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_ LIBRARY
Michigan State
University

 

 

 

This is to certify that the

dxssertation entitled

Three Dimensional Dynamic Analysis of
the HUman Hand for Predicting Tendon,
Ligament and Nerve Wear in the

Carpal Tunngrlsegttég yng Typ1ng

Wendy Sue Reffeor

has been accepted towards fulfillment
of the requirements for

l)og§oral degree in Phi losoghg

 

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Major professor

Date éffl %/

0-12771

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6/01 cJClRC/DmoDuopOS-DJ 5

 

Three Dimensional Dynamic Analysis of the Human Hand for
Predicting Tendon, Ligament and Nerve Wear in the Carpal
Tunnel During Typing

BY

Wendy Sue Reffeor

AN ABSTRACT OF A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Materials Science and Mechanics

2001

Professor Robert W. Soutas-Little

ABSTRACT

Three Dimensional Dynamic Analysis of the Human Hand for
Predicting Tendon, Ligament and Nerve Wear in the Carpal
Tunnel During Typing
BY

Wendy Sue Reffeor

The hand is one of the most complex parts of the human
body. The hands contain forty percent of the bones and
fifty percent of the muscles in the human body. In
addition, the opposable thumb is one of two features that
separates primates from other animals.

This study develops a three dimensional, dynamic
mathematical model that may be used to predict the relative
tendency of an activity to cause carpal tunnel syndrome.
The model can be used to calculate both the forces in and
the motion of the tendons in the hand. The forces and the
deflections of the tendons are combined to determine a
measure of the energy lost in the carpal tunnel because of
the friction between the tendons and the tunnel itself.

An analysis is performed on the index finger for the

typing of one sentence. The purpose of this analysis is to

determine if the model provides valid results. In
addition, in providing this analysis, the accuracy of the
measuring system is determined and shown to be adequate for

measuring the motion and forces on the hand.

 

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DEDICATION

I dedicate this manuscript to my family: Bruce and
Charlotte Reffeor and Cindy, Patrick, Stephanie and Annette
Kehoe. Without their constant and unfailing support, this

work would not have been possible.

 

 

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ACKNOWLEDGEMENTS

I take this opportunity to thank those who helped me
through this project.

First and foremost, I’d like to thank Dr. Robert
Soutas-Little. Thank you for your constant support and
encouragement. You not only helped me to finish this
degree, but also helped with my teaching and kept me
focused on what is important. Thank you for sharing your
knowledge and more.importantly,.your wisdom.

Without Patricia Soutas-Little and Claudia Angeli, I
would have been unable to complete the experimental
sections of this work. Thank you both.

To my committee—-Dr. Gary Cloud, Dr. Melissa Crimp,
Dr. Thomas Pence, and Dr. Vorro—thank you for all of your
time and assistance.

I’d also like to thank all of my fellow graduate
students and colleagues at Grand Valley State University,
without whose support I would not have been able to

complete this work.

To the ladies in the department office, JoAnn
Peterson, Iris Taylor, Lorna Coulter, and Debbie Conway,
your help is priceless. You are very appreciated and make

it possible for everyone in the department to succeed.

vi

ABSTRACT

DEDICATION
ACKNOWLEDGEMENTS

TABLE OF FIGURES

TABLE OF TABLES

LIST OF ABBREVIATIONS
CHAPTER l-INTRODUCTION

CHAPTER 2—LITERATURE REVIEW
Biomechanical Contributions to the Study of Hand Function
a Kinematic Modeling
Kinetic Models
Collection of position data
Optimization of Biological systems
Linear Optimization Criteria
Nonlinear Optimization Criteria
Ergonomic considerations in the wrist
CHAPTER 3-DEVELOPMENT OF DYNAMIC HAND MODEL
Kinetic model development
Kinematic model development

Accelerations
Tendon Displacement

Pulley Model

CHAPTER 4—EXPERIMENTAL PROCEDURE

Testing protocol

vii

II

IV

XII

XIII

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14
15
18

29

30
32
35

38

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46

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63
65

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Measurement System 85

Position Measurement 85
Force Measurement 89
Data Analysis 91
Filtering 91
Segment Lengths 92
Segment Unit Vectors 93
Joint Angles 96
Center of Gravity 98
Differentiation 98
Local Coordinates 99
Masses and Moments of Inertia 100
Model Implementation 100
Optimization 101
Energy Calculation 103
Calibration 104
Qualifying Tests 106
CHAPTER S-RESULTS AND DISCUSSION 109
Analysis Methods 109
dynamic versus quasi-static analysis 118
optimization results 120
Energy calculation 126
System accuracy 126
CHAPTER 6--CONCLUSIONS 132
APPENDIX AFTENDON LOCATIONS 135

APPENDIX B-PHYSIOLOGICAL CROSS-SECTIONAL AREA FOR ALL HAND

MUSCLES 138
APPENDIX D--CALIBRATION CURVES FOR KEYS 140
APPENDIX E--CALIBRATION CURVES FOR KEYS 141
APPENDIX F--OPTIMIZATION RESULTS 145

viii

BIBLIOGRAPHY l 5 7

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TABLE OF FIGURES

FIGURE 1--PALMER VIEW OF THE SUPERFICIAL INTRINSIC MUSCLES OF THE HAND.

TAKEN FROM SPENCE(SPENCE, 1990) , PG. 223. ................. 11
FIGURE 2--SUPERFICIAL POSTERIOR MUSCLES OF THE RIGHT FOREARM AND HAND.
TAKEN FROM SPENCE(SPENCE, 1990) , PG. 220. ................. 12
FIGURE 3--DEEP ANTERIOR MUSCLES OF THE RIGHT FOREARM. TAKEN FROM
SPENCE(SPENCE, 1990) , PG. 220. .......................... 12
FIGURE 4--DEEP POSTERIOR MUSCLES OF THE RIGHT FOREARM AND HAND. TAKEN
FROM SPENCE(SPENCE, 1990), PG. 223. ...................... 13
FIGURE 5—- PALMER VIEW OF THE INTEROSSEI MUSCLES OF THE HAND. TAKEN
FROM SPENCE(SPENCE, 1990), PG. 223. ................. . ..... 14
FIGURE 6—JOINT MODELING USING INTERMEDIATE LINK ...... . ........... 26
FIGURE e-MODEL OF INTERACTION OF TENDON FORCE AND MEDIAN NERVE ...... 41
FIGURE 9-GRAPH OF REACTION FORCE ON MEDIAN NERVE VERSUS TENDON FORCE . 42
FIGURE lO—GLOBAL COORDINATE SYSTEM ............................. 50
FIGURE 12—SEGMENTAL COORDINATE SYSTEM .......................... 51
FIGURE 13—DIMENSIONS FOR MOMENT OF INERTIA AND MASS CALCULATIONS ..... 52

FIGURE 14-ROTATION OF TENDON VECTOR CONNECTING TWO POINTS AT ENDS OF
SYNOVIAL SHEATHSAAS FINGER SEGMENTS ROTATE RELATIVE TO EACH OTHER

(ARROWS REPRESENT VECTOR) .. ................................ 54
FIGURE 15—FREE BODY DIAGRAM OF FINGER D‘ISTAL PHALANx .............. 56
FIGURE 16—FREE BODY DIAGRAM OF FINGER MIDDLE PHALANx . ., ............ 57
FIGURE 17—FREE BODY DIAGRAM OF FINGER PROKIMAL PHALANK ............ 58
FIGURE 18—FREE BODY DIAGRAM OF .THUMB DISTAL SEGMENT ............... 6 0
FIGURE 19—FREE BODY DIAGRAM OF THUMB PROKIMAL SEGMENT ............. 60
FIGURE 20—FREE BODY DIAGRAM OF THUMB METACARPAL .................. 61
FIGURE 21--LANDSMEER'S EXTENSOR TENDON MODEL. TAKEN FROM

LANDSMEER. (LANDSMEER, 1961) .............................. 66
FIGURE 22--LANDSMEER'S SECOND MODEL. TAKEN FROM LANDSMEER. (LANDSMEER,

1961) ................................................. 67
FIGURE 23--LANDSMEER'S THIRD MODEL. TAKEN FROM LANDSMEER. (LANDSMEER,

1961) ................................................. 68
FIGURE 24—PERCENT DIFFERENCE BETWEEN THREE LANDSMEER MODELS FOR TENDON

EXCURSION ............................................... 69
FIGURE 25--LENGTHS OF TENDON SHOWN ON FINGER .................... 75

FIGURE 26--CRoss-SECTION OF WRIST SHOWING LOCATIONS OF TENDONS IN THE
CARPAL TUNNEL. THE DEEP TENDONS ARE MARKED WITH THEIR RESPECTIVE
ROMAN NUMERALS. TAKEN FROM LANDSMEER(LANDSMEER, 1976) , PG. 14. 78

FIGURE 27--CROSS-SECTION OF THE WRIST SHOWING THE LOCATION OF THE CARPAL

CANAL. TAKEN FROM KAPLAN(KAPLAN, 1965) , PG. 103 . ......... 79
FIGURE 28—LABORATORY SETUP FOR TESTING .......................... 85
FIGURE 29—TARGETING SCHEMATIC FOR FINGERS ....................... 87
FIGURE 30-INSTRUMENTED KEYBOARD USED FOR MEASURING FINGER FORCE ON KEYS

DURING TESTING ........................................... 89

FIGURE 31—INSTRUMENTED KEY USED FOR MEASURING FINGER FORCE ON KEYS DURING

TESTING ................................................ 90
FIGURE 32—FREQUENCY DOMAIN RESPONSE OF THE CHEBYCHEV FILTER ......... 92
FIGURE 33—CALIBRATION CURVE FOR J KEY ......................... 105
FIGURE 34—GRAPH OF COMPARISON OF ORIGINAL, REGRESSED, AND MODIFIED

CURvES FOR THE DIP ANGLE ................................. 112
FIGURE 35—GRAPH OF THE DIP VERSUS PIP ANGLES SHOWING ACTUAL POINTS,

LINEAR REGRESSION AND MODIFIED LINEAR CURVE .................. 112
FIGURE 36-FLEXION/EXTENSION ANGLES FOR THE DIP AND PIP JOINTS . . . . 114
FIGURE 35—EULER ANGLES FOR MCP JOINT . . . . . . . . ....... . . . . ...... 115
FIGURE 38—EULER ANGLES FOR THE WRIST .......................... 116
FIGURE 37-—POSITION OF DISTAL FINGER SEGMENT AND APPLIED FORCE VS. TIME

FOR DETERMINING TIMING OF DATA . . .................... . ..... 117
FIGURE 38--MAGNITUDE OF INERTIAL TERMS ON PROXIMAL SEGMENT VERSUS TIME

........ . ................... 119

FIGURE 39--MAGNITUDE OF INERTIAL TERMS ON MIDDLE SEGMENT VERSUS TIME 119
FIGURE 40--MAGNITUDE OF INERTIAL TERMS ON MIDDLE SEGMENT VERSUS TIME 120

FIGURE 41--X-COMPONENT OF APPLIED FORCE ....................... 121
FIGURE 42--Y-COMPONENT OF APPLIED FORCE ....................... 121
FIGURE 43--Z-COMPONENT OF APPLIED FORCE ................ . ..... . 122

FIGURE 44--GRAPH OF FLEXOR DIGITORUM PROFUNDUS FOR TYPING TRIAL . . . . 124
FIGURE 45--GRAPH OF, FLEXOR DIGITORUM SUPERFICIALIS FOR TYPING TRIAL . 125
FIGURE 46--GRAPH OF THE RADIAL'BAND OF THE EXTENSOR AND THE Y-COMPONENT
OF THE APPLIED FORCE FOR TYPING ‘TRIAL . . . . ...... . ....... . . . . . 125
FIGURE 47—ACCURACY OF CALIBRATED SPACE USING ONLY THOSE POINTS
ACCURATELY TRACKED . . . . . . .................. . . . . . ......... 128
FIGURE 48—GRAPH OF ANGLE BETWEEN THE DISTAL X-AxIS AND THE FINGER Z-
AxIS....... .......................................... 131

xi

TABLE OF TABLES

TABLE l—TENDONS AND MUSCLES INVOLVED IN HAND FUNCTION .............. 48
TABLE 2—COEFFICIENTS OF EXCURSION MODELS (INDEX FINGER) (MM) ...... 73
TABLE 3—POLYNOMIAL COEFFICIENTS FOR RELATIONSHIP BETWEEN (p3 AND (p4 . 110
TABLE 4—RANGE OF MOTION FOR JOINTS DURING TEST .................. 113
TABLE 5-ACCURACY OF CALIBRATED SPACE .......................... 127
TABLE 6—LENGTHS AND STANDARD DEVIATIONS FOR INDEX FINGER SEGMENTS . . . 129

xii

LIST OF ABBREVIATIONS

ADD Adductor Pollicis

APB Abductor Pollicis Brevis
APL Abductor Pollicis Longus
CMC Carpometacarpal

CTS Carpal Tunnel Syndrome

DIP Distal Interphalangeal

EDC Extensor Digitorum Communis
EMG Electromyographic

EMI Electromagnetic Imaging

EPB Extensor Pollicis Brevis
EPL Extensor Pollicis Longus

ES Extensor Slip

FP Flexor Digitorum Profundus
FPB Flexor Pollicis Brevis

FPL Flexor Pollicis Longus

FS Flexor Digitorum Superficialis
IO Interosseous

IP Interphalangeal

LE Long Extensor

LU .Lumbrical

MCP MetacarpOphalangeal

OPP Oppponens Pollicis

PCSA. Physiological Cross Sectional Area
PIP Proximal Interphalangeal
RB Radial Band of Extensor

RI Radial Interosseous

TE Terminal Extensor

UB Ulnar Band of Extensor

UI Ulnar Interosseous

xiii

 

 

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CHAPTER l-INTRODUCTION

For centuries, scientists and physicians have studied
the human hand, one of the most complex biological
mechanisms known. Scientists believe that hand development
is one of the factors that helped humans develop beyond the
remainder of the animal kingdom. The human hand consists
of nineteen bones and forty-six muscles in addition to a
large number of ligaments. Many of the muscles in the hand
serve redundant functions and physicians still debate the
function of some of the muscles. This complexity is what
allows humans to utilize the opposable thumb and to control
motions that range from grasping and turning pill bottle
caps to crushing small objects to gently testing the
ripeness of a fruit.

Within the range of normal human hands, there are many
variations. Humans have different degrees of muscle cross—
over (fibers of one muscle inserting into the tendon for a
different muscle) (Leijnse, 1997b; Leijnse et al., 1992;
Leijnse et al., 1993) and tendon junctions (tendon fibers
from one tendon crossing over into another tendon) in

addition.to the anatomical variations required by size and

increases :3.

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shape differences among people. Each of these variations
increases the difficulty of modeling and understanding
human hand function.

Abnormal or diseased hands present even greater
challenges to the understanding of hand function. Hand
diseases commonly studied include rheumatoid and osteo—
arthritis and carpal tunnel syndrome (CTS). This study
focuses on CTS.

CTS costs corporations and individuals millions of
dollars annually and much work has been done to
qualitatively assess the potential of an activity to cause
CTS (Billi, Catalucci, Barile, & Masciocchi, 1998; Smutz,
Serina, &_Rempel, 1994a; Smutz, Miller, Eaton, Bloswick, &
France, 1994b; Sommerich, Marras, & Parnianpour, 1998).
However,comparatively little work has been done to assess
that potential mathematically (Bay, Sharkey, & Szabo, 1997;
Cobb, An, Cooney, & Berger, 1994; Cobb, Cooney, & An, 1996;
Keir, Bach, & Rempel, 1998a; Keir, Bach, & Rempel, 1998b)
and actually predict the potential of an activity to cause
CTS (Armstrong & Chaffin, 1979; Miller & Freivalds, 1995;
Dhoore, Wells, & Ranney, 1991; Werner, Armstrong, Bir, &
Ayland, 1997a) . The disease occurs more frequently in
ummnen than men and is generally associated with repetitive

tasks such as typing. Although the disease affects only

 

 

 

 

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the hand
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ins

one tenth of a percent of the entire population, it may
affect as many as fifteen percent of those people involved
in repetitive tasks and manual labor.

CTS is caused by irritation of the median nerve in the
carpal tunnel. This irritation is believed to result from
increased pressure in the carpal tunnel (Cobb et al., 1994;
Keir et al., 1998a; Keir et al., 1998b; Seradge, Jia, &
Owens, 1995) or from direct wear on the median nerve (Bay
et al., 1997; Nakamichi & Tachibana, 1995; Novak &
Mackinnon, 1998). Wear on the flexor tendons due to
frictional contact with the carpal tunnel and each other
can cause these tendons to swell and increase the pressure
on the median nerve (Miller & Freivalds, 1995; Smutz et
al., 1994b). This study combines the two theories as was
done by Armstrong, Miller and Nakamichi (Armstrong &
Chaffin, 1979; Miller & Freivalds, 1995; Nakamichi &
Tachibana, 1995).

This study develops the first ever model to predict
CTS based upon the input forces and the motion of the hand.
.Although other studies have provided equations of motion
:for the hand and models for determining the friction force
111 the carpal tunnel, none have combined the information
iJTtO a single model capable of predicting the tendency of a

task to cause CTS. In addition, none have analyzed the

 

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motion of the hand using infrared camera systems or studied
the inertial effects on the motion. Further work must be
done to verify that the model indeed agrees with known
trends to cause CTS and that it can be used in a clinical
situation.

Although many of the earlier studies of the hand
focused on the anatomical construction of the hand and
abnormalities thereof (Backhouse, 1968; Backhouse & Catton,
1954; Chao & Cooney, 1977; Close & Kidd, 1969; Eaton &
Little, 1969; Eyler & Markee, 1954; Fischer, 1969; Harris &
Rutledge, 1972; Kaplan, 1965; Kaplan, 1966; Landsmeer,
1949; Landsmeer, 1955; Landsmeer, 1961; Landsmeer, 1976;
Lin, Amadio, An, & Cooney, 1989; Stack, 1962; Taylor &
Schwarz, 1955; Tully, 1995), recent studies have included
attempts to model the hand mathematically in order to
predict its behavior and assist in the development of
prosthetics and muscle relocation surgeries (Amis, 1987;
.An, Chao, Cooney, & Linscheid, 1979; An, Himeno, Tsumura,
Kawai, & Chao, 1990; An, Kwak, Chao, & Morrey, 1984; An,
Berglund, Uchiyama, & Coert, 1993; An, Chao, Cooney, &
Linscheid, 1985; Armstrong, 1982; Boozer et al., 1994;
Brook, Mizrahi, Shoham, & Dayan, 1995; Buchholz &
.Armstrong, 1991; Buchholz & Armstrong, 1992; Buford,

Meyers, & Hollister, 1990; Chao, 1980; Chao & An, 1978a;

 

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363; Thomps,
& S

harke)’. 13

'I 1979;

Chao, Opgrande, & Axmear, 1976; Chao & An, 1978b; Chao &
Cooney, 1977; Chevallier & Payandeh, 1998; Cooney, An,
Daube, & Askew, 1985; Cooney & Chao, 1977; Crowninshield &
Brand, 1981; Dennerlein, Diao, Mote, & Rempel, 1998; Duque,
Masset, & Malchaire, 1995; Greenwald, Shumway, Allan, &
Mass, 1994; Hazelton, Smidt, Flatt, & Stephens, 1975;
Landsmeer, 1962; Leijnse, 1996; Leijnse, 1997a; Leijnse,
1997b; Leijnse, 1997c; Leijnse et al., 1992; Leijnse &
Kalker, 1995; Leijnse et al., 1993; Micks, Reswick, &
Hoger, 1978; Small, Bryant, & Pichora, 1992; Spoor, 1983;
Spoor & Landsmeer, 1976; Tamai et al., 1988; Thompson &
Giurintano, 1989; Toft & Berme, 1980; Uchiyama, Coert,
Berglund, Amadio, & An, 1995).

Many of the mathematical studies of the human hand
have focused on the function and uniqueness of individual
muscles (Backhouse & Catton, 1954; Close & Kidd, 1969; Cobb
et al., 1994; Dennerlein et al., 1998; Greenwald et al.,
1994; Harris & Rutledge, 1972; Kerr, Griffis, Sanger, &
Duffy, 1992; Leijnse, 1997c; Leijnse & Kalker, 1995; Lin et
al., 1989; Micks et al., 1978; Shewsbury & Kuczynski, 1974;
Spoor, 1983; Srinivasan, 1976; Thomas, Long, & Landsmeer,
1968; Thompson & Giurintano, 1989; Zissimos, Szabo, Yinger,
& Sharkey, 1994) and the static functions of the hand (An

et al., 1979; An et al., 1984; An et al., 1985; Armstrong,

 

 

 

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1982; Buchholz & Armstrong, 1992; Buchner, Hines, & Hemami,
1985; Chao, 1989; Chao et al., 1976; Chao & An, 1978b;
Close & Kidd, 1969; Cooney & Chao, 1977; Hirsch, Page,
Miller, Dumbleton, & Miller, 1974; Keir et al., 1998b;
Leijnse, 1996; Leijnse, 1997a; Leijnse, 1997b; Leijnse et
al., 1992; Leijnse & Kalker, 1995; Leijnse et al., 1993;
Micks et al., 1978; Shewsbury & Kuczynski, 1974; Spoor,
1983; Spoor & Landsmeer, 1976). These works have led to
the knowledge base necessary to facilitate the study of the
dynamic motion of the human hand (Brook et al., 1995;
Buchner, Hines, & Hooshang, 1988; Esteki & Mansour, 1997)
which is necessary in order to predict the tendency of an
adtivity to cause CTS.

In order to better understand the link between CTS and
typing, a three-dimensional, dynamic model of the human
hand is formulated. The theoretical development of this
model includes all four fingers and the thumb as three
link, six degrees of freedom bodies and includes both
kinematic and kinetic analyses. Although the hand could be
modeled as a whole, each finger is modeled independently to
limit the size of the system of equations being solved.
.Although much of this modeling is based upon earlier works,
the incorporations of all fingers and the thumb, the use of

a dynandc system accounting for the accelerations of the

 

 

 

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fingers and the three-dimensional model are formulated in
this work.

The fingers of the hand act essentially independently
because each has its own dedicated muscles. Since the
system of equations created by the model is inherently
underdetermined (muscle function in the hand is redundant),
both muscle grouping and system optimization will be used
to reduce the degrees of freedom in the system. Here, the
initial optimization criterion utilized is taken from
earlier work, however, the secondary criterion and the
optimization algorithm used are new. In addition, no
previous model has been formulated which includes both the
forces and excursions simultaneously. Outputs from the
model include the muscle.forces and tendon excursions for
the entire course of the motion being observed. These
outputs are calculated in a piecewise manner with each data
set being analyzed independently.

The forces and excursions determined using the model
are used to determine the energy lost in the carpal tunnel
through the tendons rubbing on the transverse carpal
ligament and the carpal bones that form the tunnel. Both
the means of calculating the friction force between the
tendons and the carpal tunnel and the definition of the

energy'criterion are defined in this work. Energy lost

will be calculated as the work required to move the tendons
over the tunnel assuming that the coefficient of kinetic
friction is as demonstrated in the literature (Linn, 1968),
(Shih, Ju, Rowlands, An, & Chao, 1993), (Armstrong &
Chaffin, 1979).

One trial was conducted to collect experimental data
to validate the model. This trial consisted of a single
activity conducted a single time. These data in no way can
be used to draw conclusions about the tendency of typing to
cause CTS and was collected solely for the purpose of model
validation. However, the method of collecting the data was
never used previously. .Motion analysis systems based upon
infrared light such as the BTS system used in this work
have not been applied to measuring the motion of small body
segments such as the finger.

Although the model was formulated for the entire hand
and data were collected for the entire hand during one
trial of the experimental procedure, only the index finger
was analyzed. This analysis is representative of that
which can be done for the other fingers and the entire
hand. When used in a clinical setting, the procedures
developed to implement the model can be followed to draw

conclusions about hand function and causes of CTS.

 

 

 

 

 

p4

In the future, this model can be utilized to determine
the relative tendency of two activities to cause CTS. The
total energy generated by an activity can be compared to
that from other activities (or positions during an
activity) to conclude which is more likely to cause CTS.

In the course of analyzing the data from the trial and
developing the data collection techniques used to gather
the data, additional studies were done to determine the
accuracy of the rigid body assumption for the finger
segments, the ability of the BTS motion analysis system to
resolve 3 mm markers, and the resolution and linearity of
the keyboard force transducers. In addition, work was done
to determine the nGCessity of including inertial terms in
the equations of motion. Note that this work applies only
to the typing task and should be reevaluated if this model

is to be used to analyze other tasks.

 

 

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CHAPTER 2—LITERATURE REVIEW

The human hand is a very complex mechanism which has
been studied by physicians, biomechanists and ergonomists
for most of this century. Physicians are still debating
the functions of some of the muscles in the hand and have
developed entire journals (Journal of Hand Surgery, Journal
of Hand Therapy and The Hand to name a few) to the study of
the hand. Biomechanists are developing mathematical models
of the hand in order to better Understand and describe its
movement and functionality, and ergonomists are studying
the effect of workplace habits on the function of the hand.

In order to form a model of the hand to study the
effects of typing on the tendons in the carpal tunnel,
expertise must be drawn from the fields of anatomy,
physiology, biomechanics and ergonomics. Anatomy and
physiology yield the details of the functions and locations
of each of the muscles and ligaments in the hand as well as
the structure of the carpal tunnel. Biomechanics
contributes a means of modeling the origins and insertions

of each of the muscles as well as modeling the structure of

10

 

 

the fingers and the hand. It also contributes information
as to the functiOn of the hand as understood from
mathematical models. The proper application of
optimization theory to biological systems. Ergonomicists
have studied the effects of carpal tunnel syndrome on
individuals and populations. Each of these fields has
contributed considerable knowledge to the current study of
the hand.

For clarity, diagrams of the muscles of the hand are

given in Figure 3-5.

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Figure 1--Pa1mer View of the Superficial Intrinsic Muscles
of the Hand. Taken From Spence(Spence, 1990), pg. 223.

11

 

 

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Figure 2--Superficia1 Figure 3--Deep Anterior
Posterior Muscles of the Muscles of the Right Forearm.
Right Forearm and Hand. Taken From Spence(Spence.
Taken From Spence(Spence, 1990), pg. 220.

1990) 1 P9. 220.

 
  
 
 
 
 
 
   
   
   
  
   
  
  

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Figure 4--Deep Posterior Muscles of the Right Forearm and
Taken From Spence(5pence, 1990), pg. 223.

 

 

 

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Figure 5-- Palmer View of the Interossei MUscles of the
Hand. Taken Frqm Spence(8pence, 1990), pg. 223.

As this study focuses on the biomechanics of the hand,

this field will be reviewed first.

BIOMECHANICAL CONTRIBUTIONS TO THE STUDY OF HAND FUNCTION

Biomechanists have developed two forms of mathematical
models to explain the function of the human hand.
Kinematic modeling has been used to determine the muscles
necessary to maintain balanced motion, to understand muscle
function and to depict anatomical relationships between the

joints. Kinetic modeling has been used to determine the

14

 

 

 

 

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forces in each of the muscles during particular motions,
the reactions at the joints, and the muscles active during

certain activities.

Kinematic Modeling

Kinematic modeling has been used extensively to
enhance the understanding of the function of the human
hand. Kinematic models have been used to develop
relationships between the motion of the proximal
interphalangeal (PIP) and distal interphalangeal (DIP)
joints, to determine the limits on motion of the finger, to
describe the redundancy of the muscles in the hand, and to
describe the functiOn of the lumbricales muscle.

Since the motion of the PIP and DIP joints are coupled
in most people, a relationship that allows the two joints
to be modeled as a Single joint was developed by Spoor and
Landsmer in 1976 (Spoor & Landsmeer, 1976) as a portion of
the study by the authors of the zig-zag motion of the
finger. The zig-zag motion is described as the motion that
allows the metacarpophalangeal joint to be extended while
the interphalangeal joints are flexed. The authors showed
that the zig-zag motion could be predicted using either
kinematic or kinetic models and that the two models provide

comparable results.

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Leijnse and his associates used a kinematic model to
determine the limits on the possible lifting motions of the
finger (Leijnse et al., 1992), to determine the coupling of
the motions of multiple fingers on the same hand (Leijnse
et al., 1993), and to describe the function of the
lumbricales muscle (Leijnse & Kalker, 1995). From a six
tendon--flexor digitorum profundus (FP), flexor digitorum
superficialis (FS), extensor digitorum communis (EDC),
interosseus (IO), radial band of extensor (RB), and ulnar
band of extensor (UB)——model in which slack variables (a
constant--zero if the tendon is taut and positive if the
tendon is slack--subtracted from the displacement equation
for the tendon) were used to describe the inactive tendon
positions, Leijnse (Leijnse et al., 1992) drew multiple
conclusions about the possible constraints on the muscles
generating the lifting motion of a single human finger.
The following constraint combinations were allowed: 1) zero
excursion of the ED, active FS, inactive FP, 2) zero
excursion EDC, active FP, inactive FS, 3) zero excursion
FS, FP active, 4) zero excursion FF, 5) zero excursion IO.
In this paper, Leijnse and his associates showed that
although many of the muscles of the fingers are coupled,

independent motion of the fingers can be achieved through a

16

 

 

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limited range of motion due to the redundancy of the finger

muscle system.

The motion of the fingers on a given hand are coupled
in two ways—musCle fiber cross-over and interconnections of
the tendons. The coupling effects of the interconnections
of tendons upon the fingers of the hand were studied by
Leijnse in 1993 (Leijnse et al., 1993). The model created
showed the interconnections as two dimensional,
inextensible cords. These interconnections limit the
relative motion between two fingers because of coupling of
the two motions.

The lumbrical muscle is different from most muscles in
that it both originates and inserts at tendons rather than
bones. Its origin is on the flexor digitorum profundus
(FF) and its insertion is on extensor digitorum communis
(EDC). In order to study the function of the lumbricales
(LU) muscle in the hand, Leijnse and Kalker, (Leijnse &
Kalker, 1995) created a five tendon, two dimensional model
of the finger. Since the lumbrical muscle originates on the
FP, the FF is taken as being in two segments in the model;
one proximal to the origin of the lumbrical and one distal
to the origin. The proximal segment is modeled as being in
series with both the distal segment and the lumbricals

which are in turn parallel with each other. Since the FP

17

 

 

 

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is inserted on the anterior side of the hand and the LU is
inserted on the posterior side, the PP and the LU work
against each other when both are active and create a
“locking” of the DIP and the PIP. This “locking” allows
these joints to be controlled by the LU and the FP
independently of the position of the MCP joint. When the
LU is slack and the distal FF is taut, the FP acts to flex
the DIP-PIP. When the LU is taut and the distal segment of
the FF is slack, the FP acts to extend the DIP-PIP.

From these three two dimensional models, Leijnse and
his associates were able to explain many functions of the
human hand. They were able to show which motions are
possible given certain muscular constraints, describe the
coupling of finger motions and develop a greater
understanding of the function of the lumbricales muscle.
Further, Spoor and Landsmeer developed a model, that helped
describe the coupling of the PIP and DIP joints, of the
zig-zag condition of the finger using only kinematic

inputs.

Kinetic Models

.Although some work has been done on developing purely
kinematic models of the hand, most work includes both

kinematic constraints and an analysis of the forces

18

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involved in the motion. These models are referred to as
kinetic models. Kinetic models can be broken into two
catagories, static or quasi-static and dynamic.

Static models refer to those in which there is no
motion. Examples are pinching a key or grasping an object.
Since many of the tasks done by the hand is, in fact,
static, many people have studied static models of the hand.
Quasi-static models analyze dynamic motions by looking at
them in a piecewise manner. Quasi-static models do not
take into account the inertial effects of the mass of the
bodies involved, but do not take into account the speed of
the muscle contraction. Since muscle behavior is rate
dependent, this is a significant distinction.

Dynamic models take into account the inertial effects
of the bodies involved and the speed of the muscles. These
inodels are the most complete models used to analyze motion,

however, they are also very complex and are, therefore,

seldom used.

Static and quasi—static models

SinCe many of the actions performed by the hand are

related to gripping or grasping an object, and so are

static functions, models which describe the static

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functions of the hand give insight into the forces involved
in many of the normal daily functions of the hand.

In 1968, Thomas and his associates (Thomas et al.,
1968) performed a static analysis of the human finger in
order to study the contribution of the lumbrical muscle.
This model included both the active (contraction) and
passive (elastic response) contributions of the muscles and
used both kinetic and kinematic analysis of the system.

The conclusion reached was that the equivalent IP segment
(based on coupling of the PIP and DIP joints) cannot be
extended without the presence of the intrinsics (lumbrical
and interosseus muscles). -Specifically, the lumbrical
muscle allOWS'the extension of the IP joint to be performed
with lower all-around force in the muscles than if the
extension were to be performed by the interosseus alone.

Two more models were proposed between 1968 and 1976.
JHirsch and his associates (Hirsch et al., 1974) proposed a
sinmde static model of the thumb to evaluate the forces in
a netacarpophalangeal (MCP) joint of the thumb. In order
tx> reduce the underdetermined system of equations,
electromyographical (EMG) data were used to eliminate
inmactive muscles during the particular activities of
jJTterest (“wine jug” or open and “key” or flat pinch). The

conclusion reached was that the maximum reaction force at

20

the MCP joint of the thumb during the two described
activities was ten times the load applied at the tip of the
thumb. Spoor and Landsmeer (Spoor & Landsmeer, 1976)
described the zig-zag motion of the MCP joint using a
static kinetic model as well as the kinematic model
described earlier. They found that the results of the
kinetic model compared well with those of the kinematic
model.

The first substantial three-dimensional work was
performed by a group of researchers, lead by Edmond Chao,
at the Mayo Clinic in the mid to late 19705 and into the
19809. Although this work was for static analysis of the
hand, it is the groundbreaking work in the field of
biomechanics of the hand. In 1976, a three dimensional
static analysis of the kinetics of the hand in four
actions—tip pinch, lateral pinch, ulnar pinch and grasp—was
performed (Chao et al., 1976). The model was formulated
'using two coordinate systems per joint and allowing the
positions of the tendons to be accurately represented
'without having to account for the joint angle. Euler

angles were used to define the position of the joint in all

jpositions. The first rotation, o (representing
flexion/extension), was performed about the fixed (more

jproximal of two bodies being considered) Z-axis; the second

21

rotation, 9 (representing abduction/adduction), about the
line of nodes which corresponds to a y-axis and the final
rotation, w (representing axial rotation), was about the
moving (more distal of two bodies being considered) x-axis.
The model assumed that the distance between the two
coordinate systems defining a joint was fixed. A direct
consequence of this assumption is that there can be no
translations at the joint. The statically indeterminate
system was reduced by systematically eliminating four of
the nine unknowns in the equations. The system was solved
using each of the 126 possible combinations of active and
inactive forces,.and inadmissible solutions were
eliminated.’ Solutions were considered inadmissible if any
of the tendons was carrying a compressive load, any of the
joint reaction forces was tensile, any of the results were
‘unreasonably high, or the extensors exceed the limit for
Ibeing defined as passive elements. All of these conditions
iuould violate the basic assumptions of the model. The
«conclusions drawn in the study were: 1) in pinch, the
tendons have force magnitudes that obey the following
FP>FS>RI and UI>LU; 2) in grasp, the intrinsic muscles are
responsible for a greater load than the flexors; 3) the
extensors are passive during grasp and active during pinch;

4) jpinch creates higher contact and forces which cause

22

 

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hyperextension at the DIP and PIP than does the grasp
function; 5) the normal contact force at the MCP joint is
higher in grasp than in any other hand function; and 6)
radial deviation and axial twisting are greatest at the MCP
joint in all actions studied. In a later work, (Cooney &
Chao, 1977) the quantitative results of the model above are
given.

In 1978, An and his associates (including Chao)
published a paper that reported the results of a detailed
anatomical study to determine the locations and lines of
actions of the finger and thumb tendons in the hand. They
used various techniques including Xeray analysis of metal
markers placed in the tendons (invasive) , ultrasonic
imaging,.tomographic xerography technique and
electromagnetic imaging (EMI) body scanner (last three are
all non-invasive). Based upon results from ten cadaveric
specimens, they established the unit vectors for all of the
tendons in the hand and the normalized locations for each
(of the tendons at each joint. These locations were all
<determined using the X-ray images. Of the three non-
invasive techniques used, the only one that showed any

}oromise was the EMI body scanner which utilizes computer

‘tomography.

23

In 1977, Berme and his associates (Berme, Paul, &
Purves, 1977) studied the effects of the ligamentous
structures of the MCP joint. This study showed that during
tap turning and pinching, the ligaments do carry a load.

In general, this load is described by the moments at the
joints and is not explicitly assigned to ligaments.

Toft and Berme (Toft & Berme, 1980) developed a three-
dimensional model of the thumb. This model included the
ligamentous structures and predicted the forces in the
ligaments, tendons and joints for squeeze and squeeze and
pinch activities. Two conclusions can be drawn from the
data presented: 1) the collateral ligaments at the IP
joint of the thumb do not carry load during the activities
observed, however, the.collateral ligaments at the MCP
joint do carry a significant load; 2) the minimum reaction
forces at the IP joint were approximately two times the
applied force and at the MCP joint were three times the
applied force. However, these results did not include the
effects of antagonistic muscles which would act to increase
the joint reactions.

In 1988, Buchner and his associates (Buchner et al.,
1988) developed a model of the human hand that included
inertial effects due to the motion of the body segments.

This model introduced a method for determining the tendon

24

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the

displacement based upon joint angles. In addition, a
weighting factor was introduced to the lateral and central
bands of the extensor in order to explain variations in the
relative positions of the PIP and DIP joints. The results
of the model are smooth force and displacement curves which
would be expected in a normal hand.

In 1995, Brook and his associates (Brook et al., 1995)
expanded upon the work of Buchner and developed a
relationship between angular position of the joints and the
displacement of the tendons. In addition, in their
modeling, they modified the constraint relationships on the
intrinsic muscles and the portions of the extensor
communis. This expansion of the constraints allowed the
effect of the uneven approach of the two lateral bands of
the extensor communis to be accounted for in the model.

An innovative approach to determine the equilibrium
equations was proposed in 1979 by Storace and Wolf. The
model developed was based on the principle of virtual work.
This is the only example of such a development in the
literature for modeling of the human hand. This model
yielded the equilibrium equations in a simple, easy to use
method.

Other models have been developed to study various

aspects of the hand. In 1995, Giurintano and his

25

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associates (Giurintano, Hollister, Buford, Thompson, &
Myers, 1995) modeled the thumb as a five-link Chain. Since
both the carpal joint and the MCP joint in the thumb have
two non-perpendicular non—concurrent axes, the authors
modeled the joints as links connected at each end by a
hinge joint rather than point contact joints. The axes of
rotation for these hinges are not perpendicular to the axis
of the thumb. See Figure 6 for an illustration of the use
of the intermediate link. Therefore, this model featured
non-orthogonal coordinate systems (Euler angles) to
describe the rotations and translations of the links. The

model agreed very well with experimental results.

proximal phalange metacarpal

  
  
  

 

Ab/Adduction Flexion/Extension

Figure 6—Joint Modeling Using Intermediate Link

Seirig and Arvikar (Seirig & Arvikar, 1989) presented
time only full hand model found in the literature. All of
time other models modeled one finger at a time. Although
they did not give any details on how the model was formed,

it 3nielded results for each of the muscles and each of the

26

 

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joints in the hand for pulling and pinch activities. Their
paper also included locations of the tendons and ligaments
relative to the joint centers and a description of each of
the muscles of the hand and their functions.

Leijnse published four papers describing different
kinetic models of the human hand. In 1996, Leijnse
(Leijnse, 1996) proved that a bi-articular chain cannot be
controlled by two parallel antagonistic muscles. Thus, a
third muscle is required to control the chain. In
addition, if the lines of action of the two muscles are not

parallel, the chain cannot be held in equilibrium.

In a later paper, Leijnse (Leijnse, 1997b) described
the effect of intertendinous forCe transfers. These force
transfers are the result of two anatomical constructs—
coactivation and tendon cross-overs. In the case of muscle
coactivation, fibers from one muscle body insert into the
tendon of another muscle body, thereby causing some
concurrent activation. The second, cross-overs in the
tendons themselves is referred to as passive connection.
leijnse presented a detailed model which includes both
ypes of interconnection. He then experimentally verified
as model by eliminating the cross-overs in both the model
ld hand and showed that the model described the

perimental results very well. This model is two-

27

 

 

 

 

 

 

 

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dimensional and assumes that the cross—overs are
inextensible and one dimensional (of zero length).

In the third paper in the series, Leijnse (Leijnse,

1997a) showed through a Simple kinetic model that the
lumbrical is never the limiting muscle in unloaded

activities and thus is correctly sized anatomically.

Finally, in the fourth paper, Leijnse (Leijnse, 1997c)

showed that the flexor profundus is better positioned

anatomically than the flexor superficialis for control of

the biarticular finger .

Dynamic Modeling
Dynamic modeling includes the effects of the rate of

extension on the muscles.. There is only one example of

dynamic modeling in the literature.

In 1997, Esteki and Mansour (Esteki & Mansour, 1997)

developed a dynamic model of the human hand that included

force-velocity and length-tension parameters in the muscles

of the hand. Although the muscle parameters were dynamic,

the model was used to study inherently static conditions

{pinch and grasp). From the information given in the

aper, it is very difficult to determine how the model was
aveloped and therefore, difficult to understand the

inclusions drawn.

28

 

 

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Kinetic models have led to a greater understanding of

the functions of the human hand and the muscle forces which

drive the hand in order to perform various functions. They

have been used to better understand the function of the

lumbrical muscle, the reaction forces in the MCP joint, the

internal muscle forces in pinch, grasp and squeeze

functions, the forces in the ligaments of the fingers, and

the effects of interconnections between the tendons.

COLLECTION OF POSITION DATA

Until recently, no one has actually collected position

data on moving fingers. In December, 1999, Rash and his

associates (Rash, Belliappa, Wachowiak, Somia, & Gupta,

1999) published a paper in which they describe a study
comparing motion data collected using a three camera, three

dimensional video motion analysis to data collected using

two dimensional lateral view fluoroscopy. Markers were

placed on each of the joints of the index finger and the

finger was flexed and extended while recording data with

both systems simultaneously. The researchers found that

the two systems agreed well and therefore concluded that

the video motion analysis systems are capable of collecting

data for motion of the fingers.

29

OPTIMIZATION OF BIOLOGICAL SYSTEMS

As in all biological systems, the human hand is a

redundant system. This redundancy allows the hand to

continue to function in case of injury and also allows for

the hand to perform high force, low frequency tasks such as

grasping an object as well as low force, high frequency

tasks such as typing. For the investigator, this

redundancy presents a problem. The redundant systems cause

the system of equations formed when modeling the hand to be

underdetermined. Thus, in order to solve the system of

equations some form of system reduction must be used.
There are many methods found in the literature to

reduce the underdetermined system of equations created when

modeling biological systems. Most of these methods use

some physiological reasoning to justify the reduction.

Physiological reduction is the result of reasoning

based upon the function of the body. In each method, sound

reasoning is used to develop the optimization. criteria,

however, because of the difficulty in performing in vivo

testing, little direct experimental evidence has been found

to support one line of physiological reasoning over

another. However, there are facts about the hand which

lead to criteria for evaluating the various optimization

methods. For example, it is known that antagonistic

30

muscles act during most motions of the hand. These

antagonistic muscles allow the hand to move in a variety of

ways as well as lending stability to the joint. Another

cuiterflx1for judging the validity of a given optimization

cmiteria is the smoothness of the force-time curves. It is
unlikely that the normal hand or any other biological
system has discontinuous force-time curves during any
activity.
Of the criteria which have been proposed in the
The

literature, some are linear and others are nonlinear.

linear criteria all favor the muscle with the largest

moment arm (Tsirakos, Baltzopoulos, & Bartlett, 1997).

Some of the criteria will allow this muscle to be loaded up

to a predetermined limit, at which time the other muscles

are required to take the remainder of the load. In

addition, linear criteria do not ever predict antagonistic

muscle activity and thus do not realistically determine the

Nonlinear criteria, on the

muscle forces in the hand.

other hand, allow for muscles other than those with the

greatest mechanical advantage to begin load sharing at

lower levels. In addition, many nonlinear criteria predict

antagonistic muscle forces.

31

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Linear Optimization Criteria

Many linear optimization criteria have been proposed

in the literature. The most frequently used are force

minimization, stress minimization and weighted force and/or

stress minimization .

The principle behind stress minimization is that the

muscles will attempt to minimize the total stress in all or

each of the muscles involved in a given activity. Stress

in a muscle is defined as the force generated by the muscle
divided by the physiological cross sectional area (PCSA).

There are two approaches to utilizing the stress

minimization principle. An'and his associates (An et al.,
1997c) chose

1984; An et al., 1985) and Leijnse (Leijnse,

to minimize the stress in each individual muscle.

Crowninshield and Brand (Crowninshield & Brand, 1981) and
Giurintano and his associates (Giurintano et al., 1995)
Both

chose to minimize the total stress in the system.

methods yield results although the results were somewhat

different.
Cooney and Chao utilized EMG data to reduce the number

(Cooney & Chao, 1977). They

of unknowns in their model

combined the flexor brevis and opponens pollicis due to EMG

results that show the two muscles are active

simultaneously. Also Hirsch and his associates (Hirsch et

32

al , 1974) utilized EMG reduction to eliminate the flexor

and extensor pollicis longus and the extensor brevis in

Toft and Berme (Toft & Berme,

their model of the thumb.
However,

1980) used EMG data to reduce their thumb model.

they also pointed out the fact that EMG data are difficult

to use for any activity other than isometric contraction

because as motion progresses in a dynamic activity, some of

the muscles which were initially inactive become active and

vice versa. There are some very large disadvantages to
First, using EMG is limited to those

using EMG data.
In addition, noninvasive

activities where EMG data exist.
EMG data can be obtained only for surface muscles.

Finally, continuous models cannot be created because

muscles activate and deactivate over the course of a

motion.
Seirig and Arvikar (Seirig & Arvikar, 1989) described

an optimization criterion they called the merit criterion

in which a linear combination of the muscle forces,

constraint forces and constraint moments was used as the

They were able to obtain results

optimization criterion.
for all of the internal forces using this optimization
:riterion; however, since the criterion was linear, they

ere not able to predict antagonistic muscle activities.

33

In 1978, Chao and An (Chao & An, 1978b) suggested many
optimization criteria based upon: 1) minimum force in a
given muscle, 2) minimum reaction moment at a given joint
in a given direction, 3) minimum sum of forces, minimum sum
of reaction moments in each of the coordinate directions,
and 4) minimum sum of reaction moments in the y and z
coordinate directions. From the thirty linear optimization
criteria described in the paper, only six acceptable
solutions arose. Penrod and his associates (Penrod, Davy,
& Singh, 1974) also used a weighted total force
optimization criterion.

In Chao and.An’s 1978 paper (Chao & An, 1978a) , based
upon the fact that there is little verification that any of
the physiological methods is the correct one, the authors
utilized a method in which a number of muscles equal to the
degree of indeterminancy was set equal to zero. All such
combinations (a total of one hundred twenty) were
calculated and those solutions that met the basic criteria
were retained as feasible solutions. A solution space was
constructed and overlaps in the space were said to be
viable solutions.

In conclusion, although many linear optimization
criteria have been utilized to predict hand forces, few can

allow any muscle other than the one with the largest moment

34

arm1x>carry load and none are able to predict antagonistic

muscle activity.

Nonlinear Optimization Criteria
There are as many nonlinear optimization criteria as

there are linear optimization criteria in the literature.

These criteria allow the forces in biological systems to be

more accurately estimated. Most importantly, nonlinear

criteria predict antagonistic forces where linear criteria

do not. Since antagonistic forces are present in almost

all human motions, the fact that linear optimization

criteria do not predict antagonistic forces has been an
overriding concern with the linear optimization criteria.
Nonlinear criteria have also been introduced which take

into account dynamic muscle characteristics such as force-

velocity and force-displacement characteristics. Taking

these characteristics into account tends to smooth the

force-time curves.
The first nonlinear optimization criterion to be used

was the sum of the square of the muscle forces. This

criterion was introduced by Pedotti and his associates in

1978 (Pedotti, Krishnan, & Stark, 1978). .Although this

criterion keeps the muscle forces low, thereby limiting

muscle energy consumption, it does not take into account

35

.v‘

physiological limits on the muscles and will allow a small

muscle to carry a large load. Pedotti and his associates

compared the results of minimizing the sum of the squares

of the muscle forces to the results from three other

criteria. The other criteria were the sum of the muscle

forces, the sum of the muscle forces normalized by the
maximum muscle force and the sum of the squares of the
muscle forces normalized by the squared maximum muscle

force. When they compared the temporal patterns for each

of the optimization criteria to those from EMG for each of

the muscles used, they found that the linear criteria did
not yield results which compared well with EMG data. In

addition, they found that summing the squares of the muscle

forces was not accurate. Therefore, they concluded that

the best choice of those criteria examined was the

normalized muscle stress squared.

Energy minimization is an attempt to minimize the

amount of energy used by the muscles to perform a given

task. This method was utilized by Nubar and Contini in

1961 (Nubar & Contini, 1961) and is based on the Lagrange

multiplier method in dynamics. The mathematical equations
of the model were derived for the dynamic case but solved

For a static example.

36

 

I(’

I)!

l’.’

Muscle stress limits were introduced in a criterion

based upon a least squares approach that minimizes the sum

of each of the individual muscle stresses squared. This

criterion is believed to minimize the energy used by the

entire system of muscles and was used by Buchner and his

associates (Buchner et al., 1988) and by Brook and his

associates (Brook et al., 1995). This method does take

into account the relative sizes of the muscles, but still

it does not incorporate physiological criteria such as

muscle speed and elongation.
In 1981, Crowninshield and Brand (Crowninshield &
Brand, 1981) introduced a criterion that incorporated the

physiological properties of muscles. This criterion is

based upon the forceaendurance relationship originally
proposed by Grosse-Lordemann and Muller (Grosse-Lordemann,
1937). This relationship stated that the endurance of the
muscle is related to the muscle force raised to a power, n.

Thus, the criterion proposed by Crowninshield and Brand is

to minimize the sum of the muscle forces raised to the same
,powery 11. Since n is an experimentally determined constant

that varies from individual to individual, this criterion

allows for flexibility depending on the individual being

tested. However, Crowninshield and Brand analyzed the

effects of changing n on the results of the optimization

37

arui found that although there is a large difference in the

results of the optimization between n = 1 and n - 2, there

.is little comparative change between n e2 and n infinity.
Experinentally, n falls between 2.54 and 3.14. Since there
is such.a small change in the optimization criterion based
upon.the power, Crowninshield and Brand chose n = 3 as an
average value and used that for all subsequent
calculations. Using Crowninshield and Brand's optimization
criterion incorporates physiological criteria into the
optimization as well as predicting active antagonistic
muscles. The only remaining disadvantage is that the model
does not enforce smoothness in the muscle force-time

curves. Since it is not likely that the body operates in a

discontinuous manner, the muscle force-time curves should

be smooth.

ERGONOMIC CONSIDERATIONS IN THE WRIST

Considerable work has been done to determine the
causes of carpal tunnel syndrome (CTS). It is believed
that there are two possible causes for CTS; either the
median nerve is compressed because of increased pressure in
the carpal tunnel or movement of the median nerve is
restricted causing stretching of the nerve. Proposed

causes of the increased pressure in the carpal tunnel are

38

frictional wear on the tendons in the carpal tunnel causing

inCursion of the lumbrical

fraying of the tendons, edema,
muscle into the tunnel, and position variations. It is

also believed that the median nerve can be compressed by

direct pressure from the tendons in the carpal tunnel.

In 1995, Seradge and his associates (Seradge et al.,

1995) published the results of a study of the in-vivo
carpal tunnel pressure. They concluded that the average
carpal tunnel pressure in individuals with CTS is higher

than that in individuals without CTS. This could lead to

the conclusion that higher carpal tunnel pressure is a

symptom of CTS rather than a cause. However, they also

concluded that certain postures—making a power fist and
grasping a small object firmly followed by wrist extension,
wrist flexion and isometric flexing of the fingers to a

much lesser degree-~resulted in higher pressures in both
individuals with and without CTS. Therefore, activities

that include these types of motions could cause CTS through

increased carpal tunnel pressure.

Werner and his associates (Werner, Armstrong, Bir, &
(ylard, 1997b) also studied the effects of hand, wrist, and

inger positions in causing increased carpal tunnel

ressure. They agreed with previous researchers as to the
Isitions that increased carpal tunnel pressure.

39

 

'

I.)

n.‘

Keir and his associates (Keir et al., 1998b) showed
that loading the fingertip by both pinching and pressing
caused increases in carpal tunnel pressure, although the
pinching task showed a much greater increase. They (Keir
et al., 1998a) also showed that finger position affects
carpal tunnel pressure. They concluded that as the MCP
angle increased from neutral in either flexion or
extension, carpal tunnel pressure decreased. They also
showed that for all angles of MCP tested, the minimum
carpal tunnel pressure occurred at a wrist angle of
approximately twenty degrees flexion and maximized at
maximum extension. 'Although there is a variation in carpal
tunnel pressure with MCP joint angle, the pressures in the
postures tested in this study are significantly lower than
those found during making a fist or grasping an object.
Therefore, it is possible that for typing, increased carpal
tunnel pressure is not the main factor in causing CTS.

A second proposed cause of carpal tunnel syndrome is
direct pressure on the median nerve by the flexor tendons.
Investigators (Armstrong & Chaffin, 1979; Miller &
Freivalds, 1995; Moore et al., 1991) have developed models
based upon the model of a belt on a pulley to determine the
:normal force on the median nerve imposed by the flexor

tendons passing over it under load. Armstrong’s model

40

IS

'1

 

(Armstrong & Chaffin, 1979) gave a linear relationship
between the tendon force and the reaction force on the
median nerve. The force on the median nerve was also
linearly related to the sine of the wrist flexion/extension
angle divided by two. Figure 7 illustrates the model used
to determine this relationship.

Therefore, the reaction force can be described by nearly
linear lines radiating out from zero degrees and zero
tendon force. Figure 8 is a graph of median nerve reaction
force versus flexion/extension angle for various values of
tendon force. From this model he was able to predict that
the tendency to develop CTS was related to the wrist
flexion/extension anglefand‘the tendon force during an
activity. This agreed with observations although the model

was very simple.

 

Figure 7-Mode1 of Interaction of Tendon Force and Median
:Norve

41

Resultant Force on Nerve vs Wrist Angle
w I 1 I I I I

 

Resultant Force (N)

 

 

 

 

 

 

9100 '75 ‘50 ’25 0 25 50 75 100
F lexion/Extension Angle (deg)

— Ft=5N

""" Ft=10 N

— ' Ft=15 N

- ' ' Ft=20 N

-— Neutral position

Figure 8—Graph of-Reaction Force on Median Nerve Versus
Tendon Force

Moore and his associates (Moore et al., 1991)
developed a more complicated model in which the tendon
radius for the wrist is a function of the angle of contact
between the tendon and the wrist, the excursion of the
tendon with respect to the proximal end of the wrist joint
required to achieve the current wrist joint angle in
reference to the neutral, and the moment arm of the tendon
when the wrist angle is zero degrees. The angle of contact
is a simple angle based only upon flexion and extension of

the wrist. The pressure on surrounding tissues caused by a

42

given tendon is then a function of the tendon radius, the
force in the tendon, the coefficient of friction, the width
of the tendon and the angle of contact. The pressure
relationship is developed from the relationship for
friction of a belt on a pulley. See Figure 7 for a
schematic of the belt and pulley model. Externally applied
forces were measured using transducers and then scaled
using relationships developed by An (An et al., 1985) for
grasping to determine the tendon forces. In the
conclusions, the authors reported that the tendon force in
the equation caused the model to predict CTS due to high
force activities and the excursions of the flexor tendons
predicted CTS due to high repetition. It was concluded
that the work from friction best described the total
influence of an activity in causing CTS. This is because
the frictional work incorporates both the excursion of the
tendon and the force in the tendon in a multiplicative
manner.

In 1995, Miller and Freivalds (Miller & Freivalds,
1995) used a model very similar to that described by Moore
and.his associates to predict total cumulative damage in a
tendon. Using this model, they predicted that women,
because of having sharper wrist radii, would be more likely

to develop CTS than men. In addition, they noticed an

43

 

«var-Ira;

.
v
oak-

-

=" w:

d.a\"

"e n;

a“-

.-
A: ln'fi‘
U‘ Von

:0 the
uECI‘e:
in the
be Ca"
by 31:.

increase in the stress in the tendons from both grasp force
and wrist deviation from neutral. This is in general
agreement with statistics of CTS in the general population.
Although the model predicted the general trends expected,
the numerical incidences did not compare well with reports
of CTS.

In 1994, Smutz and his associates (Smutz et al.,
1994b) studied the relationship between repetitive low
force activities and tendon fraying. Although no visible
signs of fraying existed after testing, tendon force distal
to the wrist decreased significantly with no corresponding
decrease in force proximal to the wrist. The authors
proposed three explanations for the apparent lack of change
in the tissue: '1)-compression of the median nerve may not
be caused by fraying of the tendons themselves, but instead
by direct compression of the median nerve, 2) the test
duration may not have been long enough, 3) the nonhuman
primate used in the test may not adequately model the human
wrist, and 4) tendon damage may have occurred, but was not
observed.

Another possibility for a cause of the increased
pressure in the carpal tunnel is incursion of the lumbrical
muscle into the carpal tunnel. This possibility was

investigated by Cobb and his associates (Cobb et al.,

44

1994). By placing wires into cadaveric lumbrical muscles
on intact hands, they discovered that incursion of the
lumbrical muscle into the carpal tunnel is a normal
occurrence. However, the mass of the lumbrical muscle
varied greatly from individual to individual. Therefore,
in hands with larger lumbrical muscles, increased pressure
in the carpal tunnel could occur. The incursion of the
lumbrical into the carpal tunnel is consistent with studies
that show that carpal tunnel pressure increases with finger
flexion.

In 1997, Bay (Bay et al., 1997) and his associates
performed a cadaveric study in which they concluded that a
probable cause of CTS is stretching of the median nerve.
They concluded that this stretching could be caused by two
mechanisms—direct stretching of the nerve caused by
increasing the distance over which it must act and shear
from the tendons sliding over the nerve. Their study
showed that the greatest elongation of the nerve occurred
in extension of the wrist and this agrees with studies of

the causes of CTS.

45

CHAPTER 3-DEVELOPMENT OF DYNAMIC HAND MODEL

The dynamic hand model for predicting the tendency of
typing to cause carpal tunnel syndrome utilizes three
steps. These are the kinetic model, which is a study of
the forces acting on the hand, the kinematic model, which
is the study of the motion of the hand, and finally the
combination of the two in a simple pulley model to
determine the energy lost in the wrist due to the friction
of the flexor tendons on the transverse carpal ligament and

carpal bones.

KINETIC MODEL DEVELOPMENT

The hand is an extremely complex mechanism consisting
of nineteen bones and 46 muscles in addition to numerous
tendons, ligaments and flesh. In order to adequately
model such a complex mechanism, simplifying assumptions
must be made. In addition, methods of analysis from
engineering mechanics must be utilized in determining the
equations of motion and modeling the wear of the tendons in
the wrist. A three-dimensional model is developed and all
of the assumptions incorporated in that model are
described.

In this model, it is assumed that all of the bones act

as rigid bodies, the tendons act as inextensible cords, and

46

the joints were idealized. All interphalangeal joints and
thumb metacarpophalangeal joints are treated as hinges
allowing only flexion/extension and the finger
metacarpophalangeal and thumb carpometacarpal joints are
treated as universal joints allowing flexion/extension and
abduction/adduction. Although the metacarpophalangeal
joints and thumb carpometacarpal joint do not have active
(voluntarily muscle controlled) axial rotation, this is
left as a degree of freedom because of the strong coupling
of abduction/adduction and axial rotation from the joint
geometry (saddle shaped).

A list of muscles considered in this model and their
abbreviations/ taken from the work of An and Chao (An et
al., 1979) is shows in Table 1.

In addition to the general assumptions made about the
modeling of the tissues in the hand—those given above in
addition to neglecting the ligaments and motion of the
flesh (skin and fatty tissue)-some assumptions were made
about the individual muscles involved in the modeling. The
extensor indicis and extensor minimi muscles were grouped
with the extensor communis for their respective fingers,
thus eliminating two unknowns. Since in each case the
specialized extensor muscles act along a line similar to

that of the extensor communis for their respective fingers,

47

Table l—Tendons and muscles involved in hand function

 

Hand
Element

Joint

Unknown Tendon and Intrinsic Muscle
Forces

 

Fingers

DIP

Terminal Extensor (TE)
Flexor Profundus (FP)

 

PIP

Extensor Slip (ES)
Radial Band (RB)
Ulnar Band (UB)
Flexor Subliminus (FS)

 

MCP

Long Extensor (LE)
Radial lnterossseous (RI)
Ulnar Interosseous (Ul)
Lumbrical (LU)

 

Thumb

 

IP

Flexor Pollicis Longus (FPL)
Extensor Pollicis Longus (EPL)

 

MCP

. Extensor- Pollicis Brews" (EPB)

Abductor Pollicis Brevis (APB)
Flexor Pollicis Brevis (FPB)
Adductor Pollicis. (ADD)

 

 

CMC

 

- Abductor Pollicis Longus (APL)

Opponens Pollicis (OPP)

 

 

although without the branching at the individual joints,

this assumption will yield a combined total extensor force

rather than individual forces for each muscle.
to combining the extensor muscles,
proposed four constraint equations based upon
of the extensor tendon complex and the origin

of the lumbical muscles.

48

Chao (Chao

In addition
& An, 1978a)
the geometry

and insertion

These are given below:

IE=aRB+JJB

2 1
RB=3LU+-LE

6
UB=lUI+lLE (l)
3 6
l 1 1 1
ES=§LU+ELE+§RI+§UI

The Newton-Euler equations of motion for the hand were
derived by analyzing each of the finger segments separately
beginning with the distal segment and working proximally.
There are two coordinate systems utilized in this
derivation.

The first is the global system relative to the
laboratory in which the input data for the model were
gathered. This system is Composed of a y-direction which
is perpendicular to the floor pointing upward, a z-
direction which points from left to right on the keyboard,
perpendicular to the y-axis and the x—axis which can be
oriented by crossing the y and z axes. This system is

illustrated below in Figure 9.

49

 

 

 

keyboard

NW

 

 

 

 

subject

 

 

 

y-directionisouoithepage

Figure 9—Global Coordinate System

The second coordinate system is actually a series of
coordinate systems called segmental systems. There is one
segmental system on each finger segment. In these systems,
the x-direction is along the long axis of the finger
segment pointing proximally, the y-direction is normal to
the finger segment pointing dorsally, and the z-direction
is in accordance with the right hand rule. The base of
this system is the proximal joint center for each segment.

This system is illustrated below in Figure 10.

5O

View of Fine: Segment Looking at Dorsal
Surface

(fetal and proximal end
-"—'—-—_-.

fl
'\ M.
/'

y-direction is out of the paper

Figure 10-Segmenta1 Coordinate System

In the equations of motion, a is the absolute
acceleration andllis the angular momentum of the segment

being considered. Iiis defined according to the Newton-

Euler equations of motion as:

§=7-Z+ax7-a ‘ (2)

where Iis the inertia matrix for the body. Since the
coordinate system used for the equilibrium equations is
chosen to be the principal axes of the body and is located
at the center of mass of the body, all of the product

moment of inertia terms in the inertia matrix are zero.

The time derivative of the angular momentum reduces to:

H, = Ina, +(Iz -I”)a)ywz (3)
Hy =Iyyay+(In—In)wxwz (4)
H, = lad, +(1,y Jump, (5)

The moments of inertia and the mass of the finger
segment were determined assuming the finger segment can be
modeled as a cylinder with an elliptical cross section.

This shape was chosen because it closely approximates the

51

shape of the finger segment. Although an ellipsoid appears
to model the segment more accurately, it was shown by
Buchholz (Buchholz & Armstrong, 1991; Buchholz & Armstrong,
1992) that ellipsoids do not accurately model the finger
segments mathematically. In addition, the ellipsoids add
unnecessary complexity to the model. The mass is
determined as:

m=p7rabh (6)
In this equation, p is the mass density of the finger

and is estimated as 1.1 g/cm3(Esteki & Mansour, 1997)

(Brand(Brand & Mosby, 1985) used 1.02 g/cm9). The

dimensions of the elliptical cylinder are a, the width of
the segment at the center; b, the thickness of the segment

at the center; and h, the length of the segment. See Figure

11 for how these dimensions were defined.

H7

   

 

Figure 11—Dimensions for Moment of Inertia and Mass
Calculations

52

The moments of inertia were calculated using the
following formulas for the moments of inertia of an

elliptical cylinder:

In=%(az+b2) (7)
b2 1:2
Iyy=m(T+-f2') ('8)

Izz=m(gzz'+%) (9)

The unit vectors for the tendon forces were defined
using the method developed by Chao (Chao et al., 1976).
One point on the tendon is taken on the distal side and
another on the proximal side of the joint at the ends of
the synovial sheaths in a neutral position. Since each
point is specified in the local segmental coordinate
system, these points will remain relatively stationary
during motion. However, the unit vector formed by taking
one point on each of the two attached segments will change.
Figure 7 illustrates this point. Note also the change of
length of the tendon from the motion can be seen in this

illustration.

53

Proximal Segment Distal Segment

Proximal Segment

Distal Segment

Figure 12—Rotation of Tendon Vector Connecting Two Points
at Ends of Synovial Sheaths as Finger Segments Rotate
Izeelative to Each Other (Arrows Represent vector)

A table containing the points, taken from Chao (Chao
eat: al., 1976), is found in Appendix A. These values are
koaased on an average of fifteen specimens. Each point is
cieefined in its respective cobrdinate system and therefore,
:11) order to calculate the unit vector for the tendon, the
£>Jroximal point must be transformed into the distal
<:<>ordinate system according tovlhe following equation:
FD=RTDP+Z (10)

where PD is the vector representing the proximal point

expressed in the distal system, Ris the Euler angle

transformation matrix between the two systems being
examined, Fpis the vector representing the proximal point

expressed in the proximal system, and Zis the vector
representing the distance, expressed in the distal system,

bet-T‘Meen the proximal system and the distal system.

Once all points were expressed in the distal

coordinate system, a unit vector for each force is

constructed using the following equation:

,. -D
IPD'DI

St:

A

where f is the unit vector for the force under
consideration, Dis the column vector representing the

distal point on the tendon and .130 is as defined before.

All position vectors, F for the moment equations, were

defined by the following equation:

F =D-cg‘ (12)
where cg is the vector representing the location of

the center of gravity of the segment in the distal

coordinate system. Since the finger segment is being

represented by an elliptical cylinder, c§=[-h/2,O,O]T.
the free body diagram

For the distal finger segment,

is given in Figure 13:

55

   
  

Reaction Moment (M3)
Joint Reaction Force (R3)

Flexor Profundus (F P3)

‘ -

T Applied Force (F)

Figure 13—Free Body Diagram of Finger Distal Phalanx

In both the free body diagrams of the finger and thumb

segments and in the equations of motion, the numeric

subscripts'signify the. joint at which the force is applied

(e.g. 1 = metacarpophalangeal joint, 2 = proximal

interphalangeal joint and 3 = distal interphalangeal

joint). From the free body diagram above of the distal

segment, the Newton-Euler equations of motion are:

ZF=F+T§+FE+§3+m3§=m353 (13)
EA?=rpxF+rmxTE+ran3+1rl3=fi3 (l4)

Zklthough the reaction, R, and the moment, M, at the
joint are shown as being general, three dimensional
Vectors, due to the specification of the joint as a hinge
joint . the component of the moment vector in the z
direction is zero. In addition, wx,wy,a, andary are all zero

56

and therefore, H3z =0, 1:13y =Oand H3, =Izzarz . The applied

force, F, and the weight of the segment are in the global y

direction. This assumption is definitely true for the

weight, and is an approximation for the force F . Since

typing is the activity being studied, this approximation

should be fairly accurate.
Each of the remaining two finger segments will be

handled in a similar manner. The free body diagram of the

finger middle phalanx is:

 
 
 
    
 
  

Ulnar Band (UB)
Extensor Slip (ES)
Radial Band (RB)

Reaction Moment (M2)

Terminal Extensor (TE) ._...———
Reaction Moment (M3)
Joint Reaction Force (R,)

F lexor Profundus (F PQR x
- Joint Reaction Force (R2)

____'_, Flexor Profundus (FPZ)
_ , Flexor Superficialis (F82)

“
Z

\
‘------
.

-~.

Figure 14—Free Body Diagram of Finger Middle Phalanx

The equations of motion for the middle phalange are:

ZF=3+za+Fg+E§+Ra+ua+Fgmam, (15)
+ m2§=m252
Z M = F” xR3+Fm xTE'+i",,,,3 x17133 +753 xE§+FRB XRB

+ 5’”, xUB+i",,,,.2 x FP2 +Fm xFS2 +sz sz +M2 + M3 = H2
The components of the reaction moment and time

(16)

d .
erlvative of the angular velocity for the middle phalange

57

are simplified in precisely the same manner as those for
the finger distal phalange.

The free body diagram of the finger proximal phalange
is:

Ulnar Band (UB)
Extensor Slip (ES)
Radial Band (RB)
Reaction Moment (M2) “

Joint Reaction Force (R2)

  
   
 
      
   

Flexor Profundus (FPz)
Flexor Superficialis (F82)

Long Extensor (LE)
Lumbrical (LU)
Reaction Moment (M1)
Ulnar Interosseous (UI)

oint Reaction Force (R)
x

Flexor Profundus (FP,)
Radial Interosseous (RI)

Figure 15—Free Body Diagram of Finger Proximal Phalanx

The equations of motion for the proximal phalange are:
ZF=R2 +1:2'S"+RB+U1§+FII52 +1573"2 +LU+RT+UI+FS§ +1375l
-+LE+JZ+1m§=an
254:?” xi?2 +73 xE§+fM xR§+FUB xU§+7m x1732
+ijm><Fi§z+iiwxLU-I—i’mxRi-I-i"w><U7+iimx1575l (18)

Him xFS, +F,_E xLE+Fm xRl +M2 +Ml =H,

(17)

For the proximal phalange, the reaction moments about

both the y and 2 directions are zero. Unlike the previous

58

two segments, none of the angular velocities or angular
accelerations is zero and therefore, the full equations for
the time derivative of the angular velocity must be used.

Although the system of equations above consists of
eighteen scalar equations, only four of the equations can
be used to solve for the unknown muscle forces. The
remainder of the equations were used to solve for the
reaction forces and moments at the joints. The constraints
presented earlier, based upon the geometry of the extensor
complex and lumbrical muscle, provide four more equations
to solve the system. Therefore, since there are ten
unknown tendon forces, the degree of indeterminacy of the
System is two.

The equations for the thumb were derived in a similar
manner. There are three free bodies to be considered when
QXamining the thumb—the distal segment, the proximal
8egment and the metacarpal bone.

The free body diagram of the distal thumb segment is

Shown in Figure 16:

59

   
   

Reaction Moment (M3)
, Joint Reaction Force (R3)

Flexor Pollicis Longus (FPL3)

‘ -'

T Applied Force (F)

Figure lS—Free Body Diagram of Thumb Distal Segment
From this free body diagram, the following equations

Of motion are derived:

2F=F+EPL3+FPZ3+R3+m3§L=m353 (19)
2 Me, x Fug,“ xEPL, um, x FPZ, +5, xii, + M, = 11 (20)

The thumb proximal segment can be modeled as shown in

1='i§3ure 17:

 
        
 
 

Extensor Pollicis Longus (EPL2)
Extensor Pollicis Longus (EPLQo—-— mam Pollicis Brevis (seep

Reaction Moment (M3)
Joint Reaction Force (R3) Adductor Pollicis (ADD K
Flexor Pollicis Longus «=ng '5

5

Reaction Moment (M2)
Abductor Pollicis Brevis (AP82)

. Joint Reaction Force (R2)

‘ - Qatar Pollicis Brevis (FP82)
--------- Flexor Pollicis Longus (FPL2)

Figure 17-Free Body Diagram of Thumb Proximal Segment

From this free body diagram, the equations of motion

are:

60

2 F‘ =1?le3 + FPZ3 + 1";va2 + FPZ2 + ADD2 + EPBZ + FPEZ + APE2 + R‘,

_. (2 1)
+ R2 + ng = "1252
215! 2'5,“ x 17:101.3 + rm, x FPL‘3 + rm2 x EPL2 + rm2 x 1?sz
+ r4002 x ADD2 + r5,“ x EPE2 + rI-‘PBZ x FPS2 + rm” x APE2 (22)

+rmx1§3 +rR2 sz HI}, +1I7i2 =I-'I2
The thumb metacarpal is modeled as shown in Figure 18:

Extensor Pollicis Longus (EPLZ)

Extensor Pollicis Brevis (EPB )
Reaction Moment (M2) 2 K.

Joint Reaction Force (F32) Abductor Pollicis Brevis (APBZ)

AdductOr Pollicis (ADDZ)

 
 
 
 

F Iexor Pollicis Longus (FPL:)\

 
 
 
 
   
   
 

\
\

Opponens Pollicis( _Pp) bductor/Pfllicis Longus (APL)
Adductor PO'JiCiS (A001) AMuctor Pollicis Brevis (APB1)

\
I

l

|
t

Extensor Pollicis Longus (EPL1)
Extensor Pollicis Brevis (EPB,)

IN

Flexor Pollicis Longus (FPL1)

Flexor Pollicis Brevis (FPB,)
, .1 Joint Reaction .Foroe (R2)

Reaction Moment (M2)

5
Figure 18—Free Body Diagram of Thumb Metacarpal

From this free body diagram, the equations of motion

are :

2: F“ =EII>L2 + Fri:2 + ADD, + 5P5, + FPE2 + APE, + EPL, + FPZ,
+ADD,+EP§,+FP§,+AP§,+0PP+APZ+R’2+R, (23)
+M§=Wa

Z 1‘? em x EPL, + rm2 x FPZZ + rm, x ADI)2 + rm2 x EPB’,
+ rm” x FPS2 + rm” x APE2 + rim x EPL, + rlwl x FPZ,
+ rm, x ADD, + rm, x 5P5: + r,,,,, x FPB’, + rm, x APE, (2 4 )
+r0PP x0P13+rAM x APZ+rR2 xi?2 +rm xR,

+192 HI}, =1?!1

61

Note that again in the case of the thumb, only four of
these eighteen equations were useful for determining the
unknown muscle forces. Since there were eight unknown

muscle forces in the thumb, this leaves a system that is

undetermined by a degree of four. Unlike with the fingers,

there have been no relationships developed in the
literature to reduce the degree of indeterminacy in the
system of equations of motion for the thumb.

In addition to the constraint equalities provided by

the equations of motion, the following inequalities will be

applied when solving for the muscle forces.

0 SE/PCSA,SO.2Mpa (25)

where Pi is the force in the ith muscle and PCSA is the

Physiological cross sectional area. The PCSA is defined as

tllhe volume of the muscle divided by the mean fiber length.
A table of the PCSAs for the muscles in the hand, taken
from Chao and his associates (Chao, 1989) , is found in
Appendix B. Equation 25 constrains the muscle stresses,
and therefore forces, to be tensile and to not exceed the
rnaIntimum possible muscle stress as reported in the
literature (Burke, 1973,- Esteki & Mansour, 1997) .

Given this set of inequalities, the system is then

OINT—imized using two optimization criteria:

62

Minimizez (E. / PCSA, )3 (2 6)

MinimizeZlFUj ) — F(tJ-_1)]2 (2 7)

The first inequality, equation 26, is the criterion
developed by Crowninshield and Brand (Crowninshield &
Brand, 1981) to optimize biological systems. As was
pointed out in the literature review, this criterion is
based upon muscle fatigue and yields results that include
active antagonistic muscles.

The second inequality is being introduced in this
research. The purpose of this inequality is to force
smoothness of the force-time curves. It minimizes the sum
of the squares of the differences between the force at the
current time increment and the force at the previous time
increment for each muscle. It has been pointed out in the
literature (Siemienski, 1992) that the force-time curves
should be smooth as it is unlikely that the body changes
its choices of muscles during a motion. In most cases, a
change in muscle selection would be the only explanation

for a discontinuity in the force-time curves.

KINEMATIC MODEL DEVELOPMENT

Accelerations

The accelerations of each segment of the finger were

found using numerical differentiation of the position data

63

obtained through laboratory testing (described in the
experimental procedure section of this document). For

this, a five-point central difference formula is used

 

(Mathews, 1987). This formula is given below in equation

28 .

f' = -f(‘i+2)+16f(’i+1)'30f(ti)+15f(’i-1)—f(‘i-2) (28)
12At2

As will be described in the experimental procedure
section, At = 0.01 s. f is the value of the function at

the increment given in the subscript. Although two data
points are lost at both the beginning and end of the data
file, this did not cause a loss of useful data. As the
hand was moved into position to begin typing, data were
recorded. These data were not used in the model. Also, at
the end of the file, data were recorded as the subject
rested. This data assured that the entire motion was
included in the data file. These resting data were also
not needed for the model.

In addition, the angular velocities and angular
accelerations for each body were found by numerically
differentiating the Euler angles for the relative position
of two adjacent finger segments using the same central

difference formula.

Tendon Displacement

There have been a number of means to determine the
displacement of tendons mentioned in the literature. These
methods served different purposes depending upon the needs
of the model being presented. Landsmeer introduced the
first of these methods (Landsmeer, 1961). He developed
three different models for determining the length of the
tendon.

The first and simplest is the model, shown below in
Figure 19, that Landsmeer chose to use for extensor tendons
in which the change in length of the tendon is equal to the
change in arc length at the joint. This change in arc
length is calculated using the simple formula

A - :8 (29)
Landsmeer considered this model to be accurate for extensor

tendons because these tendons rest on the bones of the
joint and the radius of curvature for the joints can be

estimated fairly accurately.

65

 

 

 

 

 

Figure 19--Landsmeer's Extensor Tendon Model. Taken from
Landsmeer. (Landsmeer, 1961)

The second model Landsmeer recommended, shown below in
Figure 20, was for use with flexor tendons. Because these
tendons would tend to bowstring without the synovial
sheaths and the sheaths are free to rotate around the
joint, Landsmeer assumed that the synovial sheath would
remain stationary at the midpoint of the joint. Given this

assumption, the change in arc length is given by

A - 2rsin(l/2 9) (30)
Note that for small angles, this reduces to the first model

(Using sin 7:7 for small angles).

66

 

 

 

 

 

 

 

Figure 20--Landsmeer's Second.Model. Taken from
Landsmeer . (Landsmeer, 1961)

The third model, shown in Figure 21, is much more
complex than the first two. It allows for bowstring of the
tendon in a flexible sheath that is fixed to each of the
bones comprising the joint. The change in length of the

tendon in this case is

A . 0n + y{2-6/tan(6/2)} (31)
where y represents the distance from the point of

attachment of the synovial sheath to the bone and d
represents the distance from the center of the finger bone

to the tendon. The larger the value of y, the more this

67

model varies from the other two. This is a result of the
fact that bowstring will increase with greater distance
between the joint and the attachment of the synovial
sheaths to the bone. If d, y and r are held constant, the
variation between each of the models with angle of flexion

can be determined.

 

Figure 21--Landsmeer's Third Model. Taken from
Landsmeer . (Landsmeer, 1961)

In order to compare Landsmeer’s three methods of
calculating tendon displacement, each was used to calculate

the FS tendon displacement for the distal interphalangeal

68

joint of the index finger. Values for the constants, r, d
and y, were taken from An(An, Ueba, Chao, Cooney, &
Linscheid, 1983) in order to make the comparison. Figure
22 illustrates the percent difference between each of
Landsmeer's models. Note that the first model always
yields a larger displacement than the second. The third
model has lower displacements at small angles than either
of the other two models, however at larger angles, the
third model yields higher displacements. In each case, the
percent difference was calculated assuming that the later

model was the standard.

Percent Difference For Landsmeer Models
m I I I I I I I

 

°/o Difference

 

 

 

 

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Angle (rad)
—’ Model 3 vs 1
""" Model 3 vs 2
— ' Model 1 vs 2
" ' ' 45 degrees

Figure 22—Percent Difference Between Three Landsmeer Models
for Tendon Excursion

69

As can be seen in Figure 22, the maximum difference
between the first two models is 11.1% at the extreme of the
motion. Although this is a considerable error, if the
motion is constrained to act in the range of rotation of
less than forty-five degrees that is generally true for
typing with the normal hand, this error reduces to 2.6%.
Given that each of these models is an approximation, a 2.6%
difference would tend to suggest using the simpler of the
two. The percent difference between the third and second
models is 34.0% at 90 degrees and 17.2% at 45 degrees.
Also, the percent difference between the third and first
models is 26.7% at 90 degrees and 15.0% at 45 degrees.

This large deviation can be explained by the large amount
of bowstringing of the flexor tendons that is accounted for
in the third model and not accounted for in either of the
first two models.

In 1978, Armstrong and Chaffin (Armstrong & Chaffin,
1978) developed an empirical model based upon the joint
thickness and the joint angle for the wrist and fingers.
Although the finger model predicted the displacement values
very well, it was only based upon four hands and did not
account for variations in the size of hands. There is no
apparent advantage to choosing this model over one of the

three proposed by Landsmeer. The model for the wrist,

70

however, is the only one found in the literature and will,
therefore, be used and is described below.

Following is the equation taken from Armstrong and
Chaffin (Armstrong & Chaffin, 1978) as modified by Miller
and Freivalds (Miller & Freivalds, 1995) and subsequently
modified to use the angle in radians and give the wrist

displacement in mm.

EW = (0.9181,), + 0.1745,), t+ 3.700;), t i] — 003351)), I i2)1t:10'3 (32)

where:
¢i = wrist flexion/extension angle in radians at the ith

time interval

t = thickness of the wrist

t=\[(-:762-b2) . _ (33)

i1 = 0 for extension, 1 for flexion

 

12

0 for the superficialis tendon, 1 for the
profundus tendon

c wrist circumference

b wrist breadth
In 1995, Brook and his associates (Brook et al., 1995)
derived equations for the excursion of each of the tendons
in the hand based upon Landsmeer’s models. Although they
derived equations for each of the tendons in the hand, the

current model only uses the excursions of the flexor

tendons and, thus, only those excursions will be described

71

herein. Using Brook’s notation modified to label joints as
described in this work, the excursions of the flexor

tendons were:

i w

¢3/ ¢2/
EIFDP=¢3ideP+2nyP 1___ 2 r+¢21dFDP+2nFDP 1_ 2 >

“(7%). “(7%)

A.
+ ¢1id1FDP + zylFDP 1_ / +(bFDP III-"0119‘?

tel—“7)

(42/ (41/
15st =¢2,d{DS +2y§'"1’S<1————2 +¢,,de5 +2yIFDS<1-————2

tan(¢2%) tan£¢l%) (35)

 

 

‘ (34)

 

 

+(beS ”5054.?!“

In the above equations, 01 is the flexion/extension

th

angle at the 1 time interval and 9: is the

th time interval. This is

abduction/adduction angle at the 1
consistent with the choices of Euler angles used throughout
this work. The subscripts used in the equations represent
the joints with 1 being the metacarpophalangeal joint, 2
the proximal interphalangeal joint and 3 the distal
interphalangeal joint. d and y were as defined by
Landsmeer and were approximated for the index finger in
Table 2 below. Finally baanxirn were constants based upon

the modification of Landsmeer’s model III as a second order

polynomial. This modification was published by Buchner

72

 

(Buchner et al., 1988) based upon data from Fischer

(Fischer, 1969). ha and h.a can be found in Table 2 which is
modified from Brook (Brook et al., 1995). The coefficients
in Table 2 were calculated from data collected by An (An et

al., 1983).

Table 2-Coefficients of Excursion Models (Index finger)
(m)

Joint Tendon d y ba ha

DIP FP 2.97 3.96
PIP FS 4.13 6.73
FP 5.76 7.5

MCP FS 9.56 8.14 1.1 0.68
FP 8.32 8.32 0.52 0.66

 

 

 

 

 

 

 

 

 

 

 

 

 

By summing the excursion for the finger motion and
that for the wrist motion, the total excursion of the FP
and F8 for the index finger can be found. Since the values
for the constants to use Brook’s model were only available
for the index finger, a different way of determining the
excursions for the other fingers must be used.

In order to determine those other tendon excursions,
the distance between the distal and proximal points on the
tendon, Chao (Chao et al., 1976), is used to determine the
tendon length at the joints. This assumes that the tendon
bowstrings between the two points (one on each side of the
joint). The difference between this model and Landsmeer's

third model is the difference between the arc length

73

connecting two points on the hypothetical circle and the
ray connecting the same two points. This difference is
linearly dependent upon the radius of the circle; however,
the percent error between the two models is only dependent
upon the angle. The difference increases with the angle of
flexion as illustrated in Figure 22.

The distance between the two tendon points was already
obtained in order to form the unit vectors for the tendon
for the kinematic model. By summing the distances at each
joint, the tendon length for each of the tendons can be
determined. From this length, the incremental change in
length can be determined. The equation for the total

tendon length is:
5(6): L2(tr)+L1(ti)+ L0(ti)+ J3(‘i)iL J2(’i)+ J1(’i)+ EW(ti)
J3(‘i)=lp02(’i)’53(’ix
J2(ti)=lle(ti)-52(tix
11(‘i)=(1300(‘i)-D1(‘i1

(36)

The distances are as shown below in Figure 23. Since
In, La and.Ig are constant and AB is obtained by subtracting
the length at ti from that at tr“, when calculating the
instantaneous change in tendon length, they cancel out.
Thus the equation for the instantaneous change in tendon

length becomes:

74

 

 

 

 

Figure 23--Lengths of Tendon Shown on Finger

115(1))=((13020))‘5301'141301004320)!+|1300(tr)-51(tr1)+ EW(ti)J-
[(11302 (ti+1)-53(ti+11+|fi01(ti+l)- 132(ti+11+|1300(tr+1)-51(1)411)“ EW (041)]

(37)

PULLEY MODEL

According to the principal of conservation of energy,
the heat energy dissipated into the carpal tunnel by the
tendons rubbing on the carpal tunnel is equal to the

frictional work done by those tendons.

75

Therefore, in order to determine the amount of heat
energy dissipated in the carpal tunnel during a given
activity, the instantaneous displacement of the tendon is
multiplied by the frictional force of the tendon acting on
the carpal tunnel. Since the displacements have already
been determined, only the development of the equations for
the frictional force need be described.

The model used to determine the frictional force
generated by the tendons rubbing on the carpal tunnel is
similar to the model of a belt on a pulley developed in
most statics texts. The relationship between the tension
in the belt at the end leading into the motion and that

trailing the motion is

110.) =We.) (38)
T201)
In this equation, 13 is the leading edge tension, T2 is

the trailing edge tension, u is the coefficient of static

friction and a is the angle of contact between the belt and
the pulley. The friction force can be obtained using the

following

f(‘i)=T1(‘i)-T2(ti) (39)

Finally, simplifying these two equations yields an
equation for the friction, one in terms of T3 and the other

in terms of T1.

76

f(tr)=T2(ti)(em(ti)-1)l (40)
f(ti)=T1(ti)(1-e’”"("))

For the wrist, the situation is somewhat complicated
by the fact that the direction of tendon motion changes.
Since the tendon forces have been calculated for the hand
side of the wrist and are unknown for the forearm side, the
hand side forces must always be used to compute f. For
flexion, the hand side forces are equivalent to T3 in the
above equations and for extension, the hand side forces are
equivalent to T2. .Also, the instantaneous extension given
above is positive for flexion and negative for extension.

Therefore, the friction force f can be written, using the
Heaviside step function as
f(t.-)=H(AE(t.-))T2(t.-)(e””(“)-1)+H(AE(t.-))T1(t.-)(1-e"”"("')) <41)

All other variables in equation 41 are as described
before. The coefficient of friction used in this model is
0.01 as it is the only value which is contained in each of
the ranges for the coefficient of friction in a joint found
in the literature (Linn, 1968), (Shih et al., 1993),
(Armstrong & Chaffin, 1979).

The angle of contact, a, is defined as the

flexion/extension angle of the wrist. Since the transverse

carpal ligament runs perpendicular to the long axis of the

77

forearm and the tendons run predominantly along that axis,
the primary contact of the tendons on the ligament is along
the angle defined by flexion/extension. Pronation and
suppination of the wrist will cause the tendons to slide
across the ligament slightly and will not significantly
influence the angle of contact. Figure 24 and Figure 25
show the anatomy of the wrist and can be utilized to
visualize the motion of the tendons in the carpal tunnel.
Although axial rotation of the wrist may cause a small
change in the contact angle, the change will not be

significant.

 

Figure 24--Cross-section of Wrist Showing Locations of
Tendons in the Carpal Tunnel. The deep tendons are marked
with their respective roman numerals. Taken from
Landsmeer(Landsmeer, 1976), pg. 14.

78

Dorsal
Trapezoid metacarpocarpal

Trapezium (basil ligament

(nonarticular
surface)

     
 
   
 
 
 
  

 

__ M71 Capitate
"1  ; ’}<(base)

' g .. . '- a ~
. , 3. W,” 3"“ k Hamete (base)
I y ' ")1" ’ ‘ b“

Extensor pollicis
Iongustendon

 
 

3" Deep branch of

Extensor pollicis ulnar nerve

brevis tendon

Abductor pollicis ‘ Pisiform

longus tendon ‘
Pisohamate

Trapezium ligament
(artri'cular Hook
su ace) Transverse carpal of hamate

First ligament
carpometacarpal Flexor carpi Volar

joint capsule radians Ridge of metacarpocarpal

tendon trapezium ligament

Figure 25-6Cross-section of the Wrist Showing the Location
of the Carpal Canal. Taken from.Kaplan(Kaplan, 1965), pg.
103. ‘ ‘

The frictional force between the tendons and the
transverse carpal ligament or bones of the wrist can be
calculated using the approach outlined above. The
instantaneous energy dissipated can be calculated by
multiplying the instantaneous frictional force by the
instantaneous displacement of the tendon. For a particular
activity, the total energy dissipated is equal to the sum

of the instantaneous energies over the entire activity and

over each of the tendons flexor tendons.

79

Energy=ZZAE(t,-)jf(ti)j (42)
t J

where AE(tflj is the instantaneous change in the
extension of tendon j at time interval i and f(tflj is the
instantaneous friction force in tendon j at time interval
i.

By calculating the force in each of the tendons in the
hand and using those data to determine the frictional force
in the tendons passing over the transverse carpal ligament
and then multiplying that force by the instantaneous
displacement of the tendons, a total energy dissipated in
the wrist from a given activity can be calculated. This
value can be compared to_values generated by activities to
give a relative tendency of an activity to cause carpal

tunnel syndrome.

80

CHAPTER 4-EXPERIMENTAL PROCEDURE

In order to verify the validity of this model,
experimental position and force data were taken during the
typing of a trial sentence. Once all of the data were
accumulated, it was analyzed for use in the model and the
model was verified.

In addition, tests were run on both the force and
position measurement systems in order to verify the
measurement systems were capable of sufficient resolution

to gather data for use in the model.

TESTING PROTOCOL

One set of data was acquired according to the
procedure to follow. These data were solely for the
purpose of validating the model and were not intended as a
clinical test from which major conclusions could be drawn.
Testing was conducted under UCRIS approval, IRB # 93580.

Ideally, data would be gathered for the entire hand
during a single test. The BTS camera system was incapable

of resolving markers on the entire hand simultaneously due

81

to the proximity of the markers on the hand. This
proximity caused the markers to be superimposed with
respect to the cameras during the test. When two markers
are superimposed, the camera cannot differentiate between
the two markers and therefore the system cannot resolve
each target.

Since the system was unable to resolve markers on the
entire hand, each finger was targeted and tested
individually. Although this does not allow the hand as a
whole to be modeled as precisely as if a single test were
used, the fingers do act independently with the exception
of a small degree of interconnectedness(Leijnse, 1997b;
Leijnse et al., 1992; Leijnse et al., 1993). The
independent motion of the fingers combined with the fact
that this model assesses cumulative effects, allows test
data acquired for each finger independently to accurately
model the behavior of the entire hand when combined.

A test sentence was composed that would provide the
most keystrokes by the fingers of the right hand in a short
period of time (preferably about 10 seconds with an average
typist). The test sentence was, “A kind, jolly person
helps bumpkins." This sentence included each of the keys

on the right hand side at the following frequencies: Y-l,

82

U-l, I-2, 0-2, P-3, H-l, J-l, K-2, L-3, Semi-colon-O, N-3,
M—l, Comma-1, Period-1.

The test sentence was typed three times for each
finger. The tests for a given finger were conducted
consecutively and the hand was retargeted for the next
finger immediately following the third test. When
retargeting, the markers on the hand and wrist were not
moved. Since the time required to complete all of the
tests resulted in only 165 seconds of total typing time
over a six-hour testing period, muscle fatigue was not
considered to be a problem. Given the redundancy of the
test, however, the skill level and familiarity of the test
subject with the sentence, did result in improved typing
times as the tests progressed. This improved typing speed
could skew the results versus a single test, as force
generated in a muscle is a function of the speed of motion
(Bigland & Lippold, 1954).

During the typing trials, the subject was seated in a
comfortable typing chair that was adjusted to the subject's
liking. The positioning of the subject in the workspace
can be seen in Figure 26. In addition, the subject was
asked if there was any difference between the feel of the
instrumented keys and the non-instrumented ones. Keys were

adjusted until the subject felt no difference. This

83

allowed the testing to accurately imitate an actual typing
situation.

At the start of the test, in order for the BTS system
to allow tracking of the data points, the subject was asked
to lift the right hand and angle it toward cameras 3 & 4.
Although the motion analysis system recorded the position
data as the subject moved from this position to the typing
position, this was not considered part of the test for data
analysis.

Between tests, the test subject was asked to relax.
This period was only approximately five minutes between
tests of a single finger. Changing of the markers to a
different finger required approximately fifteen to twenty
minutes.

Position and force data were synchronized using the
maximum force and minimum global y coordinate for the first
keystroke. Since the minimum global y coordinate
corresponds with the bottom of the keystroke, it was
assumed to also correspond to the maximum key force. The
validity of this assumption will be discussed in the

results section.

84

MEASUREMENT SYSTEM

Both motion and force data were needed to verify the
accuracy of the model generated in this work. A BTS four—
camera 100 Hz motion analysis system was used to collect
the position data for each of the tests. The force exerted
on the keyboard keys was measured using a standard computer
keyboard with strain gages mounted on each key under the

keycap. The laboratory setup can be seen in Figure 26.

 

Figure 26-Laboratory Setup for Testing

Position Measurement

During each test, the hand was targeted with eleven
retroreflective markers. Three markers were used to define
each wrist, hand and proximal finger segment. The
remaining two finger segments were each defined using two

markers because it was assumed that these segments were

85

only free to flex and extend and therefore remain in plane
with the proximal segment. Analysis was performed to
verify this assumption.

A targeting schematic is shown in Figure 27. In this
figure, each target is identified by its anatomical
position on the body segment and, in the case of the finger
segments, a number indicating which segment it is on (2-
proximal segment, 3-middle segment, 4-distal segment). In
addition, the targets are numbered to facilitate
identifying them later in this document. Although only the
targeting schematic for the index finger is shown, the
targeting system was consistent for each of the remaining
digits.

During testing,.position and force data were recorded
at 100 Hz. This frequency is well over the actual
frequency of controlled human movement, generally
considered to be below 8 Hz(Winter, 1987).

In order for the camera system to determine the three-
dimensional location of any given target, two cameras must
be capable of “seeing” that target. In some of the frames
of data, this criterion was not met for target 1. In those
cases, that target was replaced mathematically in the

following manner.

86

 
 
  

Medial Hand

Medial WIISt ,. i t

Figure 27-Targeting Schematic for Fingers

A relationship was determined between the
flexion/extension angle for the PIP joint and that for the
DIP joint. The assumption that there is a relationship
between these two angles and that the DIP joint is not
capable of fully independent motion is supported in the
literature (Buchner et al., 1988; Harris & Rutledge, 1972;
Thomas et al., 1968). Both the EDC and the FP muscles
cross both the DIP and PIP joints and are the only two

muscles controlling the distal finger segment, therefore,

87

with no other muscles to allow independent motion of the
distal segment, its motion is dependent upon the motion of
the PIP joint. The relationship developed between the two
angles was used to determine the DIP joint angle for the
missing markers. The location of the marker 1 was then
calculated using the average length of the distal segment

and the calculated DIP joint angle using the equation

{Positionl} = {PositionZ} + [Rm ] lR¢4 J- {length4} (4 3 )

In Equation 43, {Positionl} is the position of target 1 in
the global coordinate system, {PositionZ} is the position of
target 2 in the global coordinate system" [R ]‘is the

rotation matrix between the global coordinate system and

the middle segment COOrdinate system, [RM] is the rotation

matrix between the middle segment coordinate system and the
distal segment coordinate system and {length4} is the vector
between targets 2 and 1 expressed in the distal segment
coordinate system.

Once the missing markers were reconstructed, the file
containing the three dimensional position of all eleven

markers throughout the motion was complete.

88

Force‘Measurement

Forces were measured using a specially designed
keyboard (see 9

'Figure 28). Each of the keys on the right hand of the
keyboard was instrumented using a strain gage. A picture
of one such key is shown in Figure 30. The strain gages
were calibrated immediately after the testing to determine

the force versus output voltage relationship.

-+ 10» era-5'“
‘; ' I ‘ .

' 4 I"
z. x- at ‘

 

Figure 28—Instrumented Keyboard used for Measuring Finger
Force on Keys during Testing

89

 

Figure 30—Instrumented Key used for Measuring Finger Force
on Keys during Testing

Each key was produced by removing the key cap and
sanding down the surface of the key. This was to allow the
strain gage to be mounted on the top of the key without
increasing the overall height of-the key. In addition, the
key was then much weaker making it deflect more under the
applied loads and thus giving larger strain readings. Once
the key was sanded, a hole was drilled in the key for the
strain gage wires. Finally, the strain gage was mounted on
the key.

Output from the strain gages was recorded using a
National Instruments strain indicator and Labview. Data
were taken at 100 Hz so that the force and position data

could be synchronized.

90

DATA ANALYSIS

In order to utilize the position and force data in the
model, they first had to be filtered and differentiated to
provide the inputs necessary for the model—centroidal
accelerations, angular velocities, angular accelerations,
tendon displacements and external forces were calculated

from measured data.

Filtering
Both the position and the force data were filtered to
reduce the effects of electronic noise. All position data

0th order , Chebychev

were filtered using a single pass 1
filter with a pass frequency of 8 Hz, a stop frequency of
8.5 Hz and an attenuation factor of 1000. The frequency
domain response of this filter is shown in Figure 31.
Although the frequency domain response of this filter is
quite good, there is a time domain shift in the filtered
data. This shift was calculated and final data use
accounted for it.

Filtering was attempted at 6 Hz and 10 Hz to determine
the effects of changing the cutoff frequency on the
filtered data. It was found that there was not a

significant difference between the signals output by the

three filters.

91

Frequency Response of Chebychev Filter

 

 

 

 

' I I I I I
g 08- 4
.9
E
.5 0.6 "' .‘
E
8
g 0.4 " -
{I
II- 0‘2 L- —.

0 l J l l l

0 2 4 6 8 IO 12 14
Frequency (Hz)

Figure 31—Frequency domain response of the Chebychev filter

The force data were edited rather than filtered. The
signal to noise ratio in the force data was over 10 to 1
and therefore,.those data points which fell below a certain
threshold were forced to equal zero. For the x-component
of the applied force, this threshold was 0.2 N. For the y-
component the threshold was 0.175 N; and for the 2-

component, it was 0.1 N.

Segment Lengths

The filtered position data were used to determine the
lengths for each segment. These lengths were determined by
using the distance between the distal and proximal markers
and were later used to verify the accuracy of the rigid

body assumption and to reconstruct markers which were lost

92

because of obstructed camera views. For example, the
length of the distal segment was calculated using equation

44. All others were calculated similarly.
Iength4 = I{position1}- {positionZH ( 4 4 )

Here, length4 is the length of the distal finger and

the other variables are as defined previously.

Segment unit Vectors

The filtered position data were also used to calculate
the unit vectors for each segment. Since the markers were

placed in the center of the joint in the local z-direction,
the unit vector in the x-direction, a), could be calculated
using equation 45.

:- _ {position2}-{positionl} - -- ~ ~-
ld - |{position2}-{positionl}| (4 5)

The unit vectors in the x—direction for the middle and
proximal finger segments were calculated using a similar
equation.

The unit vector of the z-axis of the proximal two

segments of the finger was then found by taking the cross

product of i and in, as shown below in equation 46. The

P
order assured correct orientation of the z-axis in

accordance with the right hand rule. This method would

result in a singularity only in the case that f and finare

P

93

collinear. During the course of typing with the normal
hand, this does not occur as the finger is naturally arched

to position the fingertip over the keys.

A

. fxf
_ ._ P m

. . (46)
'ip ximl

 

The unit vector for the z—axis of the distal segment

A

was found by correcting the kp to be perpendicular to ii-

A

This was done by subtracting that portion of kp that was

parallel to a, from ép and dividing by the magnitude of

that vector. This is shown mathematically in equation 47.

I; __ (zp "(lip 321).:

- . . . (47)
d lkp ’(kp "(1M

 

Finally, the unit vectors for the y-axes were
calculated by taking the cross product between each
segments' unit vectors for the x and z-axes. This
procedure was used for all of the finger segments and an

example is given in equation 48.
jd=kded (48)

In order to form the coordinate systems for the hand,
the x-axis was first formed to lie along the third

metacarpal. This was accomplished by subtracting

coordinates of target 6 from the mean of the coordinates of

94

targets 7 and 8 and then dividing by the magnitude of the
vector formed. See equation 49 for the procedure.

{position7 }+ {positionS}

 

 

 

. {position6}
i}, = 2 ’ ( 4 9 )
{position 7}+ {position8} _ {position 6}!
2

 

A second axis in the plane of the hand was then formed
by subtracting the coordinates of target 7 from those of

target 8 and dividing by the magnitude of that vector.

.. _ {position8}—{position7}
vh — I{position8}-{position7}| (50)

9h was then crossed with the ah and that vector was

divided by its magnitude to form ]h(it was necessary to

divide the cross product by its magnitude since the two

unit vectors being crossed were not necessarily

 

perpendicular).

A, 17 xi

1}): ." 1’ <51)
(th‘hl -

Finally, the unit vector for the z-axis was formed by
crossing f}, with h.

£h=fhxjh (52)

A similar procedure to the above was used for the
forearm. The unit vector of the x-axis was formed by
subtracting the mean of the coordinates target 9 and target

10 from the coordinates of target 11.

95

{position9}+{position10}

 

 

 

{positionl 1}
lw=* { ,t. 9}3{ .t. 10 (53)
{positionl 1} [903! ran 2 posr Ion

 

A second axis in the plane of the wrist was then
formed by subtracting the coordinates of target 10 from
those of target 9 and dividing by the magnitude of the
vector obtained.

‘3 _ {position9}-{position10} (54)
w — l{position9}—{position10}|

 

The 9W was crossed with the a” and that vector was
divided by its magnitude to form jw.
A, Pwaw
J = . -_. (55)
W lvwxrwl

Finally, kw was formed by crossing a” with jw.

 

Iéw=fwxjw (56)
Joint Angles

Once the unit vectors for the segmental coordinate
systems were formed, the joint angles (Euler angles) were
determined. For the DIP and PIP joints, since these were
assumed to only allow flexion and extension, the rotation
angle was calculated by taking the arc cosine of the dot
product between the two adjacent segments’ local x-unit
vectors. An example of this for the DIP joint is shown
below in equation 57. Although, this method does not yield

the sign of the angle, hyperextension of these joints in a

96

normal person is not expected and therefore, the negative
angle should not occur.
¢4=acos(fm-id) (57)

For the MCP and wrist joints, a slightly more
complicated procedure was necessary due to the unrestricted
rotation of those joints. To calculate the rotations of
these joints, rotation matrices were formed using the unit
vectors for each segment expressed in the global system.
Then the joint rotation matrix was formed by multiplying
the distal segment rotation matrix by the transpose of the
proximal segment rotation matrix. The Euler angle rotation

matrix for this system is

cos (6)-cos(¢) I ' ' cos(9)-sin( ) -sin(6)
-cos (y)-sin(¢) + sin (y)-sin(¢)-cos (0) cos (y)-cos (d) + sin (y)-sin(¢)-sin(6) sin(-y)-cos (0)
sin(y)-sin(¢) + cos (y)-cos (4)) - sin(0) —sin(y)-cos (¢) + cos (y) - sin(¢) . sin(0) cos (y) - cos (0 )

(58)
The first rotation, ¢ (representing flexion/extension),
was performed about the fixed (more proximal of two bodies
being considered) Z-axis; the second rotation, 0
(representing abduction/adduction), about the line of nodes
which corresponds to a y-axis and the final rotation, w

(representing axial rotation), was about the moving (more

distal of two bodies being considered) x-axis.

97

This matrix was set equal to the joint rotation

matrices and the joint angles were obtained for each joint.

Center of Gravity

The filtered raw data were also used to compute the
center of gravity for each of the finger segments. The
center of gravity was assumed to be located midway between
the proximal and distal markers in the local coordinate
system x and 2 directions. In the local y-direction, the
center of gravity was assumed to be half the thickness
measurement for the relevant section below the two markers.
See equation (59 for an example of the computation of the

center of gravity for the distal finger segment.

{cg4} = {positionl}; {positionZ} + l R 4]. {offset} ( 5 9 )

Here, £34} is the location of the center of gravity of

 

the distal segment in the global coordinate system, [R4] is
the transformation matrix from the local distal coordinate
system to the global system and fiwfia} is a vector in the

local coordinate system allowing the center of gravity to
be shifted from the surface of the segment to the center of

the segment with respect to the thickness.

Differentiation

Once the angles and centers of gravity were known,

each was filtered using the same Chebychev filter as was

98

used on the raw data. In gait analysis, the filter is
applied to the raw data and then again to the data after
each numerical differentiation. In this research, the
second derivatives of the data were obtained directly and,
therefore, it is not necessary to apply the filter after
the first differentiation. Since both differentiation and
filtering are considered to be linear operators, the order
of operation is theoretically irrelevant.

The data obtained from the second filter are
differentiated using the following five-point central

difference formula for the second derivative.

- . +16. —30.+J .-. »
fl = fl+2 f‘H-l f2: 6-f‘t-l fi-Q (6 o)
12At
Once the data were differentiated, it was again filtered

using the same Chebychev filter.

Local Coordinates

All of the previous work was done with the data in the
global coordinate system. In order to utilize the data in
the equations of motion, they were transformed into the
local coordinate systems. This was achieved by multiplying
the vectors in the global system by the rotation matrix
from the global system to the local system.

For the angular acceleration data of the proximal

finger segment, a somewhat different approach needed to be

99

used. Since the angles, angular velocities and angular
accelerations are based upon the non-orthogonal Euler angle
directions, transformation equations for the above-

mentioned quantities were developed. These are

a2x = 72+)52-sin(¢2)sin(72) (s1)
azy =éz-cosm)+52.sin(62)cos(yz) (62)
(122 = -652 . sin(72) + 52 ~cos(6’2) cos(72) ( 6 3 )

In these equations, the angular accelerations about
the x, y, and z-axes for the local proximal finger segment
coordinate system are calculated by multiplying the Euler
angle angular accelerations by functions of the Euler
angles for the proximal finger segment. The angular
velocities were then transformed into the correct
coordinate system using the same transformations as were

used on the angular accelerations.

Masses and Moments of Inertia

The masses, moments of inertia and tendon unit vectors
were calculated in accordance with the procedure outlined

in Chapter 3.

MODEL IMPLEMENTATION

All of the inputs-unit vectors, accelerations and
forces—were input into the system of equations formed by
the equations of motion and the constraints due to the

extensor mechanism. These equations, as well as the

100

optimization criteria and the stress limits on the muscles,

were used to solve for the forces in the tendons.

Optimization

A Quasi-Newtonian linear search method was utilized to
solve the underdetermined system of equations. MATLAB
automatically selected this search because all of the
constraint equations were linear. Because of the inherent
instability of optimization, the results obtained from the
optimization were highly dependent upon the initial
conditions supplied. Therefore, a fairly elaborate set of
initial conditions was supplied to the optimization
routine.

It was assumed that the joints would absorb the
majority of the applied force since the tendons are unable
to support a compressive force and the applied load was
compressive.

The moment about the z-axis was assumed to be
constrained by the tendons since there is no applied moment
constraint. Since Fy (y-component of the applied force) is
responsible for the majority of the moment about the z-
axis, all tendon initial conditions were based upon it. If
FY is positive, this indicates that the angle between the

palmer side of the distal finger segment and the vertical

101

is less than ninety degrees. If it is negative, that same
angle is greater than ninety degrees. When the angle is
less than ninety degrees, depressing the key causes a
moment that extends the finger if unrestricted. Therefore,
a larger flexor force is necessary to maintain equilibrium.
However, when the angle is greater than ninety degrees, the
moment caused by depressing the key tends to flex the DIP
and perhaps even the PIP joints depending on the magnitude
of the angle while still extending the MCP joint.
Therefore, the extensor muscle must be used to maintain
equilibrium of the distal two segments, but flexor muscles
must be used to maintain equilibrium of the proximal
segment. In order to maintain this complex condition of
equilibrium, the LU, RI and UI muscles must be activated.

These assumptions led to the initial conditions
described below:

Case 1, applied force is zero--all forces and moments
are set to zero.

Case 2, applied forces are non-zero, angle between

distal finger segment and keyboard is less than ninety

degrees:
J”.Rxdip, Rxpip and Rxmcp were set equal to Fx.
2. Rydip, Rypip and Rymcp were set equal to Fy.
:3.deip, Rzpip and Rzmcp were set equal to F2.
‘4.All moments (deip, Mydip, Mxpip, Mypip and Mxmcp)

were set equal to zero.

102

E5.The tendon forces were assigned the following values:

a. PP = FS = Fy*10
b. TE = LU = Fy/6*10

c. RB = UB = E8 = Fy/12*1o
d. LE = Fy/2*1o

e. RI = UI = FY/30*10

Case 3, applied forces are non-zero, angle between
distal finger segment and keyboard is less than ninety

degrees:

Rxdip, Rxpip and Rxmcp were set equal to Fx.

Rydip, Rypip and Rymcp were set equal to Fy.

deip, Rzpip and Rzmcp were set equal to F2.

. All moments (deip, Mydip, Mxpip, Mypip and Mxmcp)
were set equal to zero.

5. The tendon forces were assigned the following values:

FP = FS = 33/12

TE=2Fy/3

RB UB=ES=RI=UI=LU=Fy/3

LE=Fy

#WNH

QOU‘W

Energy Calculation

Once the equations of motion were solved to determine
the tendon forces, the tendon forces were utilized to
determine the friction force between each flexor tendon and
the transverse carpal ligament. Each friction force was
then multiplied by the respective tendon displacements to
calculate the energy dissipated in the carpal tunnel due to
friction between the tendon and the transverse carpal
ligament. The total energy dissipated was then calculated

by summing the energies for the independent tendons.

103

CALIBRATION

The BTS system was calibrated using a custom
calibration stand with 4 rows and 7 columns of 5 mm
retroreflective markers in a 50 mm by 50 mm grid. Four
planes each separated by 150 mm were used for the standard
calibration procedure including calibrating the cameras for
both position and distortion. The cameras were placed in a
relatively symmetric pattern to maximize convergence of the
system when obtaining marker positions. Actual calibration
parameters and camera locations are given in Appendix D.

Calibration of the BTS camera system allows the eleven
unknown transformation constants to be found. There are
only two direct linear transformation equations used in
finding these transformation constants, one for each
coordinate direction in camera space (a two-dimensional
space). Therefore, a minimum of six markers must be used
to determine the eleven constants. If six are used, the
system is overdetermined. The method of least squares is
used to solve the overdetermined system. This method
becomes more accurate as more known points are used. With
the before stated number of rows, columns and planes used
in the calibration, a total of 112 known points was used to

solve for the transformation constants.

104

The keyboard used to measure force data was also
calibrated. Immediately following the tests, each key was
loaded in 1-ounce increments to 6 ounces and the electrical
response of the strain gages on the keys was recorded.

The weights were then removed one at a time while the
strain gage response was again recorded. A curve was
fitted to the force-voltage data to obtain the slope and
the intercept of the data. These values were then applied
to the test voltages to yield the force time curves. The
calibration curve for the j key is shown in

Figure 32. The calibration curves for all other keys

can be found in Appendix F.

Calibration 'Curvc for j

 

 

 

 

l " \ l l

4 '- -
E
E
:3 2 I— —

0 l l - l

‘900 “850 '800 ”750 ‘700

Strain (microstnin)
XXX jraw data

_ j fitted line

Figure 32—Calibration Curve for j Key

105

QUALIFYING TESTS

Since this model depends upon obtaining accurate
position and force data, the accuracy and repeatability of
both the BTS camera system and the keyboard were measured
in order to assure the validity of the final test results.
An additional concern with the position data was soft
tissue motion. The effects of this were also determined
using the test data.

In order to verify accuracy and repeatability of the
BTS camera system, two 3-mm retroreflective markers were
set at a fixed distance of 17.38 mm from each other. These
were then moved about in the calibrated space for 2 seconds
yielding two.hundred data points with which to verify the
accuracy of the space. These-data were then analyzed to
determine the variation in the distance between the two
markers. In addition, the entire file was tracked using
every combination of two cameras (a total of six
combinations) to determine the location of the markers so
that any bias to a particular camera or set of cameras
could be detected.

In order to verify the accuracy of the keyboard keys,
each key was tested using calibrated weights. The keys
were loaded from zero to 16.68 N (60 ounces) in 1.39 N (5-

ounce) increments. This range was chosen because previous

106

research suggested that the maximum force generated when
depressing a key in normal typing is 5.3 N (Rempel,
Dennerlein, Mote, & Armstrong, 1994). The weights were
then removed one at a time. This procedure was repeated
three times for each key. During this testing, data were
taken at 10 Hz. This allowed for averaging of the force
values at each step without having an unnecessarily large
amount of data. Averaging the data was necessary because
of slight motion of the weights on the keys causing
variation of the gage readings.

In order to verify that soft tissue motion was not
significant, the length of the finger segments was assumed
to be constant throughout the test. If, in fact, the
finger segments are rigid bodies as is being assumed, the
length of each segment should be constant. Any variation
in the length can be attributed to two causes—inaccuracy of
the measurement system and soft tissue motion. Under the
forces involved, it is safe to assume that the bones
themselves do not deflect significantly. The inaccuracy of
the system itself was evaluated utilizing the constantly
spaced markers. Although there is no way to isolate the
soft tissue motion from the system inaccuracy, some
conclusions can be drawn about soft tissue motion by

comparing the magnitudes of the errors in the test with the

107

two constantly spaced markers and the errors in the

calculation of the length of the finger segments.

108

CHAPTER S-RESULTS AND DISCUSSION

In addition toformulating and testing the model for
predicting CTS, the test data were examined to determine
the necessity of modeling the typing task utilizing
inertial terms as well as the stability of the optimization
technique. The accuracy of the BTS motion analysis system
in tracking position data for the hand and the keyboard
used for meaSuring force data-was tested to determine their
capalfljities in acquiring position and force data

respectively for the hand.

ANALYSIS METHODS

In order to simulate the positions for which the
markers were not visible to two cameras, a relationship was
developed between the PIP and the DIP. This was used in
conjunction with the average length of the distal segment
to determine the position of the distal target on the
distal finger segment as outlined in the experimental
procedures section. The relationship between the PIP and

DIP angles was determined first by using a first order

109

regression algorithm. In addition, coefficients were

calculated for polynomials of up to fifth order. Note,
that there is not a significant increase in the correlation
the

values as the order of the polynomial increases. Also,

performance of the higher order polynomials at higher
values of $4, the flexion/extension angle of the PIP joint,

is not better than that for the first order polynomial.

Below, in Table 3, the coefficients and R? correlation

values for each of the polynomials tested are listed.

Table 3—Polynomial Coefficients for Relationship Between o3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

and $4

C0 C1 C2 C3 C4 C5 R2
1 0.894 -0.277 -- -- -- -- 0.952
2 0.508 0.196 .-0,051 -- -- -- 0.964
3 -0.93 2.414 -l.043 'C.202 -- -- 0.966
4 -1.016 1.841 -0.319 0.105 0.03 -- 0.966
5 -40.893 139.83 ~186.572 121.633 -37.948 4.592 0.969

Although the R? correlation for the first order

equation is 0.952, a relatively strong correlation, the
equation was weakest when $4 was the greatest. ¢4 was the

greatest at those points that needed to be replaced and

therefore,

this was not the best equation to use.

The

Tequation was modified to get better correlation at those

points where the angle was the greatest.

Inanually and the Rf'value was calculated.

equation was

110

This was done

The resulting

 

¢4 = O.9¢3 — 0.25 (64)

This equation also yielded an R? correlation of 0.952,
however, it gave a smaller deviation from the actual values
at large angles.

Figure 34 below shows the values of the three curves
(original, generated using linear regression values and
generated using modified values) over time. Figure 35 is a
graph of ¢3 versus ¢4 for the actual data (shown as +’s) and
the two lines created by linear regression (solid line) and
the modified linear equation chosen (dashed line). Note
that the modified curve gives better results at higher
flexion values of the angle:

Once the equation for the relationship between the PIP
and DIP joint angles was determined and the points for the
distal target were reconstructed, the Euler angles for each
joint were calculated as well as the positions for the
center of gravity for each segment. The Euler angles for
the entire test are shown below in Figure 36 -

Figure 38. In addition, the ranges of motion for the

‘test are given in Table 4.

111

Comparison of Original and Generated DIP

 

 

 

 

 

 

‘0 I r I I I 1 I I I I T
I l’
30" ’1 "'1
a - '
é if: I)
O a. '
‘3 20- up A. -I
2 .j '-
e '
a I
A \
m— I: , —
H‘J’:
0 '~'I I I J I I I I4 I I J J I I I 4
o 05 I Is 2 25 3 35 4 4.5 s 55 6 65 7 75 a as 9
Time(s)
—OriginalData
""" Regression
—' Modified

Figure 34-Graph of Comparison of Original, Regressed, and
Modified Curves for the DIP Angle

DIP Versus PIP Angles

 

30"

 

PIP Angle (degrees)

20"

 

 

 

45 49 53 57 61
+++ actual points

— linear regression
— ' modified linear

:Figure 35—Graph of the DIP versus PIP Angles Showing Actual
IPoints, Linear Regression and Modified Linear Curve

112

The orientation for the hand and wrist coordinate
systems is not initially aligned with those of the finger.
Therefore, the absolute values of these angles cannot be
compared with the positions of the finger, however, the
ranges of motion for abduction/adduction and axial rotation
of the MCP joint and all motion of the wrist joint are
valid since these ranges do represent the total motion of

the joints.

Table 4—Range of Motion for Joints During Test

 

 

Joint Flexion/ Range Abduction/ Range Axial Range
Extension Adduction Rotation
(deg) (Pronation/
Suppination)
DIP -s to 39 44 --------------------

 

PIP 20 to 60 4O ....................

 

MCP 7 to 53 ' 46- . . *9 to 11~- 20 ~ 11 to 29 18

 

 

Wrist 32 to 64 . 32. -23 to -S 18 -8 to 6 l4

 

 

 

 

 

 

 

 

Note that the range of motion of the MCP joint and the
wrist is much larger for flexion/extension than for either
abduction/adduction or axial rotation. This is because the
Inotion of the fingers in typing is primarily to depress the
keys, which is achieved through flexion of the finger.
.Abduction/adduction provides fine control to relocate the
fingers over the chosen keys while gross control is

supplied by the wrist and forearm. Therefore, the

113

necessary range of motion for abduction/adduction is

considerably smaller than that for flexion/extension.

As noted earlier, there is a close correlation between

the PIP and DIP flexion/extension angles. This is clearly

shown in Figure 36. Although the correlation is not exact

(R2: 0.952 for the linear coefficients described above),

there is a very close relationship between the two angles.

flexion/Extension for DIP and PIP Joints
l I l l j {I l

 

O
O
O
..‘-‘-..‘-

Angle (deg)
:

zo—o““-

 

 

 

0 I ' I I
m n . n n M w w n

— flexion/extension DIP
'''' flexion/extension PIP

Figure 36—Flexion/Extension Angles for the DIP and PIP
Joints

Figure 35 shows the relationship between the Euler

angles of the MCP joint. The MCP joint is saddle shaped

‘which causes some degree of coupling between
abduction/adduction and axial rotation at the joint. Note
that although the relationship is not as strong as that for

the flexion/extension angles in the DIP and PIP joints, the

eabduction/adduction angle and the axial rotation angle

114

follow similar trends. Also, the flexion/extension angle
appears to be independent of the other two angles as would
be expected since flexion/extension is controlled by
different muscles than the other two motions.
Flexion/extension is controlled primarily by the FP, FS and
ED muscles while abduction/adduction is controlled

primarily by the IO and LU muscles.

Euler Angles for the MCP Joint

 

 

’10
'15

 

 

Melendez)
8
o llllTllTlllll

— abduction/adduction MCP
""" flexion/extension MCP
— ° Axial rotation MCP

Figure 35—Euler Angles for MCP Joint

115

Euler Angles for Wrist

 

6 I I I I T I I I
60- ; - .' ..:
55- . ‘ : ' . ‘ ; A
50* .’ g ,' ‘\ ;' ~. " ‘ .' ‘ ' ‘. _-' 4
45" " " ‘ ‘l ’0' . ' 'I .’ .i .' '
40p ........ 1'" ,2 :5 -
35- '1: -I
30- 4
:3,“ 25- -
E 20- -
“go 15* -
< 10" -
5
o
-5
'10
'15
~20
-2s

 

 

 

 

310 ll 12 l3 14 15 l6 17 18 19

— abduction/adduction for wrist

""" flexion/extension for wrist

— ‘ Pronation/suppination for wrist
Figure 38—Eu1er Angles for the Wrist

Figure 38 is a graph of the Euler angles for the
wrist. The range of motion for the wrist is smaller than
that for any of the other joints. This is because there is
very little gross motion of the wrist in typing and the
fingers can accomplish most of the motion. Also, although
the range of motion for abduction/adduction of the wrist is
eighteen degrees, for the majority of the test, this motion
was constrained to less than eleven degrees with the

remaining seven only occurring when the operator used the

enter key. A similar large motion would be expected in

116

order to reach any of the keys on the outer edge of the

keyboard. It is
Euler angles for
truly capable of

In order to

hand, force data

also interesting to note that each of the

the wrist is independent as the wrist is

controlled three-dimensional motion.

complete the analysis of the motion of the

must be combined with position data.

Since the computers utilized in collecting the force and

the position data were not synchronized, the fact that

maximum key force will occur at the bottom of keystroke was

utilized to synchronize the data.

From Figure 37,

it can

be seen that there is good correlation between the peak of

‘ Distal Finger Position and Applied Force

 

0‘ ~I
l.-o-P-ooq---W

'
0"
.

-.-‘
0

Position (mm) and Force (N)

 

1 I

u-I

T I I

:-

o
a.-.'
0.....-QQDOI.OO\..
.

o
.uo--..-
5'!-

8

-
-----.--'...'---.-...

‘-
C

I
. a "O. a.
I. '

A

 

 

310

390

— Applied Force
""" Global y Coordinate/10

Zero Line

870

950

Figure 37--Position of Distal Finger Segment and Applied
Force vs. Time for Determining Timing of Data

117

the force magnitudes and the minimum global y position of
the distal segment although this correlation seems to
become worse with increasing time. This declining
correlation could be due to the different and

unsynchronized clock speeds of the two computers taking

data.

DYNAMIC VERSUS QUASI-STATIC ANALYSIS

Prior to calculating the tendon forces, the magnitudes
of applied force (force between the keys and the finger)
and the inertial terms in the equations of motion were
compared to determine if it would be necessary to include
the inertial terms in the calculation of the tendon forces.
If the inertial terms are included in the analysis it is
considered to be a dynamic analysis. If not, the analysis
is considered to be quasi-static.

Figure 38 -

Figure 40 show the magnitudes of the inertial terms
for the proximal, middle and distal segments respectively.
lflote that the maximum magnitude of any of the inertial
'terms is 0.06 N. The magnitude of this term is very low
<iue to the low mass of the finger segments (“meMn1= 0.014

kg, muddle = 0.00554 kg and mdistal = 0.00377 kg).

118

Inertial Terms Proximal Segment vs. Time

 

0.05 "'

0.04 h

0.03 '-

 

 

 

0.02 '-

 

Magnitude of Inertial: Terms (N)

 

 

 

0.01 k-

 

 

 

 

Tirne (s)

Figure 38--Magnitude of Inertial Terms on Proximal Segment
Versus Time

Inertial Terms on Middle Segment vs Time
°-°3 I I I I I I I n

 

0.025 "'

.o
8
I

 

 

0.01 '-

Map'fldeoflnatialTermsm)
2
G
I
2

 

 

 

 

 

 

 

 

 

 

The (a)

Figure 39--Magnitude of Inertial Terms on Middle Segment
Versus Time

119

Inertial Terms on Distal Segment vs Time
°~°2 I I I - n I I I T

 

0.015 ’— '1

0.01 '-

 

 

Mayiitude of Inertial Terms (N)
l

 

 

 

 

 

 

Figure 40--Magnitude of Inertial Termm on Middle Segment
Versus Time

The force applied to the keys is between 0.5 N and 4
N, at least two orders of magnitude higher than the
inertial forces. Because of this difference, inertial

effects were neglected in determining the tendon forces.

OPTIMIZATION RESULTS

The optimization program was run to obtain the tendon
forces throughout the motion. Below, the results are shown
including the input forces and the results.

The input forces are shown in Figure 41 — Figure 43.

'These are shown for comparison with the output tendon

forces.

120

x-Component of Key Reaction Force vs. Time

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘ I Y I I W T I T Y
3 5 I- 4
3 _ _
2.5 ~ ..
5
§ 2 - -
0
II.
1.5 '- -l
1 )- -4
d5» I
o r 4L I l I h 7 I, l I I
0 100 200 300 400 500 600 700 800 900 1000

Tim e (sec'100)

Figure 41--x-Component of Applied Force

Y-‘Component of Key Reaction Force vs. Time

0‘5 f I I T I I fl I I

 

° Il IH IIIfl

 

 

 

“0.5 i- 4

E -1 _ . -l
0
2

E 45. .

-2L 1

-2.5 - .

 

 

 

 

 

0 100 200 300 400 500 600 700 800 900 1000
Tim 0 (sec'100)

Figure 42--Y-Component of Applied Force

121

Z-Component of Key Reaction Force vs. Time

0 . . . .717. r
l l

 

 

 

-0.4 - J

 

 

 

 

 

 

 

 

 

 

Force (N)

-1- .

 

 

 

 

 

 

-1.4 g I I I I L I I I
0 100 200 300 400 500 600 700 800 900 1000

Time (sec'100)

 

Figure 43--z-Component of Applied Force

Although data were output for each of the tendon
forces and reaction forces and moments, only the FP, FS and
RB forces are discussed so the remainder of the graphs are
presented in Appendix H. PP and F5 are discussed because
they are relevant to the completion of this work. The RB
force is discussed because it is typical of the extensor
forces.

Figure 44 shows the force in the FP muscle and Figure
45 shows the force in the FS muscle throughout the trial.
As is expected given the constraints (all tendon forces are
tensile), the forces are positive throughout the motion.

In addition, their magnitudes are approximately what would

122

be expected given the applied loads and is slightly lower
than results obtained by Chao and An(An et al., 1985; Chao
& An, 1978b) who predicted that the FP force should be
1.93-2.08 times the applied force for tip pinch.

Comparison is made with tip pinch because of the similarity
in location and direction of the applied loads in the two
situations.

Although the force is positive throughout the motion,
there are some points where the force is much larger than
the expected value (points 695 - 700, 716). These spikes
occur where a valid solution to the systems of equations
was not found. This phenomena can be more clearly seen in
Figure 46 which shows the force in the radial band of the
extensor complex and the y-component of the applied force
versus time. Both are shown to illustrate the relationship
between the y-component of the applied force and those
points for which the optimization technique was incapable
of finding a solution to the system of equations. Note
that the points where a negative value of the radial band
force were points 245, 695 - 700, 716 and 778. In all
cases the y-component is less than zero and therefore, the
(angle between the palmer surface of the distal segment of
theIfinger and the surface of the keyboard is greater than

Ininety degrees. The model is capable of predicting the

123

forces in the tendons when the y-component is negative, but
small (between ninety and ninety-five degrees). However,
when that angle is larger than ninety-five degrees, as is
the case for points 695 - 700 and 716, the model is
incapable of predicting the forces. This behavior is due
to the complex nature of forces in this case.

In general, the model is capable of predicting the
forces in the tendons of the finger, however, it does not
predict those forces when the angle between the distal
finger segment and the keyboard is large. This occurs when
the typist reaches the keys on the bottom row of the

keyboard.

Flexor Digitorum Profundus Force \B. Tune
10 I I T I I I I I

 

 

 

 

 

 

 

100 200 300 400 500‘ 600 700 800 900 1000
Tune (sec‘100)

Figure 44--Graph of Flexor Digitorum Profundus for'Typing
Trial

124

Flexor Digitorum Superficialis Force vs. Time
10 I I T I I T I I

 

 

 

 

FDS (N)

 

 

L

-10 I I I I I I I I
100 200 300 400‘ 500 600 700 800 900 1000

TIme (sec'100)

 

Figure 45--Graph of Flexor Digitorum.Superficialis for
Typing Trial

Radial Band Force and Y-Component oprplied Force vs. Time

10 I I I I I I T f I

 

 

 

R8(dashed) and YvComponent of Appliedisolid) (N)
O
“4:
J)
4

 

 

 

 

100 200 300 400 500 600 700 800 900 1000
Time (sec'100)

Figure 46--Graph of the Radial Band of the Extensor and the
Y-component of the Applied Force for Typing Trial

125

ENERGY CALCULATION

The energy lost due to friction in the wrist was
calculated in accordance with the procedure described in
Chapter 4. It was found that 1.217 x.10“‘J'per activity
were lost due to the motion of the tendons of the index
finger in the carpal tunnel. For this value to be useful,
extensive clinical trials will need to be performed to
verify that the method described herein is both accurate
and repeatable. In addition, studies are needed to
correlate energy values found using this method with known
tendencies of activities to cause CTS. Once these studies
have been performed, the true usefulness of this model will

be known.

SYSTEM ACCURACY

The accuracy of the BTS system was verified as
specified in the experimental procedure. The values for
the mean and standard deviations for the distance between
the two markers are given in Table 5 for each of the camera

combinations.

126

Table S—Accuracy of Calibrated Space

 

 

 

 

 

 

 

 

 

Cameras Mean Standard Minimum Maximum Range
Distance Deviation (mm) hmn) (mm)
(mm) (mm)
1&2 17.365 0.412 16.463 19.234 2.771
3&4 17.222 0.735 14.352 21.035 6.683
1&3 17.143 0.744 14.904 19.431 4.527
2&4 17.324 0.591 11.999 19.243 7.235
1&4 17.321 0.727 12.525 20.262 7.738
2&3 17.397 0.428 16.491 119.988 2.497
W/O Errors 17.390 0.303 16.491 18.164 1.673

 

 

 

 

 

 

After careful examination, it was found that the above
analysis contained some tracking errors. Due to the size
and proximity of the markers, the BTS motion analysis
system would not automatically track the markers. As a
result, the markers needed to be identified manually in
each frame of data.

In many cases, as the markers were moved through the
camera space, the two markers would appear to trade
positions in the camera views (in one frame, target one
would be the higher target and in the next, it would be the

lower target). It was very difficult to determine when

127

 

this occurred and as a result, in some cases, the markers
were misidentified. When this occurred, the distance
between the markers was incorrect. Ninety—four of the data
points had identical distance values regardless of the
cameras used to track them. Due to the above-mentioned
difficulties, these values were taken to be the only valid
data points.

The data were reexamined and it was found that the
mean distance between the points using only the ninety-four
points was 17.380 mm and the standard deviation of the
values was 0.303 mm. A histogram of these values is shown

below in Figure 47. -The marking points are given at the
mean, and i‘1 thru 4 standard deviations from the mean.

From this figure, it can be seen that the distribution is

approximately normal about the mean.

Histogram of Distances Between 2 Markers
30 I I I I I I I
25 '-

20'-
15"
10'-

5..

 

J

Occurances

      

 

 

     

. l J l l
96.17 16.47 16.78 17.08 17.38 17.68 17.98 18.29 18.59
Distance (mm)

 

Figure 47-Accuracy of Calibrated Space Using Only Those
Points Accurately Tracked

128

The maximum value of the distance was 18.164 mm and
the minimum was 16.491 mm yielding an overall range of
1.673 mm. Given that the range of motion being studied is
approximately 30 mm, this variation is acceptable.
However, it does imply that a limited amount of “noise” is
to be expected in the actual test data. This “noise”
causes large-scale inaccuracies in the acceleration data
and therefore imposes the need for filtering of the data.

In addition to determining the accuracy of the
calibrated space, soft tissue motion was measured and the
rigid body assumption was verified by calculating the
length of each finger segment throughout the typing trials.
The mean lengths and standard deviations for each of the
finger segmentsare shown below in Table 2.

Table 6-Lengths and Standard Deviations for Index Finger
Segments

 

 

 

 

 

Segment Mean Standard Maximum Minimum Range
Length Deviation (mm) (mm) (mm)
(mm) (mm

Proximal 54.006 1.416 57.991 49.567 8.424

Middle 29.543 1.055 31.800 27.491 4.309

Distal 23.976 0.614 25.405 22.632 2.773

 

 

 

 

 

 

 

Note that the soft tissue motion decreases for the

more distal finger segments. This is because the range of

129

motion and amount of soft tissue are also decreasing and is
to be expected. In the above results, it is not possible
to separate the inaccuracy of the BTS motion analysis
system from the soft tissue motion. However, due to the
relative magnitudes of the errors in the finger segment
lengths and the accuracy of the calibrated space, it is
reasonable to conclude that there is soft tissue motion in
both the proximal and middle segments and minimal soft
tissue motion in the distal segment.

In order to verify the assumption that the motion of
the finger segments is planar, the dot.product between the
z-unit vector for the proximal and middle segments and the
x-unit vector for the distal finger segment was taken and
the angle between the two vectors was calculated utilizing
the definition of the dot product (Equation 65). This was
then graphed and the results are shown in

Figure 48.

Ill=cos"(/3p-?d) (65)

130

Distal Segment Angle From X to Z axis
I I I I I I I

A ll
”VI 11 III. I. IN

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

Figure 48—Graph of Angle Between the Distal x-Axis and the
Finger Z-Axis

From these data, it was found that the average angle

between the two vectors was 93.358° with a standard

deviation of 2.615°. The angle should be 90°as the two
vectors should be perpendicular if the motion of the DIP
and PIP joints is purely planar, but this variation is
relatively small. There are two possible causes for this
variation. One is that the interphalangeal joints are not
spherical, but are condoloidal in nature. The other could
be inaccuracy in the marker placement for the test.
Markers were aligned on the finger visually, which could
introduce error. The error in the direction of the z-axis
for the distal segment was corrected as described in the

methods section.

131

CHAPTER 6 - - CONCLUSIONS

A model for determining a relative measure of the
tendency of an activity to cause carpal tunnel syndrome was
developed. For the results of this model to be used
clinically, verification of the model's accuracy and
repeatability must be performed. In addition, analysis
should be done to attempt to correlate the results obtained
from this model to known tendencies to cause carpal tunnel
syndrome.

Although the analysis was performed only on the index
finger for this work, the model is intended to analyze full
hand motion. The results from each finger will be added
together to determine the total energy for an activity.
This total energy can be compared to the energy from other
activities or different postures of the same activity to
determine which activity will have a greater chance of
causing CTS. The higher the energy dissipated, the higher
the chance of causing CTS.

In the trial performed, the model predicted the tendon

forces well for those finger positions where the angle

132

between the distal finger segment and the keyboard was less
than 90°.~ When the angle was greater than 90°, the model
was incapable of predicting the forces. The angle is
greater than 90° when the person reaches for keys on the
bottom row of the keyboard.

For applied forces between Zero and five Newtons, the
reSulting tendon forces were between zero and ten Newtons.
These magnitudes are comparable to results found in the
literature.

When analyzing the typing task, it is appropriate to
utilize a quasi-static method as the influence of the
inertial effects on the tendon forces is negligible when
compared with the influence of the applied force. This
conclusion is based upon the magnitude of the applied force
being two orders of magnitude higher than the magnitude of
the inertial terms. Since typing is a low force, high
velocity activity, having relatively high inertial effects
when compared to other activities, the quasi-static
assumption can also be used when analyzing other
activities.

An equation, ¢4=0.9¢3—0.25, was found to relate the
PIP, ¢4, and DIP, ¢3, angles. The R? correlation between

this equation and the data from the trial is 0.952.

133

The standard deviation for the length of the finger
segments was 0.614 mm, 1.055 mm and 1.416 mm for the
proximal, middle and distal finger segments respectively.
This indicates that there is soft tissue motion in the
fingers. The increasing standard deviations with
increasing proximity to the hand is from the greater amount
of flesh on the more proximal segments of the finger.

In addition, the systems utilized to collect data for
implementation in the model are adequate.

The motion analysis system was capable accurately
determining the location of the targets to i 1 mm at the
six-sigma level. However, improvements should be made on
the force transducers utilized to record keystroke force to
ensure that force is accurately recorded and the force can
be resolved into components rather than assuming that the
entire applied force is in the global y-direction. In
addition, before large-scale clinical use can be made of
the model, motion measurement systems must be improved to
facilitate easier data tracking.

Further work must be done to determine if this model
is clinically valid. Clinical trials must be performed to
determine if results are repeatable. Also, results must be
compared with known data on incidences of CTS to determine

if the model accurately predicts the tendency to cause CTS.

134

APPENDIX A—TENDON LOCATIONS

Tendon locations in thumb (mean value of five specimens).

 

 

 

Distal Point Proximal Point 1
Joint Tendon X Y Z X Y Z
EPL 0.000 0.192 -0.057 -0.050 0.201 —0.044
IP FPL -0.007 -0.224 0.049 0.100 -0.318 0.034
EPL 0.000 0.280 -0.157 -0.050 0.247 -0.224
FPL -0.062 -0.318 0.009 0.100 -0.521 0012
MP ADD -0.062 -0.224 -0.280 0.100 -0.575 -0.346
EPB 0.000 0.265 0.057 -0.050 0.268 -0.019
FPB -0.062 -0.094 0.285 0.100 -0.416 0.435
APB -0.062 0.007 0.288 0.100 -0.160 0.533
EPL 0.000 0.179 -0.385 -0.050 0.225 -0.076
FPL -0.067 -0.476 -0.046 0.100 -0.152 -0.276
A00 0067 -0.065 -0.395 0.100 0.269 -0.589
CMC EPB 0.000 0.302 0.029 -0.050 0.184 0.132
FPB -0.067 -0.351 -0.284 0.100 0.004 -0.848
APB -0.067 -0.140 1.098 0.100 -0.273 0.410
OPP _ -0.067 -0.236 0.090 0.100 -0.493 -0.074
APB ' -0.067 0.346 0.212 ' 0.100 0.136 0.239

 

135

Tendon locations in index finger (mean value of 15

specimens) .

 

 

 

 

 

 

 

Distal Point Proximal Point
Joint Tendon X Y Z X Y 2
TE 0.004 0.199 -0.010 0.000 0.196 -0.009
DIP FP 0.004 -0.184 0.026 0.300 -0.245 0.054
PP 0212 -0.308 0.009 0.400 -0.409 0.027
RB -0.112 0.186 0.223 0.100 0.181 0.268
PIP UB 0112 0.151 —0.290 0.100 0.131 0312
FS 0212 0249 0.015 0.400 -0.311 0.028
ES ~ -0.038 0.278 -0.027 0.000 0.266 0026
PP 0118 -0.386 0.031 0.300 -0.619 0.004
FS 0118 ' -0.477 -0.074 0.300 -0.689 0114
RI 0318 -0.033 0.443 0.400 -0.362 0.629
MCP LU -0.318 -0.148 0.370 0.400 -0.704 0.541
Ul -0.318 -0.039 -0.461 0.400 -0.379 0442
LE -0.018 0.421 -0.033 0.000 0.483 -0.026
Tendon locations in middle finger (mean value of 15
specimens) .
— . Distal Point Proximal Point
Joint Tendon X Y Z X Y 2

TE -0.036 0.157 -0.014 0.000 0.169 -0.017
DIP FP 1-0.036 ' 40.158 0.054 ' 0.300 -0.239 0.050
FP -0.267 -0.308 0.009 0.400 -0.251 -0.007
RB -0.167 0.206 0.237 0.100 0.132 0.262
PIP UB 0167 0.132 -0.262 0.100 0.079 0290
FS 0267 -0.217 0.054 0.400 -0.248 0.023
ES -0.017 0.241 -0.019 0.000 0.234 -0.009
FP -0.317 -0.334 0.009 0.300 —0.522 0.001
FS 0185 -0.355 0.065 0.300 -0.593 0.063
RI 0185 0.011 0.340 0.400 -0.499 0.491
MCP LU -0.385 -0.174 0.311 0.400 -0.680 0.403
UI 0385 0.011 0135 0.400 -0.185 0119
LE 0085 0.352 0.015 0.000 0.416 -0.013

 

136

Tendon locations in ring finger (mean value of 15

 

 

 

spec imens)
— Distal Point Proximal Point
Joint Tendon X Y Z X Y Z
TE -0.054 , 0.141 -0.016 0.000 0.154 -0.021
DIP FP -0.054 -0.160 0.001 0.300 —0.239 0.027
PP 0276 -0.281 0.01 1 0.400 -0.306 -0.007
RB 0176 0.142 0.176 0.100 0.092 0.256
PIP UB -0.176 0.141 -0.215 0.100 0.088 0238
FS 0276 -0.218 0.048 0.400 -0.263 0.029
ES 0026 0.221 0.004 0.000 0.204 0.023
FP -0.204 -0.302 0.022 0.300 -0.509 0.053
FS -0.204 -0.352 0.035 0.300 -0.567 0.057
RI 0404 -0.035 0.284 0.400 -0.302 0.316
MCP LU -0.404 -0.1 12 0.186 0.400 -0.477 0.265
Ul -0.404 0.047 -0.197 0.400 -0.240 0244
LE 0104 0.313 0.062 0.000 0.352 0.052

 

Tendon locations

in little finger (mean value of 15

 

 

 

spec imens) . _
— Distal Point Proximal Point
Joint Tendon X Y Z X Y 2

TE 0.010 0.196 -0.077 0.000 0.193 -0.079

DIP FP 0.010 -0.232 -0.041 0.300 -0.238 -0.003
F P -0.196 -0.333 0.040 0.400 -0.364 0002
RB 0096 0.198 0.220 0.100 0.131 0.253

PIP UB 0096 0.093 -0.317 0.100 0.120 0298
F8 -0.196 -0.268 0.050 0.400 -0.345 0008
ES 0.054 0.259 -0.010 0.000 0.254 0.014
FP -0.044 -0.427 0.080 0.300 0.628 0.170
FS -0.044 -0.508 0.111 0.300 -0.708 0.170
RI -0.244 0.027 0.418 0.400 -0.182 0.497

MCP LU -0.244 -0.169 0.364 0.400 -0.553 0.469
A00 0244 -0.023 -0.486 0.400 -0.309 -0.625
LE 0.056 0.154 0.061 0.000 0.190 0.133

 

137

APPENDIX B—PHYSIOLOGICAL CROSS-SECTIONAL AREA FOR ALL HAND

MUSCLES

 

 

 

PCSA for Extrinsic Muscles

Muscle Volume (cm"3) Fiber Length (cm) PCSA (cm"2) % Volume % PCSA
BR 46.9 1 22.0 15.8 1 5.6 2.9 1 0.7 8.51 1.5 2.9 1 0.3
ECRL 32.4 1 10.1 8.0 1 1.0 4.0 1 1.0 6.2 1 0.9 4.1 1 0.8
ECRB 29.2 1 11.7 5.8 1 1.0 4.9 1 1.6 5.3 1 0.2 4.9 1 0.4
SUP 24.0 1 11.6 3.5 1 0.8 7.3 1 4.4 4.3 1 1.1 6.8 1 2.4
E002 6.5 11.4 6111.4 1.1 1 0.3 1.3 1 0.4 1.11 0.2
EDC3 12.8 1 10.1 6.8 1 1.7 1.7 1 0.8 2.3 1 1.2 1.8 1 0.8
EDC4 8.1 1 2.0 6.8 1 0.8 1.2 1 0.4 1.7 1 0.7 1.3 1 0.4
EDCS 3.0 1 2.0 3.8 1 2.6 0.5 1 0.4 0.7 1 0.5 0.7 1 0.6
ECU 18.1 1 14.6 .. 4.8 1 1.9 3.51 2.1 3.4 1 2.1 3.9 1 2.4
APL 14.8 1 5.6 3.9 1 1.2 3.9 1 2.0 2.8 1 0.7 4.0 1 1.5
EPB 6.0 1 3.8 4.2 1 0.8 1.3 1 0.7 . . 1.0 1 0.4 1.3 1 0.5
EPL 10.5 1 5.8 5.21 1.1 1.9 1 0.8 1.8 1 0.5 1.9 1 0.6
EIP 6.9 1 3.6 4.9 1 1.0 1.3 1 0.6 1.3 1 0.5 1.4 1 0.6
£00 8.8 1 3.9 62 1 2.8 1.51 0.9 1.6 1 0.2 1.5 1 0.5
PT 34.2 1 14.7 5.3 1 1.1 6.6 1 2.7 6.3 1 1.2 6.5 1 1.3
FCR 27.3 1 11.4 5.2 1 0.7 5.2 1 1.9 5. 0 1 0.5 6.0 1 0.7
PL 6.8 1 3.2 4.4 1 0.9 1.5 1 0.6 1.2 1 0.2 1.2 1 0.4
FCU 34.4 1 13.6 3.3 1 0.7 10 1 3.0 6.2 1 0.3 10.2 1 1.0
FSD 10.0 1 11.6 4.0 1 0.5 2.4 1 2.8 1.5 1 1.7 2.0 1 2.4
F82 15.11 8.1 4.2 1 0.9 3.6 1 2.1 2.8 11.1 3.6 11.6
F83 29.5 1 15. 9 6.5 1 1.0 4.2 1 1.8 5.3 1 1.8 4.2 1 0.7
FS4 17.8 1 10.4 6.8 1 1.9 2.4 1 1.2 2.9 1 1.4 2.2 1 0.7
F85 9.3 1 5.2 4.4 1 0.6 2.1 1 1.4 1.7 1 0.7 2.2 1 1.1
FPL 23.5 1 10.4 4.6 1 1.2 5.1 1 2.6 4.2 1 0.5 5.0 1 1.7
FP2 27.6 1 16.1 6.7 1 0.7 4.1 1 2.4 4.8 1 1.7 3.8 1 1.2
FP3 27.8 1 11.0 6.7 1 0.6 4.1 11.4 5.2 1 0.9 4.1 1 0.7
FP4 24.8 1 9.6 6.4 1 0.7 3.7 1 1.1 4.7 1 1.0 3.9 1 0.8

II FP5 14.8 1 5.8 5.9 1 0.8 2.5 1 0.9 3.0 1 1.2 2.7 1 1.1
1 P0 10.0 1 5.2 3.1 10.9 3.5 12.1 1.9 1 0.8 36 11.7

 

 

138

 

PCSA for Intrinsic Muscles

 

 

 

 

 

Muscle Volume (cm’) Fiber Length 1cm) PCSA (cmz) % Volume %PCSA
ABP 4.8 1 1.8 3.2 1 0.6 1.5 1 0.6 6.2 1 1.4 4.4 1 1.0
OPP 6.1 1 3.0 2.3 1 0.6 2.8 1 1.3 7.3 1 1.7 7.5 1 2.7

ADPT 3.4 1 1.6 3.8 1 0.6 0.9 1 0.4 4.2 1 1.4 2.5 1 1.0

ADP2 2112.0 1.7116 0610.6 2411.9 1.6116

ADP3 6.1 1 3.7 3.5 1 0.8 1.8 1 1.2 7.8 1 3.5 5.2 1 2.8

ADPacc 1.6 1 0.6 1.8 1 0.2. 0.8 1 0.3 2.0 1 0.3 2.4 1 0.6

FPBsup 3.9 1 1.2 3.1 1 1.0 1.3 1 0.6 5.41 2.4 4.1 1 1.6

FPBdeep 2.1 1 1.2 2.1 1 0.3 1.0 1 0.5 2.8 1 1.4 3.0 1 1.5

DIO1 R 6.0 1 2.0 2.8 1 0.6 2.1 1 0.5 7.8 1 1.6 6.5 1 2.3

DIO1U 3.5 1 1.5 1.7 1 0.5 2.0 1 0.8 4.2 1 1.4 5.5 1 1.6

DIOZR 1.8 1 1.2 1.2 1 0.2 1.4 1 1.0 2.0 1 0.7 3.7 1 1.8

DIOZU 1.9 1 0.9 1.3 1 0.2 1.4 1 0.8 2.5 1 1.0 4.4 1 2.4

DIO3R 1.4 1 0.9 1.3 1 0.3 1.0 1 0.8 1.6 1 0.8 2.7 1 1.4

DIO3U 1.6 1 0.8 1.3 1 0.3 1.2 1 0.7 2.0 1 0.4 3.6 1 1.3

DIO4R 1311.0 1.1102 1.1108 1510.9 2811.4

DIO4U 1.4 1 0.8 1.3 1 0.3 1.1 1 0.7 1.7 1 0.5 2.9 11.0

ADPF2" 1.6 1 0.6 0.0 1 0.0 0.0 1 0.0 2.0 1 0.3 0.0 1 0.0
DIO1F3" 0.3 1 0.5 0.7 1 0.9 0.1 1 0.2 0.3 1 0.5 0.4 1 0.7
PIO1F4“ 2.5 1 0.7 1.7 1 0.2 1.4 1 0.4 3.3 1 0.7 4.1 1 0.9
DIO1F5‘ 1.2 1 0.7 . 1.6 1 0.2 0.7 1 0.4 1.5 1 0.7 2.0 1 0.9
DIO1F6’ 1.1 1 0.4 .1 .6 1 0.3 - 0.7 1 0.2 1.5 1 0.4 2.0 1 0.6
PlO1F7' 2.21 0.7 1.71 0.1 ~ . . 1:2 1 0.3 - 2.8 1 0.4 3.5 1 0.7
DIO1F8‘ 1.0 1 0.4 1.6 1 0.2 0.6 1 0.2 1.3 1 0.4 1.9 1 0.6
PIO1F9* 2.2 1 0.7 1.6 1 0.1 1.3 1 0.4 2.9 1 0.5 4.0 1 1.1
L2 1.7 1 0.7 ' 4.7 1 0.9 0.3 10.1 2.1 1 0.4 1.0 1 0.0
L3 1.2 1 0.4 5.0 1 1.4 0.2 1 0.0 1.6 1 0.4 0.7 1 0.2
L4 1.0 1 0.1 4.6 1 1.5 0.2 1 0.0 1.4 1 0.4 0.7 1 0.3
L5 0.7 1 0.3 3.5 1 0.8 0.2 1 0.0 0.9 1 0.1 0.6 1 0.1

A008 3.9 1 2.0 4.3 1 1.0 0.8 1 0.3 4.8 1 1.2 2.5 1 0.5

A000 3.1 1 1.2 3.4 1 0.9 0.9 1 0.2 3.9 1 0.7 2.7 1 0.7
FDQ 1.111.o 7711.2 0410.4 1511.0 1,311.0

OPPL 3.8 1 1.4 1.31 0.2 2.9 1 1.1 5.0 1 1.1 8.4 1 2.6

 

139

 

 

 

Appendix D--BTS Camera Calibration Constanta

 

[Subject Path: [data Imurewhand-aynm-zocol Test Date: 1211199 I

 

I BTS Calibration Setup I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Calibrated By:
Date: Protocol Code:
TVC Configuration: X MSU l BTS

Current: WC: 4 Planes: 4

ZD Grid: Rows: 4 Columns: 4
3D Grid: Rows: 4 Columns: 7 Mesh: 50 mm
Height: 770 mm Pl. Dist.: 150 mm Width: 2 mm
TVC 0 (D K x (mm) y (mm) 2 (mm)
1 -18 20 -14 330 1180 870
2 -14 -20 15 -380 1250 860
3 -12 150 0 350 1070 -510
4 -10 -160 1 -280 1090 -510

 

 

 

 

 

 

 

 

0; represents rotation about the X axis, tilt up and down.
@: represents rotation about the Y axis, panning.
It represents rotation about the Z axis, side to side.

140

Load (02)

Load (02)

APPENDIX F--CALIBRATION CURVES FOR KEYS

Calibration Curve for Comma

 

6 I l l

l l

 

 

 

'01100 “1050 ‘1000 ‘950
Voltage (microstrain)

XXX comma raw data
— comma fitted line

Calibration Curve for k

‘900

 

 

 

 

4 " l i l
2 F- “
0 l l
‘900 ’850 '800 '750

Voltage (microstrain)
XXX k raw data
'— k fitted line

141

’700

Load (02)

Load (oz)

Load (02)

Calibration Curve for b

 

 

 

 

 

 

 

 

 

 

 

 

 

6 l l l 1
4 - —
2 r- 1
0 l L l l
'1100 “1080 “1060 “1040 -1020 '1000
Voltage (microstrain)
XXX b raw data
“““" b fitted line
Calibration Curve for m
l l l l
5 '“ ..
O I g 1 1
“1200 “1180 “1160 “1140 “1120 “1100
Voltage (microstrain)
XXX m raw data
— m fitted line
Calibration Curve for n
" 1 I 1 1
5 - _
X
0 1 1 1 l v
“1100 “1050 “1000 “950 “900 ' “850
Voltage (microsuain)
XXX n raw data

— n fitted line

142

Load (oz)

Load (02)

Load (02)

Calibration Curve for j

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l " l T l
4 - ..
2 - _
0 l l l
“900 “850 “800 “750 “700
Voltage (microstrain)
xxx j raw data
— j fitted line
Calibration Curve for o
6 l I 1
4 - —
2 — "l
0 1 ' i l I
“ 800 “ 780 “760 “ 740 "’ 720 " 700
Voltage (microstrain)
XXX 0 raw data
0 fitted line
Calibration Curve for p
6 r- ..
4 - A
2 l— x .—
0 l l l
“1000 “950 “900 “850 “800
Voltage (microstmin)
XXX p raw data
— p fitted line

143

Load (02)

Load (02)

Load (02)

Calibration Curve for period

 

 

 

 

 

6 l" l l T l

4 "“ _

2 '“ .—

0 l J l I u l

“900 “850 “800 “750 “700 “650 “600

Voltage (microstrain)
XXX period raw data
— period fitted line

Calibration Curve for l

 

 

 

 

 

 

 

 

 

 

6 l . l T l l
4 - —
2 ‘ a
0 l J l 1
“1000 “950 “900 “850 “800 “750 “700
Voltage (microstrain)
XXX 1 raw data
— l fitted line
Calibration Curve for u
6 I l
4 '“ —
2 - q
0 a!
“1200 “1150 “1100 “1050 “1000
Voltage (microstrain)
XXX u raw data

 

u fitted line

144

TE (N)

10

APPENDIX H—-OPTIMIZATION RESULTS

Terminal Extensor Force vs. Time

 

Y 1 T T I I l T

 

 

 

 

 

 

 

 

 

100 200 300 400 500 600 700 800
Tlme (sec'100)

145

900

1 000

UB (N)

Radial Band Force vs. Time
10 r r I T r r t

 

 

 

 

 

 

P

 

o A A v J ‘y ‘ f
-2 _ l

 

 

100 200 300 400 500 600 700
Tlme (sec'100)

Ulnar Band Force w. Time

800

900

1000

 

10 I 1 Y ‘r 1 fi fi

 

 

 

l

 

 

 

100 200 300 400 500 600 700
Time (sec'100)

146

800

900

1000

ES (N)

RI (N)

10

10

Extensor Slip Force vs. Time

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- i -l, ( .l
1
100 200 300 400 500 600 700 800 900 1000
Time (aec'100)
Radial Interosseous Force vs. Tlme
.. 1L Jl
l j r
100 200 300 400 500 600 700 800 900 1000

Time (sec'100)

147

Ul (N)

LU (N)

Ulnar Interosseous Force vs. Tlme
10 I I Y 1 l 1 T 1 Y

 

 

 

 

 

 

 

 

 

 

 

100 200 300 400 500 600 700 800 900 1000
Time (sec'100)

Lumbricalis Force vs. Tlme

 

10 I T l I I T Y I I

 

l 717“!

 

 

 

 

 

 

 

100 200 300 400 500 600 700 800 900 1000
Tlme (sec'100)

148

Rxpip (N)

Rydip (N)

10

1O

Distal Interphalangeal Reaction Force x-Component vs. Tlme

 

T

T I I Y T

 

 

_L I A

I

T

L

T

 

 

100

200 300 400 500 600

700

800

900

 

 

 

 

 

 

Time (sec'i 00)

149

1000
Time (see'iOO)
Distal Interphalangeal Reaction Force y-Component vs. Time
J. a. v .L_Lu
.1
100 200 300 400 500 600 700 800 900 1000

deip (N)

Rxpip (N)

10

O

I
N

L

10

Distal Interphalangeal Reaction Force z-Component w. Time

 

 

l 1 U I I I T I T

 

 

 

L 4

 

100 200 300 400 500 600 700 800 900 1000
Tlme (sec'100)

Proximal Interphalangeal Reaction Force x-Compone‘nt vs. Time

 

I T T T Y 1 1 F l

 

 

 

 

W .

 

 

100 200 300 400 500 600 700 800 900 1000
Tlme (sec‘lOO)

150

Rypip (N)

Rzpip (N)

10

O

I
N

L

10

Proximal Interphalangeal Reaction Force y-Component vs. Time

 

 

I I I I 1 I I U I

 

 

1

 

100 200 300 400 500 600 700 800 900 1000
Time (sec'100)

Proximal Interphalangeal Reaction Parcel-Component vs. Time

 

 

T W I 7 I I T— j T

 

 

A;

 

100 200 300 400 500 600 700 800 900 1000
Time (88c'100)

151

Rxmcp (N)

Rymcp (N)

10

10

Metacarpophalangeal Reaction Force x-Component w. Tlme

 

 

I I I I I I I I I

 

 

 

 

100 200 300 400 500 800 700 800 900 1000
Tlme (sec'100)

Metacarpophalangeal Reaction Force y-Component vs. Tlme

 

 

I I I I I I I I I

 

 

100 200 300 400 500 600 700 800 900 1000
Time (sec'100)

152

Rzmcp (N)

Mxpip (N-mm)

10

-2

10

Metacarpophalangeal Reaction Force z-Component vs. Time

 

 

I r I I I I I I I

 

 

 

100 200 300 400 500 600 700 800 900 1000
Time (sec'100)

Proximal Interphalangeal Reaction Moment x-Component vs. Time

 

n l I I I I I I I

 

 

 

 

100 200 300 400 500 600 700 800 900 1000
Time (sec'100)

153

Mypip (N-mm)

deip (N-mm)

10

10

N

O

-2

Proximal Interphalangeal Reaction Moment y-Component to. Time

 

I I I I I I

 

 

I

I

I

 

l‘ “ ”fir—“j? ‘l

 

100 200 300 400 500 600
Tune (sec't 00)

700

800

900

Distal Interphalangeal Reaction Moment x-Component vs. Tlme

 

T I I I I I

I

T

I

 

 

l

 

100 200 300 400 500 600
Time (sec‘100)

154

700

800

900

 

 

Mydip (N-mm)

10

Distal interphalangeal Reaction Moment y-Component vs. Time

 

I

I

I

I I I

I

I

 

 

“"l

l l

 

 

100

200

300

400 500 600
Time (sec'100)

155

700

800

900 1000

Mxmcp (N)

10

Metacarpophalangeal Reaction Moment x-Component vs. Time

 

 

 

 

 

100 200 300 400 500 600 700 800 900 1000

Time (sec'100)

156

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