Biomechanics of Total Wrist Arthroplasty

by

Bardiya Akhbari

B.Sc., Sharif of University Technology, 2014

M.Sc., The University of Kansas, 2016

A dissertation submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in the Biomedical Engineering program, a joint program in the

Division of Biology and Medicine and the School of Engineering at Brown University

Providence, Rhode Island

May 2021

© Copyright 2021 by Bardiya Akhbari

iii

This dissertation by Bardiya Akhbari is accepted in its present form

by the Biomedical Engineering program, a joint program in the Division of Biology and

Medicine and the School of Engineering, as satisfying the dissertation requirement for the

degree of Doctor of Philosophy.

Date ______________ ___________________________________

Joseph. J. Crisco, Advisor

Recommended to the Graduate Council

Date ______________ ___________________________________

Braden C. Fleming, Reader

Date ______________ ___________________________________

Benjamin B. Kimia, Reader

Date ______________ ___________________________________

David H. Laidlaw, Reader

Date ______________ ___________________________________

Arnold-Peter C. Weiss, Reader

Date ______________ ___________________________________

Scott W. Wolfe, Reader

Recommended to the Graduate Council

Date ______________ ___________________________________

Andrew G. Campbell, Dean of the Graduate School

iv

Curriculum vitae

Bardiya Akhbari’s current research focus is on orthopedics, biomechanics, and medical

imaging. Throughout his PhD at Brown University, Bardiya worked with Prof. Joseph

(Trey) Crisco to investigate the biomechanics of wrist and total wrist arthroplasty using

advanced imaging systems such as biplane videoradiography and optical motion capture

systems. During his time in graduate school, Bardiya also taught Dynamics, Dynamics

Simulation, and Statistical Analysis, and acquired two teaching certifications from The

Harriet W. Sheridan Center for Teaching and Learning. Bardiya has obtained his BSc

degree in Mechanical Engineering from Sharif University of Technology (Tehran, Iran),

and MSc degree in Mechanical Engineering from The University of Kansas (Lawrence,

Kansas, USA) where he received the best Mechanical Engineering thesis award. Bardiya

has authored 12 peer-reviewed publications and has presented his research at more than 10

national conferences. In his free time, he enjoys reading books about science and history,

and running down random streets.

Selected Publications

1. Akhbari et. al, 2021. Total Wrist Arthroplasty Alignment and its Potential Association

with Outcomes, Journal of Wrist Surgery.

2. Akhbari et. al, 2020. Proximal-Distal Shift of the Center of Rotation in a Total Wrist

Arthroplasty is More Than Twice of the Healthy Wrist, Journal of Orthopaedic

Research. Journal of Orthopaedic Research

3. Akhbari et. al, 2019. Predicting Carpal Bone Kinematics using an Expanded Digital

Database of Wrist Carpal Bone Anatomy and Kinematics, Journal of Orthopaedic

Research. Journal of Orthopaedic Research

v

Acknowledgments

This dissertation would not have been possible without the help of several people. First, I

will always be indebted to my doctoral advisor and mentor, Dr. Joseph (Trey) Crisco who

trusted my potential and significantly contributed to my personal growth. I thank my

committee members, Drs. Fleming, Laidlaw, Kimia, Weiss, and Wolfe, and I appreciate

the time they spent advising me and teaching me how to critique my work.

I thank my colleagues and collaborators. I specifically want to thank Amy Morton and

Douglas Moore for their assistance in data acquisition, data interpretation, and manuscript

writing. Amy taught me how to write codes and talk to computers, Doug taught me how to

write scientific documents and talk to others. I am thankful to my colleagues in Brown

Biomechanics: Rohit for showing me how the Kuka works, Kal for his clinical feedback

on the manuscripts, Srinidhi for her crucial feedback on my first conference abstract, Elee

for the hours that she put in to track the bones inside the blue radiographs, Brian for his

determinism in publishing the soft-tissue artifact manuscript, Steven for helping out getting

everything I need to make my research move forward smoothly, Cyndi for being a great

clinical coordinator and arranging all patients' schedules, Josephine for improving all

manuscripts by reading them critically, Edgar for teaching me how you can always find

time for friends, and Sean for being a great office mate and his great book and podcast

suggestions. I found great friends while completing this dissertation, and I am grateful.

This journey could not have been possible without my friends outside the laboratory who

made my life easier and gave more meaning to all this. Thank you.

Ultimately, whatever I have achieved so far is dedicated to my family, and I am always

thankful for their love and support.

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Table of Contents

Curriculum vitae ................................................................................................................ iv

Acknowledgments............................................................................................................... v

Table of Contents ............................................................................................................... vi

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

List of Illustrations ........................................................................................................... xiii

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

Motivation ........................................................................................................... 1

Background ......................................................................................................... 3

Wrist Biomechanics .................................................................................... 3

Wrist Pathology and Treatments ................................................................. 4

Total Wrist Arthroplasty (TWA) ................................................................ 5

In vivo Methods of Studying the Wrist and TWA ...................................... 7

Specific Aims ...................................................................................................... 8

References ......................................................................................................... 10

Predicting Carpal Bone Kinematics Using an Expanded Digital Database of

Wrist Carpal Bone Anatomy and Kinematics ................................................................... 17

Introduction ....................................................................................................... 19

Methods............................................................................................................. 21

Overview ................................................................................................... 21

Database Description – Data Acquisition ................................................. 21

Database Description – Data Analysis ...................................................... 23

Carpal Bones Motion in the RCS.............................................................. 24

Mathematical Modeling ............................................................................ 25

Statistical Analysis .................................................................................... 26

Results ............................................................................................................... 27

Discussion ......................................................................................................... 31

Author’s Contribution ....................................................................................... 34

Acknowledgments............................................................................................. 35

References ......................................................................................................... 35

Accuracy of Biplane Videoradiography for Quantifying Dynamic Wrist

Kinematics 39

Introduction ....................................................................................................... 41

Methods............................................................................................................. 42

Specimen preparation and imaging ........................................................... 43

BVR and OMC Instruments...................................................................... 44

Data Acquisition ....................................................................................... 44

Image Processing and Data Reduction ..................................................... 46

Wrist Kinematics ...................................................................................... 48

Statistical Analysis .................................................................................... 49

vii

Results ............................................................................................................... 49

Discussion ......................................................................................................... 52

Acknowledgments............................................................................................. 56

References ......................................................................................................... 56

Kinematic Accuracy in Tracking Total Wrist Arthroplasty with Biplane

Videoradiography Using a Computed Tomography-Generated Model............................ 59

Introduction ....................................................................................................... 61

Methods............................................................................................................. 62

Specimen Preparation and Imaging .......................................................... 63

Instrumentation ......................................................................................... 64

BVR and OMC Data Acquisitions ............................................................ 64

Implant Model Generation and Data Reduction ....................................... 65

Statistical analyses .................................................................................... 68

Results ............................................................................................................... 68

Discussion ......................................................................................................... 71

Acknowledgments............................................................................................. 75

References ......................................................................................................... 75

Proximal-Distal Shift of the Center of Rotation in a Total Wrist

Arthroplasty is More Than Twice of the Healthy Wrist ................................................... 78

Introduction ....................................................................................................... 80

Methods............................................................................................................. 81

Subjects ..................................................................................................... 81

CT Image Acquisition ............................................................................... 81

Biplane Videoradiography ........................................................................ 82

Data Analysis ............................................................................................ 85

Coordinate System Definitions ................................................................. 85

Center of Rotation Calculations ................................................................ 88

Statistical Analysis .................................................................................... 90

Results ............................................................................................................... 91

Discussion ......................................................................................................... 95

Author’s Contribution ....................................................................................... 99

Acknowledgments............................................................................................. 99

References ......................................................................................................... 99

In-vivo Wrist Motion in Total Wrist Arthroplasty versus Healthy Wrist 104

Introduction ..................................................................................................... 106

Methods........................................................................................................... 107

Results ............................................................................................................. 109

Discussion ....................................................................................................... 113

Acknowledgments........................................................................................... 117

References ....................................................................................................... 117

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Total Wrist Arthroplasty Alignment and its Potential Association with

Outcomes 120

Introduction ..................................................................................................... 122

Materials and Methods .................................................................................... 122

Study Subjects ......................................................................................... 122

2D Alignment from Radiographs............................................................ 123

3D Alignment from CT Images .............................................................. 124

Clinical Outcomes ................................................................................... 125

TWA Kinematics and Range-of-Motion (Biplane Videoradiography) .. 126

Statistical Analysis .................................................................................. 126

Results ............................................................................................................. 127

Radiographic Measurements Validity..................................................... 128

Radial Component Alignment ................................................................ 129

Carpal Component Alignment ................................................................ 130

Discussion ....................................................................................................... 131

References ....................................................................................................... 134

In-vivo Articular Contact Kinematics of a Total Wrist Arthroplasty Device

137

Introduction ..................................................................................................... 139

Methods........................................................................................................... 140

Recruitment and Data Acquisition .......................................................... 140

Model Generation and Kinematics ......................................................... 141

Contact Analysis ..................................................................................... 144

Sensitivity Analysis ................................................................................ 145

Statistical Analysis .................................................................................. 146

Results ............................................................................................................. 146

Discussion ....................................................................................................... 151

Acknowledgements ......................................................................................... 154

References ....................................................................................................... 154

Conclusion .............................................................................................. 158

Summary ......................................................................................................... 158

Clinical Significance ....................................................................................... 160

Limitations ...................................................................................................... 161

Future Directions ............................................................................................ 162

References ....................................................................................................... 163

Autoscoper (Bone/Implant Tracking Software).................................. 165

Wrist Anatomy and Kinematics Data Collection................................ 166

ix

List of Tables

Table 1.1. The complication rate and survival rate of 3rd and 4th generation TWA designs

in follow-up (f/u) years, along with the percentage of patients who received the implant

because of osteoarthritis (OA) and number of patients (n). ................................................ 7

Table 2.1. Breakdown of our open-source carpal database. Forty-six wrists of 46 healthy

subjects in a study of carpometacarpal (CMC) joint from 2012 to 2015, fourteen wrists of

14 healthy subjects from 2008 to 2010, and sixty healthy wrists (30 subjects, for both sides)

from 2000 to 2006. The total number of unique wrist postures was 1215 (120 neutral, 1095

others). .............................................................................................................................. 22

Table 2.2. Root-mean-square error (RMSE), R2, and model error’s bias of 40 second-order

algebraic fit to every DOFs on the test set (20 subjects, 30 wrists). Degrees-of-freedoms

are: supination-pronation (SP), flexion-extension (FE), radial-ulnar deviation (RU), distal-

proximal translation (DPT), radial-ulnar translation (RUT), and volar-dorsal Translation

(VDT). Translations RMSE is scaled back by the cube root of the average capitate volume

(~ 3700 mm3) for a better demonstration of RMSEs. ....................................................... 28

Table 2.3. The lower confidence interval (LCI) and upper confidence interval (UCI) of the

slope of the path that generates a minimal carpal bone motion (MM slope). Linear

regression was used to calculate the MM slope. The comparison for flexion-extension (FE)

and volar-dorsal translation (VDT) revealed different patterns of wrist movement that

generates minimal motions for the bones in the proximal row (slopes < 0.3), and the bones

in the distal row (slopes > 0.6). ......................................................................................... 30

Table 3.1. The agreement of biplane videoradiography (BVR) with the gold standard in

evaluating the overall wrist joint motion in terms of bias and limit of agreement (LOA) for

x

all tasks. BVR in all tasks had a subdegree and submillimeter bias, and LOA was less than

1.5° and 1.4 mm for all tasks except pronation................................................................. 51

Table 3.2. The bias and precision of biplane videoradiography in measuring rotational

components of the wrist joint motion in all tasks. Bias was less than 0.5° for all tasks. The

least agreement was seen in pronation/supination angle which had 1.5 to 2 times a precision

than other rotational components. ..................................................................................... 51

Table 3.3. The bias and precision of translational components of wrist joint motion in all

tasks. Bias was less than 0.5 mm for all tasks, and the worst precisions were seen in

measuring the radial/ulnar translation and volar/dorsal translation which had a motion

approximately parallel to the X-ray beams. ...................................................................... 52

Table 3.4. Limits of agreement (LOA) between biplane videoradiography and the gold

standard, optical motion capture, in tracking the individual bones of the wrist joint (radius

and the third metacarpal). Translations LOA were mostly submillimeter, and rotations had

an LOA of within ±1.8°. ................................................................................................... 52

Table 4.1. Overall root-mean-squared-error (RMSE) of the differences between OMC and

BVR for rotations (°) and translations (mm) for all tasks. For each task, RMSE rotations

are reported for the components of flexion/extension (FE), radial/ulnar deviation (RU), and

pronosupination (PS). RMSE translations are reported for the components of radioulnar

(RU), volar/dorsal (VD), and proximal/distal (PD). ......................................................... 70

Table 4.2. Differences (mean ± std.) in instantaneous center of rotation location (mm)

between BVR and OMC for the motion of the carpal component relative to the radial

component. Tasks are Flexion-Extension (FE), Radial-Ulnar deviation (RU), and

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Circumduction (CIRC). The axis directions are Distal (-)/Proximal (+), Ulnar (-)/Radial

(+), and Dorsal (-)/Volar (+). (NA – measurement not applicable) .................................. 71

Table 5.1. Proximal-distal, volar-dorsal, and radial-ulnar location of the center of rotation

(COR) of the replaced wrist for pure rotations in capitate’s coordinate system, which is

located on its mid-axis and its most distal surface. The mean and 95% confidence intervals

(CI) were calculated using generalized estimating equations. COR for pure flexion and

extension was computed in the sagittal plane, while the COR for radial and ulnar deviation

was calculated in the frontal plane. The centers of the major and minor curvatures were

located at 3.1 mm and 22.8 mm relative to the most distal point on the capitate’s surface.

........................................................................................................................................... 92

Table 5.2. Proximal-distal, volar-dorsal, and radial-ulnar location of the center of rotation

(COR) of the healthy wrist for pure rotations in capitate’s coordinate system, which is

located on its mid-axis and its most distal surface. The mean and 95% confidence intervals

(CI) were calculated using generalized estimating equations. .......................................... 92

Table 6.1. Clinical Outcomes.......................................................................................... 109

Table 6.2. Range of motion (ROM) comparison between controls and TWAs as measured

on clinical assessment using a hand-held goniometer. ................................................... 109

Table 6.3. Range of motion (ROM) comparison between controls and TWAs as calculated

using biplane videoradiography. ..................................................................................... 110

Table 6.4. The envelope of circumduction. .................................................................... 112

Table 6.5. Orientation of the principal axis for flexion-extension and radial-ulnar deviation

tasks................................................................................................................................. 112

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Table 7.1. Clinical outcomes (pain scores and grip strength) and maximum range-of-

motion capability of 6 non-rheumatoid patients with Freedom® wrist. A higher score for

PROMIS demonstrates better outcomes (maximum score is 56.4), while a lower score for

PRWHE and QuickDASH depict a better outcome. See Methods and supplementary

materials for a description of grip strength normalization. ............................................. 127

Table 7.2. The difference between radiographic and three-dimensional measurements

demonstrated submillimeter and subdegree biases (mean differences) except for the

measures calculated between the carpal component and third metacarpal. .................... 128

Table 7.3. Carpal component and radial component alignment defined from the 3D models

for all subjects as shown in Figure 3. Each component’s alignment is defined by angular

parameters of volar (+)/dorsal (-) tilt (VDT), radial (+)/ulnar (-) tilt (RUT), and translational

offset parameters of radial (+)/ulnar (-) offset (RUO) and volar (+)/dorsal (-) offset (VDO).

......................................................................................................................................... 129

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List of Illustrations

Figure 1.1. A dorsal x-ray of a healthy wrist (left). A dorsal x-ray of a wrist with a

Freedom® system (middle). An explanted Freedom® TWA system showing the carpal

component, polyethylene cap, and radial component (right). ............................................. 1

Figure 1.2. Wrist motion is due to the articulation of eight carpal bones (Scaphoid (SCA),

Lunate (LUN), Capitate (CAP), Triquetrum (TRQ), Pisiform (PIS), Hamate (HAM),

Trapezoid (TPD), and Trapezium (TPM)) together, while they are interacting with the

radius (RAD) and ulna (ULN) proximally and the metacarpals (MC1-5) distally. ............ 3

Figure 2.1. Wrist motions within the carpal dataset for all 120 wrists. Wrist motion was

defined as the motion of capitate in the radial coordinate system, and each point depicts the

motion of the wrist in a single task. .................................................................................. 21

Figure 2.2. RCS and HAM parameters. n is a vector defining the orientation of the screw

axis (nx, ny, nz), and φtot is the rotation about the axis. This angle can be decomposed into

rotational components. ...................................................................................................... 23

Figure 2.3. Training set (motions used to construct the model) from 86 wrists and test set

(motions used to evaluate the model) from 30 wrists were randomly selected from the

database. Each data point has 42 other dimensions for 7 carpal bones and 6 degrees-of-

freedom. ............................................................................................................................ 25

Figure 2.4. The flexion-extension of scaphoid (SCAFE) as the function of wrist motion for

the database (Left), quadratic model’s prediction (Middle), and the model error (Right).

........................................................................................................................................... 29

Figure 2.5. Mathematical model errors for scaphoid flexion-extension (SCAFE), the

histogram of errors based on the wrist movement for each octant of RU and FE. The middle

xiv

figure shows the model error across kinematics space, and every histogram shows the

errors in every subdivision. The octants are defined based on the relationship between

radial (R)/ulnar (U) deviation and flexion (F)/extension (E) of the wrist. For example, UE

defines the region that the ulnar deviation is larger than extension, and FR describes the

region that flexion is larger than radial deviation. ............................................................ 29

Figure 2.6. Wrist paths that generate minimal flexion-extension, radial-ulnar deviation,

radial-ulnar translation, and volar-dorsal translation of carpal bones. Different patterns of

wrist paths were seen for the carpal bones in the distal row (i.e., hamate, capitate, trapezoid,

and trapezium) and proximal row (i.e., triquetrum, lunate, and scaphoid). ...................... 31

Figure 3.1. Marker clusters on the hand (four markers for tracking the third metacarpal),

and on the forearm (four markers for tracking the radius), as well as 3D models of the

radius and the third metacarpal constructed from the CT images. For visualization, just the

distal forearm and hand are depicted (CT scan was from the whole arm). ...................... 43

Figure 3.2. Experimental setup for biplanar videoradiography capture (right-side wrist is

depicted). The intra-beam angle of 110°, with the source-to-image distance of ~130 cm for

both X-ray sources. The specimen’s arm was secured, and the wrist and forearm were

manipulated manually with a dowel attached the distal side of the hand. ........................ 45

Figure 3.3. Bone features were enhanced using Sobel and contrast filters on the

radiographs, and the digitally reconstructed radiographs (bolded in white) were tracked in

the radiographs. From left to right, the tracked metacarpal and radius are visualized from

flexion to extension in one source for a left wrist. ............................................................ 47

Figure 3.4. Representative wrist kinematics calculated from both methods (BVR: biplane

videoradiography, OMC: optical motion capture). PS (+pronation/-supination), FE

xv

(+flexion/-extension), and RU (+ulnar/-radial deviation) demonstrate the rotational

components. ...................................................................................................................... 50

Figure 4.1. Marker positioning visualized from a rendered CT scan. Five retro-reflective

markers were fixed directly to the radius, and five retro-reflective markers were clustered

on a thermoplastic plate, rigidly fixed to the third metacarpal via nylon screws. ............ 63

Figure 4.2. Photo of a Universal2™ carpal component (left), and a 3-D digital model

generated via thresholding and manual editing of CT images (right). ............................. 65

Figure 4.3. A) Neutral posture of the components along with their respective coordinate

system; red, green, and blue vectors depict the x-axis (pronation/supination), y-axis

(flexion/extension), and z-axis (radial/ulnar deviation). B, C) The edges of the carpal and

radial components of the implanted Universal2™ TWA super-imposed on the neutral

frame radiographs as captured in the BVR cameras. D, E) The silhouettes of the carpal and

radial components of the implant on the neutral frame radiographs. ............................... 67

Figure 4.4. Definition of rotation angles and planar instantaneous center of rotation (ICR)

for the motion of the carpal components relative to the radial component (this figure depicts

only a sagittal plane intersection). In HAM parameters, n is the vector defining the

orientation of the screw axis (nx, ny, nz), and φtot is the rotation about the screw axis. This

angle can be decomposed into rotational components (φtot.nx, φtot.ny, φtot.nz). The screw

axis intersects each plane of the radial component coordinate system, providing a plane-

specific ICR. ..................................................................................................................... 68

Figure 4.5. Bland-Altman plots of carpal component rotations throughout each task

(Flexion-Extension, Radial-Ulnar Deviation, and Circumduction) calculated from the

biplane videoradiography (BVR) and optical motion capture (OMC) data. Columns report

xvi

the rotation angles in the radial component’s coordinate system for each task (Rows).

Across all tasks and directions, there was a bias of less than 1°, and the limits of agreement

were less than 2° for all tasks. ........................................................................................... 69

Figure 4.6. Bland-Altman analysis of carpal component translations throughout each task

(Flexion-Extension, Radial-Ulnar Deviation, and Circumduction) calculated from the

biplane videoradiography (BVR) and optical motion capture (OMC) data. Columns report

the translations in the radial component’s coordinate system for each task (Rows). The

Bland-Altman analysis demonstrates a trivial bias of less than 0.2 mm, and the limit of

agreement of less than 1 mm for all tasks. ........................................................................ 70

Figure 5.1. Three-dimensional models of a healthy wrist (radius, capitate, and third

metacarpal), and a replaced wrist (resected radius, radial component, polyethylene cap,

carpal component, resected capitate and third metacarpal) in the neutral pose. For the sake

of clarity, other carpal bones are omitted.......................................................................... 83

Figure 5.2. The tracked third metacarpal and radius for the healthy wrist (left) and carpal

component and radial component for the replaced wrist (right) for one of the radiographic

views. The image features of radiographs are enhanced using Sobel edge filter and intensity

thresholding to maximize the similarity between the bones/implants and radiographs. .. 84

Figure 5.3. Depiction of bones’ and implants’ coordinate systems demonstrated as X-axis

(red), y-axis (green), and z-axis (blue).............................................................................. 85

Figure 5.4. The screw axis was transferred to the origin of the radius coordinate system and

based on its orientation and projection the azimuth (azi) and elevation angles were

calculated. X-axis (red), y-axis (green), and z-axis (blue) demonstrate the radius coordinate

system. .............................................................................................................................. 87

xvii

Figure 5.5. Center of minor and major curvatures of the ellipsoidal shape of the

polyethylene cap. Curvatures were detected using the least-squares fitting of an ellipsoid

to the surface points of the polyethylene cap. ................................................................... 88

Figure 5.6. The projected center of rotation (COR) was defined for the healthy wrists as a

point on the mid-axis of the capitate which had the shortest distance from the axis of

rotation (red). The polyethylene cap’s mid-axis was used to define the projected COR for

the replaced wrists (TWA). ............................................................................................... 89

Figure 5.7. Center of rotation (COR) on the resected capitate for the replaced wrist (top

panel) and capitate (bottom panel) for the healthy wrist. The replaced wrist had a COR

located slightly distal to the center of curvature in flexion-extension (top left panel; radial

view), while it was slightly proximal to the center of curvature in radial-ulnar deviation

(top right panel; volar view). Centers of curvatures are shown as black dots, and the

standard deviation of COR in both directions are shown as colored ellipses. .................. 91

Figure 5.8. The proximal-distal shift of the projected center of rotation (COR) as a function

of wrist motion (for all tasks). COR shifted in a sinusoidal pattern (solid black line with

confidence interval as a shaded region) in proximal (+) and distal (-) direction from the

most distal point on capitate (i.e., 0 on the figures) for both cohorts. The healthy wrist’s

COR traveled an approximately 7.2 mm while the replaced wrist’s COR traveled about

17.1 mm. ........................................................................................................................... 93

Figure 5.9. The axis of rotation’s elevation angle of wrist followed a sinusoidal pattern,

while the replaced wrist had mostly a negative elevation angle. The average (solid black

line) and standard deviations (shaded black region) were calculated at 4 anatomical and 4

coupled wrist motions. ...................................................................................................... 94

xviii

Figure 5.10. The shortest distance from the screw axis to the x-axis of capitate (l). This

distance for the replaced wrist was approximately 0 throughout the wrist motion, while the

healthy wrist had slightly larger variations. The average (solid black line) and standard

deviations (shaded black region) were calculated at 4 anatomical and 4 coupled wrist

motions .............................................................................................................................. 94

Figure 5.11. The overall pattern of screw axis orientation and location at four anatomical

(F: flexion, E: extension, R: radial deviation, U: ulnar deviation) and four coupled wrist

motions (UF: ulnar-flexion, UE: ulnar-extension, RE: radial-extension, RF: radial-flexion)

for Freedom® replaced wrist (top panel) and a typical healthy wrist (bottom panel) in radial

view (left panel) and volar view (right panel). In both healthy and replaced wrists, rotation

axes for pure flexion-extension and radial-ulnar deviation were orthogonal and consistent

with the motion. In healthy wrists, dart-thrower’s (RE to UF) and anti dart-thrower’s (RF

to UE) followed the same pattern, while in the replaced wrist the coupled motions had

dissimilar and complex patterns........................................................................................ 95

Figure 6.1. Experimental Setup. ..................................................................................... 108

Figure 6.2. Bland-Altman between the calculated range of motion by biplane

videoradiography and clinically measured active range-of-motion. Bias in blue, and %95

limit of agreement in red. ................................................................................................ 110

Figure 6.3. Histogram of Wrist and Replaced Wrist Motions. ....................................... 111

Figure 6.4. Flexion-Extension and Radial-Ulnar Deviation Descriptive Analysis. Dotted

lines demonstrate the average, and dashed lines demonstrate the standard deviations. . 111

Figure 6.5. Circumduction Descriptive Analysis. Dotted lines demonstrate the average, and

dashed lines demonstrate the standard deviations. ......................................................... 112

xix

Figure 7.1. Posteroanterior view (PA, left panel) and lateral view (right panel) of the right

hand of a subject with total wrist arthroplasty. Blue lines show the reference lines of the

radial (R) and carpal components (C) and red lines show the reference lines of the third

metacarpal and radius. For each component, radial tilt (+RU) and offset (perpendicular

black arrows) were defined in PA view, and volar tilt (+VD) and offset (perpendicular

black arrows) were defined in lateral view. In this figure, radial and carpal components are

tilted radially and dorsally. ............................................................................................. 124

Figure 7.2. The orthogonal coordinate systems for the (A) radial component, (B) carpal

component, (C) resected radius, and (D) the third metacarpal are shown as red (x-axis),

green (y-axis), and blue (z-axis). .................................................................................... 125

Figure 7.3. Overall flexion-extension and radial-ulnar deviation range of motion (ROM)

increases as the volar tilt of the radial component increases. Reconstructions from CT scan

illustrate alignments of indicated data points. An increase of 3.7° flexion-extension and

1.6° radial-ulnar deviation with each degree increase of volar tilt. ................................ 130

Figure 7.4. Overall flexion-extension and radial-ulnar deviation range of motion (ROM)

increases as the volar offset of the radial component increases. An increase of 10.8°

flexion-extension and 4.2° radial-ulnar deviation for every millimeter increase of volar

offset was observed. ........................................................................................................ 130

Figure 8.1. The coordinate system (CS) of the carpal component was constructed using the

minor and major axes of the ellipsoidal surface of the polyethylene cap and the carpal

plate’s stem central axis. The radial component’s CS was constructed using the minor and

major axes of its ellipsoidal surface and the central axis of the radial stem. The origins are

xx

shown with black circles. The geometric center of the radial component was 4.2 mm ulnar

and 3.6 mm volar to the origin of the radial component’s coordinate system. ............... 143

Figure 8.2. Surface-to-surface distances were calculated using the proximity value of each

component after its kinematic transformation was calculated from biplanar

videoradiography. Proximity values greater than 0.70 mm were excluded, and the

remaining values were used to calculate the center of contact (white circles). .............. 144

Figure 8.3. Each wrist posture was randomly perturbed 1,000 times within the range of

accuracy of biplanar videoradiography (left panel), and the standard deviation of

calculating the center of contact was computed at threshold values of 0 to 1.5 mm in

increments of 0.05 mm for the carpal component (middle panel) and the radial component

(right panel). An optimal threshold value of 0.70 mm was selected when the optimal

resolution criteria of 0.41 mm (red dashed line) was met............................................... 147

Figure 8.4. (A) The center of contact of the carpal component moved from dorsal to volar

side from full wrist extension (red color) to wrist flexion (blue color), (B) while it moved

from volar to dorsal side of the radial component throughout the same path. ................ 148

Figure 8.5. The postures of the bones (third metacarpal, resected capitate, and resected

radius) and implant components (carpal component and its polyethylene cap, and radial

component) at (A) maximum wrist flexion and (B) extension. Potential impingement of

the components at the extreme extension can be seen in both the radiographic image and

the three-dimensional models. The white circles on the components are demonstrative of

the center of contact. ....................................................................................................... 148

xxi

Figure 8.6. (A) The center of contact of the carpal component moved from its radial side

to its ulnar side during wrist movement from radial deviation to ulnar deviation, (B) while

it slightly moved from the ulnar side toward its radial side on the radial component. ... 149

Figure 8.7. he three-dimensional models of bones and implant components at (A)

maximum wrist ulnar deviation and (B) radial deviation. Complete contact between

components can be seen in maximum ulnar deviation in both radiographs and three-

dimensional models. The white circles on the components are demonstrative of the center

of contact. ........................................................................................................................ 149

Figure 8.8. Predicted and 95% confidence interval (CI) behavior of the centers of contact

movement throughout pure flexion-extension and radial-ulnar deviation was computed

based on mixed models. Flexion-extension range-of-motion is demonstrated from 60°

flexion to 60° extension in 20° steps, and radial-ulnar deviation range-of-motion is

demonstrated at 0°, 10°, 15°, and 20° in both radial and ulnar deviation. ...................... 150

Figure 8.9. Throughout circumduction for all 6 patients (right panel; color-coded based on

patients), the centers of contact on average moved around the dorsal-radial side of the

carpal component (top left panel) while the centers of contact moved slightly on the radial

component (bottom left panel). The average and standard deviation of movements are

shown by the white circles and white dashed-ellipses, respectively. ............................. 150

1

INTRODUCTION

1.

Motivation

Total Wrist Arthroplasty (TWA) is a surgical solution for severe wrist joint pathology that

aims to both restore the function of the joint and reduce the patient’s pain (Figure 1.1) [1–

3]. The survival of earlier TWA designs have been historically lower (~81% prior to 8

years [4,5]) compared to arthroplasty of large joints such as the hip (~93% up to 10 years

[6]) and the knee (~96% up to 10 years [7]). Although recent TWA designs have improved

the survival rates (e.g., 97% at 7 years [8]), they still suffer from a high complication rate

(e.g., 50% incidence of radiographic loosening as well as 15% revision rate after 7 years

[9]). Unfortunately, patients’ wrist range of motion is also not significantly improved after

joint replacement (post-operative) compared to the patients’ pre-operative ROM [10,11].

Figure 1.1. A dorsal x-ray of a healthy wrist (left). A dorsal x-ray of a wrist with a Freedom®

system (middle). An explanted Freedom® TWA system showing the carpal component,

polyethylene cap, and radial component (right).

To date, TWA designs are developed empirically and in the absence of comparable

datasets on wrist arthroplasty biomechanics. In contrast, hip and knee arthroplasty designs

have been optimized for biomechanical survivorship through decades of evaluation using

2

kinematic datasets on healthy and post-arthroplasty subjects [12–15]. Based on hip and

knee in vivo studies, it has been suggested that sub-optimal kinematics of TWA systems

compared to healthy wrists may cause instability and loosening of the carpal component

[16,17]. Yet, the in vivo biomechanics of TWA designs have not been studied to date.

To assess the role of biomechanics in the success or failure of TWA surgery, the

complex system of rotations and translations of the eight carpal bones of the wrist must

also be evaluated. Previously, carpal bone kinematics have been examined in vitro and in

vivo during isolated wrist motions such as flexion/extension, radial/ulnar deviation, and the

dart thrower’s motion (DTM) [18–23]. While these studies have determined how

individual bones move relative to each other (e.g., minimal motion of scaphoid relative to

capitate in DTM [20], or rigid motion of hamate, capitate, and trapezoid [23]), they have

not evaluated the wrist kinematics as a whole, which can enable a comparison of the

behavior of TWA designs to individual carpal bones.

The primary objective of this project was to understand the biomechanics of a TWA

design. Therefore, because all TWA designs assume one general pattern of motion for the

wrist joint, we first created a mathematical model to evaluate this assumption. Next,

because advanced imaging methods have been mostly used to study hip and knee joints,

and because there are no validated non-invasive in vivo methods for studying the wrist and

TWA, we validated these methods before utilizing them to study healthy and replaced wrist

(TWA) biomechanics. Lastly, we used our validated imaging method to study the in vivo

biomechanics of the wrist and TWA. The findings of this project can be used for improving

previous wrist arthroplasty devices and designing novel data-driven devices with hopes of

improving the clinical and functional outcomes for patients.

3

Background

Wrist Biomechanics

The complex biomechanics of the wrist is due to the complex articulation of the wrist’s

eight small carpal bones (Figure 1.2). These bones move in different motion patterns to

facilitate efficient and stable positioning of the hand through a wide range of motion.

Because there are only minimal direct tendon and muscular insertions to carpal bones [24],

the passive wrist motion is only driven by the shape of the bones, ligamentous constraints,

and the compression forces from their distal structure.

Although these 8 bones do not individually articulate with the same pattern, their

overall articulation seemingly results in a two degrees-of-freedom (DOF) wrist motion,

which is described by the movement of third metacarpal (MC3) or capitate [25], relative to

the radius. Theories of column and row carpal bones [26–28] have been developed in the

past few decades; however, to date, only a few studies have tried to predict carpal bone

motion using overall wrist movement [23,26]. Hence, there is a lack of literature analyzing

the 2 DOF wrist motion assumption. The accuracy of this assumption can affect diagnoses,

treatment strategies, and replacement designs that aim to replace these bones.

Figure 1.2. Wrist motion is due to the articulation of eight carpal bones (Scaphoid (SCA),

Lunate (LUN), Capitate (CAP), Triquetrum (TRQ), Pisiform (PIS), Hamate (HAM),

Trapezoid (TPD), and Trapezium (TPM)) together, while they are interacting with the radius

(RAD) and ulna (ULN) proximally and the metacarpals (MC1-5) distally.

4

Previous studies have revealed that the center of rotation (COR) of the wrist moves

around the proximal pole of the capitate, and thus the wrist is not a simple ball-and-socket

joint [25,29]. Notably, it has been shown that the envelope of healthy wrist range of motion

is elliptically-shaped and it is oriented oblique to the anatomical axes of the wrist [30,31],

with the greatest ranges of motion in radial-extension and ulnar-flexion (~65°, and ~110°)

and much less in ulnar and radial deviation (~40° and ~20°, respectively). This path of

motion, from radial-extension to ulnar-flexion (the DTM path), is crucial for activities of

daily living (ADL) and occupational hand use [32,33]. However, it is unknown if the DTM

is preserved in pathological wrists or in the currently approved wrist arthroplasty designs.

Wrist Pathology and Treatments

In cases of severe injury to the carpal bones or in the presence of arthritis (which affects

one in seven people in the United States alone [34]) the carpal bones lose their shape and

the cartilage between them degenerates. These changes have debilitating effects on patients

by prohibiting the optimal performance of the wrist in ADL.

Although common treatment strategies for carpal injuries or arthritis can be

conservative managements such as immobilization, anti-inflammatory medications, or

corticosteroid injection, these treatments only relieve the symptoms for a brief period of

time and cannot stop the progression of the cartilage degeneration. Therefore, surgical

approaches such as partial wrist fusion (radioscapholunate-STT, or scaphoid excision and

4 corner fusion), partial row carpectomy (when the capitate is healthy), or osseous excision

(distal scaphoid and pisiform) are sometimes advised [35–37].

However, the treatments for pancarpal arthritis can only be of 3 categories [38–40].

Denervation is an approach that is only effective in the short-term. It has a high rate of

5

pain recurrence and it does not prevent progression of arthritis. Denervation may also affect

adjacent joints and may limit ROM in the long term [41]. Wrist Arthrodesis (or, wrist

fusion) is an excellent pain relief [42]. It preserves grip strength and has good functional

outcomes [38]. However, it yields limited wrist motion due to its design and thus, it

significantly limits the ADL for patients. Total Wrist Arthroplasty (TWA) aims to

provide both functional ROM and relieve pain [17,43]. TWA is traditionally reserved for

low demand patients to help them with ADL and personal hygiene [44]. TWA patients are

generally satisfied with the pain relief and wrist function, and studies have also shown that

TWA is more cost-effective than wrist arthrodesis [45,46]. However, TWA designs suffer

from a high complication rate in the long term.

Total Wrist Arthroplasty (TWA)

The first recorded TWA, an ivory ball-and-socket with two fixation pegs in the

metacarpals, was performed in 1890 by Themistocles Gluck [47]. TWA designs have

evolved and passed through many iterations since then, and can mainly be categorized into

four “generations” of TWA designs [2].

The 1st generation of TWA designs (i.e., Swanson designs) were made out of 1-

piece silicone, and they served as a hinge joint or dynamic spacer. These implants achieved

stability potentially by scar tissue over the implant; however, about 50% of them failed

after 2.5 years, possibly due to biocompatibility issues [48].

The 2nd generation of TWA designs were the ball-and-socket joint designs of Meuli

and Volz [49,50]. These designs had a fixed COR; thus, they were not simulating the

healthy wrist motion and they potentially were stressing the bone-component interface of

the implants. These TWA designs had a 35% reoperation rate within 2 years of first surgery

6

[51] along with a 44% rate of complications [50], such as loosening, dislocation, and

muscle imbalance.

Using in vitro studies of the wrist and carpal bone kinematics, the 3rd generation of

TWA designs (e.g., Biaxial [DePuy], Universal [Kinetikos Medical], Trispherical [Weber])

aimed to mimic the COR of healthy wrist motion [52,53]. These implants were cemented

and had an ulnar and volar offset for their carpal component’s stem to reproduce the

“anatomic” COR. These designs were semi-constrained (ellipsoidal or toroidal), and

achieved better long term outcomes of 93% survival [52]; yet, the distal component failure

was still a reoccurring problem for patients [54].

The latest generation of implants (Universal II and Freedom [Integra LifeSciences],

ReMotion [Stryker]) were designed to essentially eliminate the midcarpal joint and replace

the radiocarpal articular surface with a toroidal or ellipsoidal shaped articulation. These

implants, which are the ones currently available to surgeons and patients, typically

approximate center of rotation with an ellipsoid surface to produce different axes for

flexion-extension and radial-ulnar deviation motions. The updated designs also minimize

metacarpal stem fixation and include bony in-growth stems for fixation improvements.

Recently, other novel devices such as Motec (Swemac Orthopaedics), and Amandys

(Tornier) have also been designed and are currently being studied clinically for long-term

survival and complication rates.

Nevertheless, unfortunately, even the 3rd and 4th generations of TWA designs suffer

from a high complication rate of more than 25% after 5 years (Table 1). The complications,

such as loosening or osteolysis, can lead to a later failure of the implant. Therefore, to

increase the survival rate and achieve improved clinical outcomes in the long-term, we

7

need to understand the biomechanics of TWA and the underlying factors that are

potentially causing these high complication rates.

Table 1.1. The complication rate and survival rate of 3rd and 4th generation TWA designs in

follow-up (f/u) years, along with the percentage of patients who received the implant because of

osteoarthritis (OA) and number of patients (n).

Prosthesis

Publication Year n =

Avg.

f/u (y) %OA Survival Complications

Maestro [55]

2012 23 2.2 74 96%

30%: Infection, instability,

contracture

ReMotion [10]

2012 215 4.0 40 92%

28%: 14% loosening, 5%

revision

Universal II [56]

2012 21 3.1 10 91%

42%: No instability or

revision

Motec [57]

2012 30 3.2 100 93%

37%: 2 fusion, 1 loosening,

17% osteolysis

ReMotion [58]

2013 35 3.3 100 92%

23%: 2 revisions, 17%

osteolysis

Universal II [59]

2016 85 4.5 0 91%

31%: 3 fusion, 3 revision,

re-operation

Universal II [9]

2018 48 7.0 29 80%

27%: 15% revision, 8%

CTR, 50% loosening

Motec [60]

2018 25 4 80 -

16%: 4% loosening, 4%

dislocation, 8% fusion

Motec [3]

2018 110 5 - - 33%: loosening, infection

Universal II [5]

2019 26 11.0 46 81%

20%: 3 loosening, 1

luxation, 1 synovitis

ReMotion [8]

2019 39 7.0 0 97%

33%: 13% revision, 13%

impingement

Various Designs [61]

2020 136 10 24 92% 0% to 37.5% loosening

In vivo Methods of Studying the Wrist and TWA

Dynamic in vivo assessment of healthy and replaced wrist motion can help us to understand

the joint’s function during various activities and assess its biomechanics. Traditionally,

optical motion capture (OMC) techniques are used for studying joint biomechanics;

8

however, these techniques are associated with significant errors due to the relative motion

between the skin-based reflective markers and the underlying bones when they are applied

to complex joints such as the wrist [62,63].

Biplane videoradiography (BVR) is a technology that has been used to study the

dynamic motion of bones and implants before and after knee and hip replacement [62,64–

72], but it has not previously been used in the study of the wrist. BVR is a system that

combines image series acquired by two x-ray sources with a bone model acquired from

computed tomography (CT), or an accurate CAD model of an implant, to find the bone or

implant’s exact position and orientation in 3D space. Digitally reconstructed radiographs

(DRRs) are constructed from the density-based image volumes using ray casting

algorithms and then are registered to each frame of the radiographs [62,73,74].

However, using BVR to study wrist function in healthy and TWA patients is not

straightforward. In healthy wrists, tracking the carpal bones is not achievable due to their

overlap in the x-ray images, and tracking the third metacarpal is arduous and needs a novel

methodology due to the overlap of the middle metacarpals in the radiographs. In replaced

wrists, a different BVR methodology is needed, because accurate CAD models of

assembled carpal components cannot be generated a priori, since these components are

fixed in part with screws placed at surgeon-selected orientations. Because the orientations

of the screws can be different for each patient, the models of the implants need to be

different among patients, as well.

Specific Aims

In this project, we first expand our previous digital database of in vivo carpal kinematics

[75], and then we construct a mathematical model of wrist motion (Specific Aim 1). Next,

9

we evaluate the agreement of an advanced image-based method, biplane videoradiography

(BVR), with optical motion capture (OMC) in studying the kinematics of TWA and healthy

wrists (Specific Aim 2). Lastly, we use BVR in an in vivo study to understand how a current

TWA design behaves during anatomical and functional tasks (Specific Aim 3).

Based on previous studies of the wrist, hip, and knee joints, we focus our 3rd specific

aim on answering four distinct problems. First, we study the functional axis of the

Freedom® arthroplasty design and evaluate its post-operative range of motion. Although

Singh et al. demonstrated that the orientation of the functional axis of a TWA is smaller

than the native wrist (12 ± 4° compared to 25 ± 15°) by studying the Universal II® TWA

design [76], this is unknown for the Freedom® implant. Furthermore, previous studies have

shown pre- and post-operation ROM is similar for TWA patients, and only one TWA

design (Maestro, discontinued [77]) can achieve the functional range of motion after

surgery [59,78,79]. Second, to generate kinematics datasets for a healthy wrist, to design

a method for comparing TWA designs, and to provide benchmarks for novel TWA designs,

we study the center of rotation (COR) of the implant and the healthy wrist. For the wrist,

the COR is determined to be at the proximal side of the capitate bone, with minimal distal-

proximal (up and down) movement [25,28]; however, the COR dynamic shifts are

unknown for either replaced or healthy wrists. Third, the alignment of the implant has

been studied extensively for the hip and knee arthroplasty designs [80], but no similar data

exists for the wrist arthroplasty designs. Clinical consequences of alignment errors in total

knee replacements and total hip replacements have led to the accurate evaluation of surgical

techniques, and such studies might also help in devising new TWA surgical techniques.

Fourth, we focus on studying the TWA design at the contact level. Contact level studies

10

have improved total hip and knee replacement designs by detecting impingement regions

[81], but, currently, it is unknown if impingement occurs for a TWA design, and identifying

these potential regions will aid researchers in modifying the design to avoid this problem.

Briefly, the specific aims of this project are:

Specific Aim 1: Develop a mathematical model of carpal bone kinematics as a function of

wrist flexion-extension and radial-ulnar deviation based on an expanded carpal bone

kinematic database of healthy subjects.

I. Develop a mathematical model of carpal kinematics as a function of wrist flexion-

extension and radioulnar deviation to predict individual carpal bone kinematics.

II. Determine paths of wrist motion that result in minimal carpal bone movement.

Specific Aim 2: Determine the accuracy of BVR for quantifying in vivo motion of (I)

healthy wrist and (II) replaced wrist kinematics.

Specific Aim 3: Determine in vivo kinematics of TWA and the wrist in functional and

range-of-motion tasks for both TWA patients and healthy controls.

I. Evaluate the range of motion and orientation of the functional axis of the TWA.

II. Determine and assess the center of rotation of the wrist and TWA.

III. Develop methods to define the alignment of TWA components and determine its

influence on clinical outcomes.

IV. Assess the TWA contact pattern and determine the potential regions of

impingement.

References

[1] Adams, B. D., 2013, “Wrist Arthroplasty: Partial and Total,” Hand Clin, 29(1), pp.

79–89.

[2] Weiss, A.-P. C., Kamal, R. N., and Shultz, P., 2013, “Total Wrist Arthroplasty,” J

Am Acad Orthop Surg, 21(3), pp. 140–148.

11

[3] Reigstad, O., and Røkkum, M., 2018, “Wrist Arthroplasty Using Prosthesis as an

Alternative to Arthrodesis: Design, Outcomes and Future,” J Hand Surg Eur Vol,

43(7), pp. 689–699.

[4] Sagerfors, M., Gupta, A., Brus, O., and Pettersson, K., 2015, “Total Wrist

Arthroplasty: A Single-Center Study of 219 Cases With 5-Year Follow-Up,” J

Hand Surg Am, 40(12), pp. 2380–2387.

[5] Zijlker, H. J. A., Ritt, M. J. P. F., and IJsselstein, C. B., 2019, “Long-Term Results

of Universal 2 Total Wrist Arthroplasty,” Jnl Wrist Surg.

[6] Berstock, J. R., Beswick, A. D., Lenguerrand, E., Whitehouse, M. R., and Blom,

A. W., 2014, “Mortality after Total Hip Replacement Surgery,” Bone and Joint

Research, 3(6), pp. 175–182.

[7] Bayliss, L. E., Culliford, D., Monk, A. P., Glyn-Jones, S., Prieto-Alhambra, D.,

Judge, A., Cooper, C., Carr, A. J., Arden, N. K., Beard, D. J., and Price, A. J., 2017,

“The Effect of Patient Age at Intervention on Risk of Implant Revision after Total

Replacement of the Hip or Knee: A Population-Based Cohort Study,” Lancet,

389(10077), pp. 1424–1430.

[8] Froschauer, S. M., Zaussinger, M., Hager, D., Behawy, M., Kwasny, O., and

Duscher, D., 2019, “Re-Motion Total Wrist Arthroplasty: 39 Non-Rheumatoid

Cases with a Mean Follow-up of 7 Years,” Journal of Hand Surgery (European

Volume), p. 175319341986611.

[9] Kennedy, J. W., Ross, A., Wright, J., Martin, D. J., Bransby-Zachary, M., and

MacDonald, D. J., 2018, “Universal 2 Total Wrist Arthroplasty: High Satisfaction

but High Complication Rates,” J Hand Surg Eur Vol, 43(4), pp. 375–379.

[10] Herzberg, G., Boeckstyns, M., Sorensen, A. I., Axelsson, P., Kroener, K.,

Liverneaux, P., Obert, L., and Merser, S., 2012, “‘Remotion’ Total Wrist

Arthroplasty: Preliminary Results of a Prospective International Multicenter Study

of 215 Cases,” J Wrist Surg, 1(1), pp. 17–22.

[11] Boeckstyns, M. E. H., 2014, “Wrist Arthroplasty--a Systematic Review,” Dan Med

J, 61(5), p. A4834.

[12] Astephen, J. L., Deluzio, K. J., Caldwell, G. E., and Dunbar, M. J., 2008,

“Biomechanical Changes at the Hip, Knee, and Ankle Joints during Gait Are

Associated with Knee Osteoarthritis Severity,” Journal of Orthopaedic Research,

26(3), pp. 332–341.

[13] Lim, L. A., Carmichael, S. W., and Cabanela, M. E., 1999, “Biomechanics of Total

Hip Arthroplasty,” Anat. Rec., 257(3), pp. 110–116.

[14] Indelli, P. F., 2016, “Is Normal Knee Biome-Chanics Reproduced by Modern to-

Tal Knee Arthroplasty Designs? The Role of Fluoroscopy,” Osteol Rheu-matol

Open J, 1(1), pp. 6–9.

[15] Uvehammer, J., Kärrholm, J., and Brandsson, S., 2000, “In Vivo Kinematics of

Total Knee Arthroplasty,” Bone & Joint Journal, 82(4), pp. 499–505.

12

[16] Ma, J.-X., and Xu, Y.-Q., 2016, “The Instability of Wrist Joint and Total Wrist

Replacement,” Chinese Journal of Traumatology, 19(1), pp. 49–51.

[17] Halim, A., and Weiss, A.-P. C., 2017, “Total Wrist Arthroplasty,” J Hand Surg Am.

[18] Carelsen, B., Bakker, N. H., Strackee, S. D., Boon, S. N., Maas, M., Sabczynski,

J., Grimbergen, C. A., and Streekstra, G. J., 2005, “4D Rotational X-Ray Imaging

of Wrist Joint Dynamic Motion,” Med Phys, 32(9), pp. 2771–2776.

[19] Choi, Y. S., Lee, Y. H., Kim, S., Cho, H. W., Song, H.-T., and Suh, J.-S., 2013,

“Four-Dimensional Real-Time Cine Images of Wrist Joint Kinematics Using Dual

Source CT with Minimal Time Increment Scanning,” Yonsei Med. J., 54(4), pp.

1026–1032.

[20] Crisco, J. J., Coburn, J. C., Moore, D. C., Akelman, E., Weiss, A.-P. C., and Wolfe,

S. W., 2005, “In Vivo Radiocarpal Kinematics and the Dart Thrower’s Motion,” J

Bone Joint Surg Am, 87(12), pp. 2729–2740.

[21] Kobayashi, M., Berger, R. A., Nagy, L., Linscheid, R. L., Uchiyama, S., Ritt, M.,

and An, K. N., 1997, “Normal Kinematics of Carpal Bones: A Three-Dimensional

Analysis of Carpal Bone Motion Relative to the Radius,” J Biomech, pp. 787–93.

[22] Moritomo, H., Apergis, E. P., Herzberg, G., Werner, F. W., Wolfe, S. W., and

Garcia-Elias, M., 2007, “2007 IFSSH Committee Report of Wrist Biomechanics

Committee: Biomechanics of the so-Called Dart-Throwing Motion of the Wrist,” J

Hand Surg Am, 32(9), pp. 1447–1453.

[23] Taleisnik, J., 1976, “The Ligaments of the Wrist,” J Hand Surg, 1, pp. 110–8.

[24] Patterson, R. M., Williams, L., Andersen, C. R., Koh, S., and Viegas, S. F., 2007,

“Carpal Kinematics during Simulated Active and Passive Motion of the Wrist,” J

Hand Surg Am, 32(7), pp. 1013–1019.

[25] Neu, C. P., Crisco, J. J., and Wolfe, S. W., 2001, “In Vivo Kinematic Behavior of

the Radio-Capitate Joint during Wrist Flexion-Extension and Radio-Ulnar

Deviation,” J Biomech, 34(11), pp. 1429–1438.

[26] Sandow, M. J., Fisher, T. J., Howard, C. Q., and Papas, S., 2014, “Unifying Model

of Carpal Mechanics Based on Computationally Derived Isometric Constraints and

Rules-Based Motion – the Stable Central Column Theory,” J Hand Surg Eur Vol,

39(4), pp. 353–363.

[27] Craigen, M. A., and Stanley, J. K., 1995, “Wrist Kinematics. Row, Column or

Both?,” J Hand Surg [Br], 20, pp. 165–70.

[28] Rainbow, M. J., Wolff, A. L., Crisco, J. J., and Wolfe, S. W., 2016, “Functional

Kinematics of the Wrist,” J Hand Surg Eur Vol, 41(1), pp. 7–21.

[29] Werner, F. W., Green, J. K., Short, W. H., and Masaoka, S., 2004, “Scaphoid and

Lunate Motion during a Wrist Dart Throw Motion,” J Hand Surg Am, 29(3), pp.

418–422.

[30] Palmer, A. K., Werner, F. W., Murphy, D., and Glisson, R., 1985, “Functional

Wrist Motion: A Biomechanical Study,” J Hand Surg Am, 10(1), pp. 39–46.

13

[31] Crisco, J. J., Heard, W. M. R., Rich, R. R., Paller, D. J., and Wolfe, S. W., 2011,

“The Mechanical Axes of the Wrist Are Oriented Obliquely to the Anatomical

Axes,” J Bone Joint Surg Am, 93(2), pp. 169–177.

[32] Wolff, A. L., and Wolfe, S. W., 2016, “Rehabilitation for Scapholunate Injury:

Application of Scientific and Clinical Evidence to Practice,” J Hand Ther, 29(2),

pp. 146–153.

[33] Wolff, A. L., Garg, R., Kraszewski, A. P., Hillstrom, H. J., Hafer, J. F., Backus, S.

I., Lenhoff, M. L., and Wolfe, S. W., 2015, “Surgical Treatments for Scapholunate

Advanced Collapse Wrist: Kinematics and Functional Performance,” J Hand Surg

Am, 40(8), pp. 1547–1553.

[34] Akhondi, H., and Panginikkod, S., 2020, “Wrist Arthritis,” StatPearls, StatPearls

Publishing, Treasure Island (FL).

[35] Hayden, R. J., and Jebson, P. J. L., 2005, “Wrist Arthrodesis,” Hand Clin, 21(4),

pp. 631–640.

[36] Bielak, K. M., Kafka, J., and Terrell, T., 2013, “Treatment of Hand and Wrist

Injuries,” Prim Care, 40(2), pp. 431–451.

[37] Hausman, M., 2004, “Conservative Surgical Treatment of Wrist Arthritis,” Instr

Course Lect, 53, pp. 23–30.

[38] Weiss, A. C., Wiedeman, G., Quenzer, D., Hanington, K. R., Hastings, H., and

Strickland, J. W., 1995, “Upper Extremity Function after Wrist Arthrodesis,” J

Hand Surg Am, 20(5), pp. 813–817.

[39] Nydick, J. A., Watt, J. F., Garcia, M. J., Williams, B. D., and Hess, A. V., 2013,

“Clinical Outcomes of Arthrodesis and Arthroplasty for the Treatment of

Posttraumatic Wrist Arthritis,” The Journal of Hand Surgery, 38(5), pp. 899–903.

[40] Kadiyala, R. K., and Lombardi, J. M., 2017, “Denervation of the Wrist Joint for the

Management of Chronic Pain,” J Am Acad Orthop Surg, 25(6), pp. 439–447.

[41] Biswas, S., 2015, “Persistent Wrist Pain,” Eplasty, 15.

[42] Wei, D. H., and Feldon, P., 2016, “Total Wrist Arthrodesis: Indications and Clinical

Outcomes,” J Am Acad Orthop Surg.

[43] Weiss, A.-P. C., and Akelman, E., 2012, “Total Wrist Replacement,” Med Health

R I, 95(4), pp. 117–119.

[44] Murphy, D. M., Khoury, J. G., Imbriglia, J. E., and Adams, B. D., 2003,

“Comparison of Arthroplasty and Arthrodesis for the Rheumatoid Wrist,” J Hand

Surg Am, 28, pp. 570–6.

[45] Cavaliere, C. M., and Chung, K. C., 2008, “A Systematic Review of Total Wrist

Arthroplasty Compared with Total Wrist Arthrodesis for Rheumatoid Arthritis,”

Plast. Reconstr. Surg., 122(3), pp. 813–825.

[46] Cavaliere, C. M., and Chung, K. C., 2010, “A Cost-Utility Analysis of Nonsurgical

Management, Total Wrist Arthroplasty, and Total Wrist Arthrodesis in Rheumatoid

Arthritis,” J Hand Surg Am, 35(3), pp. 379-391.e2.

14

[47] Ritt, M. J., Stuart, P. R., Naggar, L., and Beckenbaugh, R. D., 1994, “The Early

History of Arthroplasty of the Wrist. From Amputation to Total Wrist Implant,” J

Hand Surg Br, 19(6), pp. 778–782.

[48] Kistler, U., Weiss, A.-P. C., Simmen, B. R., and Herren, D. B., 2005, “Long-Term

Results of Silicone Wrist Arthroplasty in Patients With Rheumatoid Arthritis,”

Journal of Hand Surgery, 30(6), pp. 1282–1287.

[49] Meuli, H. C., 1984, “Meuli Total Wrist Arthroplasty,” Clin. Orthop. Relat. Res.,

(187), pp. 107–111.

[50] Menon, J., 1987, “Total Wrist Replacement Using the Modified Volz Prosthesis,”

J Bone Joint Surg Am, 69(7), pp. 998–1006.

[51] Beckenbaugh, R. D., and Linscheid, R. L., 1977, “Total Wrist Arthroplasty: A

Preliminary Report,” The Journal of Hand Surgery, 2(5), pp. 337–344.

[52] Kraay, M. J., and Figgie, M. P., 1995, “Wrist Arthroplasty with the Trispherical

Total Wrist Prosthesis,” Semin Arthroplasty, 6(1), pp. 37–43.

[53] Cobb, T. K., and Beckenbaugh, R. D., 1996, “Biaxial Total-Wrist Arthroplasty,” J

Hand Surg Am, 21(6), pp. 1011–1021.

[54] Lorei, M. P., Figgie, M. P., Ranawat, C. S., and Inglis, A. E., 1997, “Failed Total

Wrist Arthroplasty. Analysis of Failures and Results of Operative Management,”

Clin. Orthop. Relat. Res., (342), pp. 84–93.

[55] Nydick, J. A., Greenberg, S. M., Stone, J. D., Williams, B., Polikandriotis, J. A.,

and Hess, A. V., 2012, “Clinical Outcomes of Total Wrist Arthroplasty,” The

Journal of Hand Surgery, 37(8), pp. 1580–1584.

[56] Morapudi, S. P. K., Marlow, W. J., Withers, D., Ralte, P., Gabr, A., and Waseem,

M., 2012, “Total Wrist Arthroplasty Using the Universal 2 Prosthesis,” J Orthop

Surg (Hong Kong), 20(3), pp. 365–368.

[57] Reigstad, O., Lütken, T., Grimsgaard, C., Bolstad, B., Thorkildsen, R., and

Røkkum, M., 2012, “Promising One- to Six-Year Results with the Motec Wrist

Arthroplasty in Patients with Post-Traumatic Osteoarthritis,” J Bone Joint Surg Br,

94(11), pp. 1540–1545.

[58] Boeckstyns, M. E. H., Herzberg, G., Sørensen, A. I., Axelsson, P., Krøner, K.,

Liverneaux, P. A., Obert, L., and Merser, S., 2013, “Can Total Wrist Arthroplasty

Be an Option in the Treatment of the Severely Destroyed Posttraumatic Wrist?,” J

Wrist Surg, 2(4), pp. 324–329.

[59] Badge, R., Kailash, K., Dickson, D. R., Mahalingam, S., Raza, A., Birch, A.,

Nuttall, D., Murali, S. R., Hayton, M. J., Talwalkar, S., Watts, A. C., and Trail, I.

A., 2016, “Medium-Term Outcomes of the Universal-2 Total Wrist Arthroplasty in

Patients with Rheumatoid Arthritis,” Bone Joint J, 98-B(12), pp. 1642–1647.

[60] Giwa, L., Siddiqui, A., and Packer, G., 2018, “Motec Wrist Arthroplasty: 4 Years

of Promising Results,” J Hand Surg Asian Pac Vol, 23(3), pp. 364–368.

15

[61] Fischer, P., Sagerfors, M., Jakobsson, H., and Pettersson, K., 2020, “Total Wrist

Arthroplasty: A 10-Year Follow-Up,” J Hand Surg Am, 45(8), p. 780.e1-780.e10.

[62] Miranda, D. L., Schwartz, J. B., Loomis, A. C., Brainerd, E. L., Fleming, B. C., and

Crisco, J. J., 2011, “Static and Dynamic Error of a Biplanar Videoradiography

System Using Marker-Based and Markerless Tracking Techniques,” Journal of

Biomechanical Engineering, 133(12), p. 121002.

[63] Miranda, D. L., Rainbow, M. J., Crisco, J. J., and Fleming, B. C., 2013, “Kinematic

Differences between Optical Motion Capture and Biplanar Videoradiography

during a Jump-Cut Maneuver,” J Biomech, 46(3), pp. 567–573.

[64] Banks, S. A., and Hodge, W. A., 1996, “Accurate Measurement of Three-

Dimensional Knee Replacement Kinematics Using Single-Plane Fluoroscopy,”

IEEE Trans Biomed Eng, 43(6), pp. 638–649.

[65] Flood, P. D. L., and Banks, S. A., 2016, “Automated Registration of Three-

Dimensional Knee Implant Models to Fluoroscopic Images Using Lipschitzian

Optimization,” IEEE Trans Med Imaging.

[66] Scott, G., Imam, M. A., Eifert, A., Freeman, M. a. R., Pinskerova, V., Field, R. E.,

Skinner, J., and Banks, S. A., 2016, “Can a Total Knee Arthroplasty Be Both

Rotationally Unconstrained and Anteroposteriorly Stabilised? A Pulsed

Fluoroscopic Investigation,” Bone Joint Res, 5(3), pp. 80–86.

[67] Tsai, T.-Y., Li, J.-S., Wang, S., Lin, H., Malchau, H., Li, G., Rubash, H., and Kwon,

Y.-M., 2013, “A Novel Dual Fluoroscopic Imaging Method for Determination of

THA Kinematics: In-Vitro and in-Vivo Study,” J Biomech, 46(7), pp. 1300–1304.

[68] Yamazaki, T., Watanabe, T., Nakajima, Y., Sugamoto, K., Tomita, T., Yoshikawa,

H., and Tamura, S., 2004, “Improvement of Depth Position in 2-D/3-D Registration

of Knee Implants Using Single-Plane Fluoroscopy,” IEEE Trans Med Imaging,

23(5), pp. 602–612.

[69] Kaptein, B. L., Valstar, E. R., Stoel, B. C., Rozing, P. M., and Reiber, J. H. C.,

2003, “A New Model-Based RSA Method Validated Using CAD Models and

Models from Reversed Engineering,” Journal of Biomechanics, pp. 873–882.

[70] Banks, S. A., and Hodge, W. A., 2004, “Implant Design Affects Knee Arthroplasty

Kinematics during Stair-Stepping,” Clin. Orthop. Relat. Res., (426), pp. 187–193.

[71] Tashman, S., and Anderst, W., 2003, “In-Vivo Measurement of Dynamic Joint

Motion Using High Speed Biplane Radiography and CT: Application to Canine

ACL Deficiency,” J Biomech Eng, 125(2), pp. 238–245.

[72] Brainerd, E. L., Baier, D. B., Gatesy, S. M., Hedrick, T. L., Metzger, K. A., Gilbert,

S. L., and Crisco, J. J., 2010, “X-Ray Reconstruction of Moving Morphology

(XROMM): Precision, Accuracy and Applications in Comparative Biomechanics

Research,” J Exp Zool A Ecol Genet Physiol, 313(5), pp. 262–279.

16

[73] You, B. M., Siy, P., Anderst, W., and Tashman, S., 2001, “In Vivo Measurement

of 3-D Skeletal Kinematics from Sequences of Biplane Radiographs: Application

to Knee Kinematics,” IEEE Trans Med Imaging, 20, pp. 514–25.

[74] Bey, M. J., Zauel, R., Brock, S. K., and Tashman, S., 2006, “Validation of a New

Model-Based Tracking Technique for Measuring Three-Dimensional, in Vivo

Glenohumeral Joint Kinematics,” J Biomech Eng, 128(4), pp. 604–609.

[75] Moore, D. C., Crisco, J. J., Trafton, T. G., and Leventhal, E. L., 2007, “A Digital

Database of Wrist Bone Anatomy and Carpal Kinematics,” J Biomech, 40(11), pp.

2537–2542.

[76] Singh, H. P., Bhattacharjee, D., Dias, J. J., and Trail, I., 2017, “Dynamic

Assessment of the Wrist after Total Wrist Arthroplasty,” J Hand Surg Eur Vol, p.

1753193417690472.

[77] Schmidt, I., 2018, “A Critical Appraisal to the Decision by the Company Zimmer

Biomet to Withdraw the MaestroTM Wrist Reconstructive System from the

Marketplace,” Trauma Emerg Care, 3(2).

[78] Gil, J. A., Kamal, R. N., Cone, E., and Weiss, A.-P. C., 2017, “High Survivorship

and Few Complications With Cementless Total Wrist Arthroplasty at a Mean

Followup of 9 Years,” Clin. Orthop. Relat. Res., 475(12), pp. 3082–3087.

[79] Yeoh, D., and Tourret, L., 2015, “Total Wrist Arthroplasty: A Systematic Review

of the Evidence from the Last 5 Years,” J Hand Surg Eur Vol, 40(5), pp. 458–468.

[80] Rivière, C., Lazic, S., Boughton, O., Wiart, Y., Vïllet, L., and Cobb, J., 2018,

“Current Concepts for Aligning Knee Implants: Patient-Specific or Systematic?,”

EFORT Open Reviews, 3(1), pp. 1–6.

[81] Brown, T. D., and Callaghan, J. J., 2008, “Impingement in Total Hip Replacement:

Mechanisms and Consequences,” Curr Orthop, 22(6), pp. 376–391.

17

PREDICTING CARPAL BONE

KINEMATICS USING AN EXPANDED DIGITAL

DATABASE OF WRIST CARPAL BONE

ANATOMY AND KINEMATICS

2.

Bardiya Akhbari, Douglas C. Moore, David H. Laidlaw, Arnold-Peter C.

Weiss, Edward Akelman, Scott W. Wolfe, Joseph J. Crisco

Journal of Orthopaedic Research 37: 2661–2670, 2019

https://doi.org/10.1002/jor.24435

18

Abstract (250 Words)

The wrist can be considered a two degrees-of-freedom joint with all movements reflecting

the combination of flexion-extension and radial-ulnar deviation. Wrist motions are

accomplished by the kinematic reduction of the forty-two degrees-of-freedom of the

individual carpal bones. While previous studies have demonstrated the minimal motion of

the scaphoid and lunate as the wrist moves along the dart-thrower’s path or small relative

motion between hamate-capitate-trapezoid, an understanding of the kinematics of the

complete carpus across all wrist motions remains lacking. To address this, we assembled

an open-source database of in-vivo carpal motions and developed mathematical models of

the carpal kinematics as a function of wrist motion. Quadratic surfaces were trained for

each of the 42-carpal bone degrees-of-freedom and the goodness of fits were evaluated.

Using the models, paths of wrist motion that generated minimal carpal rotations or

translations were determined. Model predictions were best for flexion-extension, radial-

ulnar deviation, and volar-dorsal translations for all carpal bones with R2 of more than 0.8,

while the estimates were least effective for supination-pronation with R2 of less than 0.6.

The wrist path of motion’s analysis indicated that the distal row of carpal bones moves

rigidly together (< 3º motion), along the anatomical axis of wrist motion, while the bones

in the proximal row undergo minimal motion when the wrist moves in a path oblique to

the main axes. The open-source dataset along with its graphical user interface and

mathematical models should facilitate clinical visualization and enable new studies of

carpal kinematics and function.

19

Introduction

The wrist joint can be considered a two degrees-of-freedom (DOF) joint with all

movements reflecting combinations of flexion-extension (FE) and radial-ulnar deviation

(RU). These two DOFs are accomplished by kinematic reduction of the forty-two DOFs of

seven carpal bones. The pisiform, while identified as a carpal bone, is not considered a

significant factor as it has a minimal role in wrist kinematics.1 The passive motion and the

reduction in the DOFs is due to the minimal direct tendon and muscular insertions to carpal

bones.2,3 Carpal bone motion is thus driven by the contact forces from their distal structures

(i.e., metacarpals), proximal structures (i.e., triangular fibrocartilage complex and radius),2

and their surrounding ligamentous constraints.4,5

To describe the carpal bone motion patterns, two major kinematic theories of row

and column have been proposed.6 Although the row theory (describing the distinct motion

patterns for proximal and distal carpal rows),7–11 column theory (assuming three medial-

central-lateral carpal columns as an inner mechanism for the wrist motion),12,13 and their

combinations14,15 have helped in devising and evaluating clinical procedures,16 they are not

predictive or specific about individual carpal bone kinematics within the wrist motion.

Most previous studies have focused on individual carpal bone or groups of

two/three bones during specific wrist motions such as FE, RU, or the dart thrower’s motion

(DTM).13,17–21 While these studies have demonstrated how individual bones move relative

to each other—importantly, the minimal motion of scaphoid and lunate in the DTM19—or

how a group of carpal bones moves relative to each other (e.g., small relative motion

between hamate, capitate, and trapezoid),13 the ability to comprehensively model the entire

carpus as a function of wrist motion (FE and RU; 2 DOF) could help us to better understand

20

wrist function. Such a model could also illuminate how individual carpal bone kinematics

are altered after an injury, or how to study the biomechanics of total wrist arthroplasty

designs which currently reduce the wrist to a two-DOF joint.22

A model’s success is assessed by its ability to predict data from a large dataset that

the model has not seen.23 Thus far, a predictive model for the carpal bones has not been

developed, perhaps in part because of the lack of a detailed kinematic database. Previous

attempts at constructing a predictive and informative model of carpal bone motion have

been primarily based on radiographic or cadaveric observations.6,16,24,25 Due to the

variations in motion patterns of the carpal bone articulations among wrists and lack of large

sample sizes, none of these models have been rigorously evaluated for predictive ability.

Recently, a stable central column theory26 of carpal bones was proposed by modeling the

isometry of ligament lengths on an in-vivo dataset, however, the study was limited to a

single specific task (in RU direction) with a small sample size (ten wrists). Computational

modeling and finite element analysis are powerful tools for evaluating wrist contact forces

in mostly static postures,27–29 however, to date, they have not been used for kinematic

analysis and prediction.

Previously, our group published a database of in-vivo carpal kinematics and

anatomy for 60 healthy wrists.19,30–33 We postulate that expanding the database with

additional studies,34–39 would provide an approximately complete picture of carpal

kinematics. In this study, our first aim was to assemble and describe an expanded open-

source database of in-vivo wrist motions from 120 previously-studied wrists. Using the

database, our second aim was to develop a mathematical model of the carpal kinematics as

a function of two DOFs of wrist motion to predict the individual carpal bone kinematics.

21

Our third aim was to use the model to determine paths of wrist motion that result in minimal

carpal bones movement. In addition, a graphical user interface (GUI) of the database and

the mathematical model were developed to enable investigators to qualitatively and

quantitively observe the wrist motions available in the database and build upon the

proposed mathematical models.

Methods

Overview

This study has integrated data from four NIH-funded CT-image based in-vivo studies on

wrist and thumb kinematics.30,34–39 The database used in this study has been also made

freely available through Simtk.org/projects/carpal-database. The current database includes

CT-derived carpal bone models from 90 subjects

(120 wrists) and carpal bone kinematics in 1,215

unique wrist positions (Table 2.1 and Figure 2.1).

Database Description – Data Acquisition

Healthy subjects were recruited after institutional

review board approval and were all pre-screened for

a history of wrist injuries by board-certified

orthopedic hand surgeons. The previously published

database,30 containing datasets for 30 subjects, has

been previously described (Table 2.1). The expanded

database contains data from an additional 60

subjects: 14 of which were studied in extreme wrist

flexion, extreme wrist extension, and five positions

Figure 2.1. Wrist motions within the

carpal dataset for all 120 wrists. Wrist

motion was defined as the motion of

capitate in the radial coordinate

system, and each point depicts the

motion of the wrist in a single task.

22

along the path of DTM. Forty-six of these participants were in a study of carpometacarpal

joint biomechanics in which the thumb and wrist were in various poses (thumb neutral

pose, adduction, abduction, flexion, extension, jar twist, jar grasp, and key pinch)40 (Table

2.1). The neutral pose was defined by aligning the dorsum of the third metacarpal with the

forearm’s dorsal surface using a goniometer in functional, combined, and incremental

orthogonal cohorts.30 In the CMC cohort, the neutral position was defined using a splint

placing the wrist in an anatomic neutral posture (approximately 0° flexion/extension and

ulnar/radial deviation).41 Two subjects (4 wrists) neutral position did not follow the

acquisition protocol, thus they were excluded for mathematical modeling.

Table 2.1. Breakdown of our open-source carpal database. Forty-six wrists of 46 healthy subjects

in a study of carpometacarpal (CMC) joint from 2012 to 2015, fourteen wrists of 14 healthy

subjects from 2008 to 2010, and sixty healthy wrists (30 subjects, for both sides) from 2000 to

2006. The total number of unique wrist postures was 1215 (120 neutral, 1095 others).

Group Description

Gender Age Side # Postures

Male

(M)

Female

(F)

Young (<

45 yrs.)

Old (> 45

yrs.)

Righ

t

CMC

Cohort34,40,41

CMC joint in this

study has

different poses;

however, the

wrist motion was

unconstrained

21 25

21

(10 M, 11

F)

25

(11 M, 14

F)

36 530

Functional

Cohort35-39

Wrists were

tested in five

hammering tasks,

extreme flexion,

and extreme

extension tasks

7 7 14 - 14 165

Combined

Cohort30-33

Wrists were in

specific anatom-

ical ROM poses

and DTM tasks

10 10 20 - 20 360

Incremental

Orthogonal

Cohort30-33

Wrists were

tested in

anatomical ROM

tasks

5 5 10 - 10 160

TOTAL # 43 47 65 25 40 80 1215

The bone surface models have been constructed from the CT scans (Lightspeed®

16. GE Medical, Milwaukee, WI) that were obtained of the wrist in the aforementioned

23

poses.30,42 The CT scan resolutions differed between the datasets and ranged from 0.2 ×

0.2 to 0.4 × 0.4 mm2 in the transverse plane of the hand, and 0.625 to 1 mm along the axis

of the forearm. Digital models of the outer cortical surface of radius, ulna, carpal bones,

and metacarpals were obtained from the neutral posture CT images using Mimics v12-19

(Materialise, Leuven, Belgium) by employing thresholding and edge detection algorithms.

No cartilage was modeled from the CT images.

Database Description – Data Analysis

Kinematic transformations were calculated from the neutral wrist position to each

target position using a tissue-classified distance fields algorithm to register the bone models

in the neutral position to all other posture’s CT scans, creating six-DOF global

transformations from the neutral scan to each subsequent position as described before.43

Using the bones’ inertial properties, an orthogonal coordinate system for each carpal bone

was constructed with the origin at the bone models’ volumetric centroid.32

A radial coordinate system (RCS) was calculated based on the modification of the

ISB recommendation and the distal radius’ anatomical

landmarks (Figure 2.2).20,44,45 The x-axis direction was

defined by the central axis of the distal radius shaft,

and the y-axis was defined by a line from the center of

the sigmoid notch to the styloid process of the radius,

projected onto the distal radius surface. The z-axis was

the cross product of the other axes. The origin was the

projection of the intersection of the x-axis direction

and y-axis direction on the distal radius surface.

Figure 2.2. RCS and HAM

parameters. n is a vector defining

the orientation of the screw axis (nx,

ny, nz), and φtot is the rotation about

the axis. This angle can be decomposed into rotational

components.

24

The database and wrist motion in all postures can be observed and evaluated both

qualitatively and quantitatively by the GUI provided with the database. Written with

MATLAB 2018b (The MathWorks, Natick, MA), the GUI enables users to investigate the

carpal bones position and rotation in any wrist motion available in the database on an

average male or female bone model. Users are also capable of importing subject-specific

bone models (captured at neutral position) to observe the wrist motions available on the

database on their imported models.

Carpal Bones Motion in the RCS

Wrist motion was defined in terms of the FE and RU of the capitate bone (CAP)

because it has been previously shown that the capitate moves almost identically to the third

metacarpal.33 The 6-DOF kinematics of the scaphoid (SCA), lunate (LUN), triquetrum

(TRQ), trapezium (TPM), trapezoid (TPD), and hamate (HAM) were described as a

function of the wrist motion.

The motion of each carpal bone was calculated in the RCS with respect to the

neutral pose and described with the helical axis of motion (HAM) parameters. HAM

parameters characterize the motion as a single rotation (ϕ) about and translation along the

unique screw axis (Figure 2.2). The rotational components of the bone motion were

decomposed using ϕ angle and the screw axis’ orientation to construct supination-pronation

(SP), FE, and RU angular components. Translations were defined as the displacement of

the origin of bone’s inertial coordinate system in the RCS in the distal-proximal (DPT),

radial-ulnar (RUT), and volar-dorsal directions (VDT). Translations were scaled by the

cube root of capitate volume to eliminate the influence of size.46

25

Mathematical Modeling

To create a predictive relationship between the wrist and carpal motion, the

mathematical models were constructed on a training set and then were evaluated on a test

set. Before modeling, 20 subjects’ datasets (30 wrists, 259 wrist motions) were randomly

selected and held out to assess the accuracy of the mathematical models (test set). If the

subject had bilateral data, both sides’ datasets were included in the test set to remove any

biases in the selection. The datasets of remaining 68 subjects (86 wrists, 804 wrist motions)

were used for training the model (Figure 2.3). In total, the carpal kinematics for 116 wrists

from 88 subjects in a total of 1179 wrist postures, which resulted in 1063 calculated

motions (i.e., # of total postures – # of neutral poses) were used for mathematical modeling.

For each carpal bone DOF (BoneDOF), a second-

order quadratic surface with the independent variables of

wrist FE and RU (CAPFE and CAPRU) was constructed

(Eq. 1):

BoneDOF = p10×CAPRU + p01×CAPFE + p20×CAPRU2 +

p11×CAPRU×CAPFE + p02×CAPFE2 (1)

, where p10, p01, p20, p11, and p02 are the coefficients

of the quadratic surface. The quadratic surface equation

was used to improve the predictions at the extreme of

motions. Higher-order polynomials were not used

because they resulted in overfitting and unnatural

behavior of the bone motions. A cross-validation

technique with a leave-one-out strategy was performed

on the training set, and the coefficients were calculated

Figure 2.3. Training set (motions

used to construct the model) from

86 wrists and test set (motions

used to evaluate the model) from

30 wrists were randomly selected

from the database. Each data point

has 42 other dimensions for 7

carpal bones and 6 degrees-of-

freedom.

26

using the least-squares method in each iteration. The best model was selected as the model

with the lowest root-mean-squared-error (RMSE) in the cross-validation procedure. The

database’ kinematics and mathematical models were visualized using Delaunay

triangulation47 of every three-dimensional data point (CAPFE, CAPRU, BoneDOF), color-

coded by the magnitude of that DOF rotation/translation. The face color of Delaunay

triangles was the average of the value for each vertices for an interpretable visualization.

To explore carpal kinematics predicted by the models, we sought to identify paths

of wrist motion along which carpal DOFs were minimal (MM wrist paths). For instance,

the path of wrist motion that generates minimal FE movement for the scaphoid was

identified as the MM wrist path for SCAFE. The MM wrist paths were calculated

numerically using grid-points limited by the minimum and maximum ranges of our dataset

(90° Extension, 120° Flexion, 40° Radial Dev., 60° Ulnar Dev.) with the interval of 0.5°.

Statistical Analysis

The model’s generalizability (i.e., how well the model predicts the motion of carpal bones

from a test set) was evaluated by r-squared (R2), RMSE, and the average of model’s error

on the test set (randomly selected 30 wrists). Since R2 and RMSE can be statistically

biased,23 wrist motions were separated into octants based on the relationship of wrist FE

and RU rotation angles for further analysis of the behavior of the generated model in

different regions of wrist motion. The histograms of differences were assessed in each

octant of RU and FE by measuring the mean and standard deviation of errors.

To analyze and compare the patterns of MM wrist paths for the carpal bone DOFs,

linear regression (p < 0.05) was used to calculate the lower and upper confidence intervals

(LCI and UCI) of the MM wrist path’s slope on a plot of wrist motion. The slope

27

demonstrates the ratio of the wrist’s FE and wrist’s RU when the carpal bone moves only

minimally. The MM wrist paths that did not follow a linear pattern were described by points

along a curve based on the wrist FE or RU.

Results

The published database (https://simtk.org/projects/carpal-database) includes CT-

generated carpal bone anatomy models from 90 healthy subjects (120 wrists) and the carpal

bone kinematics in 1215 unique wrist positions from four NIH-funded studies. A GUI was

also developed to maximize user interaction with this database and the mathematical model

constructed in this study.

The mathematical models (42 models) performed well on the 30 held-out wrists

(test set) in predicting FE (R2 > 0.9, and RMSE < 6.0°) for all carpus bones (Table 2.2).

The models also performed well for RU (R2 > 0.6, and RMSE < 5.0°), volar-dorsal

translation (R2> 0.8, and RMSE < 2.5 mm; except triquetrum), but they performed poorly

in predicting radial-ulnar and dorsal-proximal translations (0.3 < R2 < 0.9, and RMSE <

3.1 mm), and supination-pronation (R2< 0.6, and RMSE < 8°). The mean errors (which

reflect the overall bias of the models) were submillimeter or sub-degree for all predicted

DOFs and carpal bones—except supination-pronation of the capitate which had a bias of -

1.2° (Table 2.2).

28

Table 2.2. Root-mean-square error (RMSE), R2, and model error’s bias of 40 second-order

algebraic fit to every DOFs on the test set (20 subjects, 30 wrists). Degrees-of-freedoms are:

supination-pronation (SP), flexion-extension (FE), radial-ulnar deviation (RU), distal-proximal

translation (DPT), radial-ulnar translation (RUT), and volar-dorsal Translation (VDT).

Translations RMSE is scaled back by the cube root of the average capitate volume (~ 3700 mm3)

for a better demonstration of RMSEs.

Bone Root Mean Square Error (RMSE)

SP (°) FE (°) RU (°) DPT (mm) RUT (mm) VDT (mm)

Capitate 5.2 - - 1.2 1.1 1.8

Scaphoid 3.5 4.2 3.2 0.9 1.1 1.1

Lunate 3.6 5.9 3.6 0.9 1.2 1.0

Hamate 5.2 3.1 2.2 1.4 1.4 2.3

Triquetrum 4.3 6.0 3.8 1.5 1.5 1.6

Trapezoid 7.3 4.0 5.0 2.0 3.1 2.5

Trapezium 6.0 2.7 4.8 1.8 2.9 2.1

Bone R2

SP FE RU DPT RUT VDT

Capitate 0.2 - - 0.9 0.9 0.9

Scaphoid 0.5 1.0 0.7 0.8 0.7 0.9

Lunate 0.3 0.9 0.6 0.7 0.5 0.8

Hamate 0.2 1.0 1.0 0.8 0.9 0.8

Triquetrum 0.6 0.9 0.7 0.5 0.3 0.3

Trapezoid 0.2 1.0 0.9 0.7 0.6 0.8

Trapezium 0.2 1.0 0.9 0.7 0.8 0.8

Bone Model Error’s Bias

SP (°) FE (°) RU (°) DPT (mm) RUT (mm) VDT (mm)

Capitate -1.2 - - 0.1 0.1 0.0

Scaphoid -0.3 0.1 -0.3 0.1 -0.1 0.0

Lunate -0.1 0.0 -0.5 0.0 -0.1 -0.1

Hamate -0.9 0.3 0.2 0.2 0.2 -0.1

Triquetrum -0.5 -0.2 -0.1 0.0 0.0 -0.2

Trapezoid -0.5 -0.2 -0.4 0.3 -0.2 0.2

Trapezium -0.5 0.0 -0.7 0.2 -0.4 0.0

The Delaunay visualization of the carpal bone kinematics, the mathematical model,

and the model’s error demonstrated that the model performed well in the mid-region (i.e.,

mid-FE and mid-RU) of wrist positions, and it performed less well at the extreme range of

29

motions where fewer data were available (Figure 2.4; SCAFE as a representative). The

histogram of errors of the mathematical model based on the position of the wrist revealed

that the model error was normally distributed for all models and DOFs, except supination-

pronation. For example, for the SCAFE, the bias of less than 1°, and the standard deviation

of less than 5° was calculated for all octants (Figure 2.5; scaphoid FE as a representative).

Figure 2.4. The flexion-extension of scaphoid (SCAFE) as the function of wrist motion for the

database (Left), quadratic model’s prediction (Middle), and the model error (Right).

Figure 2.5. Mathematical model errors for scaphoid flexion-extension (SCAFE), the histogram of

errors based on the wrist movement for each octant of RU and FE. The middle figure shows the

model error across kinematics space, and every histogram shows the errors in every subdivision.

The octants are defined based on the relationship between radial (R)/ulnar (U) deviation and

flexion (F)/extension (E) of the wrist. For example, UE defines the region that the ulnar deviation

is larger than extension, and FR describes the region that flexion is larger than radial deviation.

30

The wrist’s FE/RU ratio of the MM wrist path (MM slope) of each bone and DOF

demonstrated different patterns of wrist movement for the bones in the proximal and distal

carpal row (Figure 2.6). The MM slopes were statistically different between proximal and

distal rows in both FE and VDT (p < 0.01) (Table 2.3). The MM slopes for FE were close

to 0 for all bones in the distal row (hamate, trapezoid, and trapezium), while they were

between 0.6 to 1.2 for the proximal row bones (triquetrum, lunate, and scaphoid) (Table

2.3). The same comparison for VDT demonstrated a -0.3 to 0.3 range for the bones in the

distal row and 1.1 to 1.7 range for the bones in the proximal row. MM wrist paths for RUT

and RU were not linear, thus they were compared at incremental wrist positions, and

showed the paths occurred at different positions of the wrist for bones in a proximal and

distal row. For instance, the MM wrist path in RU for the hamate, trapezoid, and triquetrum

had a wrist RU of less than 4° at a flexion angle of 100°, reduced to 0° at the neutral pose,

and increased to less than 3° wrist RU at extension angle of 80°. For triquetrum, lunate,

and scaphoid the path occurred at a much larger wrist RU, which went from 15° in flexion,

to 0 at neutral, and about 40° in extension (Figure 2.6). Because of the weaker prediction

of the model for PS and PDT, the MM wrist paths were not compared in those DOFs.

Table 2.3. The lower confidence interval (LCI) and upper confidence interval (UCI) of the slope

of the path that generates a minimal carpal bone motion (MM slope). Linear regression was used

to calculate the MM slope. The comparison for flexion-extension (FE) and volar-dorsal

translation (VDT) revealed different patterns of wrist movement that generates minimal motions

for the bones in the proximal row (slopes < 0.3), and the bones in the distal row (slopes > 0.6).

Flexion-Extension MM

Slope’s CI

Volar Dorsal Translation MM

Slope’s CI

Bone LCI UCI Bone LCI UCI

Hamate 0.09 0.11 Hamate 0.2 0.3

Trapezoid -0.09 -0.08 Trapezoid -0.3 -0.2

Trapezium -0.1 -0.09 Trapezium -0.3 -0.2

Triquetrum 0.6 0.7 Triquetrum 1.1 1.3

Lunate 1.1 1.2 Lunate 1.5 1.7

Scaphoid 0.7 0.8 Scaphoid 1.1 1.3

31

Figure 2.6. Wrist paths that generate minimal flexion-extension, radial-ulnar deviation, radial-

ulnar translation, and volar-dorsal translation of carpal bones. Different patterns of wrist paths

were seen for the carpal bones in the distal row (i.e., hamate, capitate, trapezoid, and trapezium)

and proximal row (i.e., triquetrum, lunate, and scaphoid).

Discussion

The purposes of this study were to assemble a large database of in-vivo wrist motions, to

construct mathematical models that predict carpal bone kinematics as a function of wrist

FE and RU using the database, and to determine the wrist motion paths that generated

minimal motions for each of the carpal bones. The predictive quadratic models were

developed using a subset of the database as a training set, and they were validated using

the remainder of the database as a test set. The models’ predictions were best on the test

set for FE, RU, and VDT DOFs. The models also revealed different patterns of wrist paths

that generates carpal bones minimal motions in the distal row (i.e., hamate, capitate,

trapezoid, and trapezium) and proximal row (i.e., triquetrum, lunate, and scaphoid).

Three-dimensional understanding of individual carpal bone motion as the wrist

moves in different motion paths is needed for clinicians to diagnose and deliver effective

32

solutions for patients following injury or disease. The current open-source database, the

GUI available with it, and the mathematical model constructed in this study, allows one to

observe carpal bone articulations within a relatively large population both quantitatively

and visually. In addition, similar to the grand challenge competition to predict in-vivo knee

loads,48 investigators can use the current database to construct elaborate models to predict

the kinematics of individual carpal bones using more complex mathematical models, bone

shapes, or finite element models.

Our model demonstrates a distinct pattern of minimal motion between the proximal

and distal row of carpal bones, but it does not explicitly prove or disprove any particular

theory of carpal bone motion that has been developed to date.6,12,13 The row theory7–9,49

described the kinematics of the wrist with two rows organized proximally (lunate and

triquetrum) and distally (hamate, capitate, trapezoid, and trapezium), having the scaphoid

as a bridge or connection between these two rows. Our mathematical model confirmed that

the hamate-capitate-trapezoid-trapezium complex moves relatively rigidly (within 3°),

similar to the row theory and previous studies;13,26 however, our model demonstrated

considerable variations among the bones in the proximal row. Thus, considering the bones

in the proximal row as rigid elements would not be an accurate interpretation of this data

set. Further studies using the database and mathematical modeling will be required to

evaluate the previous carpal theories or examine new ones.

To develop carpal bone kinematic models as a function of the wrist motion, we

made some assumptions about the motion’s description and model’s specification. We used

the wrist motion computed from the subject’s neutral position to remove the shape variation

of the carpal bones from the model generation process. While this assumption enables us

33

to devise a clinically relevent model, it ignores the variation in positioning of the subjects’

wrists at the neutral posture. The neutral position’s variation can be calculated by looking

at the capitate’s posture (as an alternative to third metacarpal), and it was within a 95%

confidence interval of ~10° in our database. However, this interval is an approximation,

because it also depends upon the inertial coordinate system definition of the capitate, which

varies with the bone shape. Future investigation can focus on generating a landmark-based

coordinate system for individual carpal bones to evaluate this effect or to generate posture-

based predictive models. Additionally, the offset in the mathematical model was fixed to

zero with the underlying assumption that carpal bones orientation in the neutral pose is

similar for all subjects. This assumption was ascertained by attaining minimal and

approximately zero offsets, when the offsets were accounted for in training the models.

Moreover, to construct the mathematical model, we chose the simplest model that was

reasonably accurate with close to zero overall mean error. A first-order equation was

incapable of predicting the extreme positions; thus, by increasing the degrees to a second-

order algebraic equation, we were able to model the extreme range-of-motion points, as

well as keeping the model relatively simple. More complex models would likely achieve

higher accuracy. We also assumed that all DOFs are independent in training our model,

and multivariate regression models might yield to a higher accuracy prediction.

We did not evaluate the collisions between the carpal bones in this study.

Consideration of carpal bone collision using finite element modeling might yield higher

accuracy with a refined model. Additionally, it has been shown that the lunate has two

main anatomical shapes, and two different motion paths have been proposed for it;50 we

did not consider effects of bone shapes in our modeling (although we accounted for the

34

size by scaling all carpal bones). Further studies need to examine the influence of the

differing shapes of carpal bones on the wrist kinematics. In our model, we did not include

variables, such as sex, age group, and sidedness, because they were out of the scope of this

study’s purpose; although, it has been shown that these variables are not associated with

the kinematics after scaling the translation by the cubic root of the volume of the capitate.46

Lastly, our model was not a good predictor for pronosupination of any of the carpal bones,

which was most likely because the wrist was considered as a two-DOF system without any

pronosupination, as well as the limited supination-pronation of carpal bones that is

generally less than 5° across all wrist positions.19

The expanded database and mathematical model constructed from this study should

facilitate clinical visualization of normal and pathological wrist motion patterns (using the

GUI) and will enable investigators to analyze the kinematics of the wrist joint and the

articulations of its carpal bones. The GUI created in this study can accommodate subject-

specific bone models to incorporate kinematic data (actual observed values, or modeled

kinematics) to visualize different motions to the user. As a secondary goal, our model

demonstrated that the pattern of wrist motion that generates minimal motion for the distal

row of carpal bones (i.e., hamate, capitate, trapezoid, and trapezium) is different than that

of for the proximal row bones (i.e., triquetrum, lunate, and scaphoid).

Author’s Contribution

Bardiya Akhbari was involved in analyzing and interpreting the data, as well as drafting

the manuscript. David H. Laidlaw was involved with advising on data analysis, interpreting

the data, as well as critical revising of the paper. Douglas C. Moore, Arnold C. Weiss,

Edward Akelman, and Scott W. Wolfe were instrumental in acquiring and reducing the

35

raw data from all studies, and critically revising of the paper. Joseph J. Crisco was involved

with designing the study acquiring and reducing the raw data from all studies, interpreting

the data and critically revising the manuscript. All authors provided feedback and edited

the manuscript. All authors have approved the final submitted manuscript.

Acknowledgments

This work was supported in part by NIH R01-AR044005, HD052127, AR059185 and

AR053648. The content is solely the responsibility of the authors and does not necessarily

represent the official views of the National Institutes of Health. Authors acknowledge all

researchers who have previously worked on the data acquisition of the studies incorporated

into this database.

Additional supporting information may be found in https://doi.org/10.1002/jor.24435.

References

1. Lam KS, Woodbridge S, Burke FD. 2003. WRIST FUNCTION AFTER

EXCISION OF THE PISIFORM. The Journal of Hand Surgery: British &

European Volume 28(1):69–72.

2. Patterson RM, Williams L, Andersen CR, et al. 2007. Carpal kinematics during

simulated active and passive motion of the wrist. J Hand Surg Am 32(7):1013–

1019.

3. Nanno M, Buford WL, Patterson RM, et al. 2006. Three-dimensional analysis of

the ligamentous attachments of the first carpometacarpal joint. J Hand Surg Am

31(7):1160–1170.

4. Moojen TM, Snel JG, Ritt MJ, et al. 2002. Scaphoid kinematics in vivo. J Hand

Surg [Am] 27:1003–10.

5. Horii E, An KN, Linscheid RL. 1993. Excursion of prime wrist tendons. Journal

of Hand Surgery St Louis 18:83–90.

6. Rainbow MJ, Wolff AL, Crisco JJ, Wolfe SW. 2016. Functional kinematics of the

wrist. J Hand Surg Eur Vol 41(1):7–21.

7. Bryce TH. 1896. Certain Points in the Anatomy and Mechanism of the Wrist-

Joint Reviewed in the Light of a Series of Rontgen Ray Photographs of the Living

Hand. J Anat Physiol 31:59–79.

8. Destot E. 1986. The classic. Injuries of the wrist. A radiological study. By Etienne

Destot. 1926. Translated by Atkinson,F.R.B. Clin Orthop 202:3–11.

36

9. Fick R. 1911. Handbuch der Anatomie und Mechanik der Gelenke unter

Berucksichtigung der Bewegenden Muskein. Fischer, Jena.

10. Landsmeer JM. 1961. Studies in the anatomy of articulation. I. The equilibrium of

the “intercalated” bone. Acta Morphol Neerl Scand 3:287–303.

11. Linscheid RL, Dobyns JH, Beabout JW, Bryan RS. 1972. Traumatic instability of

the wrist. Diagnosis, classification, and pathomechanics. J Bone Joint Surg Am

54:1612–32.

12. Navarro A. 1921. Luxaciones del carpo. Anales de la Facultad de Medicina

6:113–141.

13. Taleisnik J. 1976. The ligaments of the wrist. J Hand Surg [Am] 1:110–8.

14. MacConaill MA. 1941. The mechanical anatomy of the carpus and its bearings on

some surgical problems. J. Anat. 75(Pt 2):166–175.

15. Garcia-Elias M. 1997. Kinetic analysis of carpal stability during grip. Hand Clin

13:151–8.

16. Craigen MA, Stanley JK. 1995. Wrist kinematics. Row, column or both? J Hand

Surg [Br] 20:165–70.

17. Carelsen B, Bakker NH, Strackee SD, et al. 2005. 4D rotational x-ray imaging of

wrist joint dynamic motion. Med Phys 32(9):2771–2776.

18. Choi YS, Lee YH, Kim S, et al. 2013. Four-dimensional real-time cine images of

wrist joint kinematics using dual source CT with minimal time increment

scanning. Yonsei Med. J. 54(4):1026–1032.

19. Crisco JJ, Coburn JC, Moore DC, et al. 2005. In vivo radiocarpal kinematics and

the dart thrower’s motion. J Bone Joint Surg Am 87(12):2729–2740.

20. Kobayashi M, Berger RA, Nagy L, et al. 1997. Normal kinematics of carpal

bones: a three-dimensional analysis of carpal bone motion relative to the radius. J

Biomech 30:787–93.

21. Moritomo H, Apergis EP, Herzberg G, et al. 2007. 2007 IFSSH committee report

of wrist biomechanics committee: biomechanics of the so-called dart-throwing

motion of the wrist. J Hand Surg Am 32(9):1447–1453.

22. Akhbari B, Morton AM, Moore DC, et al. 2019. Kinematic Accuracy in Tracking

Total Wrist Arthroplasty With Biplane Videoradiography Using a Computed

Tomography-Generated Model. Journal of Biomechanical Engineering

141(4):044503.

23. Halilaj E, Rajagopal A, Fiterau M, et al. 2018. Machine learning in human

movement biomechanics: Best practices, common pitfalls, and new opportunities.

Journal of Biomechanics 81:1–11.

24. Werner FW, Short WH, Green JK. 2005. Changes in patterns of scaphoid and

lunate motion during functional arcs of wrist motion induced by ligament

division. J Hand Surg Am 30:1156–60.

37

25. Werner FW, Short WH, Fortino MD, Palmer AK. 1997. The relative contribution

of selected carpal bones to global wrist motion during simulated planar and out-

of-plane wrist motion. J Hand Surg [Am] 22:708–13.

26. Sandow MJ, Fisher TJ, Howard CQ, Papas S. 2014. Unifying model of carpal

mechanics based on computationally derived isometric constraints and rules-

based motion – the stable central column theory. J Hand Surg Eur Vol 39(4):353–

363.

27. Gislason MK, Stansfield B, Nash DH. 2010. Finite element model creation and

stability considerations of complex biological articulation: The human wrist joint.

Medical Engineering & Physics 32(5):523–531.

28. Carrigan SD, Whiteside RA, Pichora DR, Small CF. 2003. Development of a

three-dimensional finite element model for carpal load transmission in a static

neutral posture. Ann Biomed Eng 31:718–25.

29. Gíslason MK, Nash DH. 2012. Finite Element Modelling of a Multi-Bone Joint:

The Human Wrist. Finite Element Analysis - New Trends and Developments

[cited 2018 Nov 5] Available from: https://www.intechopen.com/books/finite-

element-analysis-new-trends-and-developments/finite-element-modelling-of-a-

multi-bone-joint-the-human-wrist.

30. Moore DC, Crisco JJ, Trafton TG, Leventhal EL. 2007. A digital database of

wrist bone anatomy and carpal kinematics. J Biomech 40(11):2537–2542.

31. Crisco JJ, Coburn JC, Moore DC, Upal MA. 2005. Carpal bone size and scaling

in men versus in women. J Hand Surg Am 30(1):35–42.

32. Coburn JC, Upal MA, Crisco JJ. 2007. Coordinate systems for the carpal bones of

the wrist. J Biomech 40(1):203–209.

33. Neu CP, Crisco JJ, Wolfe SW. 2001. In vivo kinematic behavior of the radio-

capitate joint during wrist flexion-extension and radio-ulnar deviation. J Biomech

34(11):1429–1438.

34. Crisco JJ, Patel T, Halilaj E, Moore DC. 2015. The Envelope of Physiological

Motion of the First Carpometacarpal Joint. J Biomech Eng 137(10):101002.

35. Kamal RN, Rainbow MJ, Akelman E, Crisco JJ. 2012. In vivo triquetrum-hamate

kinematics through a simulated hammering task wrist motion. J Bone Joint Surg

Am 94(12):e85.

36. Leventhal EL, Moore DC, Akelman E, et al. 2010. Carpal and forearm kinematics

during a simulated hammering task. J Hand Surg Am 35(7):1097–1104.

37. Rainbow MJ, Kamal RN, Moore DC, et al. 2015. Subject-Specific Carpal

Ligament Elongation in Extreme Positions, Grip, and the Dart Thrower’s Motion.

J Biomech Eng 137(11):111006.

38. Rainbow MJ, Kamal RN, Leventhal E, et al. 2013. In vivo kinematics of the

scaphoid, lunate, capitate, and third metacarpal in extreme wrist flexion and

extension. J Hand Surg Am 38(2):278–288.

38

39. Rainbow MJ, Crisco JJ, Moore DC, et al. 2012. Elongation of the dorsal carpal

ligaments: a computational study of in vivo carpal kinematics. J Hand Surg Am

37(7):1393–1399.

40. Halilaj E, Moore DC, Patel TK, et al. 2014. Thumb carpometacarpal joint

congruence during functional tasks and thumb range-of-motion activities. Conf

Proc IEEE Eng Med Biol Soc 2014:4354–4357.

41. Halilaj E, Rainbow MJ, Got C, et al. 2014. In vivo kinematics of the thumb

carpometacarpal joint during three isometric functional tasks. Clin. Orthop. Relat.

Res. 472(4):1114–1122.

42. Moore, Douglas C, Halilaj, Eni, Patel, Tarpit K, Crisco, Joseph J. 2014.

Computed Tomography Image-Based Kinematic Analysis: An Overview. In: Neu,

Corey P, Genin, Guy M, editors. Handbook of Imaging in Biological Mechanics,

1st ed. Boca Raton, Fl: CRC Press. p 115–126 [cited 2015 Nov 4] Available from:

http://www.crcnetbase.com/doi/abs/10.1201/b17566-14.

43. Marai GE, Laidlaw DH, Crisco JJ. 2006. Super-resolution registration using

tissue-classified distance fields. IEEE Trans Med Imaging 25(2):177–187.

44. Crisco JJ, Pike S, Hulsizer-Galvin DL, et al. 2003. Carpal bone postures and

motions are abnormal in both wrists of patients with unilateral scapholunate

interosseous ligament tears. J Hand Surg Am 28(6):926–937.

45. Wu G, van der Helm FC, Veeger HE, et al. 2005. ISB recommendation on

definitions of joint coordinate systems of various joints for the reporting of human

joint motion--Part II: shoulder, elbow, wrist and hand. Journal of Biomechanics

38:981–992.

46. Rainbow MJ, Crisco JJ, Moore DC, Wolfe SW. 2008. Gender differences in

capitate kinematics are eliminated after accounting for variation in carpal size. J

Biomech Eng 130(4):041003.

47. Lee DT, Schachter BJ. 1980. Two algorithms for constructing a Delaunay

triangulation. International Journal of Computer & Information Sciences

9(3):219–242.

48. Fregly BJ, Besier TF, Lloyd DG, et al. 2012. Grand challenge competition to

predict in vivo knee loads. Journal of Orthopaedic Research 30(4):503–513.

49. Kauer JM. 1986. The mechanism of the carpal joint. Clin. Orthop. Relat. Res.

(202):16–26.

50. Abe S, Moritomo H, Oka K, et al. 2018. Three-dimensional kinematics of the

lunate, hamate, capitate and triquetrum with type 1 or 2 lunate morphology. J

Hand Surg Eur Vol 43(4):380–386.

39

ACCURACY OF BIPLANE

VIDEORADIOGRAPHY FOR QUANTIFYING

DYNAMIC WRIST KINEMATICS

3.

Bardiya Akhbari, Amy M. Morton, Douglas C. Moore, Arnold-Peter C.

Weiss, Scott W. Wolfe, Joseph J. Crisco

Journal of Biomechanics 92, 120–125, 2019

https://doi.org/10.1016/j.jbiomech.2019.05.040

40

Abstract (250 words)

Accurately assessing the dynamic kinematics of the skeletal wrist could advance our

understanding of the normal and pathological wrist. Biplane videoradiography (BVR) has

allowed investigators to study dynamic activities in the knee, hip, and shoulder joint;

however, currently, BVR has not been utilized for the wrist joint because of the challenges

associated with imaging multiple overlapping bones. Therefore, our aim was to develop a

BVR procedure and to quantify its accuracy for evaluation of wrist kinematics. BVR was

performed on six cadaveric forearms for one neutral static and six dynamic tasks, including

flexion-extension, radial-ulnar deviation, circumduction, pronation, supination, and

hammering. Optical motion capture (OMC) served as the gold standard for assessing

accuracy. We propose a feedforward tracking methodology, which uses a combined model

of metacarpals (second and third) for initialization of the third metacarpal (MC3). BVR-

calculated kinematic parameters were found to be consistent with the OMC-calculated

parameters, and the BVR/OMC agreement had submillimeter and sub-degree biases in

tracking individual bones as well as the overall joint’s rotation and translation. All dynamic

tasks (except pronation task) showed a limit of agreement within 1.5° for overall rotation,

and within 1.3 mm for overall translations. Pronation task had a 2.1° and 1.4 mm limit of

agreement for rotation and translation measurement. The poorest precision was achieved

in calculating the pronation-supination angle, and radial-ulnar and volar-dorsal

translational components, although they were sub-degree and submillimeter. The

methodology described herein may assist those interested in examining the complexities

of skeletal wrist function during dynamic tasks.

41

Introduction

Dynamic assessment of wrist kinematics is crucial for understanding both normal

and pathological joint function to advance diagnosis and treatment strategies. An accurate

technique that measures the overall wrist motion, which is described as the motion of third

metacarpal relative to the radius (Neu et al., 2001), during dynamic tasks allows

comparison of the normal wrist motion with patients having carpal bone injuries or total

wrist arthroplasty.

Model-based tracking with biplane videoradiography (BVR) is a well-established

method that has allowed investigators to directly study the dynamic in-vivo skeletal

kinematics of the knee (Anderst et al., 2009; Bey et al., 2008a; Miranda et al., 2011; Stentz-

Olesen et al., 2017), shoulder (Bey et al., 2008b, 2006), hip (Martin et al., 2011), and ankle

(Ito et al., 2015) joints in various settings. BVR is capable of high-speed captures (up to

1000 Hz) with a low radiation dosage (e.g., ~0.03 mSv/sec for upper extremity studies),

and it can be a practical system for studying the dynamic motion of the wrist joint during

activities of daily living.

BVR tracking software packages typically use volumetric models of the bones that

are reconstructed from the CT images and have the internal structure’s information, stored

as gray-values (Miranda et al., 2011). The BVR programs then employ ray-casting

algorithms on the density-based volumes to create digitally reconstructed radiographs

(DRR) that mimic the similar attenuations that the X-ray sources generate from the bones

on the radiographs.

The objective of the model-based BVR tracking system is to match the similar

features of the DRRs and the bones’ image on the radiographs to accurately locate the

42

bones in the 3D space. DRRs are generated from the isolated and segmented portions of

the CT images specific to the bone of interest, while the radiographs are the projection of

all anatomy inside the field-of-view of X-ray sources. Therefore, bone overlap (e.g.,

metacarpals overlap in the wrist), or large surrounding soft-tissue (e.g., around the hip

joint) negatively impacts tracking accuracy because the matching images are no longer

one-to-one correspondence. The effects of surrounding soft tissue can be lessened, and the

matching similarities between DRRs and radiographs can be increased, by modifying the

X-ray acquisition parameters (i.e., kV and mA), or the captured radiographs intensity in

post-processing can be modified. However, the undesirable effect of bone overlap cannot

be reduced by changing pre- or post-processing parameters. To overcome this issue, Hill

et al. considered the set of five metatarsals as one rigid body to evaluate the metatarsals

motion (Hill, 2018). Another study by Ito et al. utilized contact optimization algorithms in

the BVR program to track the calcaneus and talus bones (Ito et al., 2015); but, contact

calculation requires tracking of all the bones which is both time-consuming and

unnecessary in calculating the wrist motion.

Accordingly, our aim was to develop a BVR setup and tracking methodology for

studying wrist kinematics and to quantify its accuracy. A feedforward tracking procedure

which uses a combined model of metacarpals (second and third) for initialization of the

third metacarpal was proposed to increase the accuracy of tracking.

Methods

To develop a BVR setup and evaluate its accuracy, we used optical motion capture

(OMC) technique as the gold standard comparator that has shown a submillimeter accuracy

in our experimental setup (Akhbari et al., 2019). For all experiments, both methods

43

simultaneously captured the wrist motion (third metacarpal motion relative to the radius),

and then they were compared for accuracy assessment.

Specimen preparation and imaging

Six intact forearms from four cadaver specimens (70.5 ± 12.3 yrs., 2 rights and 2

bilateral, 2 females) were obtained. The dorsal surface of the third metacarpal and a portion

of the radius of all specimens were exposed by removing their surrounding soft tissue.

Exposure of the radius was limited to its radial surface from 7 to 14 cm proximal to the

radiocarpal joint. Two clusters, each with four lightweight retro-reflective marker spheres

(9.5mm dia.) on nylon standoffs, were rigidly attached to the third metacarpal and the

radius by custom-made blocks of solid foam photonic-crystal fiber (Sawbones USA,

Vashon Island, Washington) (Figure 3.1). The blocks were affixed to the bones with heavy-

duty adhesives (Gorilla Glue Company, Cincinnati, OH). CT scans (Lightspeed® 16. GE

Medical, Milwaukee, WI) of the forearms were acquired at tube settings of 80 kVp and 80

mA and reconstructed with voxel dimensions of 0.39 x 0.39 mm2 in the transverse plane

of the forearm, and 0.625 mm along the forearm’s long axis.

Figure 3.1. Marker clusters on the hand (four markers for tracking the third metacarpal), and on

the forearm (four markers for tracking the radius), as well as 3D models of the radius and the

third metacarpal constructed from the CT images. For visualization, just the distal forearm and

hand are depicted (CT scan was from the whole arm).

44

BVR and OMC Instruments

The experiment was performed in the W. M. Keck Foundation biplanar

videoradiography facility at Brown University (xromm.org) (Brainerd et al., 2010;

Miranda et al., 2013). Briefly, the system includes two Varian Medical Systems X-ray

tubes (Palo Alto, CA, USA), two X-ray generators (Saint-Eustache, Quebec, Canada), two

40 cm Dunlee image intensifiers (Aurora, IL, USA), and two high-speed digital video

cameras (Vision Research, Wayne, NJ, USA). To devise a set-up that permits an in-vivo

study and have more perpendicular X-ray beams for most possible hand/forearm

orientations in the tasks (to minimize the possible overlap of the metacarpal bones in the

radiographs), we selected source-to-image distance of 130 cm, with the source-to-object

distance of 95 cm, and the inter-beam orientation of 110° for X-ray sources. BVR

acquisition was in the continuous mode with the beam current of 80 mA, and beam energy

of 68-76 kVp, with a camera shutter speed of 500 µs for both sources. The radiograph

images resolution was 0.22x0.22 mm/pixel, and they were stored in 8-bit format. OMC

data was captured using eight Oqus 5+ cameras (Qualisys, Gothenburg, Sweden), with the

start of data acquisition synchronized to the BVR by an external trigger (active low). Both

BVR and OMC acquisition rates were set to 200 frames per second. The conversion matrix

from OMC coordinate system to the BVR coordinate system was calculated by a

simultaneous capture of a custom-designed cross-calibration “cylinder” (xromm.org) in

both systems (Miranda et al., 2013).

Data Acquisition

Specimens were manipulated in the field-of-view of the X-ray systems and the

optical motion capture cameras (Figure 3.2). Each specimen was secured to a custom-made

45

L-frame, which was rigidly clamped to a sawhorse from the arm, and it was secured to a

rigid board binding its proximal phalanges from the palmar side. A dowel, fastened to the

board, facilitated remote and robust manipulation of the specimen’s hand and forearm in

one neutral static and six dynamic wrist tasks: flexion-extension, radial-ulnar deviation,

circumduction, pronation, supination, and hammering. The neutral static position, defined

by the back of the hand being coplanar with the back of the forearm, was captured for 500

milliseconds (i.e., 100 radiograph frames). The pronation and supination tasks were

recorded for 1 second each, during which the wrist and forearm were manipulated from

neutral pose to a fully pronated or fully supinated pose, respectively.

Figure 3.2. Experimental setup for biplanar videoradiography capture (right-side wrist is

depicted). The intra-beam angle of 110°, with the source-to-image distance of ~130 cm for both

X-ray sources. The specimen’s arm was secured, and the wrist and forearm were manipulated

manually with a dowel attached the distal side of the hand.

All range-of-motion tasks and the hammering task, described as the wrist motion

along a path oblique to flexion-extension and radial-ulnar deviation (Leventhal et al.,

2010), were captured for 2 seconds. The full range of motion was limited by the operator’s

subjective perception of increasing wrist and forearm stiffness. All tasks were performed

as fast as was practical for the operator to mimic in-vivo conditions. The resulting range-

46

of-motions and velocities of the tasks as an average were 53° and 53°/sec for flexion-

extension, 28° and 42°/sec for radial-ulnar deviation, 38° and 19°/sec for circumduction,

23° and 46°/sec for pronation, 13° and 27°/sec for supination, and 38° and 38°/sec for

hammering, respectively (Supp. Table 3.1).

Image Processing and Data Reduction

The radius, second metacarpal (MC2), and third metacarpal (MC3) were semi-

automatically segmented from the CT images using MIMICS® software (v19, Materialise,

Leuven, Belgium) using thresholding and manual editing. A volumetric model of the distal

radius with the length of ~60 mm was generated comparable with the length of the distal

radius scanned in the in-vivo studies. In addition to the distal radius, volumetric models of

MC3 alone and with the second metacarpal (MC2-MC3) were constructed (Figure 3.1;

models in dark-color). A transformation matrix from the MC2-MC3 model to MC3 model

was determined using an iterative closest point registration for later conversion of MC2-

MC3 kinematics to MC3 kinematics (Wrap 2017, 3D Systems, Rock Hill, SC).

The BVR radiographic images were enhanced with Autoscoper software

(xromm.org, Brown University, Providence, RI), and the kinematic data was generated for

each bone. In Autoscoper, digitally reconstructed radiographs (DRRs) were generated from

the isolated CT images of the bones using a ray-casting approach and then enhanced using

imaging filters to improve the matching cost function (Figure 3.3) (Miranda et al., 2011).

The same image filters were then used for tracking the bones in all specimens. To enhance

the edges of the bones’ image on the radiographs, a Sobel filter with a scale factor of 3 and

a blend value of 0.4, in addition to a contrast filter with an alpha (for image contrast) of

2.5, and beta (for image brightness) of 0.9 were used. To match the DRRs with the

47

radiograph, a ray intensity value of 0.35 was chosen, and a Sobel filter with 0.1 blend value

and 1.7 scale factor was used. Normalized cross-correlation was employed to measure the

similarity between DRRs and the radiographs, and the global optimization techniques of

particle swarm optimization and downhill simplex were used to find the optimized fit

between the DRR and the radiographs (Kennedy and Eberhart, 1995; Nelder and Mead,

1965). After optimization, a 4x4 transformation matrix of the DRRs in the X-ray world

was exported from the software for further processing and joint motion calculation.

Figure 3.3. Bone features were enhanced using Sobel and contrast filters on the radiographs, and

the digitally reconstructed radiographs (bolded in white) were tracked in the radiographs. From

left to right, the tracked metacarpal and radius are visualized from flexion to extension in one

source for a left wrist.

To reduce the effects of bone overlap, tracking was first performed with the model

combining the second and third metacarpals (MC2-MC3). After locating the combined

DRR position and rotation in the radiographs, the output kinematics were transformed to

the MC3 model coordinate system to seed the initial position of the MC3. The MC3 was

then tracked, and its kinematic was calculated. The accurate position of the radius in the

radiographs was also calculated during all tasks. The kinematics were filtered using a

moving average method (with a span of 5 frames) using a built-in MATLAB function

(R2018b, The MathWorks, Inc.).

48

The gold-standard OMC kinematic data was processed using Visual3D v6 (C-

Motion, Germantown, MD). The motion of the hand and radius reflective marker clusters

were calculated based on the markers’ positions and singular value decomposition method

in Visual3D (Söderkvist and Wedin, 1993). The reliability of OMC tracking was evaluated

by comparing the distances between all markers for each segment (i.e., third metacarpal

and radius) throughout all trials, which should be unchanged under the assumption of a

rigid body. Any change in marker distances of more than 0.5 mm (resolution of OMC in

our experimental setup), with respect to their average distances, was considered a violation

of rigid body assumption, and only in this case, the OMC data was considered unreliable

and removed from the comparison.

Wrist Kinematics

The wrist motion was defined as the motion of third metacarpal relative to the radius, and

both the BVR and OMC kinematic data were reported relative to the neutral wrist position

in the neutral static task in the radial coordinate system (RCS) (Coburn et al., 2007;

Kobayashi et al., 1997). The x-axis of RCS was defined by a best-fit line passing through

the centroids of the radial cross-sections. The RCS origin was the intersection of the x-axis

with the surface of the radiocarpal articulation. The y-axis was defined in the direction of

the midpoint of the sigmoid cavity toward the radial styloid, and the direction of the z-axis

was defined by the cross product of the x and y-axes.

The kinematics are described by Helical Axis of Motion (HAM) parameters, which

define rigid body kinematics between two positions in terms of an overall rotation (ϕ)

around and an overall translation (t) along with a unique axis in space (i.e., screw axis).

HAM parameters were then decomposed to three rotational (pronation-supination [PS],

49

flexion-extension [FE], and radial-ulnar deviation [RU]) and three translational (proximal-

distal, radial-ulnar, and volar-dorsal translation) components around and along the

described axes of RCS.

Statistical Analysis

The Bland-Altman analysis was used to determine the agreement of BVR- and

OMC-determined overall wrist rotation and translation (Bland and Altman, 1999). The

Bland-Altman analysis describes the accuracy of BVR compared to the OMC using a bias

(mean differences between the two methods), and a 95% limit of agreement (LOA) (mean

differences ± 1.96 standard deviations [SD] of the differences). The decomposed rotations

and translations were compared using the bias and precision (SD of the differences between

methods) (ASTM E177-14, 2014), and the individual bone motions were compared using

LOA calculated from Bland-Altman analysis. Finally, to analyze the variations between

subjects the bias and LOA of the overall wrist rotation and translation were compared.

Results

The overall wrist translation and rotation calculated with the BVR post-processing

technique were highly consistent with the gold standard OMC-derived parameters and

demonstrated a less than 0.1° and 0.2 mm biases among all tasks (Table 3.1). In the neutral

static task, BVR and OMC had a small bias and an LOA of within 0.5° and 0.2 mm or

better. The dynamic tasks showed wider LOA, which were within 1.5° for overall rotation,

and within 1.3 mm for overall translations, except pronation task, which had the widest

LOA of within 2.1° and 1.4 mm for overall rotation and translation. Biases of overall wrist

rotation or translation for all subjects were less than 1° and 1 mm, and the LOAs were

enclosed around 0° and 0 mm; thus, subjects did not skew the final accuracy measurements.

50

OMC- and BVR-derived rotational components of the wrist motion (MC3 in RCS)

demonstrated same motion patterns (Figure 3.4; flexion-extension task as representative).

There was no significant bias for the decomposed rotational and translational components,

and all demonstrated a less than 0.5° and 0.5 mm biases in all tasks (Table 3.2 and 3.3). In

the rotational components, the precision of BVR was less than 1°, with the highest spread

for calculation of pronation-supination component, which was mostly 1.5 times of other

rotational components (Table 3.2). In the translational components, the largest precisions

were seen for radial-ulnar and volar-dorsal translational components, although they were

both less than a millimeter (Table 3.3).

Figure 3.4. Representative wrist kinematics calculated from both methods (BVR: biplane

videoradiography, OMC: optical motion capture). PS (+pronation/-supination), FE (+flexion/-

extension), and RU (+ulnar/-radial deviation) demonstrate the rotational components.

Overall, for tracking the radius, the BVR/OMC agreement was within 1.7° and 0.8

mm or better, with the smallest spread for the static task (Table 3.4). Tracking MC3 resulted

in an LOA of within 1.4° and 1.0 mm or better, except for hammering and pronation tasks.

These tasks demonstrated a wider LOA, although it did not exceed 1.8° and 1.5 mm.

51

Table 3.1. The agreement of biplane videoradiography (BVR) with the gold standard in

evaluating the overall wrist joint motion in terms of bias and limit of agreement (LOA) for all

tasks. BVR in all tasks had a subdegree and submillimeter bias, and LOA was less than 1.5° and

1.4 mm for all tasks except pronation.

Task

Overall

Wrist Rotation (°)

Overall

Wrist Translation (mm)

Bias LOA Bias LOA

Neutral (Static) 0.1 -0.2 — 0.5 0 -0.2 — 0.1

Flexion-Extension 0.1 -1.3 — 1.5 0.1 -1.2 — 1.4

Radial-Ulnar Deviation 0 -1.5 — 1.5 0.2 -0.6 — 1.0

Circumduction 0.1 -1.2 — 1.4 0.1 -1.1 — 1.3

Pronation -0.1 -2.1 — 1.8 0 -1.4 — 1.3

Supination 0 -1.2 — 1.2 0.2 -0.9 — 1.3

Hammering -0.1 -1.5 — 1.3 0 -1.3 — 1.2

Table 3.2. The bias and precision of biplane videoradiography in measuring rotational

components of the wrist joint motion in all tasks. Bias was less than 0.5° for all tasks. The least

agreement was seen in pronation/supination angle which had 1.5 to 2 times a precision than other

rotational components.

Task Pronation/

Supination (°)

Flexion/

Extension (°)

Radial/Ulnar

Deviation (°)

Neutral (Static) -0.1 ± 0.3 -0.0 ± 0.1 -0.0 ± 0.1

Flexion-Extension 0.0 ± 0.7 0.2 ± 0.7 -0.1 ± 0.7

Radial-Ulnar Deviation 0.1 ± 0.9 0.3 ± 0.6 0.1 ± 0.7

Circumduction -0.3 ± 0.8 0.2 ± 0.6 0.2 ± 0.6

Pronation -0.3 ± 1.0 0.1 ± 0.4 0.5 ± 0.5

Supination -0.0 ± 1.1 -0.3 ± 0.6 -0.4 ± 0.9

Hammering -0.4 ± 0.8 0.2 ± 0.7 0.4 ± 0.5

52

Table 3.3. The bias and precision of translational components of wrist joint motion in all tasks.

Bias was less than 0.5 mm for all tasks, and the worst precisions were seen in measuring the

radial/ulnar translation and volar/dorsal translation which had a motion approximately parallel to

the X-ray beams.

Task Proximal/Distal

Translation (mm)

Radial/Ulnar

Translation (mm)

Volar/Dorsal

Translation (mm)

Neutral (Static) -0.0 ± 0.1 -0.0 ± 0.1 -0.0 ± 0.1

Flexion-Extension 0.1 ± 0.3 -0.1 ± 0.8 0.0 ± 0.7

Radial-Ulnar

Deviation 0.2 ± 0.5 -0.1 ± 0.5 -0.0 ± 0.5

Circumduction 0.0 ± 0.4 0.1 ± 0.7 -0.2 ± 0.5

Pronation 0.0 ± 0.4 0.0 ± 0.8 -0.1 ± 0.8

Supination -0.2 ± 0.4 -0.3 ± 0.7 0.5 ± 0.8

Hammering 0.0 ± 0.3 0.3 ± 0.6 -0.1 ± 0.6

Table 3.4. Limits of agreement (LOA) between biplane videoradiography and the gold standard,

optical motion capture, in tracking the individual bones of the wrist joint (radius and the third

metacarpal). Translations LOA were mostly submillimeter, and rotations had an LOA of within

±1.8°.

Task

Radius Third Metacarpal

Rotation (°) Translation

(mm) Rotation (°)

Translation

(mm)

Neutral (Static) -0.3 — 0.3 -0.1 — 0.1 -0.1 — 0.1 -0.1 — 0.1

Flexion-Extension -0.9 — 1.1 -0.5 — 0.3 -1.1 — 1.1 -1.0 — 1.2

Radial-Ulnar

Deviation -1.1 — 1.2 -0.6 — 0.3 -1.4 — 1.6 -0.6 — 0.9

Circumduction -1.7 — 1.5 -0.6 — 0.4 -0.7 — 0.9 -0.5 — 0.9

Pronation -1.5 — 0.8 -0.6 — 0.4 -1.8 — 1.8 -0.7 — 0.8

Supination -0.9 — 1.3 -0.6 — 0.6 -1.4 — 1.1 -0.5 — 0.7

Hammering -1.2 — 0.9 -0.6 — 0.8 -0.8 — 1.2 -0.8 — 1.5

Discussion

The purpose of this study was to quantify the accuracy of an approach with BVR

as a tool for analyzing wrist motion, defined as the motion of the third metacarpal with

53

respect to the radius. OMC markers rigidly fixed to each bone served as the gold standard.

The resulting approach had a bias and precision of similar magnitude to previous model-

based BVR studies in other joints (Bey et al., 2008b, 2006; Miranda et al., 2011; Stentz-

Olesen et al., 2017).

In a preliminary unpublished study, we found that tracking the isolated third

metacarpal was not feasible due to the feature-obscuring overlap from the other

metacarpals. We also found that the five metacarpals of the hand could not be assumed to

move as a single rigid body. Hence, we developed an approach that involved tracking the

combined MC2-MC3 first and then using this data to seed the initial position of the MC3.

Fourth metacarpal or other metacarpals were not considered in part of this process, because,

during the in-vivo experiments, we realized that considering other metacarpals adversely

affects the tracking. Another advantage of using the combined model of metacarpals is an

improvement in the process of initialization of the DRRs in the radiographs. Out-of-plane

rotation of just one metacarpal does not change the DRR images significantly; hence,

combining the models increases the accuracy of the initialization step.

The accuracy of model-based BVR highly relies on the quality of bone images in

the radiographs. To have minimal overlap of metacarpal bones for most wrist poses and

suitable repeatability for in-vivo testing, the path of motion for most tasks were devised in

a way to have the main axis of motion oblique to both X-ray beams. Although for most

tasks the overlap was minimized, large metacarpals overlaps were seen at the extremes of

flexion-extension, hammering, and end-points of pronation (which also had radius/ulna

overlap). These overlaps might be the cause of larger biases and wider LOAs that were

achieved for these tasks. Moreover, motions that are approximately parallel to the X-ray

54

beams of at least one of the sources result in a lower accuracy (Anderst et al., 2009), which

was seen in the case of worst precisions for pronation-supination rotational and volar-

dorsal translational components. Although our study was not designed to evaluate the

specific relationship between the direction of motion and beam angles, six different

dynamic tasks with various motion paths were studied, which demonstrates the high

accuracy in most bone/beam orientations with our experimental setup.

Despite the small size and multiple bones overlap, the bias and limit of agreement

achieved with our method are consistent with the accuracy of BVR in previous studies in

other joints. In the knee, femur and tibia bones were tracked using BVR and compared with

marker-based radiostereometric analysis (RSA), yielding a near 0° bias with the maximum

LOA of -1.7 to 1.3° for rotational components, occurred at external/internal tibial rotation

(Stentz-Olesen et al., 2017). The translations’ bias was within -0.2 mm to 0.2 mm with the

maximum LOA of -1.2 mm to 1.5 mm. Moreover, tracking the patellofemoral joint has

demonstrated a bias of -0.3 to 0.3 mm for translation, and -0.1 to 0.5° for rotation

measurement compared to a marker-based RSA (Bey et al., 2008a). In tracking the

shoulder joint, they found the bias was -0.1 to 0.2 mm on the scapula, while humerus

tracking demonstrated -0.2 to 0.1 mm bias (Bey et al., 2006).

In our study, OMC was used as the standard because it has submillimeter and

subdegree accuracy when marker clusters are used in tracking (Challis, 1995; Söderkvist

and Wedin, 1993). We refined the technique by rigidly fixing them to the bones and

assuming they acted as a rigid body. This was confirmed in our study by evaluating the

RMSE of differences between markers. The marker drop-out, or a decrease in the accuracy

of marker selection, was evaluated by considering the marker cluster as a rigid object and

55

evaluating the distances between all markers. An ideal rigid cluster must demonstrate a

close to 0 mm changes in the distances between markers; however, due to the occlusion of

markers in some orientations, the cameras were not always capable of detecting the

markers accurately. Due to this fact, a reliability threshold of 0.5 mm was selected for the

RMSE of distances between markers, and any capture that violated this criterion was

removed from the accuracy comparison (~10% of total captured frames).

There were some limitations to this study. Because OMC was used as the gold

standard, assessment of BVR accuracy is limited by OMC’s sub-millimeter accuracy in

our experiment. Bone density and muscle structure variations among individuals likely

alter the BVR images and CT generated DRRs, and potentially affect accuracy; however,

six specimens were tested in this experiment with various soft-tissue properties. Other

variations likely can be accounted for by optimizing the X-ray beam parameters (i.e., kV

and mA) during BVR acquisition or intensity-thresholding during post-processing. In this

study, we used Autoscoper software (xromm.org, Brown University, Providence, RI) for

tracking the bones, and other software might be applicable. Tracking software must be

selected carefully because the BVR accuracy depends upon several factors such as image

filtering parameters, matching algorithms (e.g., intensity-based, edge-based, or contact-

based systems), optimization function, and optimization algorithm. Not using global

optimization algorithms or low-quality filters will reduce the accuracy of the method.

Finally, we used one filter to enhance the radiograph and DRR images for all subjects to

reduce the subjectivity of BVR processing; however, using different filters might slightly

change the accuracy.

56

In this study, our aim was to develop a method and quantify BVR accuracy in

studying the normal wrist kinematics. Due to the occlusion and metacarpal bones’ overlap

on the radiographs, a feed-forward system was developed. A combined model of the second

and third metacarpals was first tracked, and then the output was transformed to initialize

the third metacarpal positions. We demonstrated that BVR has potentially high accuracy,

and future studies on the wrist joint can use this methodology to study the dynamic motion

of healthy or injured wrists.

Acknowledgments

The authors thank Peter Loan from C-Motion for his assistance with general BVR

algorithms and techniques. The authors also thank Janine Molino for her help in the power

analysis of the experiment, and Rohit Badida for his help throughout data acquisition. This

research was supported in part by the National Institutes of Health P20-GM104937 and a

grant from the American Foundation for Surgery of the Hand (AFSH).

Supplementary data can be found online at doi.org/10.1016/j.jbiomech.2019.05.040.

References

Akhbari, B., Morton, A., Moore, D., Weiss, A.-P.C., Wolfe, S.W., Crisco, J., 2019.

Kinematic Accuracy in Tracking Total Wrist Arthroplasty with Biplane

Videoradiography using a CT-generated Model. J. Biomech. Eng.

https://doi.org/10.1115/1.4042769

Anderst, W., Zauel, R., Bishop, J., Demps, E., Tashman, S., 2009. Validation of Three-

Dimensional Model-Based Tibio-Femoral Tracking During Running. Med. Eng. Phys.

31, 10–16. https://doi.org/10/cz7287

ASTM E177-14, 2014. Standard Practice for Use of the Terms Precision and Bias in ASTM

Test Methods. ASTM International, West Conshohocken, PA.

https://doi.org/10.1520/E0177-14

Bey, M.J., Kline, S.K., Tashman, S., Zauel, R., 2008a. Accuracy of biplane x-ray imaging

combined with model-based tracking for measuring in-vivo patellofemoral joint motion.

J. Orthop. Surg. 3, 38. https://doi.org/10.1186/1749-799X-3-38

57

Bey, M.J., Kline, S.K., Zauel, R., Lock, T.R., Kolowich, P.A., 2008b. Measuring dynamic

in-vivo glenohumeral joint kinematics: technique and preliminary results. J. Biomech.

41, 711–714. https://doi.org/10.1016/j.jbiomech.2007.09.029

Bey, M.J., Zauel, R., Brock, S.K., Tashman, S., 2006. Validation of a new model-based

tracking technique for measuring three-dimensional, in vivo glenohumeral joint

kinematics. J. Biomech. Eng. 128, 604–609. https://doi.org/10.1115/1.2206199

Bland, J.M., Altman, D.G., 1999. Measuring agreement in method comparison studies.

Stat. Methods Med. Res. 8, 135–160.

Brainerd, E.L., Baier, D.B., Gatesy, S.M., Hedrick, T.L., Metzger, K.A., Gilbert, S.L.,

Crisco, J.J., 2010. X-ray reconstruction of moving morphology (XROMM): precision,

accuracy and applications in comparative biomechanics research. J. Exp. Zool. Part

Ecol. Genet. Physiol. 313, 262–279. https://doi.org/10.1002/jez.589

Challis, J.H., 1995. A procedure for determining rigid body transformation parameters. J.

Biomech. 28, 733–737.

Coburn, J.C., Upal, M.A., Crisco, J.J., 2007. Coordinate systems for the carpal bones of

the wrist. J. Biomech. 40, 203–209. https://doi.org/10.1016/j.jbiomech.2005.11.015

Hill, D.A., 2018. A 3D neuromuscular model of the human ankle-foot complex based on

multi-joint biplanar fluoroscopy gait analysis (Thesis). Massachusetts Institute of

Technology.

Ito, K., Hosoda, K., Shimizu, M., Ikemoto, S., Kume, S., Nagura, T., Imanishi, N., Aiso,

S., Jinzaki, M., Ogihara, N., 2015. Direct assessment of 3D foot bone kinematics using

biplanar X-ray fluoroscopy and an automatic model registration method. J. Foot Ankle

Res. 8, 21. https://doi.org/10.1186/s13047-015-0079-4

Kennedy, J., Eberhart, R., 1995. Particle swarm optimization.

Kobayashi, M., Berger, R.A., Nagy, L., Linscheid, R.L., Uchiyama, S., Ritt, M., An, K.N.,

1997. Normal kinematics of carpal bones: a three-dimensional analysis of carpal bone

motion relative to the radius. J Biomech 30, 787–93.

Leventhal, E.L., Moore, D.C., Akelman, E., Wolfe, S.W., Crisco, J.J., 2010. Carpal and

forearm kinematics during a simulated hammering task. J. Hand Surg. 35, 1097–1104.

https://doi.org/10.1016/j.jhsa.2010.04.021

Martin, D.E., Greco, N.J., Klatt, B.A., Wright, V.J., Anderst, W.J., Tashman, S., 2011.

Model-Based Tracking of the Hip: Implications for Novel Analyses of Hip Pathology.

J. Arthroplasty 26, 88–97. https://doi.org/10/b29srz

Miranda, D.L., Rainbow, M.J., Crisco, J.J., Fleming, B.C., 2013. Kinematic differences

between optical motion capture and biplanar videoradiography during a jump-cut

maneuver. J. Biomech. 46, 567–573. https://doi.org/10.1016/j.jbiomech.2012.09.023

Miranda, D.L., Schwartz, J.B., Loomis, A.C., Brainerd, E.L., Fleming, B.C., Crisco, J.J.,

2011. Static and Dynamic Error of a Biplanar Videoradiography System Using Marker-

Based and Markerless Tracking Techniques. J. Biomech. Eng. 133, 121002.

https://doi.org/10.1115/1.4005471

58

Nelder, J.A., Mead, R., 1965. A Simplex Method for Function Minimization. Comput. J.

7, 308.

Neu, C.P., Crisco, J.J., Wolfe, S.W., 2001. In vivo kinematic behavior of the radio-capitate

joint during wrist flexion-extension and radio-ulnar deviation. J. Biomech. 34, 1429–

1438.

Söderkvist, I., Wedin, P.-Å., 1993. Determining the movements of the skeleton using well-

configured markers. J. Biomech. 26, 1473–1477. https://doi.org/10.1016/0021-

9290(93)90098-Y

Stentz-Olesen, K., Nielsen, E.T., De Raedt, S., Jørgensen, P.B., Sørensen, O.G., Kaptein,

B.L., Andersen, M.S., Stilling, M., 2017. Validation of static and dynamic

radiostereometric analysis of the knee joint using bone models from CT data. Bone Jt.

Res. 6, 376–384. https://doi.org/10.1302/2046-3758.66.BJR-2016-0113.R3

59

KINEMATIC ACCURACY IN

TRACKING TOTAL WRIST ARTHROPLASTY

WITH BIPLANE VIDEORADIOGRAPHY USING

A COMPUTED TOMOGRAPHY-GENERATED

MODEL

4.

Bardiya Akhbari, Amy M. Morton, Douglas C. Moore, Arnold-Peter C.

Weiss, Scott W. Wolfe, Joseph J. Crisco

Journal of Biomechanical Engineering 141, 044503, 2019

https://doi.org/10.1115/1.4042769

60

Abstract (250 words)

Total Wrist Arthroplasty (TWA) for improving the functionality of severe wrist joint

pathology has not had the same success, in parameters such as motion restoration and

implant survival, as hip, knee, and shoulder arthroplasty. These other arthroplasties have

been studied extensively, including the use of biplane videoradiography (BVR) that has

allowed investigators to study the in-vivo motion of the total joint replacement during

dynamic activities. The wrist has not been a previous focus, and utilization of BVR for

wrist arthroplasty presents unique challenges due to the design characteristics of TWAs.

Accordingly, the aims of this study were 1) to develop a methodology for generating TWA

component models for use in BVR, and 2) to evaluate the accuracy of model-image

registration in a single cadaveric model. A model of the carpal component was constructed

from a CT scan, and a model of the radial component was generated from a surface scanner.

BVR was acquired for three anatomical tasks from a cadaver specimen. Optical motion

capture was used as the gold standard. BVR’s bias in flexion/extension, radial/ulnar

deviation, and pronosupination was less than 0.3°, 0.5°, and 0.6°. Translation bias was less

than 0.2 mm with a standard deviation of less than 0.4 mm. This BVR technique achieved

a kinematic accuracy comparable to previous studies on other total joint replacements.

BVR’s application to the study of TWA function in patients could advance the

understanding of TWA and thus the implant’s success.

61

Introduction

Total Wrist Arthroplasty (TWA) is a therapeutic solution for severe wrist joint

pathology that is designed to improve function and reduce pain [1,2]. The survival of

current metal-on-polyethylene TWA designs is lower (~82% prior to 10 years follow-up

[3]), when compared to arthroplasty of larger joints such as the hip (~93% up to 10 years

[4]) and knee (~96% up to 10 years [5]). Hip and knee implants have been optimized for

biomechanical survivorship through decades of evaluation using large kinematic datasets

on normal and post-arthroplasty subjects [6–9]. In contrast, TWA designs have had to

develop empirically in the absence of comparable datasets on wrist or wrist arthroplasty

biomechanics. It has been suggested that sub-optimal kinematics of TWA components may

contribute to instability and loosening [10,11]. Nonetheless, the articulation of the carpal

component on the radial component has not been studied in-vivo.

Biplane videoradiography (BVR) is a technology that has been used to study the

dynamic three-dimensional (3D) motion of the knee, hip, and shoulder joints [12–15]. In

these applications, it is essential to have accurate 3D models (usually CAD models) of the

implant components. Silhouettes of the components are generated by applying ray-casting

algorithms to the implant models [13,16], and the components are “tracked” by optimizing

the fit of the silhouettes to images in the paired videoradiographs. For TWA, tracking the

radial component is relatively straightforward due to its shape and crisp edges, which are

comparable to those in femoral or humeral components of knee and hip arthroplasty.

However, tracking the carpal component, which consists of a carpal plate and two screws,

is challenging. The carpal plate is small, thin, and symmetrical, and it is pierced by fixation

screws to the distal row of carpal bones. The screws overlap the carpal plate at various

62

points in each video frame creating a different outline from the outline of the silhouette

generated from the model of the carpal plate. Hence, a model of the carpal component with

only the carpal plate will likely result in decreased tracking accuracy. In contrast, a model

that contains both the carpal plate and the screws provides a large, pronounced, feature-

rich model for reliable tracking. However, generating accurate CAD models of the

assembled carpal components a priori is difficult because the orientation of each screws is

defined at the time of surgery.

Computed tomography (CT) scanning has been commonly used to generate marker

position arrays (e.g., tantalum beads implanted into the bones) and Digitally Reconstructed

Radiographs (DRRs) for marker-based and markerless BVR analysis of skeletal motion,

respectively [17–19]. CT scanning is generally not used to generate implant models

because scanning dense metal implants result in streak artifacts [20]. However, the artifacts

associated with imaging smaller titanium implants (e.g., pedicle screws) can be modest

[21,22]. With that in mind, we sought to implement BVR for TWA by generating a

registerable model of the carpal component using CT scans, with intensions of getting its

unique, feature-rich shape. Accordingly, the aims of this study were to develop a method

for generating TWA carpal component models for use in BVR from CT images and then

to evaluate the accuracy of model-image registration.

Methods

Methodology development and kinematic analysis were performed using BVR data

generated from a single cadaver specimen. Simultaneously acquired optical motion capture

data (Qualisys, Gothenburg, Sweden) was used as the gold standard (<0.25 mm resolution

in our experimental setup) for evaluating the kinematic accuracy of BVR.

63

Specimen Preparation and Imaging

The radius and ulna of a cadaveric right arm (female, 49 years) were fixed in neutral

pronosupination with a Kirschner wire and transected 14 cm proximal to the radiocarpal

joint. The proximal bone ends were potted in fast-setting urethane resin (Smooth-Cast®

300, Smooth-On, Inc., Macungie, PA). Small size radial and carpal components of a total

wrist implant system (Universal2™, Integra LifeSciences, Plainsboro, NJ) were then

inserted by a board-certified hand surgeon. To do so, the

distal radius was broached, and the radial component was

press-fit without cement. The carpal component was fixed

to the distal carpus by press-fitting the central peg into the

capitate and inserting screws into the second metacarpal and

hamate. After implantation and closing of the soft tissues,

retro-reflective markers were attached to the bones for the

optical motion capture. A cluster of five marker spheres was

attached to the third metacarpal with nylon screws, and five

individual markers were fixed to the radius through nylon

standoffs (Figure 4.1). Finally, a single CT scan was

acquired of the wrist at the neutral position (Lightspeed®

16. GE Medical, Milwaukee, WI) at tube settings of 80 kVp

and 80 mA and reconstructed with a 20-cm field of view,

yielding transversely isometric voxels with dimensions of

0.39 mm x 0.39 mm in the transverse plane of the forearm, and 0.625 mm along its long

axis (z-direction).

Figure 4.1. Marker positioning

visualized from a rendered CT

scan. Five retro-reflective

markers were fixed directly to

the radius, and five retro-

reflective markers were

clustered on a thermoplastic

plate, rigidly fixed to the third

metacarpal via nylon screws.

64

Instrumentation

Both BVR and Optical Motion Capture (OMC) were performed in the W. M. Keck

Foundation biplane videoradiography (XROMM) facility at Brown University

(http://www.xromm.org/). The XROMM system consists of two Varian Medical Systems

Model G-1086 X-ray tubes (Palo Alto, CA, USA), two EMD Technologies model EPS 45-

80 pulsed X-ray generators (Saint-Eustache, Quebec, Canada), two 40 cm Dunlee (Aurora,

IL, USA) image intensifiers, and two Phantom v10 high-speed video cameras (Vision

Research, Wayne, NJ, USA). The inter-beam angle was ~120°, with the source-image

distances of ~140 cm for both X-ray sources. OMC data was acquired using eight (8) Oqus

5+ cameras (Qualisys, Gothenburg, Sweden), and the conversion between OMC and BVR

coordinate systems was performed using transforms calculated from a simultaneous OMC

and BVR acquisition of a cross-calibration cube [23].

BVR and OMC Data Acquisitions

The implanted specimen was rigidly mounted to a fixed baseplate through the

proximal potting. To facilitate remote manipulation of the hand, a wooden dowel was fixed

to the 3rd and 4th fingers. Motion tracking was compared for three tasks: flexion-extension

(FE), radial-ulnar deviation (RU), and circumduction (CIRC). Each task was continued for

three cycles, with the range limited by the operator’s subjective perception of increasing

wrist stiffness. The implant range-of-motion that was achieved during these tasks was

approximately 68° flexion, 41° extension, 11° radial deviation, 10° ulnar deviation, 16°

pronation, and 17° supination. The exposure settings for both X-ray tubes were 68 kVp and

100 mA, continuous, with a camera shutter speed of 500 µs. These settings result in a

radiation exposure of ~0.03 mSv/sec, which is within the guidelines that our institutional

65

review board has approved for in-vivo studies of the upper extremity. BVR and OMC were

acquired at a rate of 120 Hz, with the start of data acquisition synchronized by an external

trigger (TTL signal and active low). The BVR radiographic images were stored in 8-bit

format (resolution of ~0.22x0.22 mm per pixel), and then undistorted and calibrated using

XMA Lab software [17,24].

Implant Model Generation and Data Reduction

A 3D model of the implanted carpal component was constructed from the CT

images via threshold-based automatic segmentation using MIMICS® (Materialise, Leuven,

BE), followed by modest manual editing. The manual editing involved the slice-by-slice

closing of edge defects and removal of artefactual connections to the radial component.

Finally, a digital model of the edited carpal component was exported in STL format (Figure

4.2). An STL model of the explanted radial component was generated with the use of an

industrial 3D surface scanner (Artec Space Spider™, Artec 3D, LU) with a resolution of

0.1 mm. Generation of radial component models from CT images was unsatisfactory due

to streak artifacts that obscured the implant surfaces. The carpal component model

contained 7,098 triangles, and the radial component model contained 20,012 triangles.

The BVR and OMC kinematic data were reported in a radius-based coordinate

system defined by features of the TWA

radial component. The origin of the

radius-based coordinate system was

located at the geometric center of the

radial tray, with the y- and z-axes directed

radially and volarly, respectively, parallel

Figure 4.2. Photo of a Universal2™ carpal

component (left), and a 3-D digital model

generated via thresholding and manual editing of

CT images (right).

66

to the implant’s proximal cut-plane surface (Figure 4.3A). The x-axis was generated by the

cross-product of the y- into the z-axis. A similar coordinate system was generated for the

TWA carpal component, with the origin located at the geometric center of the proximal

face of the carpal plate, and the y- and z-axes directed radially and volarly, respectively,

parallel to the plate’s surface. The x-axis was generated by the cross-product of the y- into

the z-axis (Figure 4.3A).

The positions and orientations of the radial and carpal components were calculated

for each frame of the OMC and BVR datasets. The gold-standard OMC-derived kinematic

data was generated using a custom-written MATLAB code (R2017b, The Mathworks,

Inc.). Briefly, the retro-reflective marker signals were smoothed with a fourth-order low

pass Butterworth filter with a normalized cutoff frequency of 0.033 Hz [25], and the rigid

body transformations for the hand and radius marker clusters were calculated using the

Söderkvist singular value decomposition method [26]. The transformations from the

marker clusters to the implants coordinate system were calculated based on their relative

position in the neutral frame and then applied to the carpal and radial components with the

assumption that the marker clusters were rigidly affixed to the implant components.

The BVR kinematic data for TWA components was generated using JointTrack

Biplane open-source image registration software (sourceforge.net/projects/jointtrack/),

which utilizes two cost functions: contour-matching and intensity-matching (Figure 4.3B-

E) [14]. Within JointTrack, the intensity thresholding parameters (low and high) and edge

detection parameters (aperture and thresholding) were selected manually, based on an

assessment of implant 2D fit to the BVR images. Both intensity and contour metrics were

minimized for the radial component; however, only the intensity metric was used for the

67

carpal component since the Canny edge detection method was sub-optimal on the thread

features of the screws [14].

Figure 4.3. A) Neutral posture of the components along with their respective coordinate system;

red, green, and blue vectors depict the x-axis (pronation/supination), y-axis (flexion/extension),

and z-axis (radial/ulnar deviation). B, C) The edges of the carpal and radial components of the

implanted Universal2™ TWA super-imposed on the neutral frame radiographs as captured in the

BVR cameras. D, E) The silhouettes of the carpal and radial components of the implant on the

neutral frame radiographs.

To facilitate interpretation, implant kinematics are reported relative to the “neutral”

wrist position based on the congruency and alignment of carpal and radial component. The

kinematics are described by Helical Axis of Motion (HAM) parameters. HAM parameters

describe rigid body kinematics between two positions in terms of rotation (ϕ) about, and a

translation along a unique axis in space (i.e., screw axis). Rotational components of the

carpal component were decomposed using ϕ angle and the vector components of the screw

axis (Figure 4.4). Translations were defined as the displacement of the origin of the

coordinate system. The planar instantaneous center of rotation (ICR) was defined as the

intersection of the screw axis with each plane of the radial component coordinate system

(Figure 4.4). Since the HAM description of ICR and screw axis is unstable when the axis

is parallel to an anatomical plane, a cut-off angle of 5° was chosen before comparing the

ICR locations between the methods.

68

Statistical analyses

BVR accuracy was determined by direct

comparison of the BVR-calculated rotational

parameters (flexion-extension, radial-ulnar deviation,

and pronation-supination) and translational

parameters (radial-ulnar, volar-dorsal, and proximal-

distal displacements) to those determined via OMC

using Bland-Altman analysis. The root-mean-

squared-error (RMSE) of the differences between the

two techniques was used as an estimate of the overall

accuracy. The planar ICR was evaluated by

determining the bias and precision for each task and

intersection plane.

Results

Overall, the BVR-calculated kinematic

parameters were consistent with the gold standard

OMC-calculated parameters (Figure 4.5 and 4.6). The

bias in calculated flexion/-extension, radial/ulnar

deviation, and pronosupination angles between the

two methods was less than 0.3°, 0.5°, and 0.6° for all tasks (Figure 4.5). Among all tasks,

Bland-Altman plots of the rotation angle data demonstrated limits of agreement (95% CI)

between -1.2° to 0.9° for flexion/extension angle, -1.6° to 1.4° for radial/ulnar deviation,

and -1.8° to 0.8° for pronation/supination measurements. The maximum RMSEs of the

Figure 4.4. Definition of rotation

angles and planar instantaneous

center of rotation (ICR) for the

motion of the carpal components

relative to the radial component (this

figure depicts only a sagittal plane

intersection). In HAM parameters, n

is the vector defining the orientation

of the screw axis (nx, ny, nz), and φtot

is the rotation about the screw axis.

This angle can be decomposed into

rotational components (φtot.nx, φtot.ny,

φtot.nz). The screw axis intersects

each plane of the radial component

coordinate system, providing a

plane-specific ICR.

69

rotations were 0.4°, 0.7°, and 0.7°, respectively for the flexion/extension, radial/ulnar

deviation, and pronation/supination motions among all FE, RU, and CIRC tasks (Table

4.1). The differences in calculated translations between BVR and OMC had a bias of less

than 0.2 mm with standard deviations less than 0.4 mm (Figure 4.6), and sub-millimeter

limits of agreement among all tasks. The limit of agreement was between -0.8 mm to 0.7

mm, and the overall RMSE was less than 0.30 mm for all translational components (Table

4.1). The differences in rotation and translation between BVR and OMC did not follow a

consistent pattern in any of the tasks.

Figure 4.5. Bland-Altman plots of carpal component rotations throughout each task (Flexion-

Extension, Radial-Ulnar Deviation, and Circumduction) calculated from the biplane

videoradiography (BVR) and optical motion capture (OMC) data. Columns report the rotation

angles in the radial component’s coordinate system for each task (Rows). Across all tasks and

directions, there was a bias of less than 1°, and the limits of agreement were less than 2° for all

tasks.

70

Figure 4.6. Bland-Altman analysis of carpal component translations throughout each task

(Flexion-Extension, Radial-Ulnar Deviation, and Circumduction) calculated from the biplane

videoradiography (BVR) and optical motion capture (OMC) data. Columns report the translations

in the radial component’s coordinate system for each task (Rows). The Bland-Altman analysis

demonstrates a trivial bias of less than 0.2 mm, and the limit of agreement of less than 1 mm for

all tasks.

Table 4.1. Overall root-mean-squared-error (RMSE) of the differences between OMC and BVR

for rotations (°) and translations (mm) for all tasks. For each task, RMSE rotations are reported

for the components of flexion/extension (FE), radial/ulnar deviation (RU), and pronosupination

(PS). RMSE translations are reported for the components of radioulnar (RU), volar/dorsal (VD),

and proximal/distal (PD).

Task RMSE Rotation (°) RMSE Translation (mm)

FE RU PS RU VD PD

Flexion-Extension 0.3 0.5 0.5 0.2 0.2 0.2

Radial-Ulnar Deviation 0.4 0.5 0.5 0.2 0.1 0.1

Circumduction 0.4 0.7 0.7 0.3 0.2 0.2

Planar ICR location calculated by BVR showed an overall bias of less than 1 mm

in most of the planes. ICR location’s bias was higher than 1 mm only for YZ-plane in CIRC

and FE tasks, and for XY-Plane in RU task (Table 4.2). Higher standard deviation in ICR

71

accuracy was seen for YZ-plane since the screw axis is expected to be parallel to that plane

in most of the poses. The overall precision of ICR calculation was less than 3 mm among

all planes.

Table 4.2. Differences (mean ± std.) in instantaneous center of rotation location (mm) between

BVR and OMC for the motion of the carpal component relative to the radial component. Tasks

are Flexion-Extension (FE), Radial-Ulnar deviation (RU), and Circumduction (CIRC). The axis

directions are Distal (-)/Proximal (+), Ulnar (-)/Radial (+), and Dorsal (-)/Volar (+). (NA –

measurement not applicable)

Task Component XY-Plane XZ-Plane YZ-Plane

Flexion-Extension

x (DP) 0.1 ± 1.2 0.2 ± 1.1 NA

y (UR) -0.3 ± 2.3 NA -3.4 ± 6.5

z (DV) NA -0.2 ± 3.2 -0.4 ± 2.8

Radial-Ulnar Deviation

x (DP) 0.7 ± 3.2 -1.0 ± 2.8 NA

y (UR) -1.3 ± 4.7 NA -1.6 ± 6.4

z (DV) NA -0.3 ± 2.8 -1.6 ± 4.8

Circumduction

x (DP) 0.1 ± 1.0 0.3 ± 1.6 NA

y (UR) 0.0 ± 2.4 NA 2.0 ± 4.6

z (DV) NA -0.2 ± 1.8 -0.9 ± 2.9

Discussion

The aims of this study were to generate a carpal component model from CT image

volumes for tracking TWA kinematics using BVR, and then to evaluate the accuracy of

tracking using model-image registration. Three range-of-motion tasks were evaluated and

compared to OMC as the gold-standard. Compared to OMC, we found a submillimeter and

sub-degree bias for BVR-generated rotations and translations across all tasks. The rotation

angles and translations had limits of agreement of less than 1.8° and 0.8 mm, respectively.

72

These variations are of the same order of magnitude as differences seen in other studies for

other implants [12–14,27].

The technique reported here can detect changes in TWA kinematics of ~0.8 mm

translation and 1.8° rotation. Evaluating the TWA motion is important for understanding

its biomechanics, and its differences with normal wrist motion. Previous in-vivo studies on

TWA have used electrogoniometers and OMC systems to evaluate the overall wrist range-

of-motion after TWA [28,29]; however, these techniques have a high cross-talk error (up

to 5°) or soft-tissue artifact [23,30]. Here, we demonstrated the BVR’s high accuracy in

calculating the kinematics of the TWA; hence, investigators may be able to achieve much

higher accuracy in studying TWA kinematics in-vivo using BVR. Moreover, an accurate

measurement of the center of rotation is required for comparing the implant kinematics to

the normal joint kinematics [31]. Specifically, for the wrist joint, large control databases

exist [32] that can be used for comparing the implant ICR location in different planes of

motion. Without having an accurate measuring system, the sample size needed to evaluate

statistically significant differences among TWA designs, or between TWA and control

subjects, could be prohibitive to study.

Total Wrist Arthroplasty has not been previously studied using markerless

registration in BVR; however, total knee and hip arthroplasty have been studied in various

settings. Tsai et al. evaluated the accuracy of dual fluoroscopic systems for total hip

arthroplasties by marker-based radiostereometric analysis (RSA), and they found an

accuracy of within 0.33±0.81 mm in translations and 0.45±0.65° in the rotation in dynamic

motions [12]. Mahfouz et al. compared the kinematics of total knee arthroplasty studied by

fluoroscopy to its actual movement measured by the optical sensor. They found an RMS

73

deviation of ~0.4° in rotation and 0.1 mm of translations in the transverse plane, but up to

1.4 mm difference in translations in superior/inferior directions [14]. Here, we found a bias

of ~0.2 mm for translations, and bias of less than 0.5° for rotations, which is in the same

order of magnitude to the bias that previous studies have found.

In this study, OMC was used as the “gold standard” because of its submillimeter

accuracy. Due to the rigid fixation of the implants to the bones, we assumed rigid body

motion, which was confirmed with RMSE of less than 0.2 mm in Söderkvist method for

our marker clusters (each using 5 markers) [26,33]. Evaluating any inherent movement

between metacarpals, screws or the radial stem and the bones was not assessed here,

although the inspection of the in-situ implant components after the experiment did not

display any loosening.

There are some general limitations in studying the implant kinematics with BVR.

The obtained radiographic images and the thresholding parameters affect the outcome of

the optimized kinematic pose. Hence, we propose that future investigators optimize the

thresholding hyperparameters based on the image quality by inspecting the output of the

optimization cost function. Until a robust technique is achieved to make the process less

susceptible to image parameters, this limitation cannot be fully eliminated. Moreover, the

implant posture in the radiographic images can highly affect the accuracy of the outcome.

In this study, we found higher inaccuracies in the images where implant location was

occluded by thenar muscles, and/or two screws were overlapping each other. In contrast,

radiographs with two high-quality images that clearly demonstrated the implant’s unique

features had results that were consistent and sub-degree accurate. Reconstructing a 3D

model from CT images was unsuitable for the radial component studied here due to the

74

large streak artifacts caused by the highly attenuative solid cobalt-chromium stems. In such

cases, the radial component models will need to be generated from original CAD files, or

via surface scanning of size- and manufacturer-matched implants. This is not an

insurmountable challenge, as the number of different radial implants presently in clinical

use is relatively modest.

In addition to the inherent limitations of BVR, there are additional limitations in

our study. One specimen was studied in our experiment, but we believe that the findings

would be similar if the generated model and the quality of scans remain comparable. We

used one implant design and results might vary with others but given the similar geometry

and material of the implants, we do not expect a large difference across the current designs.

The Canny edge detection method (which filters the intensity gradients of the image using

double threshold parameters to determine potential edges) failed to detect continuous edges

for the screws of the carpal component because of the relatively high image noise in the

region of screw threads. Hence, edge-matching was not used for tracking the carpal

component. Finally, a key assumption of our tracking method is that the carpal component

and its screws are rigidly fixed relative to each other and to the bones of the hand. Loose

screws or carpal component would most likely decrease the accuracy of our tracking

approach. Future modifications to our approach may enable measurements of loosening,

which could be used to examine mechanisms behind the failures of TWA in a longitudinal

study of patients.

To summarize, we demonstrated that the CT-generated model of a TWA system

could be used in BVR for accurately measuring dynamic wrist motion. Our methodology’s

bias was on the order of a degree and submillimeter, achieving an accuracy comparable to

75

previous studies on other total joint replacements that have used the high-fidelity CAD

model of the implants for BVR tracking. Future studies employing this technique will

enable the kinematic study of TWA during various functional tasks (e.g., pitcher pouring,

hammering or twisting a doorknob) with the aim of improving the understanding of TWA

function in patients.

Acknowledgments

Authors want thank Benedict Gagliardi and Nature Lab facility in the Rhode Island School

of Design for providing the Artec 3D scanner. The research was supported in part by the

National Institutes of Health P20-GM104937 and a grant from the American Foundation

for Surgery of the Hand (AFSH).

References

[1] Adams, B. D., 2013, “Wrist Arthroplasty: Partial and Total,” Hand Clin., 29(1), pp. 79–

89.

[2] Weiss, A.-P. C., Kamal, R. N., and Shultz, P., 2013, “Total Wrist Arthroplasty,” J. Am.

Acad. Orthop. Surg., 21(3), pp. 140–148.

[3] Reigstad, O., Holm-Glad, T., Bolstad, B., Grimsgaard, C., Thorkildsen, R., and Røkkum,

M., 2017, “Five- to 10-Year Prospective Follow-Up of Wrist Arthroplasty in 56

Nonrheumatoid Patients,” J. Hand Surg.

[4] Berstock, J. R., Beswick, A. D., Lenguerrand, E., Whitehouse, M. R., and Blom, A. W.,

2014, “Mortality after Total Hip Replacement Surgery,” Bone Jt. Res., 3(6), pp. 175–182.

[5] Bayliss, L. E., Culliford, D., Monk, A. P., Glyn-Jones, S., Prieto-Alhambra, D., Judge,

A., Cooper, C., Carr, A. J., Arden, N. K., Beard, D. J., and Price, A. J., 2017, “The Effect

of Patient Age at Intervention on Risk of Implant Revision after Total Replacement of the

Hip or Knee: A Population-Based Cohort Study,” Lancet Lond. Engl., 389(10077), pp.

1424–1430.

[6] Astephen, J. L., Deluzio, K. J., Caldwell, G. E., and Dunbar, M. J., 2008, “Biomechanical

Changes at the Hip, Knee, and Ankle Joints during Gait Are Associated with Knee

Osteoarthritis Severity,” J. Orthop. Res., 26(3), pp. 332–341.

[7] Lim, L. A., Carmichael, S. W., and Cabanela, M. E., 1999, “Biomechanics of Total Hip

Arthroplasty,” Anat. Rec., 257(3), pp. 110–116.

[8] Indelli, P. F., 2016, “Is Normal Knee Biome-Chanics Reproduced by Modern to-Tal

Knee Arthroplasty Designs? The Role of Fluoroscopy,” Osteol Rheu-Matol Open J, 1(1),

pp. 6–9.

76

[9] Uvehammer, J., Kärrholm, J., and Brandsson, S., 2000, “In Vivo Kinematics of Total

Knee Arthroplasty,” Bone Jt. J., 82(4), pp. 499–505.

[10] Ma, J.-X., and Xu, Y.-Q., 2016, “The Instability of Wrist Joint and Total Wrist

Replacement,” Chin. J. Traumatol., 19(1), pp. 49–51.

[11] Halim, A., and Weiss, A.-P. C., 2017, “Total Wrist Arthroplasty,” J. Hand Surg.

[12] Tsai, T.-Y., Li, J.-S., Wang, S., Lin, H., Malchau, H., Li, G., Rubash, H., and Kwon, Y.-

M., 2013, “A Novel Dual Fluoroscopic Imaging Method for Determination of THA

Kinematics: In-Vitro and in-Vivo Study,” J. Biomech., 46(7), pp. 1300–1304.

[13] Flood, P. D. L., and Banks, S. A., 2016, “Automated Registration of Three-Dimensional

Knee Implant Models to Fluoroscopic Images Using Lipschitzian Optimization,” IEEE

Trans. Med. Imaging.

[14] Mahfouz, M. R., Hoff, W. A., Komistek, R. D., and Dennis, D. A., 2003, “A Robust

Method for Registration of Three-Dimensional Knee Implant Models to Two-

Dimensional Fluoroscopy Images,” IEEE Trans. Med. Imaging, 22(12), pp. 1561–1574.

[15] Zhu, Z., Massimini, D. F., Wang, G., Warner, J. J. P., and Li, G., 2012, “The Accuracy

and Repeatability of an Automatic 2D–3D Fluoroscopic Image-Model Registration

Technique for Determining Shoulder Joint Kinematics,” Med. Eng. Phys., 34(9), pp.

1303–1309.

[16] Kaptein, B. L., Valstar, E. R., Stoel, B. C., Rozing, P. M., and Reiber, J. H. C., 2003, “A

New Model-Based RSA Method Validated Using CAD Models and Models from

Reversed Engineering,” J. Biomech., 36(6), pp. 873–882.

[17] Brainerd, E. L., Baier, D. B., Gatesy, S. M., Hedrick, T. L., Metzger, K. A., Gilbert, S. L.,

and Crisco, J. J., 2010, “X-Ray Reconstruction of Moving Morphology (XROMM):

Precision, Accuracy and Applications in Comparative Biomechanics Research,” J. Exp.

Zool. Part Ecol. Genet. Physiol., 313(5), pp. 262–279.

[18] You, B. M., Siy, P., Anderst, W., and Tashman, S., 2001, “In Vivo Measurement of 3-D

Skeletal Kinematics from Sequences of Biplane Radiographs: Application to Knee

Kinematics,” IEEE Trans Med Imaging, 20, pp. 514–25.

[19] Tashman, S., and Anderst, W., 2003, “In-Vivo Measurement of Dynamic Joint Motion

Using High Speed Biplane Radiography and CT: Application to Canine ACL

Deficiency,” J. Biomech. Eng., 125(2), pp. 238–245.

[20] Barrett, J. F., and Keat, N., 2004, “Artifacts in CT: Recognition and Avoidance,”

RadioGraphics, 24(6), pp. 1679–1691.

[21] Elliott, M. J., and Slakey, J. B., 2014, “CT Provides Precise Size Assessment of

Implanted Titanium Alloy Pedicle Screws,” Clin. Orthop. Relat. Res., 472(5), pp. 1605–

1609.

[22] Stradiotti, P., Curti, A., Castellazzi, G., and Zerbi, A., 2009, “Metal-Related Artifacts in

Instrumented Spine. Techniques for Reducing Artifacts in CT and MRI: State of the Art,”

Eur. Spine J., 18(S1), pp. 102–108.

[23] Miranda, D. L., Rainbow, M. J., Crisco, J. J., and Fleming, B. C., 2013, “Kinematic

Differences between Optical Motion Capture and Biplanar Videoradiography during a

Jump-Cut Maneuver,” J. Biomech., 46(3), pp. 567–573.

77

[24] Knörlein, B. J., Baier, D. B., Gatesy, S. M., Laurence-Chasen, J. D., and Brainerd, E. L.,

2016, “Validation of XMALab Software for Marker-Based XROMM,” J. Exp. Biol.,

219(23), pp. 3701–3711.

[25] Robertson, D. G. E., and Dowling, J. J., 2003, “Design and Responses of Butterworth and

Critically Damped Digital Filters,” J. Electromyogr. Kinesiol. Off. J. Int. Soc.

Electrophysiol. Kinesiol., 13(6), pp. 569–573.

[26] Söderkvist, I., and Wedin, P.-Å., 1993, “Determining the Movements of the Skeleton

Using Well-Configured Markers,” J. Biomech., 26(12), pp. 1473–1477.

[27] Banks, S. A., and Hodge, W. A., 1996, “Accurate Measurement of Three-Dimensional

Knee Replacement Kinematics Using Single-Plane Fluoroscopy,” IEEE Trans. Biomed.

Eng., 43(6), pp. 638–649.

[28] Singh, H. P., Bhattacharjee, D., Dias, J. J., and Trail, I., 2017, “Dynamic Assessment of

the Wrist after Total Wrist Arthroplasty,” J. Hand Surg. Eur. Vol., p. 1753193417690472.

[29] Johnson, P. W., Jonsson, P., and Hagberg, M., 2002, “Comparison of Measurement

Accuracy between Two Wrist Goniometer Systems during Pronation and Supination,” J.

Electromyogr. Kinesiol. Off. J. Int. Soc. Electrophysiol. Kinesiol., 12(5), pp. 413–420.

[30] Kuo, M.-Y., Tsai, T.-Y., Lin, C.-C., Lu, T.-W., Hsu, H.-C., and Shen, W.-C., 2011,

“Influence of Soft Tissue Artifacts on the Calculated Kinematics and Kinetics of Total

Knee Replacements during Sit-to-Stand,” Gait Posture, 33(3), pp. 379–384.

[31] Imaeda, T., Cooney, W. P., Niebur, G. L., Linscheid, R. L., and An, K. N., 1996,

“Kinematics of the Trapeziometacarpal Joint: A Biomechanical Analysis Comparing

Tendon Interposition Arthroplasty and Total-Joint Arthroplasty,” J. Hand Surg., 21(4),

pp. 544–553.

[32] Moore, D. C., Crisco, J. J., Trafton, T. G., and Leventhal, E. L., 2007, “A Digital

Database of Wrist Bone Anatomy and Carpal Kinematics,” J. Biomech., 40(11), pp.

2537–2542.

[33] Challis, J. H., 1995, “A Procedure for Determining Rigid Body Transformation

Parameters,” J. Biomech., 28(6), pp. 733–737.

78

PROXIMAL-DISTAL SHIFT OF

THE CENTER OF ROTATION IN A TOTAL

WRIST ARTHROPLASTY IS MORE THAN

TWICE OF THE HEALTHY WRIST

5.

Bardiya Akhbari, Amy M. Morton, Kalpit N. Shah, Janine Molino, Douglas

C. Moore, Arnold-Peter C. Weiss, Scott W. Wolfe, Joseph J. Crisco

Journal of Orthopaedic Research, 2020

https://doi.org/10.1002/jor.24717

79

Abstract (250 Words)

Reproduction of healthy wrist biomechanics should minimize the abnormal joint forces

that could potentially result in the failure of a total wrist arthroplasty (TWA). To date, the

in-vivo kinematics of TWA have not been measured and it is unknown if TWA preserves

the healthy wrist kinematics. Therefore, the purpose of this in-vivo study was to determine

the center of rotation (COR) for a current TWA design and to compare its location to the

healthy wrist. The wrist COR for 6 patients with TWA and 10 healthy subjects were

calculated using biplane videoradiography as the subjects performed various range-of-

motion and functional tasks that included coupled wrist motions. An open-source

registration software, Autoscoper, was used for model-based tracking and kinematics

analysis. It was demonstrated that the COR was located near the centers of curvatures of

the carpal component for the anatomical motions of flexion-extension and radial-ulnar

deviation. When compared to healthy wrists, the COR of TWAs was located more distal

in both pure radial deviation (p < 0.0001) and pure ulnar deviation (p = 0.07), while there

was no difference in its location in pure flexion or extension (p = 0.99). Across all coupled

motions, the TWA’s COR shifted more than two times that of the healthy wrists in the

proximal-distal direction (17.1 mm vs. 7.2 mm). We postulate that the mismatch in the

COR location and behavior may be associated with increased loading of the TWA

components, leading to an increase in the risk of component and/or interface failure.

80

Introduction

Total Wrist Arthroplasty (TWA) has a history as long as total knee and hip joint

replacements;1 however, it has not demonstrated the same high survival rates.2–4 Although

current TWA designs5–8 have improved over the past decade and have started to become a

reliable option for some patients,6 high complication rates are still a major issue.9–11 While

the reasons for the complications following a TWA are debated, studies evaluating total

joint replacements of the knee, shoulder, spine, and hip have shown that kinematic

differences between the healthy and replaced joint motion can lead to implant and bone-

implant interface failures.12–16 Differences in the kinematics, as quantified by the location

of the center of rotation (COR), have been postulated as an etiology for TWA failure.17

However, none of the current TWA designs have been subjected to rigorous in-vivo

kinematic studies. Thus, it is unknown if current-generation TWA implants maintain a

similar COR as that of healthy wrists.

The COR of the healthy wrist is located within the proximal head of capitate in

wrist flexion and extension, and shifts distally 5 to 10 mm when the wrist radially and

ulnarly deviates.18–21 Studies using sequential computed-tomography (CT) scanning of

wrists have reported the COR location as slightly dorsal to the head of the capitate in

extreme extensions, slightly volar in extreme flexion, and slightly distal in radial-ulnar

deviation.18,19 However, dynamic shifting in the COR during coupled wrist motions,22 such

as circumduction or the dart-thrower’s motion, have not been established. Biplane

videoradiography is a dynamic imaging technique that can accurately determine the three-

dimensional (3D) positions of the bones and implants in-vivo, and could help illustrate the

physiological behavior of the wrist joint during dynamic coupled motion.23–27

81

The purpose of this in-vivo study was to compare the location of COR of a current-

generation TWA design with the healthy wrist. Given that the geometry of the articulating

surface of a current TWA implant is ellipsoidal in shape, we hypothesized the COR of the

TWA patients would be located at the centers of curvature of the carpal component’s

bearing surface (at the center of minor curvature in pure flexion-extension and at the center

of major curvature in pure radioulnar deviation). We further sought to determine if the

overall behavior of the COR of a current TWA differed from the COR of the healthy wrist.

Methods

Subjects

Six patients (74.7 ± 5.6 yrs, 2 females, 2 right wrists) who had a TWA (size 2

Freedom® [Integra LifeSciences, Plainsboro, NJ]) for wrist osteoarthritis and 10 healthy

subjects with no history of wrist pathology (57.0 ± 5.2 yrs, 8 females, 9 right-hand

dominant) participated in this study after institutional review board approval. The TWA

surgeries were performed by a board-certified hand surgeon (APCW) using a standard

dorsal approach. TWA patients had undergone surgery at least 6 months prior to the study

(average 22 ± 12 months).

CT Image Acquisition

A CT scan (Lightspeed® 16, GE Medical, Milwaukee, WI) was acquired of each

studied wrist at tube settings of 80 kVp and 80 mA. The CT images were reconstructed

with a 20 cm field-of-view using the Bone Plus algorithm yielding 3D volumetric images

with 0.39 mm × 0.39 mm resolution in the transverse plane of the forearm and 0.625 mm

resolution along the proximal-distal direction of the forearm/hand. CT scans of the healthy

contralateral wrists for 3 participants in the TWA cohort were also acquired using the same

82

settings to construct pre-surgery models of the radius and capitate. CT scans of the

contralateral wrists of the other 3 participants were not available at the time of study;

therefore, a shape-matching approach was used to construct the pre-surgery models.

Biplane Videoradiography

5.2.3.1. XROMM System

Biplane videoradiography (BVR) was used to capture dynamic images of implant

and wrist position while each subject performed range-of-motion (ROM) and functional

tasks described below. The BVR system has been described in detail previously (XROMM,

Brown University).28 In this experiment, the x-rays were generated with an exposure

setting of 65 to 75 kV and 80 mA in continuous mode. The source-to-hand distances were

~90 cm, and the source-to-image distances of both systems were 130 cm. Videoradiographs

were acquired at the rate of 200 Hz with camera shutter speed set at 500 µs. Two seconds

of imaging were recorded for each task (i.e., 400 BVR images). The radiographs had a

resolution of ~0.22 × 0.22 mm per pixel and were stored in an 8-bit format. The calibration

of the system and the de-distortion of images were completed using XMALab software and

protocol (Brown University, Providence, RI).29 The mean total effective dose of radiation

to each subject was approximately 0.95 mSV, equivalent to 115 days of background

radiation in the United States.30

5.2.3.2. Tasks Description

BVR was acquired for five active tasks of wrist motion: flexion-extension, radial-

ulnar deviation, circumduction, hammering, and pitcher pouring. In all tasks, the forearm’s

starting posture was at neutral rotation and unconstrained, while the elbow was supported

at the joint level, and the shoulder was in adduction. Flexion-extension and radial-ulnar

83

deviation tasks were defined as the rotation of the palm relative to the volar-dorsal and

radial-ulnar sides of the hand, respectively. Circumduction was described as the coupled

motion22 of flexion-extension and radial-ulnar deviation, and consisted of a wrist motion

that aimed to achieve maximum active ROM in every direction. Hammering was used to

elicit motion along the dart-thrower’s path.31–34 During hammering, subjects repeatedly

swung a 0.25 kg rubber mallet without hitting any surface. Pitcher pouring task utilized a

weighed pitcher (1 kg of Smooth-Cast® 300, Smooth-On Inc., Macungie, PA), for a task

that simulated pouring. The subjects followed the path of motion displayed by the

researchers throughout each capture, and for all tasks except pitcher pouring, the subjects

performed the task at a consistent pace (90 beats per minute) for more than 5 seconds during

which 2 seconds of data was acquired. The pitcher

pouring task was captured when the subjects began

performing the task.

5.2.3.3. Kinematic Analysis

An established 2D-to-3D image registration

software, Autoscoper (Brown University

[https://simtk.org/projects/autoscoper]), was used to

calculate kinematics by tracking the radial and carpal

components in the TWA patients, and the third

metacarpal (MC3) and radius in the healthy wrists

(Figure 5.1).23,35 Briefly, the software uses the

density-based volumetric image of each bone/implant

to construct digitally reconstructed radiographs using

Figure 5.1. Three-dimensional

models of a healthy wrist (radius,

capitate, and third metacarpal), and a

replaced wrist (resected radius, radial

component, polyethylene cap, carpal

component, resected capitate and

third metacarpal) in the neutral pose.

For the sake of clarity, other carpal

bones are omitted.

84

backward ray-casting algorithm (Figure 5.2).36 Normalized cross-correlation cost function

and particle swarm optimization algorithm37 were implemented to optimize the 3D position

of TWA components and bones. Optimization and radiograph filters specifications have

been reported previously.23 Hammering task data for one healthy subject was excluded

because of its poor tracking accuracy due to the large overlap of metacarpals and

indistinguishable MC3 in BVR images.

Figure 5.2. The tracked third metacarpal and radius for the healthy wrist (left) and carpal

component and radial component for the replaced wrist (right) for one of the radiographic views.

The image features of radiographs are enhanced using Sobel edge filter and intensity thresholding

to maximize the similarity between the bones/implants and radiographs.

Kinematic analysis was performed for the TWA patients via model-based tracking

of the radial component and carpal component.35 The models for the radial component and

the polyethylene cap were generated by scanning a Freedom® implant using a high-

resolution (0.1 mm) 3D laser scanner (Space Spider™, Artec 3D, LU). The model for the

carpal component, consisting of the base and the two screws, was generated via

segmentation of the CT scan using Mimics v19 software (Materialise NV, Leuven, BE).35

Additionally, the radii of the contralateral wrists of the 3 TWA patients who had CT scans

85

were segmented with the same procedure for further coordinate system construction to

describe the wrist kinematics. For the other 3 patients, the coordinate system was

constructed by utilizing a large database of patients described in the next section.

Kinematic analysis of the wrist of the healthy patients was performed via tracking

of the radius and MC3. The second metacarpal (MC2), MC3, fourth metacarpal (MC4),

capitate, and radius were segmented from the CT images using Mimics (Figure 5.1). The

bones in the CT images were segmented manually in two or three image slices, and then

an automatic gradient-based segmentation (Materialise) was used for segmentation of the

entire bone. In this study, we used a previously-reported feedforward model-based tracking

methodology to track the bones in the videoradiographs by first tracking the combined

MC2-MC3 image volumes and then using the results of this analysis to seed the tracking

of the MC3 alone.23

Data Analysis

Coordinate System Definitions

Wrist center of rotation was determined

relative to the geometry of the implant as a

function of wrist position relative to its neutral

posture defined below. Wrist position was

defined as the position of the anatomically-

aligned MC3 coordinate system (CS) with

respect to a conventional, anatomically-aligned

radius-based CS (Figure 5.3).38 Briefly, the

radial coordinate system’s x-axis was aligned

Figure 5.3. Depiction of bones’ and

implants’ coordinate systems demonstrated

as X-axis (red), y-axis (green), and z-axis

(blue).

86

with the radial shaft positive proximally, the y-axis intersected the radial styloid and the

sigmoid notch (projected to the radial articular surface) positive radially, the z-axis was

orthogonal to both x- and y-axes positive in the volar direction, and the origin was at the

intersection of the x-axis and the radial articular surface. For the TWA patients whose

proximal radii were resected and obscured by CT streak artifact from the implants, radius

morphology was restored by registration of the contralateral radius to the resected radius

using the dissimilarity-excluded Procrustes algorithm39,40 (3 subjects), or using bone

models from our large database of wrist bone anatomy38 (3 subjects). Model selection from

the database involved determining the best fit from 120 available radii based on a

dissimilarity metric as an optimization criterion.40 The MC3 CS was located at its centroid

and was defined using the inertial properties, and the centroids of MC2, MC3, and MC4

models. The y-axis was defined as the best line fit to the metacarpal centroids positive

radially, the x-axis was aligned with the MC3 diaphysis positive proximally, and the z-axis

was orthogonal to both positive volarly. For visualization, the models of the registered radii

were trimmed along the proximal surfaces of the radial component. All left-handed bone

and implant models were converted to right-hand bone and implant models

mathematically.32

Neutral position was defined as the wrist posture with flexion-extension and radial-

ulnar deviation of MC3 CS aligned with the radius-based CS. The MC3 was used to define

the wrist motion as a proxy for capitate motion since previous studies have reported the

rigid coupling of capitate-MC3 motion.18,41

Wrist kinematics were described using helical axis of motion (HAM) parameters42

calculated relative to the neutral pose. HAM parameters uniquely describe kinematics

87

using an axis of rotation or screw axis (whose orientation and location in space are

described by vectors, �⃗� 𝑥𝑦𝑧 and 𝑞 𝑥𝑦𝑧, respectively), a rotation about the screw axis, and a

translation along the screw axis. After the HAMs were calculated, the HAM rotation angle

was projected and decomposed in the radius CS using its orientation vector (�⃗� 𝑥𝑦𝑧), and the

wrist flexion-extension and radial-ulnar deviation rotations were calculated (y- and z-axes

components).32 Wrist motion was then categorized to four anatomical motions of “pure”

flexion, extension, radial deviation, and ulnar deviation for

evaluating the COR location. Pure flexion and extension were

defined when the radial-ulnar deviation was less than 10°, and

pure radial and ulnar deviation were defined when flexion-

extension was less than 10°. In overall, for pure flexion-

extension, out-of-plane motion was 0.4 ± 3.7° in radial

deviation and 1.0 ± 4.6° in ulnar deviation, while for pure

radial-ulnar deviation, the out-of-plane motion was 0.6 ± 1.8°

in flexion and 0.1 ± 1.5° in extension for replaced wrist and

healthy cohorts, respectively. The orientation of axis of

rotation was also described using azimuth angle (azi) within

the radial CS reference plane, and elevation angle out of the radial CS plane (Figure 5.4).43

COR location was described with respect to capitate-based CS in the healthy wrists,

and with respect to a carpal component-based CS in the replaced wrists. The capitate CS

was defined by the inertial properties of the bone,44 with the x-axis modified as the best-fit

line that passed through the centroids of axial cross-sections45 of the bone model (positive

proximally) and origin located at its intersection with the most distal surface. The z-axis

Figure 5.4. The screw axis

was transferred to the origin

of the radius coordinate

system and based on its

orientation and projection

the azimuth (azi) and

elevation angles were

calculated. X-axis (red), y-

axis (green), and z-axis

(blue) demonstrate the radius

coordinate system.

88

was a cross-product of x-axis and y-axis. The x-axis of the carpal component’s CS was

defined by the implant’s stem (positive distally), and the y-axis was positive radially in the

direction of the holes provided for the screws. The z-axis was the cross-product of x- and

y-axes positive volarly, and the origin was located at the intersection of the stem and the

distal surface of the carpal component’s base (Figure 5.3).

Center of Rotation Calculations

COR location was calculated as the point of intersection of the screw axis with the

capitate’s CS planes. For wrist flexion-extension, the COR was calculated as the

intersection of the screw axis with the sagittal plane (xz plane) and the intersection with

frontal plane (xy plane) for wrist radial-

ulnar deviation. The centers of

curvatures of the polyethylene cap’s

ellipsoidal shape were computed as

COR reference points for “pure”

anatomical motions: flexion/extension

and radial/ulnar deviation (Figure 5.5).

The minor and major centers of

curvatures of the articulating surface were determined by fitting an ellipsoid to surface

points of the polyethylene cap in each plane using a custom-written code (Matlab 2018a,

Mathworks, Natick, MA).46 The minor and major centers of curvatures were located 22.8

mm and 3.1 mm proximal to the origin of the capitate coordinate system.

Previous studies have shown that age does not affect healthy wrist kinematics, and

the variability resulted from sex or bone size can be removed by scaling the

Figure 5.5. Center of minor and major curvatures of

the ellipsoidal shape of the polyethylene cap.

Curvatures were detected using the least-squares

fitting of an ellipsoid to the surface points of the

polyethylene cap.

89

translations;19,47 thus, the height of capitate was used for normalization of the location of

COR. The height of capitate was defined as the distance between the origin and the most

proximal intersections of the x-axis with the capitate surface model. Because the capitate

was partially resected for the TWA cohort, a pre-surgery estimate was reconstructed by

utilizing a large database of the carpal bone anatomy models38 and the same Procrustes

registration algorithm described in the previous section. The capitate height for all subjects

in both cohorts was 22.9 ± 2.0 mm, and its average was used to normalize COR location

for all subjects.

The projected COR (ψ) was used to describe the proximal-distal shifting of the

screw axis across wrist motions (Figure 5.6). ψ was computed as the point on the capitate’s

x-axis closest to each screw axis, and its distance was measured in the capitate’s CS.

Figure 5.6. The projected center of rotation (COR) was defined for the healthy wrists as a point

on the mid-axis of the capitate which had the shortest distance from the axis of rotation (red). The

polyethylene cap’s mid-axis was used to define the projected COR for the replaced wrists

(TWA).

90

Statistical Analysis

To compare COR location of the TWA cohort to the centers of curvatures intercept-

only generalized estimating equations (GEEs) was used (SAS v9.4, SAS Institute Inc.,

Cary, NC). Comparison of COR location between TWAs and healthy wrists in pure

anatomical motions was performed with GEEs that modeled the COR location as a function

of subject within wrist motions and conditions (TWA vs. healthy). The maximum

likelihood estimators of the GEE model were adjusted for possible misspecification, and a

separate model was run for each COR location. The Holm test was used for multiple

comparisons to maintain a 2-tailed familywise alpha at 0.05. All estimates are reported as

mean values along with their 95% confidence interval (CI). Given our sample size, we had

80% power to detect 7.5, 2.9, and 2.9 mm differences between the COR locations of both

cohorts in proximal-distal, volar-dorsal, and radial-ulnar directions. Similarly, we had 80%

power to detect 2.0 and 2.7 mm differences between the TWA COR locations and centers

of curvatures.

The proximal-distal shift of the projected COR among all tasks was modeled with

two harmonic equations, ψTWA(azi) = A0 + A1cos(h1×azi) and ψHEALTHY(azi) = B0 +

B1cos(g1×azi), both as a function of the direction of wrist rotation (azimuth angle [azi]),

where A0/B0 were y-intercept, A1/B1 were amplitude, and h1/g1 were period of the sine

curves (Matlab 2018a, Mathworks, Natick, MA). Harmonic equations were chosen based

on data behavior posteriori. Root-mean-squared-error (RMSE) and adjusted R2 were used

to evaluate the robustness of the model. The association of the azimuth angle and the

average (standard deviation [SD]) of the distance between COR and capitate’s x-axis (l),

and the azimuth angle and the elevation angle were also evaluated at 4 anatomical and 4

91

coupled wrist motions. Coupled wrist motions were selected when the extent of radial/ulnar

deviation and flexion/extension were equal (resulting in four motions of radial-flexion,

radial-extension, ulnar-flexion, and ulnar-extension). Typical location and orientation of

the screw axis for both the healthy wrist and replaced wrist were evaluated using the

sinusoidal model of the projected COR behavior, average elevation angle, and distance

from the mid-axis.

Results

Average (SD) of wrist ROM for

subjects with TWA implant were 26.7°

(10.5°), 37.8° (12.1°), 15.4° (1.6°), and

20.8° (3.7°), in pure flexion, extension,

radial deviation, and ulnar deviation,

respectively, while healthy wrists were

able to attain 47.0° (13.8°), 46.3°

(11.2°), 20.1° (3.3°), and 31.6° (6.5°),

respectively.

The CORs of the TWA wrists

for anatomical wrist motions were

located approximately at the two

centers of curvature of the carpal

component (Table 5.1 and Figure 5.7).

The differences between the proximal-

distal or volar-dorsal location of the

Figure 5.7. Center of rotation (COR) on the resected

capitate for the replaced wrist (top panel) and

capitate (bottom panel) for the healthy wrist. The

replaced wrist had a COR located slightly distal to

the center of curvature in flexion-extension (top left

panel; radial view), while it was slightly proximal to

the center of curvature in radial-ulnar deviation (top

right panel; volar view). Centers of curvatures are

shown as black dots, and the standard deviation of

COR in both directions are shown as colored

ellipses.

92

TWA COR and the center of curvature in pure anatomical motions were not statistically

significant (Table 5.1). Similarly, the radial-ulnar location of COR was also not

significantly different from the center of curvature in the pure ulnar deviation (0.3 mm,

p=0.89); however, for the pure radial deviation, the COR was located significantly more

radially (1.4 mm) to the center of curvature (p=0.03).

When compared to the healthy wrist, the TWA COR was located significantly (p <

0.0001) more distal (7.9 mm) in pure radial deviation and was approaching significance (p

= 0.07) in pure ulnar deviation (8.2 mm) (Tables 5.1 and 5.2, Figure 5.7). There were no

other statistically significant differences between the location of the TWA and healthy

wrist COR (Tables 5.1 and 5.2).

Table 5.1. Proximal-distal, volar-dorsal, and radial-ulnar location of the center of rotation (COR)

of the replaced wrist for pure rotations in capitate’s coordinate system, which is located on its

mid-axis and its most distal surface. The mean and 95% confidence intervals (CI) were calculated

using generalized estimating equations. COR for pure flexion and extension was computed in the

sagittal plane, while the COR for radial and ulnar deviation was calculated in the frontal plane.

Proximal-Distal

Location

Mean (95% CI)

Volar-Dorsal

Location

Mean (95% CI)

Radial-Ulnar

Location

Mean (95% CI)

Pure Flexion COR 18.9 (16.1, 21.8) 0.2 (-0.4, 0.8) N/A

Pure Extension COR 20.0 (17.3, 22.8) 0.0 (-0.5, 0.5) N/A

Pure Radial Dev. COR 6.0 (3.5, 8.5) N/A 1.4 (0.6, 2.3)

Pure Ulnar Dev. COR 5.7 (-0.3, 11.7) N/A -0.3 (-1.1, 2.6)

Table 5.2. Proximal-distal, volar-dorsal, and radial-ulnar location of the center of rotation (COR)

of the healthy wrist for pure rotations in capitate’s coordinate system, which is located on its mid-

axis and its most distal surface. The mean and 95% confidence intervals (CI) were calculated

using generalized estimating equations.

Proximal-Distal

Location

Mean (95% CI)

Volar-Dorsal

Location

Mean (95% CI)

Radial-Ulnar

Location

Mean (95% CI)

Pure Flexion COR 21.5 (20.8, 22.2) 2.2 (0.8, 3.6) N/A

Pure Extension COR 20.8 (20.1, 21.4) -1.3 (-2.4, -0.3) N/A

Pure Radial Dev COR 13.9 (13.0, 14.8) N/A 3.9 (2.1, 5.7)

Pure Ulnar Dev COR 13.9 (13.0, 14.9) N/A 1.0 (-0.5, 2.6)

93

During coupled motions, proximal-distal shift of the TWA COR followed a

sinusoidal pattern (A0=11.9, A1=8.6, h1=-2.1; R2=0.77, RMSE=3.0 mm) with minimum

occurring at slightly distal to the center of the minor curvature in wrist’s flexion/extension

and maximum occurring at slightly proximal of the center of the major curvature in wrist’s

radial/ulnar deviation (Figure 5.8). Shifts in COR in the healthy wrists during coupled

motions followed a similar sinusoidal pattern (B0=17.5, B1=3.6, g1=-2.1; R2=0.72,

RMSE=1.6 mm), but with significantly less proximal-distal shifting (p < 0.0001). The COR

for TWA traveled proximally from 3.3 mm of the most distal point of capitate to 20.4 mm

(17.1 mm), while the COR for healthy wrist traveled in the same direction from

approximately 13.9 mm to 21.1 mm (7.2 mm).

In overall, different patterns for the orientation and location of the axis of rotation

were observed between the TWA and the healthy wrist (Figure 5.9-11). The axes of

rotations were oriented differently in radial-flexion and ulnar-extension for the TWA (with

22.4° difference), while their orientation differed only 1.7° for the healthy wrist (Figure

5.9 and Figure 5.11). The axis of rotation for TWA also had minimal volar-dorsal

Figure 5.8. The proximal-distal shift of the projected center of rotation (COR) as a function of

wrist motion (for all tasks). COR shifted in a sinusoidal pattern (solid black line with confidence

interval as a shaded region) in proximal (+) and distal (-) direction from the most distal point on capitate (i.e., 0 on the figures) for both cohorts. The healthy wrist’s COR traveled an

approximately 7.2 mm while the replaced wrist’s COR traveled about 17.1 mm.

94

orientation in full radial and ulnar deviation, while it was oriented approximately 20°

volarly for the healthy wrists. For both cohorts, the volar-dorsal orientation of the screw

axis was 0° near full flexion and extension. Moreover, the COR was located on the stem

of carpal component for the TWA throughout the coupled motions, while it was located

approximately 2 mm volarly or dorsally for the healthy wrist in flexion or extension,

respectively (Figure 5.10).

Figure 5.10. The shortest distance from the screw axis to the x-axis of capitate (l). This distance

for the replaced wrist was approximately 0 throughout the wrist motion, while the healthy wrist

had slightly larger variations. The average (solid black line) and standard deviations (shaded

black region) were calculated at 4 anatomical and 4 coupled wrist motions

Figure 5.9. The axis of rotation’s elevation angle of wrist followed a sinusoidal pattern, while the

replaced wrist had mostly a negative elevation angle. The average (solid black line) and standard

deviations (shaded black region) were calculated at 4 anatomical and 4 coupled wrist motions.

95

Discussion

The dynamic location of the COR and the orientation of the screw axis for a current-

generation TWA (Freedom®) and healthy wrists were evaluated in this study. We

demonstrated the CORs for the anatomical motions of flexion-extension and radial-ulnar

deviation occurred about the centers of curvatures of the ellipsoidal shape of the carpal

component of TWA, while during coupled wrist motions, the COR locations was shifting

between these centers. This COR shift was roughly 2 times more for the TWA when

compared to that for a healthy wrist (17.1 mm compared to 7.2 mm) illustrating a

significant mismatch in kinematics. Previous studies48–51 have shown the dissimilarity in

ROM and pattern of stress distribution between healthy and replaced wrists, which could

be the result of this mismatch in COR. In this study, the calculated healthy wrist’s COR

was similar to previous studies that have reported the COR location at the proximal pole

of capitate with 5 to 10 mm distal shift.17,18,41

Figure 5.11. The overall pattern of screw

axis orientation and location at four

anatomical (F: flexion, E: extension, R: radial deviation, U: ulnar deviation) and

four coupled wrist motions (UF: ulnar-

flexion, UE: ulnar-extension, RE: radial-

extension, RF: radial-flexion) for Freedom®

replaced wrist (top panel) and a typical

healthy wrist (bottom panel) in radial view

(left panel) and volar view (right panel). In

both healthy and replaced wrists, rotation

axes for pure flexion-extension and radial-

ulnar deviation were orthogonal and

consistent with the motion. In healthy

wrists, dart-thrower’s (RE to UF) and anti

dart-thrower’s (RF to UE) followed the same pattern, while in the replaced wrist

the coupled motions had dissimilar and

complex patterns.

96

We demonstrated that the COR of the implant was at the centers of curvatures of

the carpal component and it shifts between these locations during coupled motions. The

distal location of COR relative to the center of curvatures may indicate sliding (rotation

along with translation) of the implant between the polyethylene cap and the radial

component at times. In contrast, the proximal location of COR relative to the center of

major curvature during motions with radial-ulnar deviation suggests that implant

components are rolling without any translations. This discrepancy between the behavior of

the implant and direction of motion could be due to the muscular and soft-tissue structure

surrounding the wrist. Although this behavior should be confirmed by detailed contact

analysis, the in-vivo kinematics demonstrates a complicated implant motion based on the

direction of wrist motion.

Studies of other joint arthroplasties have verified the importance of replicating

healthy joint kinematics in the replaced joint.12–16 Malalignment of the knee replacements

has been reported as the cause of unintended implant contacts and excessive polyethylene

wear,52 and consequent inferior clinical outcomes.53 The hip joint COR after total hip

arthroplasty also influences the lever arm of the body weight and the tension of the muscles;

thus, any abnormal changes could cause an increase in pelvic balancing force and

potentially lead to the implant’s failure.54 Similarly, finite element modeling of the wrist

suggests dramatic increases in contact stress with even small (<1°) off-axis motions,55

which could lead to polyethylene wear and particle generation and subsequent osteolysis.55

Both high interface loads and bearing wear may contribute to carpal component loosening,

a leading complication following TWA.10,56

97

Previous studies have shown the importance of dart-thrower’s (occurring primarily

at the midcarpal joint) and anti dart-thrower’s motion in the activities of daily living.32,57,58

We demonstrated a consistent behavior of axis of rotation for the healthy wrists, while a

more complicated pattern for the replaced wrist was observed, indicating the implants

incapability in accomplishing these motions (Figure 5.11). This mismatch could be

potentially be due to the fact that most current implant designs are intended to replicate the

radiocarpal joint, and not the midcarpal joint’s kinematics.59

Data obtained from this study could help with designing more biomechanically-

fidelic wrist implants. The discrepancy between the amplitude (shifting) of the sinusoidal

pattern of projected COR between the cohorts might be resolvable by reducing the distance

between the centers of curvatures. One solution may be to use an elliptical polyethylene

cap which has a smaller radius for its major curvature. However, with that change, the joint

would become closer to a ball-and-socket joint, which, accordingly, provides no torsional

(supination-pronation) stability and it is instructive to note such designs have been

considered, but have been associated with high complication rates relative to other

arthroplasty designs.1,2,9,60 The mismatch of the orientarion of the screw axis in the anti

dart-thrower’s motions (radial-flexion to ulnar-extension) between healthy wrists and

TWA might also be resolvable with novel designs. Lastly, although modifying the joint’s

shape and the type of articulation might aid to simulate the biomechanics of the healthy

wrist, future studies must evaluate their clinical success and patient’s satisfaction.

Even though our mathematical models for COR location and the axis of rotation’s

orientation across patients demonstrated high R2 and low RMSE, we were limited to a

small cohort of 6 subjects with a single implant design. Although other currently FDA-

98

approved implants have similar ellipsoidal designs for the polyethylene cap, they may

reflect different behavior than the implant studied here. We did not directly discuss the

ROM between cohorts and their magnitude of relationship to COR due to the small sample

size, but similar to previous studies,50,51 we found a lower ROM for TWA patients relative

to the healthy wrists. Furthermore, although the relative alignment of TWA components to

the bones might affect the wrist’s ROM, we did not see any variations in the COR

proximal-distal shift relative to the extent of ROM. In this study, we were not able to

evaluate any associations between the alignment of the implant’s components and the COR

location because of the small size of our cohort. However, to minimize the TWA alignment

effects on COR location, we used polyethylene cap’s coordinate system as the reference

which is invariant to the component’s alignment relative to MC3.

In this study, we evaluated the dynamic behavior of the COR for both healthy wrists

and wrists that have undergone a TWA. We found that the COR of the TWA cohort is

located approximately at the centers of curvatures of the articulating surface. The COR of

a TWA, however, shifts about 2 times more than a healthy wrist during functional tasks.

This behavior of COR movement demonstrated a discrepancy between the healthy wrist

and TWA kinematics throughout functional tasks and coupled motions. The relative high

complication rate of current TWA design may be associated with abnormal forces at the

implant interface that could be a result of the mismatch reported between the replaced and

healthy wrist behavior in this study. Further studies must be done to elucidate the

relationship between the TWA kinematics, implant’s contact area and location, and clinical

outcomes.

99

Author’s Contribution

BA was involved in data acquisition, study design, data processing, and manuscript

drafting and revising. AMM and KNS were involved in data acquisition, manuscript

drafting and revising. JM was involved in supervising and performing the proper statistical

analysis. DCM was involved in data acquisition, study design, funding acquisition, and

manuscript revising. APCW and SWW were involved in designing the study and revising

the manuscript. JJC was involved in acquiring the funding, designing the study, supervising

data processing, and revising the manuscript.

Acknowledgments

Authors thank Erika Tavares for her help throughout data acquisition at the XROMM

facility at Brown University. This study was funded by partial support from the National

Institute of Arthritis and Musculoskeletal and Skin Diseases under award number

P30GM122732 (COBRE Bio-engineering Core), and a grant from the American

Foundation for Surgery of the Hand (AFSH).

References

1. Ritt MJ, Stuart PR, Naggar L, Beckenbaugh RD. 1994. The early history of

arthroplasty of the wrist. From amputation to total wrist implant. J Hand Surg Br

19(6):778–782.

2. Reigstad O, Holm-Glad T, Bolstad B, et al. 2017. Five- to 10-Year Prospective

Follow-Up of Wrist Arthroplasty in 56 Nonrheumatoid Patients. J Hand Surg Am

.

3. Berstock JR, Beswick AD, Lenguerrand E, et al. 2014. Mortality after total hip

replacement surgery. Bone and Joint Research 3(6):175–182.

4. Bayliss LE, Culliford D, Monk AP, et al. 2017. The effect of patient age at

intervention on risk of implant revision after total replacement of the hip or knee:

a population-based cohort study. Lancet 389(10077):1424–1430.

5. Badge R, Kailash K, Dickson DR, et al. 2016. Medium-term outcomes of the

Universal-2 total wrist arthroplasty in patients with rheumatoid arthritis. Bone

Joint J 98-B(12):1642–1647.

100

6. Gil JA, Kamal RN, Cone E, Weiss A-PC. 2017. High Survivorship and Few

Complications With Cementless Total Wrist Arthroplasty at a Mean Followup of

9 Years. Clinical Orthopaedics and Related Research® 475(12):3082–3087.

7. Herzberg G, Boeckstyns M, Sorensen AI, et al. 2012. “Remotion” total wrist

arthroplasty: preliminary results of a prospective international multicenter study

of 215 cases. J Wrist Surg 1(1):17–22.

8. Reigstad O, Røkkum M. 2014. Wrist arthroplasty: where do we stand today? A

review of historic and contemporary designs. Hand Surg 19(2):311–322.

9. Halim A, Weiss A-PC. 2017. Total Wrist Arthroplasty. J Hand Surg Am

42(3):198–209.

10. Yeoh D, Tourret L. 2015. Total wrist arthroplasty: a systematic review of the

evidence from the last 5 years. J Hand Surg Eur Vol 40(5):458–468.

11. Froschauer SM, Zaussinger M, Hager D, et al. 2019. Re-motion total wrist

arthroplasty: 39 non-rheumatoid cases with a mean follow-up of 7 years. Journal

of Hand Surgery (European Volume) :175319341986611.

12. Banks SA, Hodge WA. 2004. Implant design affects knee arthroplasty kinematics

during stair-stepping. Clin. Orthop. Relat. Res. (426):187–193.

13. Franta AK, Lenters TR, Mounce D, et al. 2007. The complex characteristics of

282 unsatisfactory shoulder arthroplasties. J Shoulder Elbow Surg 16(5):555–562.

14. Gregory TM, Sankey A, Augereau B, et al. 2013. Accuracy of glenoid component

placement in total shoulder arthroplasty and its effect on clinical and radiological

outcome in a retrospective, longitudinal, monocentric open study. PLoS ONE

8(10):e75791.

15. Galbusera F, Anasetti F, Bellini CM, et al. 2010. The influence of the axial,

antero-posterior and lateral positions of the center of rotation of a ball-and-socket

disc prosthesis on the cervical spine biomechanics. Clinical Biomechanics

25(5):397–401.

16. Lecerf G, Fessy MH, Philippot R, et al. 2009. Femoral offset: Anatomical

concept, definition, assessment, implications for preoperative templating and hip

arthroplasty. Orthopaedics & Traumatology: Surgery & Research 95(3):210–219.

17. Figgie HE, Inglis AE, Straub LR, Ranawat CS. 1986. A critical analysis of

alignment factors influencing functional results following trispherical total wrist

arthroplasty. The Journal of Arthroplasty 1(3):149–156.

18. Neu CP, Crisco JJ, Wolfe SW. 2001. In vivo kinematic behavior of the radio-

capitate joint during wrist flexion-extension and radio-ulnar deviation. J Biomech

34(11):1429–1438.

19. Rainbow MJ, Crisco JJ, Moore DC, Wolfe SW. 2008. Gender differences in

capitate kinematics are eliminated after accounting for variation in carpal size. J

Biomech Eng 130(4):041003.

101

20. Kaufmann R, Pfaeffle J, Blankenhorn B, et al. 2005. Kinematics of the midcarpal

and radiocarpal joints in radioulnar deviation: an in vitro study. J Hand Surg Am

30(5):937–942.

21. Kaufmann RA, Pfaeffle HJ, Blankenhorn BD, et al. 2006. Kinematics of the

midcarpal and radiocarpal joint in flexion and extension: an in vitro study. J Hand

Surg Am 31(7):1142–1148.

22. Li Z-M, Kuxhaus L, Fisk JA, Christophel TH. 2005. Coupling between wrist

flexion-extension and radial-ulnar deviation. Clin Biomech (Bristol, Avon)

20(2):177–183.

23. Akhbari B, Morton AM, Moore DC, et al. 2019. Accuracy of biplane

videoradiography for quantifying dynamic wrist kinematics. Journal of

Biomechanics 92:120–125.

24. Miranda DL, Rainbow MJ, Crisco JJ, Fleming BC. 2013. Kinematic differences

between optical motion capture and biplanar videoradiography during a jump-cut

maneuver. J Biomech 46(3):567–573.

25. Kessler SE, Rainbow MJ, Lichtwark GA, et al. 2019. A Direct Comparison of

Biplanar Videoradiography and Optical Motion Capture for Foot and Ankle

Kinematics. Front. Bioeng. Biotechnol. 7 [cited 2019 Oct 13] Available from:

https://www.frontiersin.org/articles/10.3389/fbioe.2019.00199/full.

26. Anderst W, Zauel R, Bishop J, et al. 2009. Validation of Three-Dimensional

Model-Based Tibio-Femoral Tracking During Running. Med Eng Phys 31(1):10–

16.

27. Martin DE, Greco NJ, Klatt BA, et al. 2011. Model-Based Tracking of the Hip:

Implications for Novel Analyses of Hip Pathology. The Journal of Arthroplasty

26(1):88–97.

28. Miranda DL, Schwartz JB, Loomis AC, et al. 2011. Static and Dynamic Error of a

Biplanar Videoradiography System Using Marker-Based and Markerless

Tracking Techniques. Journal of Biomechanical Engineering 133(12):121002.

29. Knörlein BJ, Baier DB, Gatesy SM, et al. 2016. Validation of XMALab software

for marker-based XROMM. Journal of Experimental Biology 219(23):3701–

3711.

30. Broga D. 2009. Ionizing Radiation Exposure of the Population of the United

States. Medical Physics 36(11):5375–5375.

31. Moritomo H, Apergis EP, Garcia-Elias M, et al. 2014. International Federation of

Societies for Surgery of the Hand 2013 Committee’s report on wrist dart-throwing

motion. J Hand Surg Am 39(7):1433–1439.

32. Crisco JJ, Coburn JC, Moore DC, et al. 2005. In vivo radiocarpal kinematics and

the dart thrower’s motion. J Bone Joint Surg Am 87(12):2729–2740.

102

33. Crisco JJ, Heard WMR, Rich RR, et al. 2011. The mechanical axes of the wrist

are oriented obliquely to the anatomical axes. J Bone Joint Surg Am 93(2):169–

177.

34. Goto A, Moritomo H, Murase T, et al. 2005. In vivo three-dimensional wrist

motion analysis using magnetic resonance imaging and volume-based

registration. J. Orthop. Res. 23(4):750–756.

35. Akhbari B, Morton AM, Moore DC, et al. 2019. Kinematic Accuracy in Tracking

Total Wrist Arthroplasty With Biplane Videoradiography Using a Computed

Tomography-Generated Model. Journal of Biomechanical Engineering

141(4):044503.

36. Glassner AS. 1989. An Introduction to Ray Tracing, 1st ed. Morgan Kaufmann.

368 p.

37. Kennedy J, Eberhart R. 1995. Particle swarm optimization.

38. Akhbari B, Moore DC, Laidlaw DH, et al. 2019. Predicting Carpal Bone

Kinematics Using an Expanded Digital Database of Wrist Carpal Bone Anatomy

and Kinematics. Journal of Orthopaedic Research [cited 2019 Aug 23] Available

from: https://onlinelibrary.wiley.com/doi/abs/10.1002/jor.24435.

39. Van Haver A, Mahieu P, Claessens T, et al. 2014. A statistical shape model of

trochlear dysplasia of the knee. The Knee 21(2):518–523.

40. Morton AM, Akhbari B, Moore DC, Crisco JJ. 2019. Osteophyte Volume

Calculation Using Dissimilarity-Excluding Procrustes Registration of Archived

Bone Models from Healthy Volunteers. J. Orthop. Res. .

41. Patterson RM, Nicodemus CL, Viegas SF, et al. 1998. High-speed, three-

dimensional kinematic analysis of the normal wrist. J Hand Surg [Am] 23:446–

53.

42. Panjabi MM, Krag MH, Goel VK. 1981. A technique for measurement and

description of three-dimensional six degree-of-freedom motion of a body joint

with an application to the human spine. J Biomech 14(7):447–460.

43. Crisco JJ, Patel T, Halilaj E, Moore DC. 2015. The Envelope of Physiological

Motion of the First Carpometacarpal Joint. J Biomech Eng 137(10):101002.

44. Coburn JC, Upal MA, Crisco JJ. 2007. Coordinate systems for the carpal bones of

the wrist. J Biomech 40(1):203–209.

45. Crisco JJ, McGovern RD. 1998. Efficient calculation of mass moments of inertia

for segmented homogeneous three-dimensional objects. J Biomech 31(1):97–101.

46. Qingde Li, Griffiths JG. 2004. Least squares ellipsoid specific fitting. In:

Geometric Modeling and Processing, 2004. Proceedings. p 335–340.

47. Crisco JJ, Coburn JC, Moore DC, Upal MA. 2005. Carpal bone size and scaling

in men versus in women. J Hand Surg Am 30(1):35–42.

103

48. Bajuri MN, Abdul Kadir MR, Murali MR, Kamarul T. 2013. Biomechanical

analysis of the wrist arthroplasty in rheumatoid arthritis: a finite element analysis.

Med Biol Eng Comput 51(1–2):175–186.

49. Schmidt I. 2019. Functional Outcomes After Salvage Procedures for Wrist

Trauma and Arthritis (Four-corner fusion, Proximal row Carpectomy, Total wrist

arthroplasty, Total wrist fusion, Wrist Denervation): Review of Literature. Open

Orthop J 13:217–231.

50. Singh HP, Bhattacharjee D, Dias JJ, Trail I. 2017. Dynamic assessment of the

wrist after total wrist arthroplasty. J Hand Surg Eur Vol :1753193417690472.

51. McCullough M BA, Adams BD, Grosland NM. 2012. Postoperative analysis of

patients who received the Universal 2 total wrist implant system. J Appl Biomech

28(4):466–472.

52. Callaghan JJ, O’Rourke MR, Saleh KJ. 2004. Why knees fail: Lessons learned1

1Benefits or funds were received in partial or total support of the research

material described in this article from DePuy, Warsaw, IN and Zimmer, Warsaw,

IN. The Journal of Arthroplasty 19(4, Supplement 1):31–34.

53. Harman MK, Banks SA, Kirschner S, Lützner J. 2012. Prosthesis alignment

affects axial rotation motion after total knee replacement: a prospective in vivo

study combining computed tomography and fluoroscopic evaluations. BMC

Musculoskelet Disord 13:206.

54. Bjarnason JA, Reikeras O. 2015. Changes of center of rotation and femoral offset

in total hip arthroplasty. Ann Transl Med 3(22) [cited 2019 Aug 13] Available

from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4701526/.

55. Grosland NM, Rogge RD, Adams BD. 2004. Influence of articular geometry on

prosthetic wrist stability. Clin. Orthop. Relat. Res. (421):134–142.

56. McBeath R, Osterman AL. 2012. Total wrist arthroplasty. Hand Clin 28(4):595–

609.

57. Rainbow MJ, Wolff AL, Crisco JJ, Wolfe SW. 2016. Functional kinematics of the

wrist. J Hand Surg Eur Vol 41(1):7–21.

58. Kane PM, Vopat BG, Mansuripur PK, et al. 2017. Relative Contributions of the

Midcarpal and Radiocarpal Joints to Dart-Thrower’s Motion at the Wrist. J Hand

Surg Am .

59. Vance MC, Packer G, Tan D, et al. 2012. Midcarpal hemiarthroplasty for wrist

arthritis: rationale and early results. J Wrist Surg 1(1):61–68.

60. Reigstad O, Røkkum M. 2018. Wrist arthroplasty using prosthesis as an

alternative to arthrodesis: design, outcomes and future. J Hand Surg Eur Vol

43(7):689–699.

104

IN-VIVO WRIST MOTION IN

TOTAL WRIST ARTHROPLASTY VERSUS

HEALTHY WRIST

6.

Kalpit N Shah, Bardiya Akhbari, Amy M. Morton, Douglas C. Moore,

Arnold-Peter C. Weiss, Scott W. Wolfe, Joseph J. Crisco

Under Review for Journal of Hand Surgery

105

Abstract

Background: Total Wrist Arthroplasty (TWA) can provide pain relief while preserving

some wrist motion for patients with severe wrist pathology. In-vivo biomechanical studies

of TWA are lacking in literature, which may help further our understanding of

complications following TWA. The goal of this study is to compare the biomechanics of a

TWA and healthy, unaffected wrists during dynamic range-of-motion (ROM) tasks.

Methods: TWA patients and control subjects were recruited and were administered a

history and physical exam (including clinical measurement of the flexion-extension and

radial-ulnar deviation using a hand-held goniometer), and outcomes surveys. Biplanar

videoradiography was used to capture dynamic wrist motion.

Results: PRWHE and QuickDASH were statistically worse in TWA patients than controls,

PROMIS showed no difference. Controls demonstrated better motion during the ROM

tasks in all direction except radial deviation (p<0.05). There was no statistical difference

between the maximum motion seen in each principal axes of wrist motion expect for ulnar

deviation during circumduction; however, the area was larger for controls than TWA

patients. The principal axes of motion for the flexion-extension and circumduction were

not significantly different between the two groups, but it was for radial-ulnar deviation.

Conclusion: The TWA patients exhibited a reduced motion during ROM tasks when

compared to control subjects. The axis of motion during the circumduction, which could

be interpreted as the principal axis of motion was similar between the TWA patients and

the controls despite the design of the TWA being optimized for the orthogonal axis of

flexion-extension and radial-ulnar deviation.

106

Introduction

Total Wrist Arthroplasty (TWA) provides pain relief while preserving some wrist

motion in patients with severe wrist pathology.1–7 However, despite being first described

in 1890, the TWA does not enjoy the high survival rates seen by other joint replacement

implants.4,8,9 Though evolving TWA designs have improved over the past decade2 and

these implants are starting to become a reliable option for patients with end-stage wrist

arthritis,1,4,6,7,10,11 high complication rates are still a major issue.6,12

While most outcomes studies report on the range-of-motion (ROM) achieved after

a TWA, the results are typically compared to preoperative values of the arthritic wrist,

which may be diminished due to intrinsic, extrinsic, or pain-related issues.1,3–7,10,11,13,14 It

is unknown if a current-generation TWA delivers similar ROM to a native, unaffected

wrist. In a systemic review of outcomes after TWA,15 Yeoh and Tourret compared the

ROM achieved by 7 different TWA designs to normative values established by an historic

article.16 Though many devices were close, only patients with the Maestro TWA achieved

functional ROM.

Studies of total joint replacements for the knee, shoulder, spine, and hip have shown

that kinematic differences between native and replaced joint motion can lead to abnormal

forces across the implants, leading to bone-implant interface failures.8,17–21 However, the

etiology for the higher complications rates following a TWA continue to be studied.22,23

There is paucity of literature on current TWA designs being subjected to rigorous in-vivo

kinematic studies to compare to native wrist joints. Accordingly, the goal of this study is

to compare the accurate in-vivo ROM of a TWA and asymptomatic, unaffected wrists

during dynamic ROM tasks using biplane videoradiography (BVR) techniques.

107

Methods

Patients and controls were enrolled into the study after approval for our institutional

review board. Inclusion criteria for the TWA patients included follow up >6 months, and

a history of non-rheumatoid osteoarthritis of the wrist. Inclusion criteria for the controls

included asymptomatic wrists. Exclusion criteria for TWA patients included any history of

connective tissue or bone disorders, and any complications with the TWA. Exclusion

criteria for the controls included wrist arthritis, history of surgical interventions for the

wrist and a history of connective tissue or bone disorders.

Six non-rheumatoid, osteoarthritic patients (74.7 ± 5.6 yrs, 2 females, 2 right wrists)

with the Freedom® TWA with >6 months follow up prior to the study (average 22 ± 12

months), and 10 control subjects (57.0 ± 5.2 yrs, 8 females, 9 right-hand dominant) without

any wrist pathology acted as controls. All study participants had a history and physical

exam performed (including clinical measurement of the flexion-extension and radial-ulnar

deviation using a hand-held goniometer), along with administration of outcomes surveys

(PRWHE, PROMIS Upper Extremity, QuickDASH)

A CT scan (Lightspeed® 16, GE Medical, Milwaukee, WI) of each wrist was

acquired to generate a three-dimensional model for motion analysis. BVR was used to

capture dynamic carpal and implant motion at 200 Hz rate (XROMM, Brown University,

Providence RI). The orientation between the image intensifiers was approximately 110°,

and the source-to-image distances for the X-ray sources were ~130 cm (Figure 6.1).

Using a previously described methodology, surface models were generated,

coordinate systems of the implants and bones were constructed, and replaced wrist

kinematics were calculated.22 Briefly, surface models of the carpal component of the wrist

108

implant, the 3rd metacarpal (MC3), and the distal

radius were generated in Mimics v19 software

(Materialise NV, Leuven, BE). Models of the

polyethylene cap and radial component were

constructed using a 3D scanner (0.1 mm

resolution, Artec Space Spider™, Artec 3D,

Luxembourg) and were superimposed on the carpal component and resected radius,

respectively. The third metacarpal and radius for the control group, and the carpal and

radial components for the TWA group were tracked in the biplane videoradiographs open-

source 2D-to-3D registration software (Autoscoper, Brown University).22,24 Wrist

kinematics was reported as the posture of MC3 with respect to the radius, relative to its

posture in neutral position. Neutral posture was defined as the wrist posture that had

minimal flexion-extension and radial-ulnar deviation in all captured postures.

TWA Patients and control subjects were asked to perform ROM tasks involving

wrist flexion-extension, radial-ulnar deviation, and circumduction. Each task was

performed for 2 seconds resulting in 6 seconds of total capture or 1,200 biplane radiographs

per subject (mean total effective dose of radiation to each subject was approximately 0.95

mSV). The detailed description of data acquisition parameters and guidelines for each task

have been reported in previous works.22 To evaluate the overall behavior of the joint, the

principal axes of motion were defined for both groups in the anatomical tasks. The principal

axis and area of the circumduction’s envelope was calculated by finding the best ellipse

fitted to the envelope using least squares criterion. The main axis of the flexion-extension

and radial-ulnar deviation tasks were computed using principal component analysis.

Figure 6.1. Experimental Setup.

109

Bland-Altman (bias and 95% limit of agreement) and correlation analysis were used

to assess the agreement of active ROM measured from BVR with ROM measured

clinically. An ordinary two-way ANOVA with Sidak’s multiple comparison test was

performed to compare the control subject’s clinical outcomes and ROM with TWA cohort

(adjusted p-value <0.05 as significant). Unpaired t-test was done to compare overall area

and orientation of the envelope of ROM during the circumduction task (p-value <0.05).

Results

TWA patients were older than control subjects (p=0.02). Patient-reported outcomes

differed between TWA patients and controls for PRWHE (0 vs 16.2 ± 20.9, p = 0.04) and

QuickDASH (0.7 ± 1.5 vs 23.9 ± 25.6, p <0.001) but not PROMIS (54.5 ± 3.2 vs 49.7 ±

10.5, p = 0.91) (Table 6.1). The ROM measured clinically, and the calculated ROM based

on BVR analysis demonstrated better ROM (Tables 6.2 and 6.3).

Table 6.1. Clinical Outcomes.

Controls TWA p-value

Mean ± SD Mean ± SD

Age (years) 57.0 ± 5.2 75.0 ± 5.9 0.02

Grip Strength (kg) 35.3 ± 15.6 24.1 ± 8.1 0.27

PRWHE 0.0 ± 0.0 16.2 ± 20.9 0.04

PROMIS 54.5 ± 3.2 49.7 ± 10.5 0.91

QuickDASH 0.7 ± 1.5 23.9 ± 25.6 0.0009

Table 6.2. Range of motion (ROM) comparison between controls and TWAs as measured on

clinical assessment using a hand-held goniometer.

Average ± SD % Average Reduction

in TWA Controls TWAs

Extension (°) 69.8 ± 8.0 41.7 ± 12.9 40.3

Flexion (°) 71.4 ± 7.2 27.7 ± 11.6 61.2

Overall Flexion-Extension (°) 141.1 ± 12.7 69.3 ± 18.3 50.9

Radial Deviation (°) 24.1 ± 8.4 17.3 ± 5.9 28.2

Ulnar Deviation (°) 39.3 ± 10.1 22.3 ± 9.5 43.1

Overall Radial-Ulnar Deviation (°) 63.4 ± 13.9 39.7 ± 9.0 37.4

110

Table 6.3. Range of motion (ROM) comparison between controls and TWAs as calculated using

biplane videoradiography.

Average ± SD % Average Reduction

in TWA Controls TWAs

Extension (°) -62.7 ± 5.6 -49.2 ± 8.4 21.6

Flexion (°) 64.7 ± 10.1 26.6 ± 12.6 58.9

Overall Flexion-Extension (°) 127.4 ± 11.3 75.8 ± 17.1 40.6

Radial Deviation (°) -23.3 ± 5.8 -16.8 ± 4.7 28.2

Ulnar Deviation (°) 38.5 ± 4.7 18.2 ± 10.4 52.8

Overall Radial-Ulnar Deviation (°) 61.9 ± 6.9 34.9 ± 6.5 43.6

Bland-Altman analysis comparing ROM as measured clinically with a hand-held

goniometer to ROM calculated using BVR analysis demonstrated a 95% limit of agreement

range of 10° or less for all measurements (Figure 6.2). The measurements calculated by

BVR were slightly lower than those measured clinically. ROM measurements for both

methods were also highly correlated (R2>0.45 and p<0.01).

Figure 6.2. Bland-Altman between the calculated range of motion by biplane videoradiography

and clinically measured active range-of-motion. Bias in blue, and %95 limit of agreement in red.

The difference in ROM as calculated by BVR analysis between the TWA patients

and control subjects for all ROM tasks shows the visual difference in the range achieved

by TWA patients and controls (Figure 6.3). The graph of the motion calculated by BVR

for TWA patients and control subjects during flexion-extension and radial-ulnar deviation

is showed in Figure 6.4.

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Figure 6.3. Histogram of Wrist and Replaced Wrist Motions.

Figure 6.4. Flexion-Extension and Radial-Ulnar Deviation Descriptive Analysis. Dotted lines

demonstrate the average, and dashed lines demonstrate the standard deviations.

The maximum motion achieved in each direction during circumduction as

measured through BVR analysis was not significantly different between TWA patients and

controls, except for ulnar deviation. (Table 6.4, Figure 6.5) However, the area of

circumduction was significantly lower for TWA patients than controls by 65% (2591.2 ±

826.6 vs 903.2 ± 529.3 deg2, p<0.001).

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Table 6.4. The envelope of circumduction.

Controls TWA % Average

Reduction Mean ± SD Mean ± SD

Extension in Circumduction (°) -43.6 ± 14.6 -32.5 ± 16.6 25.3

Flexion in Circumduction (°) 27.6 ± 18.5 13.8 ± 10.0 50.2

Radial Dev. in Circumduction (°) -20.4 ± 4.7 -15.4 ± 4.2 24.3

Ulnar Dev. in Circumduction (°) 30.7 ± 7.7 13.2 ± 8.6 57.0

Circumduction’s Area (degree2) 2591.2 ± 826.6 903.2 ± 529.3 65.1

Figure 6.5. Circumduction Descriptive Analysis. Dotted lines demonstrate the average, and

dashed lines demonstrate the standard deviations.

The principal axes of motion for the flexion-extension (-4.0 ± 9.3 vs. -7.8 ± 8.3,

p<0.44) and circumduction task (18.8 ± 9.8 vs. 13.0 ± 10.3, p>0.99) were not significantly

different between the controls and the TWA patients (Table 6.5). The axis of motion for

the radial-ulnar deviation was significantly different between the two groups (65.2 ± 8.1

vs. 48.2 ± 15.0, p=0.01). When comparing the principal axes of motion during the

circumduction task, which has been used in the past to describe the principal axis of motion

for the wrist, both the controls and the TWA patients were significantly more oblique than

the vertical axis (18.8±10.2 and 13.0±10.3, respectively; p<0.05 for both).

Table 6.5. Orientation of the principal axis for flexion-extension and radial-ulnar deviation tasks.

Controls TWA p-value

Mean ± SD Mean ± SD

Flexion-Extension Principal Axis (°) -4.0 ± 9.3 -7.8 ± 8.3 0.44

Radial-Ulnar Deviation Principal Axis (°) 65.2 ± 8.1 48.2 ± 15.0 0.01

Circumduction’s Orientation (°) 18.8 ± 9.8 13.0 ± 10.3 >0.99

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Discussion

We evaluated the ROM of a TWA and compared it to the ROM demonstrated by

controls with no clinical or radiographic evidence of wrist pathology. We found that all

TWA patients demonstrated a statistically lower ROM during simple uniplanar motion

except for radial deviation, during clinical evaluation of motion as measured with a

goniometer and also the calculated ROM using BVR. While the motion seen in each

direction during circumduction was not statistically different between the TWA patients

and controls, the area of the envelope of motion was significantly lower in TWA patients.

Finally, the principal axis for flexion-extension and circumduction tasks were not different

between the two groups but the radial-ulnar deviation axis was significantly “flatter” for

the TWA patients than the controls.

The TWA patients included in this study had a flexion-extension arc of 75.8° and

radial-ulnar deviation arc of 34.9°. This is similar to ROM reported in literature for newer

generation TWA implants. Matsui et al., reported on 20 patients with TWA in the setting

of rheumatoid arthritis with a flexion-extension arc of 60.8° 1.5 years after surgery and

48.2° at final follow up (mean 5.7 years).25 They did not report the radial-ulnar deviation

range that their patients demonstrated. Similarly, Ward et al., reported a flexion-extension

arc of 62° and radial-ulnar deviation arc of 25° at a mean of 14.5 months post-operatively.14

Froschauer et al., reported their experience with 39 non-rheumatoid TWA using the Re-

Motion total wrist system and found a flexion-extension arc of 75° and radial-ulnar

deviation arc of 45° in their cohort at a mean follow up of 7 years.26 Another recent study

reported outcomes after a fourth-generation TWA system, and a mean flexion-extension

arc of 66° at a mean follow up of 9 years.1 The authors did not report on other ROM

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parameters. Boeckstyns et al., reported on 65 TWA that were performed using the Re-

Motion system with 5-7 year follow up. They reported final flexion-extension of 60° and

radial-ulnar deviation arc of 28°.7 Interestingly, they separated out rheumatoid and non-

rheumatoid pts and reported a larger flexion-extension arc (53° vs 77°), as well as radial-

ulnar deviation arc (26° vs 35°) for the non-rheumatoid patients.

The ROM observed in the TWA patients, was significantly reduced in all directions

compared to controls by 28.2 to 61.2%. except for radial deviation. Hooke et al., performed

a cadaveric study with 6 specimen and measured the ROM possible in the native wrist and

then after implant a TWA by manually moving the wrist through the different tasks.27 They

did not find a significant difference between flexion, extension, or radial deviation tasks,

but did report that the TWA had a significantly reduced ulnar deviation than the native

wrist. However, it is unclear if the ROM during flexion, extension and radial deviation

obtained by the cadaveric specimen instrumented with a TWA can be translated to the same

degree in a patient with a TWA under voluntary muscle control.

We found that the ROM exhibited for TWA patients in radial deviation is not

significantly different than controls. It is possible that the difference seen between the two

groups did not achieve significance because of small size as even in asymptomatic, disease-

free wrists, subjects have significantly lower radial deviation than ulnar deviation. Ryu et

al., reported 17° of radial deviation compared to 40° of ulnar deviation in 40 control

subjects.28 This low value for radial deviation persists in TWA patients; Ward et al.,

reported radial deviation postoperatively to be an average of 8° (range: 0 - 35°).14

Additionally, Froschauer et al. reported radial deviation of 15° compared to 30° of ulnar

deviation in their series of TWA patients postoperatively. Boeckstyns et al., reported radial

115

deviation of 6° compared to 22° of ulnar deviation postoperatively in their TWA patients.

The latter two studies did not report on the radial deviation in disease-free wrists, but the

comparatively lower values seen for radial deviation seen in native and post-operative

wrists with TWA, along with our lower sample size may have contributed to the lack of

statistical significance between the radial deviation obtained by controls and TWA patients.

When asked to perform the circumduction task, the controls had a maximum value

for each component of the circular motion (flexion, extension, radial and ulnar deviation)

that was higher, but not statistically different than TWA patients. It can be postulated that

when performing the task, the subjects were not aiming to reach maximum wrist excursion

in each anatomic direction but rather perform the largest circumduction motion. We did

see a difference in the area of the graphed circumduction path, with the controls covering

a significantly larger area than TWA patients (2591.2 vs 903.2 deg2, p<0.001), a reduction

of 65%. Hooke et al., performed a circumduction tasks by manually manipulating their 6

cadaveric specimens before and after TWA implant placement.27 They mapped the arc of

motion for both flexion-extension and radial-ulnar deviation during the circumduction task

on the coronal and the sagittal planes. The authors did not find a significant difference in

the radius of curvature of the arc of motion. However, the radius of curvature of the arc of

motion in the two planes exhibited by their specimen does not capture the three-

dimensionality of the circumduction task.

Interestingly, the orientation of the axis of motion during circumduction did not

differ between the TWA patients and controls (18.8° vs.13.0°, p=0.3). The oblique axis of

motion is similar to the finding presented in the article by Crisco et al., where the authors

applied a 2Nm moment was applied to cadaveric wrists in 24 directions and studied the

116

moment-rotation behavior.29 They observed that the principal axis for the motion exhibited

by the wrists was 26.6°. Similarly, our study’s findings suggest that the wrist tries to

maintain an oblique axis of motion during the circumduction task, even after a TWA. The

principal axis seen in our 10 controls (18.8±10.2°) or 6 TWA patients (13.0±10.3°) was

not significantly different from the 6 cadavers (26.6±4.4°, p=0.1 and 0.0145, respectively)

studied in the article by Crisco et al.29 The latter finding is surprising given this and more-

recent TWAs are designed (via its ellipsoid articulation) to optimize motion along the

orthogonal anatomic axis of flexion-extension and radial-ulnar deviation. The mismatch

between its design and motion observed in vivo may lead to high stress in certain portions

of the implant, generate particulate wear of the polyethylene articulation and subsequent

resorption. It may potentially be the reason for the high reoperation rate, up to 46% at a

median of 3.6 years.12

There are several limitations to consider that may have affected the results of this

study. We had a relatively small sample size of 6 TWA patients and 10 control subjects.

Patients with rheumatoid arthritis have other soft tissue changes that may impact ROM7,30

and hence were excluded from the study, which limited the available patients for

recruitment and enrollment. While a larger sample size may have helped power the study

better, the statistical significances that we were able to establish for our analysis is

demonstrative of the need for further research on TWA patients. Another limitation to this

study is that we studied only a single TWA implant design, which was the only implant

used at our institution due to surgeon preference. It is possible that the ROM achieved by

TWA patients with other available implants may be different than what is achieved with

the Freedom® TWA. Finally, while we tried to instruct controls and TWA patients to only

117

use their wrist for the tasks required, it is possible that some of them had varying degrees

of motion at their shoulder and elbow joints, as these were supported but not fixed.

However, to eliminate all other motions when processing the motion, we mathematically

fixed the radius in space, and only evaluated the relative motion of the third metacarpal

bone (controls) and carpal component against the fixated radius.

Acknowledgments

Authors thank Erika Tavares for her help throughout data acquisition at XROMM facility

at Brown University. This study was funded by partial support from the National Institute

of Arthritis and Musculoskeletal and Skin Diseases under award number P30GM122732

(COBRE Bio-engineering Core), and a grant from the American Foundation for Surgery

of the Hand (AFSH).

References

1. Gil JA, Kamal RN, Cone E, Weiss A-PC. 2017. High Survivorship and Few Complications

With Cementless Total Wrist Arthroplasty at a Mean Followup of 9 Years. Clinical

Orthopaedics and Related Research® 475(12):3082–3087.

2. Srnec JJ, Wagner ER, Rizzo M. 2018. Total Wrist Arthroplasty. JBJS reviews 6(6):e9.

3. Sagerfors M, Gupta A, Brus O, Pettersson K. 2015. Total wrist arthroplasty: A single-

center study of 219 cases with 5-year follow-up. Journal of Hand Surgery 40(12):2380–

2387.

4. Reigstad O, Holm-Glad T, Bolstad B, et al. 2017. Five- to 10-Year Prospective Follow-Up

of Wrist Arthroplasty in 56 Nonrheumatoid Patients. The Journal of Hand Surgery

42(10):788–796.

5. Kennedy JW, Ross A, Wright J, et al. 2018. Universal 2 total wrist arthroplasty: high

satisfaction but high complication rates. Journal of Hand Surgery (European Volume)

43(4):375–379.

6. Fischer P, Sagerfors M, Jakobsson H, Pettersson K. 2020. Total Wrist Arthroplasty: A 10-

Year Follow-Up. Journal of Hand Surgery .

7. Boeckstyns MEH, Herzberg G, Merser S. 2013. Favorable results after total wrist

arthroplasty. Acta Orthopaedica 84(4):415–419.

8. Bayliss LE, Culliford D, Monk AP, et al. 2017. The effect of patient age at intervention on

risk of implant revision after total replacement of the hip or knee: a population-based cohort

study. The Lancet .

118

9. Evans JT, Evans JP, Walker RW, et al. 2019. How long does a hip replacement last? A

systematic review and meta-analysis of case series and national registry reports with more

than 15 years of follow-up. Lancet (London, England) .

10. Badge R, Kailash K, DIckson DR, et al. 2016. Medium-term outcomes of the Universal-2

total wrist arthroplasty in patients with rheumatoid arthritis. Bone and Joint Journal 98-

B(12):1642–1647.

11. Pfanner S, Munz G, Guidi G, Ceruso M. 2017. Universal 2 Wrist Arthroplasty in

Rheumatoid Arthritis. Journal of Wrist Surgery 06(03):206–215.

12. Pong TM, van Leeuwen WF, Oflazoglu K, et al. 2020. Unplanned Reoperation and Implant

Revision After Total Wrist Arthroplasty. Hand .

13. Brinkhorst M, Selles R, Dias J, et al. 2018. Results of the Universal 2 Prosthesis in

Noninflammatory Osteoarthritic Wrists. Journal of Wrist Surgery 07(02):121–126.

14. Ward CM, Kuhl T, Adams BD. 2011. Five to ten-year outcomes of the universal total wrist

arthroplasty in patients with rheumatoid arthritis. Journal of Bone and Joint Surgery -

Series A 93(10):914–919.

15. Yeoh D, Tourret L. 2015. Total wrist arthroplasty: A systematic review of the evidence

from the last 5 years. Journal of Hand Surgery: European Volume 40(5):458–468.

16. Palmer AK, Werner FW. 1984. Biomechanics of the distal radioulnar joint. Clinical

Orthopaedics and Related Research .

17. Damm P, Graichen F, Rohlmann A, et al. 2010. Total hip joint prosthesis for in vivo

measurement of forces and moments. Medical Engineering and Physics .

18. Galbusera F, Anasetti F, Bellini CM, et al. 2010. The influence of the axial, antero-

posterior and lateral positions of the center of rotation of a ball-and-socket disc prosthesis

on the cervical spine biomechanics. Clinical Biomechanics .

19. Mündermann A, Dyrby CO, D’Lima DD, et al. 2008. In vivo knee loading characteristics

during activities of daily living as measured by an instrumented total knee replacement.

Journal of Orthopaedic Research .

20. D’Lima DD, Patil S, Steklov N, et al. 2007. In vivo knee moments and shear after total

knee arthroplasty. Journal of Biomechanics .

21. Franta AK, Lenters TR, Mounce D, et al. 2007. The complex characteristics of 282

unsatisfactory shoulder arthroplasties. Journal of Shoulder and Elbow Surgery .

22. Akhbari B, Morton AM, Shah KN, et al. 2020. Proximal‐Distal Shift of the Center of

Rotation in a Total Wrist Arthroplasty is More Than Twice of the Healthy Wrist. Journal

of Orthopaedic Research .

23. Akhbari B, Morton AM, Moore DC, et al. 2019. Kinematic accuracy in tracking total wrist

arthroplasty with biplane videoradiography using a computed tomography-generated

model. Journal of Biomechanical Engineering .

24. Akhbari B, Morton AM, Moore DC, et al. 2019. Accuracy of biplane videoradiography for

quantifying dynamic wrist kinematics. J Biomech 92:120–125.

25. Matsui Y, Minami A, Kondo M, et al. 2020. A Minimum 5-Year Longitudinal Study of a

New Total Wrist Arthroplasty in Patients With Rheumatoid Arthritis. Journal of Hand

Surgery .

119

26. Froschauer SM, Zaussinger M, Hager D, et al. 2019. Re-motion total wrist arthroplasty: 39

non-rheumatoid cases with a mean follow-up of 7 years. Journal of Hand Surgery:

European Volume .

27. Hooke A, Pettersson K, Sagerfors M, et al. 2015. An Anatomic and Kinematic Analysis of

a New Total Wrist Arthroplasty Design. Journal of Wrist Surgery .

28. Ryu J, Cooney WP, Askew LJ, et al. 1991. Functional ranges of motion of the wrist joint.

Journal of Hand Surgery 16(3):409–419.

29. Crisco JJ, Heard WMR, Rich RR, et al. 2011. The mechanical axes of the wrist are oriented

obliquely to the anatomical axes. Journal of Bone and Joint Surgery - Series A .

30. Blazar PE, Gancarczyk SM, Simmons BP. 2019. Rheumatoid Hand and Wrist Surgery:

Soft Tissue Principles and Management of Digital Pathology. Journal of the American

Academy of Orthopaedic Surgeons 27(21):785–793.

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TOTAL WRIST

ARTHROPLASTY ALIGNMENT AND ITS

POTENTIAL ASSOCIATION WITH OUTCOMES

7.

Bardiya Akhbari, Kalpit N. Shah, Amy M. Morton, Janine Molino, Douglas

C. Moore, Scott W. Wolfe, Arnold-Peter C. Weiss, Joseph J. Crisco.

Journal of Wrist Surgery, 2021

https://doi.org/10.1055/s-0041-1725172

121

Abstract (300 Words)

Purpose: There is a lack of quantitative research that describes the alignment and, more

importantly, the effects of malalignment on total wrist arthroplasty (TWA). The main goal

of this pilot study was to assess the alignment of TWA components in radiographic images

and compare them with measures computed by three-dimensional analysis. Using these

measures, we then determined if malalignment is associated with range of motion (ROM)

or clinical outcomes (PRWHE, PROMIS, QuickDash, and grip strength).

Methods: Six osteoarthritic patients with a single type of TWA were recruited.

Radiographic images, computed-tomography images, and clinical outcomes of the wrists

were recorded. Using posteroanterior and lateral radiographs, alignment measurements

were defined for the radial and carpal components. Radiographic measurements were

validated with models reconstructed from computed-tomography images using Bland-

Altman analysis. Biplanar videoradiography (<1mm and <1° accuracy) was used to capture

and compute ROM of the TWA components. Linear regression assessed the associations

between alignment and outcomes.

Results: Radiographic measures had a 95% limit-of-agreement (mean

difference±1.96×SD) of 3° and 3mm with three-dimensional values, except for the

measures of the carpal component in the lateral view. In our small cohort, wrist flexion-

extension and radial-ulnar deviation were correlated with volar-dorsal tilt and volar-dorsal

offset of the radial component and demonstrated a ROM increase of 3.7° and 1.6° per

degree increase in volar tilt, and 10.8° and 4.2° per every millimeter increase in volar offset.

The carpal component’s higher volar tilt was also associated with improvements in patient-

reported pain.

Conclusions: We determined metrics describing the alignment of TWA, and found the

volar tilt and volar offset of the radial component could potentially influence the replaced

wrist’s ROM.

Clinical Relevance: The components’ alignment can be measured reliably in radiographs,

and it might be critical for better clinical outcomes. Future studies must evaluate its role in

a larger cohort.

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Introduction

There is a lack of quantitative research that describes alignment and its potential influence

on the functional and clinical outcomes after total wrist arthroplasty (TWA). The optimal

alignment of a TWA implant is not defined in the literature, and there is no consensus on

the ideal methodology to radiologically assess this alignment.1,2 In previous works, one

study focused on the surgeon’s ability to align the implants during the surgery,1 while

another defined the alignment only for a single prosthesis that is no longer commercially

available.2 The current generation of TWA designs,3–6 which have evolved to improve

implant stability, feature either a toroidal or ellipsoidal articular surface, and two screws

and a central peg for fixation of the carpal component.7–9 Current surgical guides

recommend alignment of the radial component’s stem with the longitudinal axis of the

radius and alignment of the peg of the carpal component with the third metacarpal (MC3)

diaphysis to achieve the ideal congruency between the articular surfaces. However, there

is no available science on the consequences of differences in the implant’s alignment.

The aim of this in-vivo pilot study was to define the alignment of TWA components

in radiographic images and compare them with accurate measurements from three-

dimensional (3D) computed-tomography (CT) models. Then, we used these alignment

measures to determine if the component alignments influence the active wrist ROM,

patient-reported outcomes, or grip strength in a small cohort of patients.

Materials and Methods

Study Subjects

Six patients with the same total wrist implant design (Freedom® size 2, Integra

LifeSciences, Plainsboro, NJ) were recruited into the study after institutional review board

123

approval. All subjects were non-rheumatoid patients, and none had a prior radius fracture

or malunion. All surgeries were performed by a single fellowship-trained expert10 hand

surgeon. At the time of enrollment (6 to 34 months post-operatively), the radiographs were

assessed to assure the absence of any loosening, osteolysis, or subluxation. To assess pain

and disability of the wrist, Patient-Rated Wrist-Hand Evaluation (PRWHE),11 Patient-

Reported Outcomes Measurement Information System (PROMIS Bank v1.2, Upper

Extremity),12 and Quick Disabilities of the Arm, Shoulder, and Hand (QuickDASH)13 were

administered, and grip strength (Jamar Hand Dynamometer, Jackson, MI) was measured

at the time of enrollment. Wrist ROM, our primary outcome, was computed directly from

biplane videoradiography (BVR), described in detail below.

2D Alignment from Radiographs

Standard14 posteroanterior (PA) and lateral wrist radiographs were obtained at the time of

enrollment. An open-source image analysis program, Fiji,15 was used to measure the

alignment of the TWA components in each radiographic view. The alignment of the radial

component was measured on PA (radial/ulnar tilt) and lateral (volar/dorsal tilt) radiographs

as the angle between the longitudinal axis of the radial shaft and the stem of the radial

component (Figure 7.1. Indicated by RRU and RVD, respectively). Radial tilt in the

coronal plane and volar tilt in the sagittal plane was defined as positive. Radial component

offset was defined as the shortest distance from the longitudinal axis of the radial shaft to

the stem’s location on the radial tray (Figure 7.1. Indicated by arrows in the direction of

radius to radial component). Carpal component tilt in the coronal and sagittal planes was

defined as the angle between the MC3 diaphysis and the carpal component’s peg. The

carpal component’s translational offset was measured on the PA (radial/ulnar offset) and

124

lateral (volar/dorsal offset) as the shortest distance from the MC3 diaphysis to the peg’s

location on the distal aspect of the carpal component’s tray (directed from MC3 to carpal

component). Alignment measures of left hands were mirrored for post-processing.

Figure 7.1. Posteroanterior view (PA, left panel) and lateral view (right panel) of the right hand of

a subject with total wrist arthroplasty. Blue lines show the reference lines of the radial (R) and

carpal components (C) and red lines show the reference lines of the third metacarpal and radius.

For each component, radial tilt (+RU) and offset (perpendicular black arrows) were defined in PA

view, and volar tilt (+VD) and offset (perpendicular black arrows) were defined in lateral view. In

this figure, radial and carpal components are tilted radially and dorsally.

3D Alignment from CT Images

CT volume images (80 kVp/80 mA, 0.39mm×0.39mm×0.625mm; Lightspeed® 16, GE

Medical, WI) of each wrist were acquired and segmented to obtain 3D models of the carpal

component, second metacarpal (MC2), MC3, fourth metacarpal (MC4), and resected radius

using a previously reported threshold-based approach in Mimics® (Materialise,

Belgium).16,17 The 3D model of radial component was generated using a 3D scanner with

0.1 mm resolution (Artec Spider™, Luxembourg). A pre-surgery model of the radius was

125

constructed to define alignment measures and analyze

kinematics (more details in Appendix).18

To define the alignments and describe the wrist

motion, coordinate systems (CSs) were constructed for

each TWA component, radius, and MC3 using previously

described methodologies (more details in Appendix). The

radial and carpal component CSs were based on their

geometrical features (Figure 7.2A-B), and the radius CS

was defined using its anatomical features (Figure 7.2C).19

The MC3 CS was defined using both MC2 and MC4

(Figure 7.2D).20

The 3D alignment measurements were defined computationally and automatically

based on the relative alignment of the TWA components to the bone coordinate systems.

The relative orientations of the individual implant components to their respective bones

were calculated using the scalar product of the x-axes and y-axes for radial and volar tilt,

respectively. For example,

Implant Radial Tilt = cos−1( Implantx−axis ∙ Bonex−axis)

The translational offsets were measured as the distance between the location of the CS of

the components and the bones in all directions. These descriptions correspond to the

metrics in the plain film-measured alignments.

Clinical Outcomes

PRWHE, PROMIS and QuickDASH total scores were calculated according to their

published guidelines.11–13 Grip strengths were normalized to account for age, sex, and

Figure 7.2. The orthogonal

coordinate systems for the (A)

radial component, (B) carpal

component, (C) resected

radius, and (D) the third

metacarpal are shown as red

(x-axis), green (y-axis), and

blue (z-axis).

126

handedness (Appendix, Section 4) before processing, based on the data provided in the

device’s guidelines.

TWA Kinematics and Range-of-Motion (Biplane Videoradiography)

Dynamic implant motion was calculated using a previously-described BVR system16

(imaging parameters: 75 kV/80 mA, 200Hz, 500µs shutter speed). BVR combines implant-

specific image volumes with movement data from videoradiographs to produce kinematics

of the replaced joint with submillimeter and subdegree accuracy. Each study participant

performed three active anatomical tasks of flexion-extension, radial-ulnar deviation, and

circumduction. Patients were instructed and trained to attempt their full range-of-motion

in each task. The implants were tracked using an open-source 2D-3D registration software

(Autoscoper) with methodology that has been described previously.17

The position and orientation of TWA components were transformed into the radius

and MC3 reference frames, and wrist motion was described as the motion of MC3 in the

radius CS, relative to the wrist neutral position. The neutral position was defined as the

position in which the MC3 CS had the least deviation from the radius CS, across all tasks.

The helical axis of motion (HAM) method was used to describe the wrist kinematics, and

ROM was computed as the maximum wrist rotation in each direction of flexion, extension,

radial deviation, and ulnar deviation among all tasks. Flexion-extension and radial-ulnar

deviation were calculated by projecting HAM rotations to the radius CS.

Statistical Analysis

Radiographic alignments were assessed three separate times by two raters, who were

blinded to the clinical outcomes. For each rater, intraclass correlation coefficient (ICC)

estimates and their 95% confidence intervals were calculated based on a single-rater,

127

absolute-agreement, 2-way mixed-effects model.21 The interrater agreement was assessed

using Pearson’s correlation coefficient (Pearson’s r). Bland-Altman plot was used to

evaluate the agreement of the radiographic measurements compared to the 3D model

alignment measurements by determining the bias (average differences between methods)

and 95% limit of agreement of the measurements (bias ± 1.96×standard deviation).22 Linear

regressions, with alpha set to 0.10 due to the small sample size, were used to evaluate the

association of component alignment, as measured on the 3D models, to the observed

clinical outcomes and ROM. With alpha set to 0.10, we had 60% to 85% power to detect

R2 of 0.55 to 0.76.

Results

Six osteoarthritic patients (75±6 yrs, 2 females, 2 right wrists) were enrolled, with reported

PRWHE, PROMIS, and QuickDASH scores of 16±21, 50±10, and 24±26, respectively

(Table 7.1). Overall, patients demonstrated 49.2±8.4° of extension, 26.6±12.6° of flexion,

16.8±4.7° of radial deviation, and 18.2±10.4° of ulnar deviation ROM as measured by

BVR. There were no significant associations between the follow-up time and any of the

ROMs (p>0.05).

Table 7.1. Clinical outcomes (pain scores and grip strength) and maximum range-of-motion capability of 6

non-rheumatoid patients with Freedom® wrist. A higher score for PROMIS demonstrates better outcomes

(maximum score is 56.4), while a lower score for PRWHE and QuickDASH depict a better outcome. See

Methods and supplementary materials for a description of grip strength normalization.

# Gender Age Follow-up

Time (m.)

Norm Grip

Strength PRWHE PROMIS QuickDASH

1 Male 69 16 -2.1 46.5 35.1 43.2

2 Female 74 34 0.1 0 56.4 2.3

3 Female 78 32 -0.8 38 37.3 59.1

4 Male 70 14 -1.0 0 56.4 0

5 Male 74 31 -0.9 12.5 56.4 36.4

6 Male 85 6 1.8 0 56.4 2.3

Average

(SD) -

75.0

(5.9)

22.1

(11.6)

-0.5

(1.3)

16.2

(20.9)

49.7

(10.5)

23.9

(25.6)

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Radiographic Measurements Validity

The plain radiographic measurements differed by less than 1° and 1mm (Table 7.2), and

had 95% limits of agreements within 3° and 3 mm of the 3D alignment measurements in

all except the sagittal alignment measurements of the carpal component (4.4° and -4.0mm

bias, respectively). For each rater, the intra-rater reliability of radiographic measurement

was highest for the radial component’s alignment measures in both PA and lateral

radiographic views (ICC>0.90). The carpal component’s alignment measures also had high

intra-rater reliability in the PA view (ICC>0.95); however, the intra-reliability was only

moderate for these measures in the lateral view (0.50<ICC<0.85). The inter-rater

agreement was high for both radial and carpal component measures (Pearson’s r > 0.85)

except for the carpal component’s offset measure in the lateral view (Pearson’s r = 0.49).

Table 7.2. The difference between radiographic and three-dimensional measurements

demonstrated submillimeter and subdegree biases (mean differences) except for the measures

calculated between the carpal component and third metacarpal.

Implant’s

Component

Alignment

Measurement

Bias of

Methods

95% Limits of

Agreement of Methods

Radial

Component

Volar/Dorsal Tilt 0.4° -3.1 — 3.9

Radial/Ulnar Tilt 0.6° -1.9 — 3.1

Volar/Dorsal Offset -0.6° -3.7 — 2.6

Radial/Ulnar Offset 0.9° -0.5 — 2.2

Carpal

Component

Volar/Dorsal Tilt 4.4 mm -3.8 — 12.7

Radial/Ulnar Tilt -0.9 mm -4.7 — 2.9

Volar/Dorsal Offset -4.0 mm -6.2 — -1.7

Radial/Ulnar Offset 0.7 mm -1.7 — 3.1

The component alignments with the bony anatomy varied largely in our cohort, with the

lowest component alignment variation (<2mm) in the volar-dorsal offset of the radial

component (Table 7.3). The radial component’s alignment ranged from 3.2° dorsal to 6.1°

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volar tilt, and from 2.8° ulnar to 20.0° radial tilt, while the carpal component ranged from

13.6° dorsal to 9.2° volar tilt, and from 2.9° ulnar to 12.0° radial tilt (Table 7.3). Within

the alignment measures, there was an association between increased volar tilt and increased

volar offset of the radial component (p<0.05, R2=0.93).

Table 7.3. Carpal component and radial component alignment defined from the 3D models for all

subjects as shown in Figure 3. Each component’s alignment is defined by angular parameters of

volar (+)/dorsal (-) tilt (VDT), radial (+)/ulnar (-) tilt (RUT), and translational offset parameters

of radial (+)/ulnar (-) offset (RUO) and volar (+)/dorsal (-) offset (VDO).

Subject #

Radial Component Alignment

VDT

(°)

RUT

(°)

RUO

(mm)

VDO

(mm)

VDT

(°)

RUT

(°)

RUO

(mm)

VDO

(mm)

1 -13.6 9.3 -5.3 11.6 -0.3 20.0 8.4 -3.2

2 1.7 12.0 -4.3 7.1 6.1 2.4 5.1 -1.4

3 -3.8 5.9 -6.4 5.5 1.0 -3.4 -1.8 -2.6

4 4.6 2.6 -8.5 6.3 -2.6 2.6 2.1 -4.3

5 9.2 -2.9 -2.5 2.2 -3.2 8.4 3.7 -4.7

6 4.6 6.7 -1.4 6.3 4.4 -2.8 0.1 -2.2

Average

(SD)

0.5

(8.1)

5.8

(4.7)

-5

(2.6)

6.5

(3.4)

0.9

(3.7)

4.5

(8.7)

4.2

(3.8)

-3.1

(1.3)

Radial Component Alignment

Comparing the component alignment to the clinical outcomes, increased flexion, radial

deviation, and ulnar deviation ROM correlated with increased volar tilt and volar offset of

the radial component. Greater volar tilt of the radial component was significantly

associated with increased flexion (p = 0.06, r = 0.55), radial deviation (p = 0. 002, r = 0.91),

and ulnar deviation (p = 0.02, r = 0.73). Larger volar offset of the radial component was

also associated with increases in these ROMs (p=0.05, 0.009, and 0.01, respectively). There

was no significant association between maximum extension ROM and volar tilt or offset

(p>0.3). There was also no significant association between radial component’s alignment

measurements and normalized grip strength, or patient reported outcomes (p>0.1).

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Total flexion-extension and radial-ulnar deviation ROM were also associated with

the volar tilt of the radial component and had 3.7° and 1.6° larger ROM per each degree

increase of volar tilt, respectively (Figure 7.3; R2 = 0.58 and 0.76). Similarly, total flexion-

extension and radial-ulnar deviation were associated with the volar-dorsal offset of the

radial component, with a ROM increase of 10.8° and 4.2° per millimeter rise of volar offset,

respectively (Figure 7.4; R2 = 0.55 and 0.57).

Figure 7.3. Overall flexion-extension and radial-ulnar deviation range of motion (ROM) increases

as the volar tilt of the radial component increases. Reconstructions from CT scan illustrate

alignments of indicated data points. An increase of 3.7° flexion-extension and 1.6° radial-ulnar

deviation with each degree increase of volar tilt.

Figure 7.4. Overall flexion-extension and radial-ulnar deviation range of motion (ROM) increases

as the volar offset of the radial component increases. An increase of 10.8° flexion-extension and

4.2° radial-ulnar deviation for every millimeter increase of volar offset was observed.

Carpal Component Alignment

Greater radial tilt of the carpal component was correlated with increased wrist flexion (p =

0.03, r = 0.67), but there was no correlation between the radial tilt of the carpal component

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and other ROM directions (p>0.10). Both PRWHE and PROMIS clinical scores were

associated with higher volar tilt of the carpal component at our follow-up time points

(p=0.04 and p=0.01). There was no correlation between the carpal component’s alignment

measurements and the QuickDash or normalized grip strength (p>0.10)

Discussion

In this study, we demonstrated that manual measurement of radiographic alignment of

TWA components on plain radiographs correlated well with computed 3D measurement

of alignment. These parameters were validated for only the Freedom® TWA design, but

we believe they are applicable to currently-approved TWA designs with similar design

features. We also identified a potential association between increased wrist ROM and

increased volar tilt and offset of the radial component, which demonstrates the alignment

parameters might influence the clinical outcomes for patients. Although our cohort was

small and we did not have access to pre-operative information to infer a broad case for

volar tilt of the implant, this potential association suggests there may be value in larger

cohort studies with more focus on the alignment measures.

Restoration of normal alignment during arthroplasty surgery has been demonstrated

to lead to increased success of hip,23 knee,24,25 and ankle arthroplasties;26 however, no

evidence-based alignment parameters exist for TWA. The optimal implant alignment

recommendations for hip and knee implants have evolved over time and have been

informed by rigorous biomechanical and clinical studies. TWA biomechanical

investigations are more difficult to perform due to fewer patients and the lack of established

methodologies to study the prosthesis in-vivo. In a cadaveric study, Ocampos et al.

investigated the alignment of the Re-Motion TWA design (Stryker, Kalamazoo, MI), and

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found inconsistency in the positioning of the prostheses and large variation in their

alignment.1 We also observed large variations in implant alignment, demonstrating the

need to define such parameters for TWA implant during the surgery. In addition, careful

attention to correct sizing of the implant and the quality of the bone in which the implant

is being placed may have an influence on implant alignment in the peri-operative period.

In this study, we addressed the lack of TWA alignment definition using an open-source

program, Fiji,15 to assess multiple alignment measurements and validated their robustness

and accuracy using a 3D modeling technique as a first step for further investigation on the

role of implant alignment on patient outcomes and motion. Finally, the high correlation of

volar tilt and volar offset of the radial component with each other is potentially due to the

initial placement of the broach in the volar half of the distal radius rather than the central

axis and impaction perpendicular to the natural volar tilt or the subtle shift of the impacted

implant once the distal tip starts to impinge against the opposite dorsal cortex forcing a

translation volarly of the proximal implant itself during seating.

Our limited dataset suggests an association between the sagittal alignment

parameters of the radial component and increased flexion, radial, and ulnar deviation. No

evidence of subluxation of the components throughout the ROM was observed; thus, the

alignment variations are possibly affecting the ROM by potentially changing the soft tissue

constraints or causing impingement. Similarly, although our observations of no significant

associations may be affected by our sample size, there was no association between wrist

extension and alignment parameters (p>0.10) possibly suggesting the role of constraints of

the soft-tissue envelope of the wrist (e.g., post-surgical scar or surgical bed changes) as the

limiting factor, in addition to the geometry of the implant. However, there is no objective

133

means to quantify those soft-tissue contributions. Additionally, although none of our

patients reported major pain or fear of moving their wrist, factors such as kinesiophobia

(i.e., limited ROM due to fear of dislocating the implant) might also affect the range of

extension in patients.

Although some earlier TWA designs accounted for the native volar tilt of the radius

as a design feature,27 the Freedom® implant’s radial component has a neutral 0° volar tilt

possibly to favor wrist extension. This built-in bias indeed favors wrist extension which is

confirmed by our findings of nearly twice as much extension than flexion. This study

suggests that the placement of an implant with the radial component tilted volarly may

increase overall ROM and favor increased flexion. This placement change could also be

used as a surrogate for a design feature that incorporates a native volar tilt of the radius.

However, its long-term outcomes have to be studied. The reasons for why patient-reported

outcomes improved with increased carpal component volar tilt can only be speculated, due

to our small sample size and may be related to both mobility and pain. While the impact of

malalignment of current TWA designs on implant survival rate remains unknown, a similar

investigation on the Trispherical TWA design has shown the association of TWA

alignment with functional clinical outcomes and durability.2 Finally, more volar tilt and

offset of the radial component might result in edge loading and possible polyethylene

particle wear after certain limits, thus it is important to study the articulation of the

components in larger cohorts and with longer follow-ups to resolve these issues.

In this study, we were limited by our small sample size and the use of one type of

total wrist implant. There was also a lack of preoperative or immediate post-operative

information for the ROM of our patients, which hampers the interpretation of our ROM

134

data. Despite this, we found a high correlation between alignment factors and ROM, which

demonstrates that further research on the relationship between TWA design and kinematics

is important. We restricted our enrollment criteria to patients with osteoarthritis, as patients

with inflammatory arthritis typically have soft-tissue involvement that could confound the

results of this study. Larger sample size may have helped power the study better and

allowed us to perform further analysis between different alignment parameters. Lastly, we

used standard PA and lateral views of the wrist to assess component alignment as

orthogonal radiographic views are important in order to enable retrospective research of

TWA designs and outcomes. A shortcoming of the lateral view is the inability to

consistently identify the MC3 contours because of bony overlap; consequently, our

correlation with computed 3D measurements in this view was less consistent. We continue

to investigate other radiographic methods to optimize visualization of the MC3.

Nonetheless, this pilot study demonstrates a convincing association between TWA

component alignment and wrist ROM and prompts additional kinematic studies to optimize

articular alignment parameters and improve patient outcomes and durability.

References

1. Ocampos M. Component alignment in total wrist arthroplasty: success rate of

surgeons in their first cases. Acta Orthop Traumatol Turc. 2014;48(3):259-261.

doi:10.3944/aott.2014.3017

2. Figgie HE, Inglis AE, Straub LR, Ranawat CS. A critical analysis of alignment

factors influencing functional results following trispherical total wrist arthroplasty. J

Arthroplasty. 1986;1(3):149-156. doi:10/b5mv4b

3. Badge R, Kailash K, Dickson DR, et al. Medium-term outcomes of the Universal-

2 total wrist arthroplasty in patients with rheumatoid arthritis. Bone Jt J. 2016;98-

B(12):1642-1647. doi:10.1302/0301-620X.98B12.37121

4. Gil JA, Kamal RN, Cone E, Weiss A-PC. High Survivorship and Few

Complications With Cementless Total Wrist Arthroplasty at a Mean Followup of 9 Years.

Clin Orthop Relat Res. 2017;475(12):3082-3087. doi:10.1007/s11999-017-5445-z

135

5. Herzberg G, Boeckstyns M, Sorensen AI, et al. “Remotion” total wrist arthroplasty:

preliminary results of a prospective international multicenter study of 215 cases. J Wrist

Surg. 2012;1(1):17-22. doi:10.1055/s-0032-1323642

6. Reigstad O, Røkkum M. Wrist arthroplasty: where do we stand today? A review of

historic and contemporary designs. Hand Surg Int J Devoted Hand Up Limb Surg Relat

Res J Asia-Pac Fed Soc Surg Hand. 2014;19(2):311-322.

doi:10.1142/S0218810414300034

7. Halim A, Weiss A-PC. Total Wrist Arthroplasty. J Hand Surg. 2017;42(3):198-209.

doi:10.1016/j.jhsa.2016.12.004

8. Kennedy CD, Huang JI. Prosthetic Design in Total Wrist Arthroplasty. Orthop Clin

North Am. 2016;47(1):207-218. doi:10.1016/j.ocl.2015.08.018

9. Hooke AW, Pettersson K, Sagerfors M, An K-N, Rizzo M. An anatomic and

kinematic analysis of a new total wrist arthroplasty design. J Wrist Surg. 2015;4(2):121-

127. doi:10.1055/s-0035-1549288

10. Tang JB, Giddins G. Why and how to report surgeons’ levels of expertise. J Hand

Surg Eur Vol. 2016;41(4):365-366. doi:10.1177/1753193416641590

11. Hoang-Kim A, Pegreffi F, Moroni A, Ladd A. Measuring wrist and hand function:

Common scales and checklists. Injury. 2011;42(3):253-258.

doi:10.1016/j.injury.2010.11.050

12. Brodke DJ, Saltzman CL, Brodke DS. PROMIS for Orthopaedic Outcomes

Measurement. J Am Acad Orthop Surg. 2016;24(11):744-749. doi:10.5435/JAAOS-D-15-

00404

13. Beaton DE, Wright JG, Katz JN, Upper Extremity Collaborative Group.

Development of the QuickDASH: comparison of three item-reduction approaches. J Bone

Joint Surg Am. 2005;87(5):1038-1046. doi:10.2106/JBJS.D.02060

14. Gilula LA, Mann FA, Dobyns JH, Yin Y. Wrist Terminology as Defined by the

International Wrist Investigators’ Workshop (IWIW). In: ; 2002. doi:10.2106/00004623-

200200001-00002

15. Schindelin J, Arganda-Carreras I, Frise E, et al. Fiji - an Open Source platform for

biological image analysis. Nat Methods. 2012;9(7). doi:10.1038/nmeth.2019

16. Akhbari B, Morton AM, Moore DC, Weiss A-PC, Wolfe SW, Crisco JJ. Accuracy

of biplane videoradiography for quantifying dynamic wrist kinematics. J Biomech.

2019;92:120-125. doi:10.1016/j.jbiomech.2019.05.040

17. Akhbari B, Morton AM, Moore DC, Weiss A-PC, Wolfe SW, Crisco JJ. Kinematic

Accuracy in Tracking Total Wrist Arthroplasty With Biplane Videoradiography Using a

Computed Tomography-Generated Model. J Biomech Eng. 2019;141(4):044503.

doi:10.1115/1.4042769

18. Akhbari B, Morton AM, Shah KN, et al. Proximal-Distal Shift of the Center of

Rotation in a Total Wrist Arthroplasty is More Than Twice of the Healthy Wrist. J Orthop

Res. Published online May 13, 2020. doi:10.1002/jor.24717

136

19. Akhbari B, Moore DC, Laidlaw DH, et al. Predicting carpal bone kinematics using

an expanded digital database of wrist carpal bone anatomy and kinematics. J Orthop Res

Off Publ Orthop Res Soc. Published online August 5, 2019. doi:10.1002/jor.24435

20. Coburn JC, Upal MA, Crisco JJ. Coordinate systems for the carpal bones of the

wrist. J Biomech. 2007;40(1):203-209. doi:10.1016/j.jbiomech.2005.11.015

21. Koo TK, Li MY. A Guideline of Selecting and Reporting Intraclass Correlation

Coefficients for Reliability Research. J Chiropr Med. 2016;15(2):155-163.

doi:10.1016/j.jcm.2016.02.012

22. Bland JM, Altman DG. Measuring agreement in method comparison studies. Stat

Methods Med Res. 1999;8(2):135-160.

23. Müller M, Duda G, Perka C, Tohtz S. The sagittal stem alignment and the stem

version clearly influence the impingement-free range of motion in total hip arthroplasty: a

computer model-based analysis. Int Orthop. 2016;40(3):473-480. doi:10.1007/s00264-

015-2845-0

24. Matsuda S, Kawahara S, Okazaki K, Tashiro Y, Iwamoto Y. Postoperative

Alignment and ROM Affect Patient Satisfaction After TKA. Clin Orthop.

2013;471(1):127-133. doi:10.1007/s11999-012-2533-y

25. Rivière C, Lazic S, Boughton O, Wiart Y, Vïllet L, Cobb J. Current concepts for

aligning knee implants: patient-specific or systematic? EFORT Open Rev. 2018;3(1):1-6.

doi:10.1302/2058-5241.3.170021

26. Greisberg J, Hansen ST, Digiovanni C. Alignment and technique in total ankle

arthroplasty. Oper Tech Orthop. 2004;14(1):21-30. doi:10.1053/j.oto.2003.11.002

27. Figgie MP, Ranawat CS, Inglis AE, Sobel M, Figgie HE. Trispherical total wrist

arthroplasty in rheumatoid arthritis. J Hand Surg. 1990;15(2):217-223. doi:10.1016/0363-

5023(90)90098-C

137

IN-VIVO ARTICULAR

CONTACT KINEMATICS OF A TOTAL WRIST

ARTHROPLASTY DEVICE

8.

Bardiya Akhbari, Amy M. Morton, Kalpit N. Shah, Douglas C. Moore,

Arnold-Peter C. Weiss, Scott W. Wolfe, Joseph J. Crisco

Under Review in Journal of Biomechanics

ABSTRACT

138

Total wrist arthroplasty (TWA) designs suffer from a relatively high complication rate

compared to other arthroplasties. Understanding the contact pattern of hip and knee

replacement has improved their design and function; however, the in-vivo contact pattern

of TWA has not been examined. Therefore, we studied the contact pattern of TWA

components. We hypothesized that the center of contact (CoC) is located at the geometric

center of the carpal component and radial component’s surface in neutral posture and that

it moves along the principal arcs of curvature throughout motion. The wrist motion of six

patients with the Freedom® total wrist implant was studied during various tasks using

biplanar videoradiography. The location of the CoC of the components was investigated

by calculating the distance fields. We found the CoC at the neutral pose was not at the

geometric center but was located 3.5mm radially on the carpal component and 1.2mm

ulnarly on the radial component. From extension to flexion, the CoC moved 10.8mm from

dorsal to volar side on the carpal component (p<0.0001) and 7.2mm from volar to dorsal

on the radial component (p=0.0009). From radial to ulnar deviation, the CoC moved

12.4mm from radial to ulnar on the carpal component (p<0.0001), and 5.6mm from ulnar

to radial on the radial component (p=0.009). The pattern of movement demonstrated a

potential for impingement around maximum flexion and extension. Future TWA designs

will benefit from these findings by targeting the elimination of the detected areas of

impingement.

139

Introduction

Identifying the articular contact of joint arthroplasty is critical for determining the

biomechanical factors that limit postoperative range-of-motion and for understanding

failure mechanisms and wear patterns of implant components (Gilbert et al., 2014; Li et

al., 2006; Steinbrück et al., 2013; Trepczynski et al., 2019). Improving implant designs to

reduce the failure and complication rate is important for total wrist arthroplasty (TWA)

designs, particularly given their stubbornly high complication rate (Berber et al., 2018;

Fischer et al., 2020; Halim and Weiss, 2017; Melamed et al., 2016; Yeoh and Tourret,

2015). Previously, investigations of hip replacements have shown the points of increased

wear (Hua et al., 2014; Kwon et al., 2012) and have led to design improvements that reduce

impingement by minimizing edge loading (Hua et al., 2016). Similarly, total knee

arthroplasty designs have been improved to mimic the contact patterns of a native knee

joint by allowing for the rollback of the distal femur on the tibial plateau (Steinbrück et al.,

2013).

TWA designs have empirically evolved to reduce complications such as loosening

and periprosthetic fracture that could occur because of the irregular motion in vivo (Berber

et al., 2018; Halim and Weiss, 2017; Kandemir et al., 2020). Abnormal interface loads,

high shear stress on the arthroplasty components, and bearing wear could result in

polyethylene particle debris and implant failure (Zhu et al., 2001). Understanding the

contact patterns, the centers of contact (CoC), and their relationship to wrist motion may

give us insight into potential points of stress and possible approaches for reducing abnormal

interface loads. Finite element models have shown that a toroidal design TWA has a more

uniform stress distribution and less contact pressure compared to a wrist affected by

140

rheumatoid arthritis (Bajuri et al., 2013) but high stress levels on the ulnar aspect of the

radial component possibly because of the geometrical configuration of the implant

(Gislason et al., 2017). Grosland et al. compared the toroidal and ellipsoidal TWA designs

and demonstrated that the ellipsoidal articulation was likely to achieve a higher stability

and more consistent contact area (Grosland et al., 2004). Although these finite element

models have led to a change in design from toroidal (Universal®, Integra LifeSciences) to

ellipsoidal (Freedom®, Integra LifeSciences) shape articulation, no one has yet studied the

actual contact pattern of a TWA design during dynamic in vivo motion.

The aim of this study was to compute the in vivo articular contact patterns and

identify the CoC of a specific TWA implant during various tasks. To do so, we used biplane

videoradiography (BVR), an imaging technique that provides direct visualization of bone

and implant motion. Based on the geometry of the components, we hypothesized that the

CoC would be located at the geometric center of the convex surface of the carpal

component and at the center of the concave surface of the radial component when the wrist

is in a neutral posture. We also hypothesized that the CoC would move along the principal

arcs of curvature of the carpal component and that it would remain seated and stationary at

the center of the concave surface on the radial component. Because the sensitivity of

calculating the CoC for TWA designs with model-based BVR is unknown, as a secondary

objective we evaluated the sensitivity of the CoC measurement.

Methods

Recruitment and Data Acquisition

Six non-rheumatoid patients (74.7 ± 5.6 yrs, 2F, 2R) with size 2 Freedom® TWA

implants (Integra LifeSciences, Plainsboro, NJ) provided informed written consent and

141

participated in this study after institutional review board approval. The standard size

polyethylene cap was used for 4 patients, while +2mm size (larger proximal-distal

thickness) was used for the other 2 patients for better restoration of carpal height. The

cohort studied herein was part of a larger project that compared the biomechanics of a

TWA to a healthy cohort from different aspects, such as range of motion, center of rotation,

and alignment (Akhbari et al., 2020).

A computed-tomography (CT) scan (Lightspeed® 16, GE Medical, Milwaukee, WI)

of each wrist was acquired at a resolution of 0.39mm×0.39mm×0.625mm. Biplane

videoradiography (BVR) was used to capture dynamic implant motion at 200 Hz with

acquisition specification of 75 kV/80 mA and 500µs shutter speed for both X-ray sources

(XROMM, Brown University). Each study participant performed 5 tasks involving active

wrist motion, including flexion-extension, radial-ulnar deviation, circumduction, simulated

hammering, and simulated pitcher pouring. Each task was performed for 2 seconds,

resulting in 10 seconds of total capture or 2,000 biplane radiographs per patient (mean total

effective dose of radiation to each patient was approximately 0.95 mSv). The angle

between the image intensifiers was ~110°, and the source-to-image distances for the X-ray

sources were ~130 cm. The accuracy of BVR in capturing the wrist motion is less than 0.7°

for rotations and less than 0.3 mm for translations (Akhbari et al., 2019b). A more detailed

description of the data acquisition parameters and tasks has been reported previously

(Akhbari et al., 2020).

Model Generation and Kinematics

Three-dimensional (3D) surface models, implant-based coordinate systems (CS),

and bone surface models were generated semi-automatically using a previously described

142

methodology (Akhbari et al., 2020). Briefly, surface models of the carpal component of the

wrist implant, the 3rd metacarpal (MC3), and the resected radius were generated using

Mimics v19 software (Materialise NV, Leuven, BE). Models of the polyethylene cap and

radial component of the TWA were generated using a 3D scanner (Artec Space Spider™,

Artec 3D, Luxembourg) and were superimposed on the carpal component and resected

radius, respectively. The resolution (i.e., the median of the edge lengths) of the

polyethylene cap and radial component surface models were 0.39 and 0.46 mm,

respectively. To reconstruct a pre-surgery model of the radius for visualization and

coordinate system construction, the contralateral radius was used for 3 patients, and best-

fit radii from a large database that included 120 intact radius bone models (Akhbari et al.,

2019a) were used for the other 3 patients.

Coordinate systems were constructed for both the carpal component and radial

component. The CS for the carpal component was placed at the center of the ellipse-shaped

surface of the polyethylene cap (corresponding to the distal surface of the titanium base)

with the positive y-axis directed radially and positive z-axis directed volarly (Figure 8.1).

The stem of the radial component was shape-registered using a cylinder in Geomagic Wrap

(3D Systems, Rock Hill, SC), and the longitudinal axis of the cylinder was used to define

the x-axis with positive directed proximally. The CS for the radial component was located

at the intersection of the x-axis and the distal articular surface, with positive y-axis directed

radially and positive z-axis directed volarly (Figure 8.1). The geometric center of the

concave surface of the radial component was 4.2 mm ulnar and 3.6 mm volar to the origin

of the radial component’s CS. Coordinate systems for the radius and the MC3 were also

constructed using standard anatomical landmarks (e.g., radius styloid, sigmoid notch) and

143

geometrical features for kinematics description with respect to the radius (Akhbari et al.,

2019a).

Figure 8.1. The coordinate system (CS) of the carpal component was constructed using the minor

and major axes of the ellipsoidal surface of the polyethylene cap and the carpal plate’s stem

central axis. The radial component’s CS was constructed using the minor and major axes of its

ellipsoidal surface and the central axis of the radial stem. The origins are shown with black

circles. The geometric center of the radial component was 4.2 mm ulnar and 3.6 mm volar to the

origin of the radial component’s coordinate system.

The implant components were tracked in the BVR in an open-source 2D-to-3D

registration software program (Autoscoper, Brown University) (Akhbari et al., 2021). The

global position and orientation of the carpal component and radial component were then

transformed to the MC3 and radius coordinate systems, respectively. Wrist kinematics

were reported as the posture of MC3 with respect to the radius, relative to its posture in

neutral position. Neutral posture was defined as the wrist posture that had minimal flexion-

extension and minimal radial-ulnar deviation, selected from all captured images. Helical

axes of motion were used to report wrist and implant rotations. Pure flexion-extension

(radial-ulnar deviation < 5% of the maximum range) and pure radial-ulnar deviation

(flexion-extension < 5% of the maximum range) were defined for further contact

processing. Pronation-supination (axial rotation of the carpal component relative to the

radial component) was minimal (0.1 ± 4.7°) throughout all acquired tasks.

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Contact Analysis

Contact between the carpal component and radial component were calculated using

the wrist kinematics and component-specific distance fields (Marai et al., 2004). Distance

fields were calculated for a given closed 3D surface model as a volumetric array of signed

distances from the surface (i.e., node-to-surface-face distance). Known affine

transformations of the array structure allowed rapid and accurate distance calculation of a

point cloud in proximity to the model surface. Tri-cubic interpolation in the distance field

was performed to yield sub-voxel accuracy. Using the distance fields, proximity values on

the surface of the polyethylene cap and radial component were calculated for each posture

(Figure 8.2). To obtain the contact patch between the components, these proximity values

were then adjusted to the resolution of the acquisition system. A distance exclusion

threshold (T) was used to determine the resolution, and its sensitivity was assessed

(described in the next section).

Figure 8.2. Surface-to-surface distances were calculated using the proximity value of each

component after its kinematic transformation was calculated from biplanar videoradiography.

Proximity values greater than 0.70 mm were excluded, and the remaining values were used to

calculate the center of contact (white circles).

The CoC was calculated as the weighted-average position of the contact patch on

each component. Each component’s distance field was weighted with (T – PV), where T

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was the optimal distance exclusion threshold and PV was the proximity value for each

triangular face of the component. The weighting factor was used to reduce the influence of

large proximity values in computing the CoC. Lastly, for consistency in evaluating the CoC

among all patients, and because the weighted center is not precisely on the surface mesh,

the weighted center was assigned to its corresponding closest point on the surface mesh.

Sensitivity Analysis

A Monte Carlo simulation that incorporated the accuracy of the BVR (0.7° and 0.3

mm) was used to determine the optimal T that achieves the optimal resolution. A priori,

0.41 mm (i.e., √0.32 + 0.22 + 0.22 = 0.41 mm based on translation accuracy of BVR) was

selected as the optimal resolution of the system. To find the optimal T, 10% of implant

positions (n = 1,142) were chosen randomly (Ip), and the CoC was calculated at threshold

values (T) of 0, 0.05, 0.10, …, 1.45, and 1.50 mm (CCTp). Then, the position and orientation

of the carpal component (Ip) was perturbed 1,000 times within the limits of the system

accuracy (< 0.7° and < 0.3 mm) in all 6 degrees of freedom (Ip,m). The relative distance

field for each Ip,m was computed, and using the threshold (T), the CoC was calculated

(CCTp,m). The Euclidean distances of all CCT

p,m from CCTp were then calculated (ET

p,m),

and for each threshold (T), the standard deviation of ETp,m was calculated (PT). The standard

deviation in calculating the CoC (PT) was then assessed with respect to T, and an

exponential decay equation:

𝑃𝑇 = 𝑎 ∗ 𝑒𝑏∗𝑇 + 𝑐 (Equation 8.1)

, where a, b, and c are coefficients, was fit to the points (Matlab 2018a, Mathworks, Natick,

MA). The model fitness was evaluated with adjusted R2 and root-mean-squared-error

(RMSE). The optimal T was selected when the model achieved 0.41 mm resolution. The

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CoC of each component was also compared to assure both centers represented the same

location.

Statistical Analysis

The location of the CoC at the neutral was calculated with its 95% confidence

interval (CI). To assess the relationship between the CoC location and the direction of

motion (see Appendix for the visualization), mixed models with a random intercept and

random slope were used (flexion-extension and radial-ulnar deviation) in SAS version 9.4

(SAS Institute Inc., Cary, NC). A separate model was run for each CoC location and

direction of motion. To assess the relative position of the CoC location with respect to the

component’s CS origin, intercept-only mixed models with a random intercept were used.

The maximum likelihood estimators of the models were adjusted for possible model

misspecification using classical sandwich estimators. Pseudo r-squared (R2) values were

calculated to assess model fit, and a p-value of 0.05 was used to determine statistical

significance.

Results

Our sensitivity analysis established 0.70 mm as the threshold to achieve the optimal

resolution of the BVR system and thus the lower limit of our CoC localization (Figure 8.3).

The exponential decay equations

𝑃𝑇𝐶𝑎𝑟𝑝𝑎𝑙 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 = 2.0𝑒−3.5𝑇 + 0.2

𝑃𝑇𝑅𝑎𝑑𝑖𝑎𝑙 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 = 1.5𝑒−3.1𝑇 + 0.2

had both R2 of 1.0 an RMSE of 0.02 and they perfectly captured the relationship between

T and the standard deviation in calculating the CoC, and determined a resolution of 0.63

and 0.70 mm for the carpal component and the radial component, respectively. Therefore,

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0.70 mm was selected as the optimal T. The distance between the CoC calculated on the

carpal component and on the radial component was less than 0.4 mm throughout all

captured motions.

Figure 8.3. Each wrist posture was randomly perturbed 1,000 times within the range of accuracy

of biplanar videoradiography (left panel), and the standard deviation of calculating the center of

contact was computed at threshold values of 0 to 1.5 mm in increments of 0.05 mm for the carpal

component (middle panel) and the radial component (right panel). An optimal threshold value of

0.70 mm was selected when the optimal resolution criteria of 0.41 mm (red dashed line) was met.

Across all patient tasks, the average maximum wrist flexion, extension, radial

deviation, and ulnar deviation were 43.3°, 60.8°, 23.1°, and 31.1°, respectively. At the wrist

neutral pose, the carpal component was oriented on average (95% CI) at 4.9° pronation

(2.4° to 7.4° pronation), 0.9° flexion (6.9° extension to 8.7° flexion), and 2.8° radial

deviation (11.9° radial deviation to 6.3° ulnar deviation) relative to the radial component.

At the neutral posture, the CoC was located 3.5 mm radially (2.7 to 4.4 mm) and 0.5 mm

dorsally (0.1 to 0.9 mm) from the carpal component’s geometric center. Similarly, the CoC

was located 1.4 mm ulnar (0.7 to 2.1 mm) and 0.6 mm dorsal (0.4 to 0.8 mm) from the

radial component’s geometric center.

Wrist motion from flexion to extension was significantly associated with volar-to-

dorsal movement of the CoC on the carpal component, shifting at a rate of approximately

1 mm per 10° (R2 = 0.97, p<0.0001), as well as dorsal-to-volar movement of the CoC on

the radial component, shifting at a rate of approximately 0.5 mm per 10° (R2 = 0.7, p<0.001)

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(Figure 8.4 and Figure 8.5). Throughout wrist flexion-extension, the average CoC on the

carpal component was located 3.4 mm radial to the geometric center of the surface of the

carpal components (p=0.04), and on the radial component the CoC was located 1.3 mm

ulnar to the geometric center of the surface of the radial component (p= 0.0006).

Figure 8.4. (A) The center of contact of the carpal component moved from dorsal to volar side

from full wrist extension (red color) to wrist flexion (blue color), (B) while it moved from volar

to dorsal side of the radial component throughout the same path.

Figure 8.5. The postures of the bones (third metacarpal, resected capitate, and resected radius)

and implant components (carpal component and its polyethylene cap, and radial component) at

(A) maximum wrist flexion and (B) extension. Potential impingement of the components at the

extreme extension can be seen in both the radiographic image and the three-dimensional models.

The white circles on the components are demonstrative of the center of contact.

149

From wrist full radial deviation to full ulnar deviation, the CoC on the carpal

component moved from a radial location to ulnar location at a rate of 3.1 mm per 10° (R2=

0.96, p< 0.001), while it moved from an ulnar location to a radial location on the radial

component, at a more modest rate of 1.4 mm per 10° (R2= 0.84, p= 0.009) (Figure 8.6 and

Figure 8.7).

Figure 8.6. (A) The center of contact of the carpal component moved from its radial side to its

ulnar side during wrist movement from radial deviation to ulnar deviation, (B) while it slightly

moved from the ulnar side toward its radial side on the radial component.

Figure 8.7. he three-dimensional models of bones and implant components at (A) maximum wrist

ulnar deviation and (B) radial deviation. Complete contact between components can be seen in

maximum ulnar deviation in both radiographs and three-dimensional models. The white circles

on the components are demonstrative of the center of contact.

150

The overall pattern of movement of the CoC in flexion-extension demonstrated an

articulation pattern that did not follow the principal curvatures of the ellipsoidal shape of

the polyethylene component (Figure 8.8). During circumduction, the CoC covered an area

of 34.2 ± 13.1 mm around the dorsal-radial side of the carpal component while it covered

an area of 21.9 ± 8.0 mm on the radial component (Figure 8.9).

Figure 8.8. Predicted and 95% confidence interval (CI) behavior of the centers of contact

movement throughout pure flexion-extension and radial-ulnar deviation was computed based on

mixed models. Flexion-extension range-of-motion is demonstrated from 60° flexion to 60°

extension in 20° steps, and radial-ulnar deviation range-of-motion is demonstrated at 0°, 10°, 15°,

and 20° in both radial and ulnar deviation.

Figure 8.9. Throughout circumduction for all 6 patients (right panel; color-coded based on

patients), the centers of contact on average moved around the dorsal-radial side of the carpal

component (top left panel) while the centers of contact moved slightly on the radial component

(bottom left panel). The average and standard deviation of movements are shown by the white

circles and white dashed-ellipses, respectively.

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Discussion

Our goal in this study was to identify the center of contact (CoC) for a single TWA

design during in vivo wrist motion. At the neutral posture, we observed the CoC was

located primarily on the radial side of the carpal component, and slightly ulnar and dorsal

on the radial component, demonstrating a potential abnormal contact pattern of the implant

in vivo. We also observed a dorsal-to-volar and radial-to-ulnar translation of the CoC on

the carpal component, and volar-to-dorsal and ulnar-to-radial translation of the CoC on the

radial component, as the wrist moved from full extension to flexion and from full radial

deviation to ulnar deviation, respectively. Lastly, the CoC shifted only moderately (less

than 10% of the articular surface area) on the radial component during circumduction,

while it circled around a large portion of the dorsoradial side of the carpal component

during the same motion.

Our findings are consistent with a previous finite element model (Grosland et al.,

2004), as we observed a less than 1.5 mm shift in the CoC, which is a mathematical

estimation of the center of pressure, on the carpal component within the first 15° of flexion-

extension. We also observed a radial position of the CoC on the carpal component while

Grosland et al. did not specify any radial positioning of the CoC. Another finite element

study determined higher stress rate on the ulnar and dorsal aspect of the radial component,

similar to our study that has shown the overall ulnar and dorsal location of the CoC on the

radial component during flexion-extension and radial-ulnar deviation (Gislason et al.,

2017).

Understanding the articulation pattern of the radial and carpal TWA components

can help identify possible impingement or zones of increased stress on the components at

152

different postures. Recent studies have shown that TWA allows for adequate wrist

functionality for activities of daily living and has a good patient satisfaction rate, but it has

much smaller ranges-of-motion compared to native wrists (Akhbari et al., 2020; Badge et

al., 2016; Kennedy et al., 2018; Singh et al., 2017). Both improved range-of-motion and

higher survivability of the implant could be affected if the impingement-free arc of motion

is maximized (Brown and Callaghan, 2008; Cho et al., 2013; Walker et al., 2011). Based

on our analysis of the in vivo flexion-extension motion, the CoC moves in opposite

directions on the radial and carpal components and it is most congruent at the radial side

of the carpal component. This opposing rotational and translational behavior might result

in impingement and restriction of range-of-motion at certain wrist postures (top right

radiographic image of Figure 5). Understanding the nature of the joint’s articulation could

also improve and validate future computational models.

While the wrist motion can be categorized to midcarpal and radiocarpal joint’s

motion (Craigen and Stanley, 1995; Rainbow et al., 2016), TWA implants simplify the

wrist joint by making a single radiocarpal articulation out of a two-joint “cardan”-type

articulation. Therefore, it is important to compare the TWA articulation to scaphoid-lunate

articulation on the radius. However, there is a lack of consensus on the movement pattern

of the CoC of the radiocarpal articulation. This could be attributed to the differences in

measurement methods and their accuracies. For example, while some investigators have

determined that the CoC of the scaphoid is located on the volar aspect of the radius overall

(Chambers et al., 2020; Short et al., 1997; Viegas et al., 1987), others have not found any

patterns in various wrist postures (Kobayashi et al., 2018). In a cadaveric study, Viegas et.

al found no significant movement of the scaphoid’s CoC on the radius in flexion but

153

observed dorsal translation in early extension and volar translation at the extreme extension

(Viegas et al., 1987). Some in vivo studies have determined that the scaphoid’s CoC is

either not moving or moving dorsally on the radius in flexion-extension (Rainbow et al.,

2013; Tang and Chen, 2012; Tang et al., 2009). They have demonstrated dorsal movement

of the CoC on both the scaphoid and lunate in both mid- and extreme extension (Tang and

Chen, 2012) and little movement of the CoC on the radius. During flexion, the CoC had a

volar/radial movement on the radius and volar movement on scaphoid (Rainbow et al.,

2013; Tang et al., 2009). Our findings for the CoC movement of the carpal component are

similar to what is reported for the scaphoid and lunate in the in vivo studies, but not for the

radial component when compared to the literature for the radius. These dissimilarities could

be due to soft tissue differences after joint replacement or the geometric differences

between the radial component and the distal radius.

Furthermore, current laboratory wear tests and computational models of TWA

simulate wrist motion with experimental simplifications (load and motion applied)

(Completo et al., 2017), which may be inaccurate (Gislason et al., 2016). Accurate and

detailed data describing contact patterns should aid investigators in validating

computational models and in the development and design of more realistic laboratory wear

testing protocols.

The main limitation of our study was the small cohort of 6 participants with a single

implant design of polyethylene articulation on metal. Satisfactory alignment of TWA

components according to the company recommendations cannot always be achieved

(Ocampos, 2014), and due to this small sample size, it is possible that the position of the

implants at the neutral posture may have affected the CoC and articulation patterns.

154

However, based on RMSE and R2 parameters calculated from our statistical analysis

(mixed models), which factors the CoC behavior for each patient separately, the

articulation of the components was not potentially affected by the malalignment. Finally,

although we evaluated the sensitivity of our contact analysis method within the limit of

accuracy of BVR, we did not validate our system using pressure sensors in cadaver models.

In this study, we computed the sensitivity of a BVR system in estimating the contact

pattern of TWA components, and we demonstrated the articulation patterns of these

components based on the direction of motion. Although we hypothesized that the center of

contact moves along the principal arcs of curvature, our assessment showed that the center

of contact is mostly located on the radial side of the convex surface of the carpal component

and the ulnar side of the concave surface of the radial component. Our findings may inform

future design considerations for TWA, help determine protocols for wear and stress testing

for TWA implants in the laboratory and contribute to the validation of computational

models.

Acknowledgements

The authors want to thank Erika Tavares for her help throughout biplanar videoradiography

data acquisition. This study was possible with support from the National Institutes of

Health P30-GM122732 (COBRE Bio-engineering Core) and a grant from the American

Foundation for Surgery of the Hand (AFSH).

References

Akhbari, B., Moore, D.C., Laidlaw, D.H., Weiss, A.C., Akelman, E., Wolfe, S.W., Crisco, J.J.,

2019a. Predicting Carpal Bone Kinematics Using an Expanded Digital Database of Wrist

Carpal Bone Anatomy and Kinematics. Journal of Orthopaedic Research.

https://doi.org/10.1002/jor.24435

155

Akhbari, B., Morton, A., Moore, D., Weiss, A.-P.C., Wolfe, S.W., Crisco, J.J., 2019b. Kinematic

Accuracy in Tracking Total Wrist Arthroplasty with Biplane Videoradiography using a

CT-generated Model. J Biomech Eng. https://doi.org/10.1115/1.4042769

Akhbari, B., Morton, A.M., Moore, D.C., Crisco, J.J., 2021. Biplanar Videoradiography to Study

the Wrist and Distal Radioulnar Joints. JoVE (Journal of Visualized Experiments) e62102.

https://doi.org/10.3791/62102

Akhbari, B., Morton, A.M., Shah, K.N., Molino, J., Moore, D.C., Weiss, A.-P.C., Wolfe, S.W.,

Crisco, J.J., 2020. Proximal-Distal Shift of the Center of Rotation in a Total Wrist

Arthroplasty is More Than Twice of the Healthy Wrist. J Orthop Res.

https://doi.org/10.1002/jor.24717

Badge, R., Kailash, K., Dickson, D.R., Mahalingam, S., Raza, A., Birch, A., Nuttall, D., Murali,

S.R., Hayton, M.J., Talwalkar, S., Watts, A.C., Trail, I.A., 2016. Medium-term outcomes

of the Universal-2 total wrist arthroplasty in patients with rheumatoid arthritis. Bone Joint

J 98-B, 1642–1647. https://doi.org/10.1302/0301-620X.98B12.37121

Bajuri, M.N., Abdul Kadir, M.R., Murali, M.R., Kamarul, T., 2013. Biomechanical analysis of the

wrist arthroplasty in rheumatoid arthritis: a finite element analysis. Med Biol Eng Comput

51, 175–186. https://doi.org/10.1007/s11517-012-0982-9

Berber, O., Garagnani, L., Gidwani, S., 2018. Systematic Review of Total Wrist Arthroplasty and

Arthrodesis in Wrist Arthritis. J Wrist Surg 7, 424–440. https://doi.org/10.1055/s-0038-

1646956

Brown, T.D., Callaghan, J.J., 2008. Impingement in Total Hip Replacement: Mechanisms and

Consequences. Curr Orthop 22, 376–391. https://doi.org/10.1016/j.cuor.2008.10.009

Chambers, S.B., Padmore, C.E., Grewal, R., Suh, N., 2020. The Impact of Scaphoid Malunion on

Radioscaphoid Joint Contact: A Computational Analysis. The Journal of Hand Surgery

S0363502320300563. https://doi.org/10.1016/j.jhsa.2020.01.009

Cho, S.H., Cho, H.L., Lee, S.H., Jin, H.K., 2013. Posterior femoral translation in medial pivot total

knee arthroplasty of posterior cruciate ligament retaining type. J Orthop 10, 74–78.

https://doi.org/10.1016/j.jor.2013.04.004

Completo, A., Pereira, J., Nascimento, A., Almeida, F., 2017. Strain shielding in distal radius after

wrist arthroplasty with a current generation implant: An in vitro analysis. Journal of

Biomechanics 52, 169–175. https://doi.org/10.1016/j.jbiomech.2016.12.011

Craigen, M.A., Stanley, J.K., 1995. Wrist kinematics. Row, column or both? J Hand Surg [Br] 20,

165–70.

Fischer, P., Sagerfors, M., Jakobsson, H., Pettersson, K., 2020. Total Wrist Arthroplasty: A 10-

Year Follow-Up. The Journal of Hand Surgery S0363502320300848.

https://doi.org/10.1016/j.jhsa.2020.02.006

Gilbert, S.L., Rana, A.J., Lipman, J.D., Wright, T.M., Westrich, G.H., 2014. Design changes

improve contact patterns and articular surface damage in total knee arthroplasty. The Knee

21, 1129–1134. https://doi.org/10.1016/j.knee.2014.07.022

Gislason, M.K., Foster, E., Bransby-Zachary, M., Nash, D.H., 2017. Biomechanical analysis of the

Universal 2 implant in total wrist arthroplasty: a finite element study. Comput Methods

Biomech Biomed Engin 20, 1113–1121. https://doi.org/10.1080/10255842.2017.1336548

156

Gislason, M.K., Foster, E., Main, D., Fusiek, G., Niewczas, P., Bransby-Zachary, M., Nash, D.H.,

2016. Mechanical testing and modelling of the Universal 2 implant. Med Eng Phys 38,

511–517. https://doi.org/10.1016/j.medengphy.2016.02.008

Grosland, N.M., Rogge, R.D., Adams, B.D., 2004. Influence of articular geometry on prosthetic

wrist stability. Clin. Orthop. Relat. Res. 134–142.

Halim, A., Weiss, A.-P.C., 2017. Total Wrist Arthroplasty. J Hand Surg Am 42, 198–209.

https://doi.org/10.1016/j.jhsa.2016.12.004

Hua, X., Li, J., Jin, Z., Fisher, J., 2016. The contact mechanics and occurrence of edge loading in

modular metal-on-polyethylene total hip replacement during daily activities. Medical

Engineering & Physics 38, 518–525. https://doi.org/10.1016/j.medengphy.2016.03.004

Hua, X., Li, J., Wang, L., Jin, Z., Wilcox, R., Fisher, J., 2014. Contact mechanics of modular metal-

on-polyethylene total hip replacement under adverse edge loading conditions. J Biomech

47, 3303–3309. https://doi.org/10.1016/j.jbiomech.2014.08.015

Kandemir, G., Smith, S., Schmidt, I., Joyce, T.J., 2020. Explant analysis of a MaestroTM wrist

prosthesis and calculation of its lubrication regime. Journal of the Mechanical Behavior of

Biomedical Materials 110, 103933. https://doi.org/10.1016/j.jmbbm.2020.103933

Kennedy, J.W., Ross, A., Wright, J., Martin, D.J., Bransby-Zachary, M., MacDonald, D.J., 2018.

Universal 2 total wrist arthroplasty: high satisfaction but high complication rates. J Hand

Surg Eur Vol 43, 375–379. https://doi.org/10.1177/1753193418761513

Kobayashi, K., Kazama, K., Sakamoto, M., 2018. In Vivo Assessment of Articular Contact at

Radiocarpal Joint during Dorsal/Palmar Flexion and Ulnar/Radial Deviation. Advanced

Experimental Mechanics 3, 215–220. https://doi.org/10.11395/aem.3.0_215

Kwon, Y.-M., Mellon, S.J., Monk, P., Murray, D.W., Gill, H.S., 2012. In vivo evaluation of edge-

loading in metal-on-metal hip resurfacing patients with pseudotumours. Bone Joint Res 1,

42–49. https://doi.org/10.1302/2046-3758.14.2000019

Li, G., Suggs, J., Hanson, G., Durbhakula, S., Johnson, T., Freiberg, A., 2006. Three-dimensional

tibiofemoral articular contact kinematics of a cruciate-retaining total knee arthroplasty. J

Bone Joint Surg Am 88, 395–402. https://doi.org/10.2106/JBJS.D.03028

Marai, G.E., Laidlaw, D.H., Demiralp, C., Andrews, S., Grimm, C.M., Crisco, J.J., 2004.

Estimating joint contact areas and ligament lengths from bone kinematics and surfaces.

IEEE Trans Biomed Eng 51, 790–799. https://doi.org/10.1109/TBME.2004.826606

Melamed, E., Marascalchi, B., Hinds, R.M., Rizzo, M., Capo, J.T., 2016. Trends in the Utilization

of Total Wrist Arthroplasty versus Wrist Fusion for Treatment of Advanced Wrist Arthritis.

J Wrist Surg 5, 211–216. https://doi.org/10.1055/s-0036-1571841

Ocampos, M., 2014. Component alignment in total wrist arthroplasty: success rate of surgeons in

their first cases. Acta Orthopaedica et Traumatologica Turcica 48, 259–261.

https://doi.org/10.3944/aott.2014.3017

Rainbow, M.J., Kamal, R.N., Leventhal, E., Akelman, E., Moore, D.C., Wolfe, S.W., Crisco, J.J.,

2013. In vivo kinematics of the scaphoid, lunate, capitate, and third metacarpal in extreme

wrist flexion and extension. J Hand Surg Am 38, 278–288.

https://doi.org/10.1016/j.jhsa.2012.10.035

Rainbow, M.J., Wolff, A.L., Crisco, J.J., Wolfe, S.W., 2016. Functional kinematics of the wrist. J

Hand Surg Eur Vol 41, 7–21. https://doi.org/10.1177/1753193415616939

157

Short, W.H., Werner, F.W., Fortino, M.D., Mann, K.A., 1997. Analysis of the kinematics of the

scaphoid and lunate in the intact wrist joint. Hand Clin 13, 93–108.

Singh, H.P., Bhattacharjee, D., Dias, J.J., Trail, I., 2017. Dynamic assessment of the wrist after

total wrist arthroplasty. J Hand Surg Eur Vol 1753193417690472.

https://doi.org/10.1177/1753193417690472

Steinbrück, A., Schröder, C., Woiczinski, M., Fottner, A., Müller, P.E., Jansson, V., 2013.

Patellofemoral contact patterns before and after total knee arthroplasty: an in vitro

measurement. Biomed Eng Online 12, 58. https://doi.org/10.1186/1475-925X-12-58

Tang, J.B., Chen, Y.R., 2012. In vivo changes in contact regions of the radiocarpal joint during

wrist hyperextension. J Hand Surg Am 37, 2257–2262.

https://doi.org/10.1016/j.jhsa.2012.08.030

Tang, P., Gauvin, J., Muriuki, M., Pfaeffle, J.H., Imbriglia, J.E., Goitz, R.J., 2009. Comparison of

the “contact biomechanics” of the intact and proximal row carpectomy wrist. J Hand Surg

Am 34, 660–670. https://doi.org/10.1016/j.jhsa.2008.12.004

Trepczynski, A., Kutzner, I., Schütz, P., Dymke, J., List, R., von Roth, P., Moewis, P., Bergmann,

G., Taylor, W.R., Duda, G.N., 2019. Tibio-Femoral Contact Force Distribution is Not the

Only Factor Governing Pivot Location after Total Knee Arthroplasty. Scientific Reports 9.

https://doi.org/10.1038/s41598-018-37189-z

Viegas, S.F., Tencer, A.F., Cantrell, J., Chang, M., Clegg, P., Hicks, C., O’Meara, C., Williamson,

J.B., 1987. Load transfer characteristics of the wrist. Part I. The normal joint. J Hand Surg

[Am] 12, 971–8.

Walker, M., Brooks, J., Willis, M., Frankle, M., 2011. How Reverse Shoulder Arthroplasty Works.

Clin Orthop Relat Res 469, 2440–2451. https://doi.org/10.1007/s11999-011-1892-0

Yeoh, D., Tourret, L., 2015. Total wrist arthroplasty: a systematic review of the evidence from the

last 5 years. J Hand Surg Eur Vol 40, 458–468. https://doi.org/10.1177/1753193414539796

Zhu, Y., Chiu, K., Tang, W., 2001. Review Article: Polyethylene Wear and Osteolysis in Total Hip

Arthroplasty. J Orthop Surg (Hong Kong) 9, 91–99.

https://doi.org/10.1177/230949900100900117

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CONCLUSION

Summary

This thesis work aimed to understand the in vivo biomechanics of total wrist arthroplasty

(TWA) and the healthy wrist to address the lack of previous comparison studies on TWA

and healthy wrist mechanics. In this dissertation, we first studied the motion of individual

carpal bones in the healthy wrist and evaluated their motion patterns. Then, we developed

methodologies for processing biplane videoradiography (BVR) data to study the healthy

and replaced wrists and assessed the system’s accuracy. Lastly, we studied the in vivo

biomechanics of healthy wrists and TWA during various anatomical and functional tasks

from 4 aspects: range of motion, center of rotation (COR), alignment, and contact pattern.

For the 1st aim, we first compiled a large database of 120 wrists and calculated the

wrist motion for 1095 postures and evaluated the detailed relationship between the carpal

bones. We computed the position of carpal bones after acquiring the computed-tomography

(CT) images of 120 subjects’ hands and created a mathematical model that uses wrist

motion to predict the motion of individual carpal bones. Our prediction confirmed the wrist

can be approximated as a 2 degrees-of-freedom system and the capitate bone can predict

the motion of other bones within a 5° limit. Our study, more importantly, demonstrated

that two distinct motion patterns exist for the bones of proximal and distal rows. For the

2nd aim, in a series of cadaveric experiments, we computed the submillimeter and

subdegree accuracy of a BVR system in studying the healthy wrist and TWA and

developed an open-source processing pipeline to aid researchers in using the same protocol

159

for other scientific purposes. Using these validation studies, we designed an in vivo

experiment to investigate the biomechanics of TWA and compare it to the healthy wrist

biomechanics. Studying the wrists of 6 patients with TWA and 10 wrists of healthy

volunteers, we calculated the range of motion and center of rotation of both cohorts,

defined metrics depicting the alignment of the components in both radiographs and CT

images, and determined their influence on clinical outcomes. We also evaluated the

articular contact pattern of the TWA components and determined how the contact pattern

changes in vivo. The presented work makes the following contributions to the

biomechanics literature:

Established the submillimeter and subdegree accuracy of biplanar videoradiography in

measuring the kinematics of the wrist joint and total wrist arthroplasty (TWA) [1, 2]

Reported a data-driven approach for designing a TWA that mimics the healthy wrist [3]

Demonstrated a total wrist replacement surgical strategy that can result in higher range-

of-motion and functionality for patients (higher volar tilt placement for the implant) [4]

Developed and validated an open-source software (simtk.org/projects/autoscoper) that

gives researchers the ability to study the biomechanics of bones/implants in a highly-

accurate biplane videoradiography system [5]

Published a large database of wrist anatomy and carpal kinematics on an NIH-funded

platform (simtk.org/projects/carpal-database) to provide medical students with an

educational visualization kit [6]

Developed a mathematical model to predict carpal bone motion from wrist motion to

provide physicians with a better understanding of wrist biomechanics [6]

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Determined that TWA patients demonstrate a smaller envelope of range of motion

(~65%) compared to healthy wrists but have an oblique functional axis similar to

healthy wrists [7]

Established that the center of rotation of the TWA design moves twice that of a wrist

joint [3]

Provided a continuous accurate representation of the center of rotation and axis of

rotation that can be helpful in designing future implants [3]

Defined reliable radiographic metrics to measure the alignment of the TWA

components [4]

Demonstrated the importance of the volar tilt of the radial component in affecting the

range of motion outcomes [4]

Determined that the center of contact location is on the radial side the carpal component

and the ulnar side of the radial component, resulting in non-uniform articulation [8]

Detected that the extreme flexion-extension regions are potential locations that might

cause impingement for the TWA components [8]

Clinical Significance

The results of this study demonstrate numerous opportunities for improving the current

TWA devices and designing biomechanically-driven novel arthroplasty devices. The

mismatch we reported between the kinematics of TWA and healthy wrists, the lack of

standards for alignment of the components, and the non-uniform articulation pattern of the

components could be reasons for the high complication rates of the implants. These

concerns and factors should be examined in detail for future devices, and these potential

concerns must be resolved before new devices are implanted in patients. The methodology

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developed and validated in this dissertation can, at least, be used in a research setting to

understand the dynamic in vivo behavior of wrists that are affected by pathologies (e.g.,

osteoarthritis or dorsal or volar intercalated segment instabilities), or to assess the

mechanics of other TWA designs. Additionally, using improved hardware and computing

resources, the methodology described herein can be translated to clinical settings as a tool

for diagnosis and prognosis of wrist joint pathologies or as a surgical guide for total wrist

replacement operations. Lastly, the results of this study and our in vivo data can be used to

drive robotic testing of various implants and to develop testing protocols for wear testing

or fatigue analysis of old and new TWA devices.

Limitations

The major limitation of the first aim of this study was our inability to evaluate the collisions

between the carpal bones. Our method was kinematically-driven and finite element

modeling might yield a higher accuracy model. Additionally, in our study, we did not

categorize carpal bones based on their shape. For example, the lunate bone has two

different anatomical shapes amongst the population and possibly two different paths of

motion. The influence of this variation on the motion is unknown and has to be measured

in future works.

The major limitation of the second aim of this study was that our investigation was

constrained to only one set of BVR acquisition parameters (kV, mA, and orientation of x-

ray sources). We believe the same experimental setup can be used reliably for studying the

wrist and replaced wrist motion and there would not be a need to change these parameters,

but if future researchers decide to change the orientation of the systems or change the

acquisition parameters, they need to be aware of the dependency of BVR system accuracy

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on experimental setup and orientation of systems. In our accuracy study, we were also

limited to 6 specimens and the variations of their bone density and muscle structure. Lastly,

the implant posture in each frame changes the accuracy of BVR systems slightly and

keeping the wrist posture of the implant perpendicular to the x-ray sources can yield a

higher accuracy.

The major limitation of the third aim of this study was our access to a small cohort

of 6 patients and 1 implant design (Freedom®). Although our cohort of TWA patients was

small, the observed patterns were mostly statistically significant and depicted a broader

need for the investigation of other designs and factors. In this study, we also did not have

access to pre-operative information to infer a broad case for the volar tilt of the implant in

the alignment chapter; however, the determined potential association suggests there may

be value in larger cohort studies with more focus on the alignment measures in future

studies. Lastly, our study cannot address the question of whether mimicking the

biomechanics of the healthy joint causes better implant outcomes; however, studies of other

joint arthroplasty designs have shown the importance of following the natural motion of

the joints.

Future Directions

There are multiple areas of research that can be built upon both the methods and the results

that are described in this dissertation. First, the mathematical model created from the carpal

database was devised based on wrist motion and using quadratic surfaces. The method’s

prediction accuracy can potentially be improved using neural network algorithms.

Similarly, designing a method that uses wrist postures (as opposed to wrist “motion”) might

yield a higher accuracy and better predictions. Additionally, categorizing carpal bones

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based on their shape (e.g., two lunate types) might also lead to an improvement in the

accuracy of the model.

The developed BVR method can be improved if enough training data becomes

available or synthetic data is generated in order to design and train novel deep learning

methods that can automatically initialize the position of the digitally reconstructed

radiographs (DRRs) on the videoradiographs. The most time-consuming part of the

registration is the initialization, and if automated, the subjective error will be significantly

reduced. Reducing the processing time subsequently reduces the processing cost and a need

for a team of engineers, and therefore, it can facilitate the transfer of this technology to

clinical settings.

The protocol and strategy described herein can be implemented to investigate other

implant designs (e.g., KinematX, Arthrosurface) in larger cohorts and with follow-up

times. Larger patient cohorts can enable a comparison of designs and outcomes to find the

optimal solutions for implant designs. Similarly, prospective or retrospective studies with

both pre- and post-operation data with follow-ups can help us to understand exactly why

these implants still suffer from high complication rates. Data provided in this thesis can be

used for robotic simulation to understand the effects of parameters such as alignment non-

invasively and provide some standards for future designs. Lastly, robotic simulations that

utilize the data provided in this dissertation along with contact sensors can help future

investigators to assess the load distribution of TWA designs.

References

1. Akhbari, B., Morton, A.M., Moore, D.C., Weiss, A.-P.C., Wolfe, S.W., Crisco, J.J.:

Accuracy of biplane videoradiography for quantifying dynamic wrist kinematics.

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Journal of Biomechanics. 92, 120–125 (2019).

https://doi.org/10.1016/j.jbiomech.2019.05.040.

2. Akhbari, B., Morton, A.M., Moore, D.C., Weiss, A.-P.C., Wolfe, S.W., Crisco, J.J.:

Kinematic Accuracy in Tracking Total Wrist Arthroplasty With Biplane

Videoradiography Using a Computed Tomography-Generated Model. Journal of

Biomechanical Engineering. 141, 044503 (2019).

https://doi.org/10.1115/1.4042769.

3. Akhbari, B., Morton, A.M., Shah, K.N., Molino, J., Moore, D.C., Weiss, A.-P.C.,

Wolfe, S.W., Crisco, J.J.: Proximal-Distal Shift of the Center of Rotation in a Total

Wrist Arthroplasty is More Than Twice of the Healthy Wrist. J Orthop Res. (2020).

https://doi.org/10.1002/jor.24717.

4. Akhbari, B., Shah, K.N., Morton, A.M., Molino, J., Moore, D.C., Weiss, A.-P.C.,

Wolfe, S.W., Crisco, J.J.: Total Wrist Arthroplasty Alignment and its Potential

Association with Outcomes. Journal of Wrist Surgery (Accepted). (2021).

5. Akhbari, B., Morton, A.M., Moore, D.C., Crisco, J.J.: Biplanar Videoradiography

to Study the Wrist and Distal Radioulnar Joints. JoVE (Journal of Visualized

Experiments). e62102 (2021). https://doi.org/10.3791/62102.

6. Akhbari, B., Moore, D.C., Laidlaw, D.H., Weiss, A.C., Akelman, E., Wolfe, S.W.,

Crisco, J.J.: Predicting Carpal Bone Kinematics Using an Expanded Digital

Database of Wrist Carpal Bone Anatomy and Kinematics. Journal of Orthopaedic

Research. (2019). https://doi.org/10.1002/jor.24435.

7. Shah, K.N., Akhbari, B., Morton, A.M., Moore, D.C., Weiss, A.-P.C., Wolfe, S.W.,

Crisco, J.J.: Total Wrist Arthroplasty Has Reduced in-vivo Motion Than a Healthy

Wrist. Journal of Hand Surgery (Under Review). (2021).

8. Akhbari, B., Shah, K.N., Morton, A.M., Moore, D.C., Weiss, A.-P.C., Wolfe, S.W.,

Crisco, J.J.: In vivo Articular Contact Pattern of a Total Wrist Arthroplasty Design.

Journal of Biomechanics (Under Review). (2021).

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AUTOSCOPER

(BONE/IMPLANT TRACKING SOFTWARE)

Bardiya Akhbari, Amy M. Morton, Douglas C. Moore, Joseph J. Crisco

Published in https://simtk.org/projects/autoscoper

Autoscoper is a 2D to 3D image registration software developed at Brown University in

2013 as a tool to investigate intra-articular joint motion during dynamic tasks. 3D position

and orientation of bones and implants can be resolved in Autoscoper using volumetric

density (CT) data and multi-view 2D radiographs acquired at high-speed

(videoradiographs; VRG). So far, Autoscoper has been used for tracking the shoulder,

spine, wrist, hip, knee, and ankle joints.

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WRIST ANATOMY AND

KINEMATICS DATA COLLECTION

Bardiya Akhbari, Douglas C. Moore, David H Laidlaw, Edward Akelman,

Arnold-Peter C. Weiss, Scott W. Wolfe, Joseph J. Crisco

Published in https://simtk.org/projects/carpal-database

The current collection includes carpal bone anatomy models from 90 healthy subjects (120

wrists), and the carpal bone kinematics in 1215 unique wrist positions. A graphical user

interface is also developed to maximize user interaction with this collection.

CT images of wrists from 90 healthy volunteers (43 males and 47 females) were acquired

in various wrist positions. The outer cortical surfaces of the carpal bones, radius, and ulna

in a 3D format, and each bone kinematics were calculated for each wrist position using a

methodology described in the README file associated with the database. The database

does not include soft tissue or the cartilage information of the wrist. Moreover, there is a

MATLAB graphic user interface (GUI) available for you to observe the database. This

dataset comes from four different NIH funding between 2001 and 2014.