

70

Obviously it is possible to study and analyze highly complex motions centered
at the tarsal joint using this technique. The disparities between the
assertions of Badoux (1987 ) and Schamhardt et a1 (1984), and the findings in

this study should be addressed in future research.

Subsequent studies in this field and using this technique should focus on
utilization of these models for clinical and research studies. Specifically, they
could be used for improving the understanding of the normal motion of the
joint, as well as the process and treatment of degenerative or injury induced
diseases located in the tarsus. Studies of the internal interactions of the joint
by the application of bone pins or three-dimensional radiography will allow a

significantly improved model of the normal motion of the equine tarsal joint.

Another area for study would be in the application of dynamic principles to
more advanced models that would include the ligaments, tendons, and
additional accessory structures in the hopes of developing a series of models
to analyze loading through and on the joint during normal and pathological
gait. Dynanfic models of this type have been used in human medicine to
evaluate the effects of proposed surgeries to evaluate their efficacy in
improving motion prior to conducting the procedure (Sellberg and
Vanderploeg, 1994). In horses, a similar technique could be employed to
evaluate the value and effects on locomotion of performing fusions or

tenectomies.

71

Finally, with a combination of the above information, accurate finite element
models could be developed with certainty to their geometric accuracy and
boundary conditions to evaluate the process of remodeling, fracture, and
degeneration in the horse, similar to those performed in the human knee
(Sathasivm and Walker, 1997 ), equine metacarpus (Les, et al, 1997), and
equine hoof (Hogan et al, 1991). There is great potential for studies in this
area having a direct and beneficial impact on the long term health and —

working life of the equine athlete.

72

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76

 

 

 

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