comparison of a novel surgical implant with the volar

Comparison of a novel surgical implant with the volar locking plate for the

treatment of distal radius fractures: a mechanical study

A Thesis Submitted to the College of

Graduate and Postdoctoral Studies

In Partial Fulfillment of the Requirements

For the Degree of Master of Science

In the Department of Mechanical Engineering

University of Saskatchewan

Saskatoon

By

Nima Ashjaee

Copyright Nima Ashjaee, August 2018. All rights reserved.

i

PERMISSION TO USE

In presenting this thesis/dissertation in partial fulfillment of the requirements for a Postgraduate

degree from the University of Saskatchewan, I agree that the Libraries of this University may

make it freely available for inspection. I further agree that permission for copying of this

thesis/dissertation in any manner, in whole or in part, for scholarly purposes may be granted by

the professor or professors who supervised my thesis/dissertation work or, in their absence, by

the Head of the Department or the Dean of the College in which my thesis work was done. It is

understood that any copying or publication or use of this thesis/dissertation or parts thereof for

financial gain shall not be allowed without my written permission. It is also understood that due

recognition shall be given to me and to the University of Saskatchewan in any scholarly use

which may be made of any material in my thesis/dissertation.

DISCLAIMER

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trade name, trademark, manufacturer, or otherwise, does not constitute or imply its endorsement,

recommendation, or favoring by the University of Saskatchewan. The views and opinions of the

author expressed herein do not state or reflect those of the University of Saskatchewan, and shall

not be used for advertising or product endorsement purposes.

Requests for permission to copy or to make other uses of materials in this thesis/dissertation in

whole or part should be addressed to:

Head of the Department of Mechanical Engineering

57 Campus Drive


Saskatoon, Saskatchewan S7N 5A9

Canada

OR

Dean

College of Graduate and Postdoctoral Studies


116 Thorvaldson Building, 110 Science Place

Saskatoon, Saskatchewan S7N 5C9

Canada

ii

ABSTRACT

Distal radius fractures are the most common osteoporotic fractures among women. The treatment

of these fractures has been shifting from a traditional non-operative approach to surgery, using

volar locking plate (VLP) technology. Surgery, however, is not without risk, complications

including failure to restore an anatomic reduction, fracture re-displacement (loss of reduction),

and tendon rupture. The objectives of this study were to optimize the design of a novel surgical

implant and compare it to the gold-standard VLP, in terms of mechanical stability (assessed by

mechanical testing) and long-term effects (assessed by computer simulation).

The implant is novel in a variety of ways. Rather than being an externally applied device,

its application is as an intramedullary device designed to fill the distal radial metaphysis to the

extent that it stabilizes the fracture. It consists of two elements: rods and spheres.

In this research, various design iterations for rods were prototyped and tested on

cadaveric specimens to obtain a balance between different number/types of rods, stability and

technical ease. A combination of radial and volar rods linked together proximally was found to

best meet the criteria. Ideally, the spheres should be porous to accommodate bone in-growth. A

design optimization study was performed to find the optimal balance between porosity and load

carrying capacity. The results showed perforated spheres have the potential to be primarily used.

To compare the long-term effects of this implant and VLP, a subject-specific finite

element model of the radius, integrated with a bone adaptation algorithm, was constructed. The final

density distributions of the two implants were compared together as a predictor of the stress shielding

damages. Our results showed that the novel implant appeared to lead to higher density distribution.

To evaluate the mechanical stability, a custom passive wrist joint simulator was designed and

built. A ten-millimeter defect (experimental fracture) in the dorsal cortex of the distal radius was

created in seven cadaveric specimens. In sequence the distal radius was first stabilized with the new

intramedullary device, and then with a VLP. Resistance to cyclic fatigue loading was evaluated for

each treatment method by measuring the change of fracture-length during testing. On average, the

change in fracture-length for the novel implant and VLP were 1.34 and 0.10 mm, respectively.

In conclusion, this study showed potential of the presented novel implant. It was

demonstrated that the novel implant provides better biocompatibility than the VLP and has the

potential to maintain near complete fracture stabilization. Further research, however, is needed to

refine the surgical technique in order to achieve fracture stability.

iii

PREFACE

Sections of this thesis have been under preparation to be submitted as multi-authored papers in

refereed journals. The research was performed by me; data analyses and manuscript preparation

were carried out by me and the co-authors contributed in editing the manuscripts for submission

to refereed journals.

1. N. Ashjaee, J. D. Johnston, “An alternative element-based approach for simulation of

bone remodeling”; Under preparation.

Author’s contribution: Nima Ashjaee was jointly responsible for the original ideas behind

the paper, constructing finite element models, data analyses, presentation of the findings,

and writing and editing of the original paper. Dr. Johnston was jointly responsible for the

original ideas, provided supervision, and was the key editor of this paper. This research is

discussed in Chapter 5 of this thesis.

2. N. Ashjaee, M. Hosseini Kalajahi, J. D. Johnston, “Analysis of material mapping

approaches on the local stiffness predictions of proximal tibia in QCT-based finite

element modeling”; Under preparation.

Author’s contribution: Nima Ashjaee was jointly responsible for the original ideas behind

the paper, constructing finite element models, data analyses, presentation of the findings,

and writing and editing of the original paper. Dr. Johnston was jointly responsible for the

original ideas, provided supervision, and was the key editor of this paper. This research is

discussed in Chapter 5 of this thesis.

The results in this study were presented at following national and international conferences:

1. N. Ashjaee, J. D. Johnston, “Investigation of an improved element-based approach for

simulating bone remodeling”. The 20th Biennial Meeting of the Canadian Society for

Biomechanics, Halifax, Nova Scotia, August 2018

iv

2. N. Ashjaee, M. Hosseini Kalajahi, J. D. Johnston, “Accounting for Young’s modulus

variability “inside” elements for subject-specific FE modeling”, 18th Annual Alberta

Biomedical Engineering Conference, Banff, Alberta, November 2017.

3. N. Ashjaee, G. Johnston, J. D. Johnston, “Assessment of novel surgical implant using

mechanical testing and extended finite element method (XFEM)”, University of

Saskatchewan Life and Health Sciences Research Expo, May 2017

4. N. Ashjaee, S.A. Kontulainen, G. Johnston, J.D. Johnston, “Bench-Testing a Novel

Surgical Implant to Stabilize Distal Radial Fractures”, 16th Annual Alberta Biomedical

Engineering Conference, Banff, Alberta, November 2015

v

TABLE OF CONTENTS

PERMISSION TO USE ...............................................................................................................................................i

DISCLAIMER ..............................................................................................................................................................i

ABSTRACT ................................................................................................................................................................ ii

PREFACE .................................................................................................................................................................. iii

TABLE OF CONTENTS ............................................................................................................................................ v

LIST OF TABLES ......................................................................................................................................................ix

LIST OF FIGURES ..................................................................................................................................................... x

LIST OF TERMS, ABBREVIATIONS, AND SYMBOLS .................................................................................... xv

Chapter 1 Introduction.......................................................................................................................................... 1

1.1 Overview ......................................................................................................................................................... 1

1.2 Scope ............................................................................................................................................................... 2

Chapter 2 Literature Review ................................................................................................................................ 3

2.1 Anatomy of the wrist ....................................................................................................................................... 3

2.1.1 Osteology ............................................................................................................................................... 3

2.1.1.1 Radius ............................................................................................................................................................... 4

2.1.1.2 Ulna ................................................................................................................................................................... 4

2.1.1.3 Carpal bones ...................................................................................................................................................... 4

2.1.2 Ligaments ............................................................................................................................................... 5

2.1.3 Myology ................................................................................................................................................. 5

2.1.3.1 Volar muscles .................................................................................................................................................... 5

2.1.3.2 Dorsal muscles .................................................................................................................................................. 6

2.2 Distal radius fracture ....................................................................................................................................... 6

2.2.1 Epidemiology ......................................................................................................................................... 7

2.2.2 Classifications ........................................................................................................................................ 7

2.3 Treatment of distal radius fractures ................................................................................................................. 8

2.3.1 Conservative treatment .......................................................................................................................... 9

2.3.2 Closed surgical treatment ...................................................................................................................... 9

2.3.3 Open reduction .................................................................................................................................... 10

2.4 Bone remodeling process .............................................................................................................................. 12

2.5 Finite element modeling ................................................................................................................................ 13

2.5.1 Quantitative Computed Tomography-based Finite Element Modeling (QCT-FE) .............................. 14

vi

2.5.2 Material mapping in QCT-FE modeling .............................................................................................. 15

2.5.2.1 Constant-E ....................................................................................................................................................... 16

2.5.2.2 Element-based ................................................................................................................................................. 16

2.5.2.3 Node-based...................................................................................................................................................... 17

2.5.3 FE modeling of bone remodeling ......................................................................................................... 17

2.6 In-vitro biomechanical testing ....................................................................................................................... 19

2.6.1 Active motion simulators ..................................................................................................................... 20

2.6.2 Passive motion simulators ................................................................................................................... 21

2.7 Summary ....................................................................................................................................................... 21

Chapter 3 Research Questions ............................................................................................................................ 22

Chapter 4 Novel surgical implant: specifications and design optimization .................................................... 23

4.1 Introduction ................................................................................................................................................... 23

4.2 General design features ................................................................................................................................. 23

4.3 Surgical procedure ......................................................................................................................................... 24

4.4 Design improvements .................................................................................................................................... 25

4.4.1 Sphere design optimization .................................................................................................................. 25

4.4.1.1 Method ....................................................................................................................................................... 25

4.4.1.1.1 Finite element model ............................................................................................................................ 26

4.4.1.1.2 Statistical analysis ................................................................................................................................. 28

4.4.1.2 Results ............................................................................................................................................................. 28

4.4.1.3 Optimal design for the spheres ........................................................................................................................ 33

4.4.2 Rod design improvements .................................................................................................................... 33

4.4.2.1 Methods........................................................................................................................................................... 33

4.4.2.1.1 CT Imaging ........................................................................................................................................... 33

4.4.2.1.2 Segmentation ........................................................................................................................................ 33

4.4.2.1.3 CAD model of the bone ........................................................................................................................ 34

4.4.2.1.4 3D printing and prototyping ................................................................................................................. 34

4.4.2.1.5 Cadaveric testing .................................................................................................................................. 35

4.4.2.2 Design iterations.............................................................................................................................................. 36

4.4.2.2.1 Iteration 1: Simple bent rods ................................................................................................................. 36

4.4.2.2.2 Iteration 2: Simple rods contoured to match the cortex ........................................................................ 36

4.4.2.2.3 Iteration 3: S-shape volar-dorsal rods ................................................................................................... 37

4.4.2.2.4 Iteration 4: Volar rod and coiled rod ..................................................................................................... 38

4.4.2.2.5 Iteration 5: Introduction of the radial rod .............................................................................................. 38

4.4.2.2.6 Iteration 6: Introduction of flat secondary dorsal rods .......................................................................... 39

4.4.2.2.7 Iteration 7: Improved radial rod ............................................................................................................ 40

4.4.2.2.8 Iteration 8: linked volar and radial rods (A).......................................................................................... 41

4.4.2.2.9 Iteration 9: Connected volar and radial rod (B) .................................................................................... 42

vii

4.5 Final design of the novel implant .................................................................................................................. 42

4.6 Discussion ................................................................................................................................................ 43

Chapter 5 Subject-specific FE modeling integrated with a bone adaptation algorithm ................................ 46

5.1 Introduction ................................................................................................................................................... 46

5.2 Method .......................................................................................................................................................... 46

5.2.1 Specimen .............................................................................................................................................. 46

5.2.2 Finite element modeling ....................................................................................................................... 46

5.2.2.1 Segmentation ................................................................................................................................................... 46

5.2.2.2 Geometry ......................................................................................................................................................... 47

5.2.2.2.1 Bone...................................................................................................................................................... 47

5.2.2.2.2 Volar locking plate ............................................................................................................................... 48

5.2.2.2.3 Novel surgical implant .......................................................................................................................... 49

5.2.2.2.4 Assembly (osteotomized radius treated with implants) ........................................................................ 49

5.2.2.3 Meshing........................................................................................................................................................... 51

5.2.2.4 Material mapping ............................................................................................................................................ 51

5.2.2.5 Bone remodeling algorithm ............................................................................................................................. 52

5.2.2.6 Numerical approach in bone remodeling simulation ....................................................................................... 53

5.2.2.7 Boundary conditions ....................................................................................................................................... 53

5.2.2.8 FE outcomes .................................................................................................................................................... 54

5.3 Results ........................................................................................................................................................... 55

5.4 Discussion ..................................................................................................................................................... 59

Chapter 6 Mechanical testing of distal radius fractures treated with the volar locking plate and novel

implant 62

6.1 Introduction ................................................................................................................................................... 62

6.2 Method .......................................................................................................................................................... 62

6.2.1 Specimens ............................................................................................................................................ 62

6.2.2 Radiography ........................................................................................................................................ 62

6.2.3 Specimen preparation .......................................................................................................................... 63

6.2.4 Mechanical testing setup ..................................................................................................................... 68

6.2.5 Mechanical testing outcomes ............................................................................................................... 70

6.2.6 Statistics ............................................................................................................................................... 71

6.3 Results ........................................................................................................................................................... 71

6.4 Discussion ..................................................................................................................................................... 73

Chapter 7 Discussion ........................................................................................................................................... 75

7.1 Overview of findings ..................................................................................................................................... 75

7.2 Study Strengths and Limitations ................................................................................................................... 76

viii

7.3 Conclusions ................................................................................................................................................... 77

7.4 Future work ................................................................................................................................................... 78

References .................................................................................................................................................................. 79

Appendix A – Optimal Design of Spheres Raw Data ............................................................................................. 97

Appendix B – Mechanical Testing Raw Data ........................................................................................................ 101

ix

LIST OF TABLES

Table 4.1. Standardized beta coefficients (β), and level of significance (p) of the regression

model (diameter, thickness, and hole-size) to predict the safety factor. Significant values are

bolded. ........................................................................................................................................... 29

Table 4.2. Safety factors of solid spheres and perforated spheres with hole size of 2 mm. ......... 32

Table 4.3. Qualitative criteria used to assess and progress each design iteration. ........................ 42

Table 6.1. Changes in fracture-length (mm) when the osteotomized bone was treated with the

novel implant and the volar locking plate. .................................................................................... 72

Table A. 1. Results of the 6-hole design. ...................................................................................... 97

Table A. 2. ANOVA for 6-hole design. ........................................................................................ 98

Table A. 3. Results of the 4-hole design. ...................................................................................... 99

Table A. 4. ANOVA for 4-hole design. ...................................................................................... 100

x

LIST OF FIGURES

Figure 2.1. A simple representation of forearm bones [7]. ............................................................. 3

Figure 2.2. Distal radius anatomy [8]. ............................................................................................ 4

Figure 2.3. (A) Superficial muscles (bold) of right posterior forearm, and (B) Deep muscles

(bold) of right posterior forearm [12]. ............................................................................................ 6

Figure 2.4. Initial radiographs of a 15-year-old male who sustained a left wrist hyperextension

injury [23] demonstrate fractures of the distal radius, and ulna. .................................................... 7

Figure 2.5. Fracture treated with external fixation device [34]. ................................................... 10

Figure 2.6. Plain radiographs immediately after volar locking plate surgery for an unstable distal

radius fracture treated. The (a) posterior-anterior and (b) medial-lateral views [42]. .................. 11

Figure 2.7. A hypothesis of the relationship between strain and bone remodeling rate. The X axis

shows the strain history rate and the Y axis shows the net rate of bone volume change [58]. ..... 12

Figure 2.8. Four integration points inside of a 2D rectangular element. ...................................... 13

Figure 2.9. Linear (left) and quadratic (right) shape functions of a 2D rectangular element [68].

....................................................................................................................................................... 14

Figure 2.10. (A) Voxel-based and (B) geometry-based QCT-FE model of the human proximal

tibia [75]. ....................................................................................................................................... 15

Figure 2.11. Schematic drawing of a random element along with nodes and integration points,

and its corresponding QCT image [76]. ........................................................................................ 16

Figure 2.12. General procedure of QCT-FE modeling. (A) image segmentation. (B) Smooth

surface reconstruction. (C) Smoothed volume generation. (D) Discretizing the volume

(meshing). (E) Constant-E mapping method. (F) Element-based mapping method. (G) Node-

based mapping method ................................................................................................................. 17

Figure 2.13. Schematic representation of bone remodeling governing equation (Eq. (2.2)), which

presents rate of density change in relation to bone remodeling stimulus (η/ρ). Lazy zone specifies

zero change in bone density, higher values of η/ρ results in bone formation, while lower values

induce bone resorption. ................................................................................................................. 19

Figure 2.14. Previous active (top row) and passive (bottom row) motion simulators. (A) first

wrist joint motion simulator reported by Werner et al. [91]. (B) An active motion simulator for

the upper limb reported by Dunning el al. [92]. (C) An active wrist motion simulator developed

xi

by Iglesias et al. [93]. (D) A passive simulator for upper limbs presented by Nishiwaki et al. [94].

(E) A wrist joint simulator presented by Foumani et al. [95]. ...................................................... 20

Figure 4.1. Simple sketch showing the general design features of the novel surgical implant. The

spheres push the rods to the cortex of bone and the rods provide structural stability. ................. 24

Figure 4.2. The surgical procedure of the novel implant. (A) Conduit created for inserting the

rods and spheres. (B) Inserting a rod. (C) Inserting the spheres to fill the medullary canal/cavity.

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

Figure 4.3. 4-hole design. The holes were equidistant from each other. ...................................... 25

Figure 4.4. 6-hole design sphere. The holes were at the same distance and angle from each other.

....................................................................................................................................................... 25

Figure 4.5. Top view of a perforated sphere with six holes. ......................................................... 26

Figure 4.6. (A) The simplified model used to model the radius. (B) A load of 300 N was applied

to the bone. (C) The proximal side of the radius was fixed .......................................................... 27

Figure 4.7. Boundary conditions of finite element models: Applied force (left), and fixed support

(right). ........................................................................................................................................... 28

Figure 4.8. Main effects of design parameters for 6-hole design. Dimensions are in millimeter. 29

Figure 4.9. Interaction plot of variables for 6-hole design. Parallel lines mean no interaction.

Dimensions are in millimeter. ....................................................................................................... 30

Figure 4.10. Main effects of design parameters for 4-hole design. Dimensions are in millimeter.

....................................................................................................................................................... 31

Figure 4.11. Interaction plot of variables for 4-hole design. Parallel lines mean no interaction.

Dimensions are in millimeter. ....................................................................................................... 31

Figure 4.12. Safety factors of solid spheres and perforated spheres with hole-size of 2 mm. ...... 32

Figure 4.13. One slice of the obtained CT image of the bone treated with the novel implant. .... 33

Figure 4.14. CAD model of the bone ............................................................................................ 34

Figure 4.15. (A) 3D printed model which mimics a bone with a hole drilled to insert the implant

into the medullary canal. (B) Half of the 3D printed bone model. ............................................... 35

Figure 4.16. Cadaveric specimen used to test the rod prototypes. A 6-mm hole was drilled to

simulate the surgery of the novel surgical implant. ...................................................................... 35

Figure 4.17. The 2D draft of the simple bent rod. Dimensions are in millimeter. ........................ 36

Figure 4.18. The 3D printed prototype of the simple rods contoured to match the cortex. .......... 37

xii

Figure 4.19. The 3D printed prototype of the s-shape rod. ........................................................... 37

Figure 4.20. CAD model (left) and 3D printed prototypes (right) of the coiled rods. .................. 38

Figure 4.21. CAD model of the design iteration with volar, coiled, and radial rods. ................... 39

Figure 4.22. CAD model of a secondary dorsal rod. It was designed to act as a barrier to sphere

extrusion. ....................................................................................................................................... 40

Figure 4.23. The CAD model of the improved radial rod showed in (A) top and (B) side views.41

Figure 4.24. CAD model of the linked volar and radial rods (A). ................................................ 41

Figure 4.25. CAD model of the linked volar and radial rods (B) [final design iteration]. ........... 42

Figure 4.26. CAD representation of the final design. A system of linked volar-radial rods, and

solid 6mm spheres determined as the final design combination for the novel implant. ............... 43

Figure 5.1. (A) CT image of the distal radius, and (B) segmented bone. Images show a transverse

reconstruction from the CT image volume. .................................................................................. 47

Figure 5.2. CAD model of the bone generated from the segmented CT image. The induced

osteotomy was approximately 10 mm wide and centered 20 mm proximal to the tip of the

styloid. ........................................................................................................................................... 48

Figure 5.3. Anatomical standard plate from Stryker (VariAx 2 Distal Radius) used to model the

volar locking plate. (B) Screw/peg angles relative to the plate, which is achieved when an aiming

block is used [113]. ....................................................................................................................... 49

Figure 5.4. Generated 3D geometries of bone with (A) novel surgical implant, and (B) volar

locking plate. ................................................................................................................................. 50

Figure 5.5. Dorsal view of the (A) novel surgical implant, and (B) volar locking plate. Plate is

located at the volar side................................................................................................................. 50

Figure 5.6. Discretized FE model meshed with tetrahedral 10-node elements: (A) bone-Novel

implant system, and (B) Meshed bone-VLP model. ..................................................................... 51

Figure 5.7. The initial distribution of material properties in bone with (A) the novel implant and

(B) VLP. Red regions indicate a density of 1.8 g/cm3 and blue regions indicate 0.02 g/cm3. ..... 52

Figure 5.8. FE model of the osteotomized radius treated with the volar locking plate with

boundary conditions. The 180 N was applied at the location of the scaphoid and the 120 N was

applied at the location of the lunate. Both forces were directed towards the centroid of the

constrained nodes. ......................................................................................................................... 54

xiii

Figure 5.9. Cross-sections examined in regional density analysis to obtain the long-term effects

of implants. Transverse cross-sections located 50, 57, and 64 mm from the subchondral plate. . 55

Figure 5.10. Stress distribution in the novel implant and VLP. (A) Maximum principal stress

distribution in the novel implant. (B) Minimum principal stress distribution in the novel implant.

(C) Von Mises stress distribution in the VLP. .............................................................................. 56

Figure 5.11. Cross-sectional view of the von Mises stress distribution in bone for novel implant

(left) and volar locking plate (right).............................................................................................. 56

Figure 5.12. Bone density changes at different transverse cross-section for both “novel implant

(NI)” and “volar locking plate (VLP)”. ........................................................................................ 57

Figure 5.13. Resultant density distribution at different transverse cross-sections when the

osteotomized bone was stabilized with the novel implant (left) and volar locking plate (right).

Red regions indicate a density of 1.8 g/cm3 and blue regions indicate 0.02 g/cm3. ..................... 58

Figure 5.14. Average resultant density values at different transverse cross-sections for both

"novel implant" and “volar locking plate". ................................................................................... 59

Figure 6.1. 2D radiographs of (A) posterior-anterior and (B) medial-lateral views. All specimens

were imaged prior to testing to confirm and characterize the distal radius fracture. .................... 63

Figure 6.2. (A) Flexor profundus tendons were identified and their surrounding soft tissues were

mobilized or removed, while maintaining their intact connectivity to fingers. (B) The carpal

tunnel was preserved for simulating natural loading condition .................................................... 64

Figure 6.3. Extensor tendons were mobilized or separated from the surrounding soft tissues while

maintaining their natural connectivity to fingers and preserving the extensor retinaculum. ........ 65

Figure 6.4. 3D printed connecting frames for fingers flexors/extensors (left) and wrist

flexors/extensors (right). ............................................................................................................... 66

Figure 6.5. Connecting frames sutured to (A) flexor wrist and finger tendons, and (B) extensor

wrist and finger tendons. ............................................................................................................... 66

Figure 6.6. Standardized osteotomy performed on all specimens. The osteotomy was 10 mm

wide and was positioned 20 mm proximal to the tip of the radial styloid .................................... 67

Figure 6.7. (A) Novel surgical implant inserted inside the osteotomized specimen, (B)

Osteotomy filled with agar around the novel surgical implant. Osteotomized specimen treated

with VLP in (C) anterior and (D) lateral views. ........................................................................... 68

xiv

Figure 6.8. Specimen placed inside a custom-built setup and MTS Bionix Servohydraulic Test

System Model 370.02 ................................................................................................................... 69

Figure 6.9. The top view of the testing system. ............................................................................ 70

Figure 6.10. (A) LVIT maximum and minimum positions. (B) Change in fracture length. ........ 71

Figure 6.11. Graphical representation of the means and standard deviation of the two data

groups. ........................................................................................................................................... 72

Figure B. 1. LVIT maximum and minimum positions (left column) and change in fracture length

(right column) for the novel implant (top row) and volar locking plate (bottom row) for the

specimen 15-03022R (test 1). ..................................................................................................... 101



specimen 15-02039R (test 2). ..................................................................................................... 102

Figure B. 3. . LVIT maximum and minimum positions (left column) and change in fracture

length (right column) for the novel implant (top row) and volar locking plate (bottom row) for

the specimen 15-06029R (test 3). ............................................................................................... 103



specimen 15- 06064R (test 4). .................................................................................................... 104



specimen 15- 05068L (test 5). .................................................................................................... 105



specimen 14-08067R (test 6). ..................................................................................................... 106



specimen 14-05024L (test 7). ..................................................................................................... 107

xv

LIST OF TERMS, ABBREVIATIONS, AND SYMBOLS

Term Definition

Anterior Located nearer the front part of an organ

Apparent density Bone specimen mass/ total bone specimen volume (g/cm3)

Ash density Bone ash mass/ total bone specimen volume (g/cm3)

Carpal tunnel The passageway on the volar side of the wrist

Cortical bone The bone tissue which covers the outer shell of the

skeleton

Distal Situated away from the center of the body

Dorsum The dorsal part of an organism

In-silico An experiment performed via computer simulation

Integration point Element integration point used to derive the element

stiffness matrix

In-vitro An experiment taking place outside a living organism.

In-vivo An experiment taking place inside a living organism

Isotropic A material with similar mechanical properties in different

directions

Lateral Situated nearer the side part of an organ

Lumbrical muscles Four short hand muscles located in the metacarpus deep

Medial Situated nearer the middle part of an organ

Metacarpophalangeal joints The joint between the metacarpal bones and phalanges

Metaphyseal flare The narrow portion of the bone between the rounded end

xvi

and the shaft

Node Element node used to connect the elements together

Orthotropic material An anisotropic material which is symmetric with respect

to three mutually orthogonal planes

PLA Polylactic Acid

Posterior Situated nearer the back part of an organ

Retinaculum A band around tendons that holds them in place

Safety factor The ratio of mechanical strength to the applied stress

Subchondral bone Bone beneath the cartilage

Trabecular bone A spongy bone which forms inner volume of bone tissue

Transverse The plane which cuts the body into top and bottom

portions

Volar Direction toward the palm of the hand, also referred to as

palmar

Voxel Three-dimensional element of space in an image

xvii

Abbreviations/Symbol Definition

2D Two dimensional

3D Three dimensional

APL Abductor pollicis longus

BMD Bone mineral density

CAD Computer-aided design

CRPS Complex regional pain syndrome

CT Computer tomography

DAQ Data Acquisition System

DRF Distal radius fracture

E Elastic modulus

ECRB Extensor carpi radialis brevis

ECRL Extensor carpi radialis longus

ECU Extensor carpi ulnaris

FCR Flexor carpi radialis

FCU Flexor carpi ulnaris

FE Finite element

HMH Half maximum height method

LVIT Linear variable inductance transducer

NURBS Non-uniform rational basis spline

PMMA Poly(Methyl Methacrylate)

QCT Quantitative Computed Tomography

QCT-FE Quantitative computed tomography-based finite element

xviii

R2 Coefficient of Determination

RMSE Root-mean-square error

SD Standard deviation

SRG Seed-based region growing algorithm

VLP Volar locking plate

𝜌 Density

𝜌QCT Radiological density

𝜌𝑎𝑝𝑝 Apparent density

𝜌𝑎𝑠ℎ Ash density

1

Chapter 1 Introduction

1.1 Overview

A fracture occurs when the external force applied to the bone exceeds the mechanical strength

(i.e., failure force) of the bone. Distal radius fractures (DRFs) are commonplace, both in children

and in adults. As bone density diminishes, particularly post-menopause, the risk of fracture

increases. Coupled with a growing tendency to fall with increasing age, women over the age of

50 years of age are especially prone to sustain a distal radial fracture from a fall on the out

stretched hand [1]. These fragility fractures are ones resulting from any fall from a standing

height or less that result in a fracture. Osteoporosis Canada reports that at least one in every three

women and one in every five men will suffer from an osteoporotic fracture [2]. Court-Brown and

Caesar [1] estimated a distal fracture rate of 195.2 per 100,000 population, which is equivalent to

approximately 72,000 new cases in Canada each year.

The traditional approach to managing a DRF has been to use “closed” non-operative

management consisting of a manipulative reduction to restore alignment, followed by typically

six weeks of cast treatment. In light of improved surgical implant technology and patient

expectations there has been a trend towards surgery [3]. Surgical repair, however, is not without

risk. Surgery introduces the risks of incomplete restoration of alignment, post-operative

infection, nerve injury, tendon disruption and implant-induced joint problems. The employment

of hospital resources is costly; Shauver et al. [4] reported that in 2007, the mean DRF-related

payment for each patient was $1.983 in the United States. Converting this into a Canadian

context, the annual cost of surgical repair for Saskatchewan and Canada is estimated in excess of

C$3,000,000 and C$100,000,000, respectively.

In terms of specific surgical approaches, a volar locking plate (VLP) is most commonly

used. It provides rigid fixation of the fracture, a feature that facilitates early active motion of the

wrist by the patient, with low risk of loss of the fracture position. Rigid internal fixation,

however, eliminates external bridging callus formation, the body’s normal earliest healing

response to a fracture. This is important because bone healing is considerably slower after rigid

internal fixation. An ideal implant for DRF fixation would be one that maintains fracture

reduction, allows early wrist motion, facilitates early fracture union, has little or no risk related to

its implantation, and minimizes hospital resource utilization. Present VLP technology represents

a step forward, but it still falls short of the ideal. The overall goal of my thesis was to evaluate a

2

novel made-in-Saskatchewan surgical implant designed not only to stabilize distal radial

fractures, but one that also should allow early wrist motion, facilitates early fracture union, has

little risk related to its implantation, and minimizes hospital resource utilization.

1.2 Scope

Chapter 2 highlights the anatomy of the wrist joint, DRF and its treatments, and in-vitro and in-

silico simulations related to evaluating implants. Chapter 3 discusses the research questions and

objectives of this thesis. In Chapter 4, an optimal design of the novel surgical implant is

presented regarding mechanical stability and ease of the surgical procedure. Chapter 5 presents a

novel subject-specific finite element (FE) model integrated, with a bone adaptation algorithm,

and compares the long-term effects of the novel implant and VLP. In Chapter 6, the two implants

are compared together in terms of resistance to cyclic fatigue loading, mimicking physiological

loading. General outcomes, novelties, limitations, and potential future work related to this

research are outlined in Chapter 7.

3

Chapter 2 Literature Review

2.1 Anatomy of the wrist

An understanding of the anatomy of the wrist is required when studying wrist joint motion and

mechanical testing. This section will discuss bony structure (osteology), ligaments, and myology

(musculature) of the wrist.

2.1.1 Osteology

The cross-sectional diameter of bones demonstrates a two-tissue layer composition, the outer

layer known as cortical bone, which is dense, and a porous core called trabecular bone [5]. Long

bones are comprised of three main regions: distal and proximal ends (metaphysis/epiphysis) and

a shaft (diaphysis) [6]. The forearm consists of two large bones: radius and ulna (Figure 2.1).

Figure 2.1. A simple representation of forearm bones [7].

4

2.1.1.1 Radius

The radius resides on the thumb side of the hand (referred to as the lateral side when standing in

a prone position with thumbs facing outwards). Two major surfaces articulate with other bones

in distal radius: the ulnar notch with interacts with the ulna, and a concave surface which

articulate with the scaphoid and lunate of the carpus, two bones which make up a part of the

wrist joint (Figure 2.2) .

Figure 2.2. Distal radius anatomy [8].

2.1.1.2 Ulna

The ulna is located medial to the radius when the forearm is in natural anatomical prone position.

During supination and pronation, the ulna articulates with the radial head through a concave

groove known as the radial notch to allow the rotation about the ulna.

2.1.1.3 Carpal bones

Carpal bones are comprised of eight short bones, which are arranged into two rows of four. The

proximal row is composed of the scaphoid, lunate, triquetrum, and pisiform, and the distal is

composed of the trapezium, trapezoid, capitate, and hamate. In this thesis, only the scaphoid and

lunate will be discussed due to their articulation with distal radius.

The scaphoid is the largest carpal bone in the proximal row and is located on the lateral

side. The outer surface on the proximal side is convex to articulate with concave distal radius. In

5

general, the scaphoid articulates with five other bones: capitate, lunate, trapezium, trapezoid, and

distal radius. The lunate articulates with four other bones: scaphoid, hamate, triquetrum, and

distal radius. The scaphoid and lunate are mainly responsible for transferring the load from the

wrist to the radius since they act as a bridge between distal radius and carpal bones [9].

2.1.2 Ligaments

Ligaments are made of collagenous fibers and they are responsible for providing binding across

different bones [10]. The ligaments in the hand are categorized into intrinsic and extrinsic

ligaments. The intrinsic ligaments link carpal bone to carpal bone, providing a rigid framework

for the wrist. The extrinsic ligaments originate outside the wrist, linking the distal radius and

ulna, principally, and the proximal metacarpals to the carpal bones.

2.1.3 Myology

Six main muscles are responsible for the motion of the wrist: flexor carpi radialis (FCR), flexor

carpi ulnaris (FCU), and abductor pollicis longus (APL), for flexion, and extensor carpi radialis

brevis (ECRB), extensor carpi radialis longus (ECRL), and extensor carpi ulnaris (ECU) for

extension (Figure 2.3). They are all extrinsic to the wrist, since they originate from epicondyles

of the distal humerus, with the exception of APL. The finger and thumb flexor and extensor

muscles originate in the forearm, and by virtue of their insertion in the fingers, they also have a

role in producing wrist flexion and extension.

2.1.3.1 Volar muscles

The FCU originates from the medial epicondyle of the distal humerus and the ulna, and it is

mainly responsible for wrist flexion and ulnar deviation. It crosses the wrist to insert on the

pisiform, the hamate, and the fifth metacarpal [11]. The FCR contributes to wrist flexion and

radial deviation. It originates from the medial epicondyle of the distal humerus and its principal

insertion is on the second metacarpal The APL is primarily responsible for wrist abduction and

thumb extension. In contrast with other flexor muscles, it originates from the radius and ulna,

and attaches to the trapezium and thumb metacarpal.

6

2.1.3.2 Dorsal muscles

The ECU is mainly responsible for extension and ulnar deviation of the wrist. It originates from

the lateral epicondyle of the distal humerus and the proximal ulna and inserts on the base of the

small finger metacarpal. The ECRL achieves wrist extension and radial deviation. It originates

from the lateral epicondyle of the distal humerus and attaches to the base of the index finger

metacarpal. The ECRB, originating from the lateral epicondyle of the distal humerus and

inserting at the base of the long finger metacarpal accomplishes wrist extension and some radial

deviation. It also stabilizes the wrist during finger flexion.

Figure 2.3. (A) Superficial muscles (bold) of right posterior forearm, and (B) Deep muscles (bold) of right

posterior forearm [12].

2.2 Distal radius fracture

A DRF is a common bone fracture which accounts for roughly 25% of all bone injuries [13]. In

the adult population post-menopausal women represent a group particularly prone to this

fracture.

7

2.2.1 Epidemiology

DRFs occur in all ages (with similar anatomical patterns); however, the frequency and gender

distribution vary remarkably between different ages. The age-related occurrence of this injury

has a bimodal distribution, with the first peak in childhood [14,15] and the second peak in later

adulthood. For children, DRFs represent up to 30% of all fractures [16]. At this age, fractures are

mostly sport-related, and they are more common in boys (Figure 2.4) [17,18]. For adult women,

DRF represents 28% of all fractures in adult women, 13% in men [19–21]. Low bone mineral

density (BMD), a propensity to fall, and limited cognitive status, are reported as important risk

factors for this injury [22].

Figure 2.4. Initial radiographs of a 15-year-old male who sustained a left wrist hyperextension injury [23]

demonstrate fractures of the distal radius, and ulna.

2.2.2 Classifications

DRFs are usually classified based on the direction of the displaced distal fragment(s). The most

common type is the dorsally angulated fracture, colloquially known as a Colles’ fracture, which

occurs as a result of a load against an extended wrist (typically by falling on the outstretched

hand). It is reported that this type of fracture represents up to 97% of all DRFs [19]. The two

other types of DRFs are Smith and Barton fractures. In a Smith fracture the distal fragment is

volarly angulated (for descriptive purposes described as a reverse Colles’ fracture). This fracture

Fracture

8

is mostly a result of trauma to a flexed wrist. The Barton fracture represents a shear fracture of

the articular surface [24].

Clinically, DRFs can be categorized as being undisplaced or displaced fractures.

Undisplaced fractures are generally stable and rarely require surgical fixation [25]. Displaced

fractures typically require reduction and fixation. This can be accomplished by a “closed” means,

wherein manipulation of the fracture is performed in the emergency room, followed by

application of a cast or splint. Alternatively, via an “open” means, manipulation of the fracture is

accomplished in an operating room and surgical fixation using a variety of plates and screws

(e.g. VLP), pins, or an external stabilizing frame. Displaced fractures comprise roughly 70% of

fractures of distal radius [21,22].

2.3 Treatment of distal radius fractures

Treatment consists of obtaining and maintaining a satisfactory, if not “anatomic” reduction of the

fracture, that is, attempting to restore the broken bone to its original position and preventing it

from moving from that position [26]. The goals of treatment are to restore patients’ wrist motion

and grip strength as quickly as possible. The AO Foundation (Association for the Study of

Internal Fixation), influential in trauma management, maintains the overall principles of fracture

management as including [27,28]:

1. Anatomic reduction

2. Stable internal fixation

3. Preservation of blood supply, and

4. Early active pain-free mobilization.

The orthopedic surgeon has various options to choose from. Treatment differs from using a

splint, casting or surgery based on the conditions of the fracture, age or activity level [3]. The

American Academy of Orthopedic Surgeons (AAOS) issued clinical guidelines on the treatment

of DRFs [3]. Although a number of different treatments were suggested in the guidelines, most

of them lacked strong supporting evidence; therefore, they were inconclusive. However, these

general recommendations have been made [3]:

▪ For all patients, x-ray imaging of the carpus is suggested for assessment of the joint

alignment

9

▪ Rigid immobilization is preferred to the use of splints in non-operative treatment

▪ For fractures with post-reduction radial shortening greater than 3 mm, surgical

fixation is preferred to cast fixation

The AAOS was unable to suggest any specific surgical method over another [3]. Despite the

benefits of surgical fracture treatment, the use of current commercially available implant

technology poses a risk to the surrounding soft tissues (tendons) [4]). The ideal treatment for

DRFs has not yet been achieved.

2.3.1 Conservative treatment

As mentioned, undisplaced fractures usually do not require fixation [25] and a plaster cast, or an

analog, might be sufficient for treatment of the fracture. In addition, displaced fractures which

could be reduced to an acceptable, or even an anatomical, position can be treated by cast

immobilization for approximately 5 weeks [29].

2.3.2 Closed surgical treatment

With unstable fractures, operative reduction is needed to obtain a satisfactory, and ideally, an

anatomical position. Several techniques exist regarding operative reduction; it can be closed,

minimally invasive or open. Surgical treatment has benefits that make it a preferable option,

including high stability and optimized alignment.

Bridging external fixation is one method of surgical management that has been used for

several decades [30]. The principles are that the soft tissue envelope around the fracture, critical

to normal fracture healing, is undisturbed, and that ligamentotaxis is employed to maintain the

fracture reduction. The premise of ligamentotaxis is the integrity of the extrinsic wrist

ligament/capsular structures and their origin on the DRF fragments. By applying axial traction on

the wrist, it is presumed that the axial pull on the ligaments will return the DRF fragments to

their pre-fracture position. Threaded pins are introduced into one or two metacarpals, and into

the distal radius proximal to the fracture. Pin clamps are applied to the pins, allowing for rods to

span the fracture from one pin cluster to the other. These rods are external to the skin. A

manipulative reduction of the fracture is performed, and the external scaffold is secured (Figure

2.5). Complications such as delayed fracture healing, loss of reduction [31], pin site infection,

10

pin loosening, nerve damage, and complex regional pain syndrome (CRPS) became associated

with bridging external fixation devices, which contributed to their limited popularity [32]. A

modified external fixation method evolved wherein the distal pins were implanted in the distal

fracture fragment; though, a relatively large distal fracture fragment is required. This non-

bridging external fixation technique permits wrist mobilization during treatment [33]. .

Figure 2.5. Fracture treated with external fixation device [34].

2.3.3 Open reduction

Formal open reduction and internal fixation (ORIF) wherein the bone fragments are surgically

exposed, reduced into position and secured (typically with a plate and screw construct) generally

is successful for cases where there is sufficiently strong bone. In those patients whose bone

density is compromised, traditional plate and screw fixation often failed to maintain screw

purchase in either the cortical bone on the opposite side of the plate, or in the cancellous bone in

the metaphysis of the distal radius, resulting in loss of fracture reduction. In recent years, ORIF

using locking plates (Figure 2.6) has become popularized for the treatment of displaced DRFs.

The essence of this technology is that the screws lock into the plate. Consistently satisfactory

results are reported for different ages [35–37]. The maintenance of reduction relies on a secure

11

locking between the plate and screws, and less reliably on screw purchase in bone. They are

sufficiently strong in terms of load carrying capacity and provide favorable clinical results [38–

40].

This treatment, however, is relatively expensive and more invasive than an external

fixation. The main advantage of using plates and screws to maintain fracture reduction is that

accurate and immediate realignment of fractured fragments is possible, and early motion can be

achieved immediately. Some complications associated with this treatment include: tendon

attrition and rupture, screw loosening, fracture re-displacement, carpal tunnel syndrome, and

CRPS [41].

Figure 2.6. Plain radiographs immediately after volar locking plate surgery for an unstable distal radius

fracture treated. The (a) posterior-anterior and (b) medial-lateral views [42].

Dorsal plates have become less popular since the introduction of VLPs; mainly due to high risk

of extensor tendon complications with some plating systems [43]. Autogenous or allograft bone

grafts (used to fill and thereby stabilize the metaphyseal cavity) are another type of fixation

device that can be used, especially in osteoporotic bones. It is reported that they may improve

12

anatomical results; but, it is unclear whether the method will advance the final functional results

[44]. Rather than being used on its own, it is usually used in conjunction with either internal or

external fixation.

2.4 Bone remodeling process

In the 19th century, Wolff suggested that bone adapts itself as a response to external forces acting

on it [45]. It is hypothesized that the structure of the bone is dependent on external load levels.

However, a certain level for bone mass is expected to be maintained through normal

physiological activities. At this level, the bone is not responsive to changes in external loads,

which is identified by “lazy zone” [46–51] or “dead zone” [51–57]. When mechanical stimulus

exceeds the normal physiological range, bone mass will increase. On the other hand, if the

mechanical stimulus in the bone goes lower than the physiological range by limited activities or

immobilization, bone loss occurs. A hypothesis of the relationship between mechanical stimulus

(e.g. strain) and bone remodeling rate is shown in Figure 2.7.

Figure 2.7. A hypothesis of the relationship between strain and bone remodeling rate. The X axis shows

the strain history rate and the Y axis shows the net rate of bone volume change [58].

13

Several formulations have been suggested to quantify Wolff’s law and describe the

functional adaptation of the bone. There is a consensus among bone remodeling researchers that

bone remodeling theories are feedback control processes. When bone detects extreme

mechanical stimulus, it will adapt by changing its structure, which in turn will change the

resultant mechanical stimulus. This process will continue until mechanical stimulus falls into

normal physiological range where shape and density of the bone remain unchanged.

2.5 Finite element modeling

A numerical approach to solving engineering problems, the FE method is used widely in

orthopedic biomechanics to study the mechanical behavior of bone and prosthetics and bone

adaptation [53,59–67]. The premise behind this numerical approach is to discretize the body into

smaller segments (known as “elements”) that are connected to each other via points, known as

“nodes”. Inside the elements are “integration points”, which are points at which the integrals are

evaluated numerically. These points are ced inside the element in such a way that the integration

for a particular element is the most accurate. Depending on the integration scheme used, the

number of these points can vary. A 2D rectangular element with four integration points is shown

in Figure 2.8.

Figure 2.8. Four integration points inside of a 2D rectangular element.

In the FE method, the domain discretization leads to finding the solution at nodes. “Shape

functions” are used to interpolate the solution between these discrete values. The order of shape

functions stipulates the accuracy of the estimated solution inside the element. Thus, there are two

14

strategies to get high-quality results in FE modeling: Smaller (more) elements with lower shape

function order, and bigger (less) elements with higher shape function order. Linear and quadratic

shape functions of a 2D rectangular element are shown in Figure 2.9.

Figure 2.9. Linear (left) and quadratic (right) shape functions of a 2D rectangular element [68].

In general, clinical follow-up of 10-15 years is required to appreciate the long-term in-

vivo effects of an implant design on bone [69]. The FE method can be used to rapidly simulate

how bone adapts to the implant, and various design features can be readily analyzed. The

knowledge obtained from FE models can further be implemented to improve implant designs, or

to evaluate the effects of different surgical procedures [69].

2.5.1 Quantitative Computed Tomography-based Finite Element Modeling (QCT-FE)

QCT-FE is a form of subject-specific FE modeling. To develop an FE model, the CAD geometry

of the interested object must first be defined. For complex anatomical models, 3D imaging (e.g.

computer tomography (CT) scan) is often used [70–72] to model the specific geometry of a

specimen. In addition to geometry, the accuracy of the FE model is also dependent on the

material properties. Since inhomogeneous material properties are unique to the specimen being

analyzed, a general material distribution (e.g., single elastic modulus E for every element) cannot

accurately model each individual specimen. To address this, 3D imaging (e.g. typically QCT

images) is used to obtain the heterogeneous material properties of each individual specimen. This

is done by converting CT-based Hounsfield units (HU) to density [73], then using

experimentally-derived density-modulus equations to define heterogeneous elastic moduli

through-out the bone.

15

QCT-FE models are categorized into two groups: voxel-based and geometry-based. With

voxel-based QCT-FE, each voxel is directly converted into one element. In this method, models have

serrated surfaces which create inaccuracy for calculating local variables, such as stress, strain and

deformation [74]. The geometry-based QCT-FE is able to create geometrically complex models with

smooth surfaces. In this method, the geometry is first generated from the segmented image, and then

is smoothed, typically via a marching cube algorithm. This method does not suffer inaccuracies

found with the voxel-based method. Voxel-based and geometry-based QCT-FE models of a

proximal tibia are shown in Figure 2.10.

Figure 2.10. (A) Voxel-based and (B) geometry-based QCT-FE model of the human proximal tibia [75].

2.5.2 Material mapping in QCT-FE modeling

The purpose of material mapping in QCT-FE modeling is to assign site-specific material

properties to FE models from QCT images. This is done by assigning material properties to

elements. In QCT-FE modeling, the elements are often bigger than QCT voxels; therefore,

different techniques are needed to efficiently map the material properties (Figure 2.11). The

material mapping methods can be grouped into three main groups: constant-E method, element-

based method, and node-based method.

16

Figure 2.11. Schematic drawing of a random element along with nodes and integration points, and its

corresponding QCT image [76].

2.5.2.1 Constant-E

In this mapping method, a constant E is assigned to the element. Generally, this method is

performed by reading and rewriting the input file, using an in-house code. In order to find the

representing E of the element, initially, nodal elastic moduli are identified from their

corresponding voxels via density-modulus equations, and the elastic modulus field is calculated

using element shape functions.

2.5.2.2 Element-based

In FE analysis, material properties are used at integration points to perform the Gaussian

quadrature [77]; therefore, in this mapping method, material properties are directly assigned to

each integration point. If the number of integration points inside each element is more than one,

the spatial variation of elastic modulus will be accounted for.

17

2.5.2.3 Node-based

This mapping method is very similar to the element-based method. The only difference being in

this method, material properties are first assigned to nodes, and then interpolated at integration

points during the analysis. The general procedure of QCT-FE modeling is shown in Figure 2.12.

Figure 2.12. General procedure of QCT-FE modeling. (A) image segmentation. (B) Smooth surface

reconstruction. (C) Smoothed volume generation. (D) Discretizing the volume (meshing). (E) Constant-E

mapping method. (F) Element-based mapping method. (G) Node-based mapping method

2.5.3 FE modeling of bone remodeling

In some cases, a stiff implant shields the bone from carrying the normal mechanical stimulus.

This biomechanical phenomenon is known as stress shielding [78,79]. A change in load

distribution promotes bone adaptation around the implant, which adversely affects density,

stiffness, architecture, and load carrying capacity of the bone, and bone resorption occurs.

18

Although bone resorption associated with stress shielding is a common trait of implants, different

implant designs promote different rate of resorption. The purpose of FE modeling of bone

remodeling is to predict which implant design promotes the least resorption.

There is no general agreement on what mechanical stimulus triggers bone adaptation.

Cowin suggested “strain” as the primary stimulus for bone adaptation while nominating “stress”

as the secondary stimulus [80]. Strain energy density (SED) has been also widely suggested as

the primary bone remodeling stimulus by Huiskes and other researchers [50,56,81–84]. Other

mechanical stimuli, such as strain rate [85,86] and damage-based theories [87,88] have been used

as well.

In bone remodeling theory developed by Huiskes and other researchers, to predict the

changes in apparent density of the bone, the rate of the change in apparent density is directly

related to the difference between the remodeling stimulus and homeostatic stimulus (ω) [50].

Bone remodeling stimulus is determined as strain energy density (SED) per unit bone mass,

which calculated as:

(2.1)

where η is SED and ρ is the apparent density of bone. The mathematical formulation of bone

remodeling is [50,56,89,90]:

(2.2)

where t is time, C is bone remodeling constant, and δ is the width of the lazy zone (see Figure

2.13). In Eq. (2.2), (1+δ)ω and (1-δ)ω are thresholds of the bone remodeling algorithm. If the

value of bone remodeling stimulus (η/ρ) is between these two thresholds, the density will remain

constant. This area is defined as the dead or lazy zone [50,56,89,90]. If the value of η/ρ is greater

than (1+δ)ω, the apparent density of bone will increase (bone formation). Bone resorption occurs

when the bone remodeling stimulus is less than (1-δ)ω. As per prior research, in this study, we

used the following settings: B = 1 g2/cm3/J/time [54], ω = 150 µJ/g [53], and δ = 0.55 [53].

=

( - (1 ) ) (1 )

0 (1- ) (1 )

( - (1- ) ) (1- )

Cd

dtC

+ +

= +

19

Figure 2.13. Schematic representation of bone remodeling governing equation (Eq. (2.2)), which presents

rate of density change in relation to bone remodeling stimulus (η/ρ). Lazy zone specifies zero change in

bone density, higher values of η/ρ results in bone formation, while lower values induce bone resorption.

2.6 In-vitro biomechanical testing

Wrist motion simulators can be categorized into two main groups: active motion simulators, and

passive motion simulators. In the former, wrist joint kinematics are produced through forces

applied to the muscle tendons, while in the latter, motion of the wrist is generated through

external forces with passive motion simulators. A number of previous simulators are shown in

Figure 2.14.

20

Figure 2.14. Previous active (top row) and passive (bottom row) motion simulators. (A) first wrist joint

motion simulator reported by Werner et al. [91]. (B) An active motion simulator for the upper limb

reported by Dunning el al. [92]. (C) An active wrist motion simulator developed by Iglesias et al. [93].

(D) A passive simulator for upper limbs presented by Nishiwaki et al. [94]. (E) A wrist joint simulator

presented by Foumani et al. [95].

2.6.1 Active motion simulators

In active motion simulations, forces are directly applied to the muscle tendons to manipulate

joint positions. In these simulations, antagonistic relationships between opposing muscles are

often considered to more accurately mimic the in-vivo condition; therefore, they are regarded as

a more accurate method to simulate joint positioning [93].

Motion is often controlled with force-position algorithms that generate the motion of the

wrist in a controlled manner [91]. The primary mover muscle is activated (usually with

displacement-control) to maintain a continuous angular velocity [92], while the opposing

muscles hold a constant force [93].

21

Linear actuators and servomotors are primary candidates to apply forces to the tendons of

interest. Linear actuators are typically relatively inexpensive, and they provide force feedback;

however, they do not have a measure of position [93]. On the other hand, servomotors are more

expensive but provide positioning feedback. However, they require additional force transducers

to record the forces during the simulation.

2.6.2 Passive motion simulators

In this group of simulators, the motion of the joint is produced by an external mechanical

apparatus, or by the researcher. With passive motion simulators, although forces are applied to

tendons (either directly or indirectly), they are not responsible for the motion of the joint. In

these simulators, although the motion of the wrist is generated using a passive controller, forces

can still be applied to muscle tendons to mimic the physiological conditions. No positional

feedback is used in these simulators [94,95]. Regularly, the extensor and flexor tendons are

loaded with constant forces (e.g. constant force springs [95]) and the tendons are attached to the

constant springs using wires. A pulley system was implemented to assure an equal distribution of

force over individual tendons.

2.7 Summary

• The trend in the treatment of DRFs is toward open reduction and internal fixation, as

much due to its reliability in maintaining fracture reduction. The complications of such

treatment, however, speak to the need for an implant which maintains the corrected

position (reduction), minimizes soft tissue disruption, mitigates risk of present-day

surgery, and does not interfere with the natural fracture healing process.

• Subject-specific FE modeling integrated with a bone adaptation algorithm, is a prominent

tool to predict internal load distribution and long-term effects of different implants.

• In-vitro joint simulators include active and passive simulators. In active simulators, the

motion is generated by activating tendon(s) while the wrist is passively motioned in

passive simulators. Although active motion simulators can more accurately generate the

spatial motion of the wrist, they are hard to control and are expensive. Conversely, the

physiological load distribution of the joint can be accurately achieved via passive motion

simulators where the muscle forces are applied to tendons.

22

Chapter 3 Research Questions

The broad goal of the project was to evaluate a novel treatment strategy for DRFs. To help

achieve this broad goal, the following research questions were formed:

1. Can design features of the novel surgical implant be optimized to improve mechanical

outcomes (e.g., safety factor) and ease of surgery?

2. How will the long-term effects of the novel implant compare to the VLP in terms of bone

adaptation?

3. How will the novel implant resist fracture displacement under cyclic loading compared to

the VLP?

To answer the research questions, the objectives were to:

1. Optimize the design of the novel implant in terms of mechanical stability (assessed via

safety factor) and ease of surgery.

2. Compare the long-term effects of the novel implant and the VLP on bone adaptation

(assessed via bone density) using subject-specific FE modeling.

3. Evaluate fracture stability of the novel implant and VLP using cyclic fatigue testing.

23

Chapter 4 Novel surgical implant: specifications and design optimization

4.1 Introduction

The trend in the treatment of the DRFs is shifting toward surgery, especially the use of the VLP

technology. However, the VLP is far from the ideal solution. To address the shortcomings of the

VLP (identified as the gold-standard in the field), a novel surgical implant was designed by Dr.

G. Johnston. The aim of this chapter was to improve the design of the novel surgical implant, in

terms of resistance to failure and ease of surgery.

The parts of the novel surgical device can be separated into two groups: rods and spheres.

Between them, spheres are the weakest link in terms of load carrying capacity. Ideally, the

spheres should be porous in order to encourage bone ingrowth. Although this accommodates

bone ingrowth, holes inside the spheres can reduce their load carrying capacity.

The first objective of this chapter was to find the optimal balance between porosity of the

spheres and resistance to failure (assessed via safety factors, which is the ratio of mechanical

strength to the applied stress). The second objective was to improve the shape of the rods in

order to enhance fracture stability. Throughout the process one had to be mindful of the principle

that the surgical technique for fracture reduction and insertion of the implant had to be both easy

to perform and as safe as possible.

4.2 General design features

Both rods and spheres are placed surgically inside the bone to stabilize the fracture from inside

(i.e., intramedullary fixation). Spheres act as springs and push the rods to the cortex of bone.

They also attempt to mimic the function of normal cancellous bone by facilitating axial load

transfer from the softer cancellous bone of the medullary cavity to the firmer cortical walls of the

radius. The rods are responsible for providing structural stability to the fractured segments.

Multiple rods can be placed at different locations (volar, dorsal, radial or ulnar), with different

shapes and sizes, to provide the appropriate structural stability required for each region (Figure

4.1).

24

Figure 4.1. Simple sketch showing the general design features of the novel surgical implant. The spheres

push the rods to the cortex of bone and the rods provide structural stability.

4.3 Surgical procedure

In brief, a hole is drilled into the dorsal radial cortex, proximal to the fracture, to create a conduit

for inserting the rods and spheres into the medullary canal (Figure 4.2A). Next the rods are

inserted (in a specific order or linked together, depending on the design; Figure 4.2B). Lastly, as

many spheres as possible are inserted (Figure 4.2C) to fill the medullary canal/cavity, to achieve

stable intramedullary fixation.

Figure 4.2. The surgical procedure of the novel implant. (A) Conduit created for inserting the rods and

spheres. (B) Inserting a rod. (C) Inserting the spheres to fill the medullary canal/cavity.

Fracture

1 cm

25

4.4 Design improvements

4.4.1 Sphere design optimization

4.4.1.1 Method

Four different designs were considered for spheres: (1) 4-hole, (2) 6-hole, (3) solid spheres, and

(4) spheres with perforations. In a 4-hole design, holes were equidistant from each another. In

order to achieve that, the 3 bottom holes need to be in 109.5 degrees from the one on top, and

120 degrees from each other (Figure 4.3). Another way to imagine this design is to cut a caltrop

from inside of a sphere. The axes of holes passed the center of sphere.

Figure 4.3. 4-hole design. The holes were equidistant from each other.

A 6-hole design (Figure 4.4) followed a more straightforward concept. All holes were equidistant

from each other, and the angle between them was 90 degrees. Similar to the 4-hole design, all

holes passed through the center of the sphere.

Figure 4.4. 6-hole design sphere. The holes were at the same distance and angle from each other.

26

Perforated design (Figure 4.5) took the idea of using 6-holes, and addressed the

mechanical weakness that they create. Holes that completely pass through the sphere weaken its

core. In order to prevent that, in a perforated design, the holes did not reach the center, but rather

only perforate the spheres up to a certain depth (2 mm in this study). This increased the load

carrying capacity of spheres. The top view of a perforated sphere is shown in Figure 4.5. For all

perforated spheres, a constant hole size of 2 mm was used.

Figure 4.5. Top view of a perforated sphere with six holes.

4.4.1.1.1 Finite element model

In this study, thickness (1, 1.5, 2 mm), diameter of spheres (5.5, 6, 6.5 mm), and hole-diameter

(1.5, 2 mm) were chosen as design parameters. Different values were assigned to each design

parameter, and various models were created. All combinations of design parameters were

generated, which resulted in 18 separate models for 6-hole design, 18 models for 4-hole design, 3

models for solid, and 3 models for perforated spheres. Hole size in the perforated design was

kept constant at 2 mm.

In order to estimate the maximum force between spheres in real life conditions, a

simplified model of the radius was created based on the work of Pietruszczak et al. [96] (Figure

4.6A). This model is obtained by rotating a simple sketch (comprised of six straight lines) along

its central axis.

A ramped quasi-static load of 300 N was applied to the radius. A force of 180 N (mimicking the

effect of the scaphoid) was applied to one side on the surface, while 120 N (mimicking the

lunate) was applied to the other side (Figure 4.6B). These values were chosen based on previous

research [96–99]. The other end of radius was treated with a fixed support (Figure 4.6C). The

27

maximum amount of 27 N was observed between spheres when different settings (spheres with

different diameters or different positions) was used. This value was used to calculate the safety

factor of different designs.

Figure 4.6. (A) The simplified model used to model the radius. (B) A load of 300 N was applied to the

bone. (C) The proximal side of the radius was fixed

FE modeling was used to assess the safety factor of different designs. The methodology

for assessing the safety factor of specific spheres was to apply the calculated force at one end of

the sphere, while fixing the other side of it, in a way to simulate the weakest setting (Figure 4.7).

The spheres were made of Norian (Norian Corporation, Cupertino, California) which is brittle;

therefore, Brittle Coulomb Mohr (BCM) was used for evaluating the safety factor of spheres

under loading and investigate the effects of each variable (diameter, hole size, and wall

thickness). The elastic modulus, tensile yield strength, and compressive yield strength of the

Norian were assumed to be 700 MPa [100], 8.33 MPa [101], and 25 MPa [101], respectively.

A B C

28

Figure 4.7. Boundary conditions of finite element models: Applied force (left), and fixed support (right).

4.4.1.1.2 Statistical analysis

In order to evaluate the effect of design variables on safety factors of spheres, a full factorial

design of experiment was constructed, where all possible combinations of design variables were

included. The significance of each variable, as well as their interactions were evaluated. Based

on the recommendation of [102], the data from each factorial design (4-hole and 6-hole) were

analyzed using a general linear analysis of variance (ANOVA), which was equivalent to

performing multiple linear regression [102]. The same statistical approach was used in similar

studies [102–105]. ANOVA specified the percentage contribution of each design parameter

(factor) to total sum of squares of the responses. These were used to identify the significance of

each factor. Standardized beta (β)-coefficients were used to find the effect of each variable on

safety factor. Statistical analyses were performed using SPSS 22.0 (IBM, Armonk, NY, USA).

4.4.1.2 Results

Raw results of FE modeling are shown in Appendix A. Table 4.1 shows the standardized beta

coefficients (β) and the level of significance (p) in 4-hole and 6-hole regression models. The R-

squared values of 4-hole and 6-hole models were 83.7% and 71.8% respectively. In the 6-hole

model, diameter had a P-value less than 0.001. The P-values of thickness and hole-size were

0.247 and 0.033, respectively. Based on the results, diameter and hole-size were significant. The

diameter had the highest effect on the results (β = 0.76). The mean effect of each design

parameter in 6-hole design is shown in Figure 4.8. Higher values of diameter and thickness

29

increased the safety factor. In Figure 4.8, X axis shows the levels of each factor, and Y axis

shows the BCM safety factors.

Table 4.1. Standardized beta coefficients (β), and level of significance (p) of the regression model

(diameter, thickness, and hole-size) to predict the safety factor. Significant values are bolded.

Safety factor

β p-value

4-hole design

Diameter 0.448 0.001

Thickness 0.697 0.00001

Hole-size -0.388 0.003

6-hole design

Diameter 0.76 0.0001

Thickness 0.171 0.25

Hole-size -0.335 0.033


30

Figure 4.9 shows the interactions of variables for 6-hole design. The variables were

independent if the lines were parallel to each other, and they followed the same pattern. Based on

the plots, thickness and hole-size were the only independent variables. Interdependence was

observed between diameter-thickness, and diameter-hole size.

Figure 4.9. Interaction plot of variables for 6-hole design. Parallel lines mean no interaction. Dimensions

are in millimeter.

The same diagrams are shown for 4-hole design. The mean results of the 4-hole design

are shown in Figure 4.10. In this design, thickness was the most prominent factor (β = 0.448)

followed by diameter (β = 0.697). The BCM safety-factor increased with the increase of

thickness and diameter. Figure 4.11 shows the interactions of design parameters for 4-hole

design. Almost all lines were parallel, and all of variables were independent. The highest

interdependency was observed between diameter and thickness.

31


Figure 4.11. Interaction plot of variables for 4-hole design. Parallel lines mean no interaction. Dimensions

are in millimeter.

32

The FEA results of solid and perforated spheres are shown in Table 4.2 and Figure 4.12.

Solid spheres had the highest safety factors among other designs, ranging from 1.8 (diameter = 5

mm) to 2.9 (for diameter = 6 mm). Safety factors of perforated spheres ranged from 0.17 to 0.97.

Relative to solid spheres, safety factors of perforated spheres decreased between 34% (diameter

= 6 mm) to 10% (diameter =5 mm).

Table 4.2. Safety factors of solid spheres and perforated spheres with hole size of 2 mm.

Diameter (mm) Solid spheres Perforated spheres

5 1.8 0.171

5.5 2.24 0.366

6 2.88 0.968

Figure 4.12. Safety factors of solid spheres and perforated spheres with hole-size of 2 mm.

33

4.4.1.3 Optimal design for the spheres

Solid spheres were the only design category which had a safety factor greater than one.

Therefore, 6 mm solid spheres were chosen as the final design for spheres (safety factor = 2.88).

The safety factors of perforated spheres were also close to 1 (safety factor = 0.968 for 6 mm

perforated sphere), and with careful design, they have potential to be used instead of solid

spheres.

4.4.2 Rod design improvements

4.4.2.1 Methods

4.4.2.1.1 CT Imaging

Since an accurate model of the radius was needed to design the shape of the rods (to match the

contour of the bone) a CT image of one distal radius, into which the first iteration of rods and

spheres had been inserted, was obtained.

Figure 4.13. One slice of the obtained CT image of the bone treated with the novel implant.

4.4.2.1.2 Segmentation

Each CT image slice was segmented from the surrounding tissue in the transverse plane with the

half maximum height (HMH) method using commercial image processing software (Analyze 10;

Mayo Foundation, Rochester, MN, USA). After obtaining the initial estimate for the tissue

threshold using the HMH method, semi-automatic segmentation was performed using a seed-

34

based region growing algorithm. The initial seed was located in a dense area in the cortical

region, and HMH thresholds were used to automatically identify voxels with higher BMD values

than the defined threshold. In sections where the seed was not able to successfully identify closed

boundaries, manual correction was performed using an interactive touch-screen tablet and a

stylus (Cintiq 21uX, Wacom, Krefeld, Germany).

4.4.2.1.3 CAD model of the bone

After segmenting the bony region, the 3D polygonal outer and inner surfaces of the cortical bone

were extracted as an object mesh file using a marching cube algorithm (ANALYZE). The 3D

object was then converted and smoothed into a non-uniform rational basis spline (NURBS)

surface. At this stage, the computer-aided design (CAD) model was checked using

GEOMAGICS (a commercial reverse-engineering software package) to ensure no topological

problems existed in the model. The final CAD model is shown in Figure 4.14. This model was

used to design various types of rods.

Figure 4.14. CAD model of the bone

4.4.2.1.4 3D printing and prototyping

The CAD model of the segmented bone and various rod prototypes were 3D printed and the

general feasibility of the rods was controlled with the 3D printed model of bone (Figure 4.15).

35

Figure 4.15. (A) 3D printed model which mimics a bone with a hole drilled to insert the implant into the

medullary canal. (B) Half of the 3D printed bone model.

4.4.2.1.5 Cadaveric testing

After testing the rods with the 3D printed model, the rods were tested with a cadaveric specimen.

A 6-mm hole was drilled through the dorsal cortex of the radius, at least a centimeter proximal to

the location of the DRF. The surgery was simulated by inserting the rods and spheres inside the

bone through the drilled hole (Figure 4.16).

Figure 4.16. Cadaveric specimen used to test the rod prototypes. A 6-mm hole was drilled to simulate the

surgery of the novel surgical implant.

36

4.4.2.2 Design iterations

In this section, a summary of major design iterations is presented, and their general features,

benefits, and disadvantages are discussed in general terms.

4.4.2.2.1 Iteration 1: Simple bent rods

This was the first design iteration which was used as a basis to generate the next design

iterations. In this design, the rods were bent (25 degrees) to follow the general contour of the

bone. The 2D draft of this design is shown in Figure 4.17.

Figure 4.17. The 2D draft of the simple bent rod. Dimensions are in millimeter.

4.4.2.2.2 Iteration 2: Simple rods contoured to match the cortex

In this design iteration, instead of bending the rods 25 degrees to match the bone, specific volar

and dorsal rods were designed which were specifically contoured to match the cortex. A 3D

printed prototype of this design is shown in Figure 4.18. In this iteration, the rods more closely

matched the contour of the cortical bone, thereby potentiating higher friction between the rod

and the bone, and improving the stability of the implant.

37

Figure 4.18. The 3D printed prototype of the simple rods contoured to match the cortex.

4.4.2.2.3 Iteration 3: S-shape volar-dorsal rods

In this design iteration, both dorsal and volar rods were combined into one s-shape rod (Figure

4.19). In addition to reducing the number of rods, which makes the surgery process easier, this

design benefited from an intrinsic spring force present in the rod, which acts on dorsal and volar

sides of the bone, when the rod is inserted. The curved shape of the rod allows it to pass through

the hole. Although the design had mechanically attractive attributes, insertion of the implant

proved to be technically difficult in the cadaveric experimentation.

Figure 4.19. The 3D printed prototype of the s-shape rod.

38

4.4.2.2.4 Iteration 4: Volar rod and coiled rod

In this design iteration, only two separate rods were used. One volar rod, as presented in iteration

2, and one coiled rod, which had both dorsal and volar ends. The idea was to provide high

stability for the volar side. Compared to the previous iteration, this design was technically easier

to perform; however, keeping the coiled rods at their desired position proved to be technically

challenging in some cases.

Figure 4.20. CAD model (left) and 3D printed prototypes (right) of the coiled rods.

4.4.2.2.5 Iteration 5: Introduction of the radial rod

In this design iteration, to further increase fracture stability, a third rod was introduced to support

the radial side of the radius. Similar to volar and coiled rods, the radial rod was shaped to match

the contour of the cortex. The CAD model of the rods of this design iteration is shown in Figure

4.21.

39

Figure 4.21. CAD model of the design iteration with volar, coiled, and radial rods.

4.4.2.2.6 Iteration 6: Introduction of flat secondary dorsal rods

After inserting the rods, the empty space between them was filled with the spheres. In order to

prevent the spheres from extruding from the drilled hole, small secondary dorsal rods were

designed. They were designed to be inserted as the last of the implants, their principal role was to

maintain the spheres within the bone. Horizontal ridges were included on one side of the rods to

make it easier for surgeons to position them accurately with a pair of tissue forceps.

40

Figure 4.22. CAD model of a secondary dorsal rod. It was designed to act as a barrier to sphere extrusion.

4.4.2.2.7 Iteration 7: Improved radial rod

In this design iteration, the shape of the radial rod was altered to make the insertion of the rod

easier. The change in radial rod design allowed for continued matching to the cortex of the radial

wall of the distal radius, both distal and proximal to the fracture, but once past the metaphyseal

flare [the narrow portion of bone between the rounded end and the shaft] into the diaphyseal

canal, it was reshaped to terminate centrally in the canal proximally (Figure 4.23A). Also, to

counter a tendency for the radial implant to roll out of position, stabilizer bars were added to both

the proximal and distal ends of the radial rod (Figure 4.23B).

In addition, by accommodating the new radial rod design, the notion of having three rods

inside the radius, as in the previous iteration, made the space inside the radius very crowded;

therefore, the coiled rod was removed in this iteration, leaving the stability of the structure to the

radial and volar rods.

41

Figure 4.23. The CAD model of the improved radial rod showed in (A) top and (B) side views.

4.4.2.2.8 Iteration 8: linked volar and radial rods (A)

In this iteration, a connection between the volar and radial rods was designed to link the rods

orthogonally, making the positioning of the rods inside the bone not only easier but also

enhancing the stability of the coupled implant and the fracture. The CAD model of the linked

volar and radial rods is shown in Figure 4.24. Two linkage stands (pegs/posts) were added to the

volar rod in order to give the surgeon the ability to adjust the length relationship of the radial and

volar rods to facilitate the best distal fit of the two rods. Horizontal ridges were added to the

volar rod to make the positioning of the structure easier.

Figure 4.24. CAD model of the linked volar and radial rods (A).

A B

42

4.4.2.2.9 Iteration 9: Connected volar and radial rod (B)

This was the final iteration of the design of the rod investigated in this thesis. In this iteration, the

posts and the post holes in the rods were switched, the posts to the radial rod, and the post holes

to the volar rod (Figure 4.25). A step-shape change to the proximal end of the volar rod was

adopted to accommodate this switch. In addition, the introduced curve of the radial rod was

moved to the center. This centralization of the radial stem further eased the insertion of rods.

Figure 4.25. CAD model of the linked volar and radial rods (B) [final design iteration].

4.5 Final design of the novel implant

Table 4.3 shows the qualitative criteria used to assess and progress each design iteration. For the

final design, solid 6mm spheres were chosen. Regarding the rods, a system of volar and radial

rods which were linked together at the proximal end (design iteration 9) was established (Figure

4.26). In the following chapters, when the novel implant is mentioned, this design is intended.

Table 4.3. Qualitative criteria used to assess and progress each design iteration.

Matching the

cortex

General easiness of the

surgery

High

stability

Positioning the

rods

Iteration 1 ✗ ✓ ✗ ✗

Iteration 2 ✓ ✓ ✗ ✗

Iteration 3 ✓ ✗ ✓ ✗✗

Iteration 4 ✓ ✗ ✓ ✗

43

Iteration 5 ✓ ✗ ✓✓ ✗

Iteration 6 ✗ ✓ ✗ ✓

Iteration 7 ✓ ✓ ✗ ✗

Iteration 8 ✓ ✗ ✓ ✗

Iteration 9 ✓ ✓ ✓ ✓

Figure 4.26. CAD representation of the final design. A system of linked volar-radial rods, and solid 6mm

spheres determined as the final design combination for the novel implant.

4.6 Discussion

The aim of sphere design optimization was to identify the safety factor of different sphere

designs and sizes. Furthermore, the importance of different design parameters was investigated

with the use of statistical factorial design. All combinations of variables were implemented, and

FE modeling was used to calculate the safety factors of spheres.

Generally, the more material that is present in a sphere design, the more load it is

expected to be able to withstand. Higher values of diameter and thickness added more bulk to

spheres; therefore, they were expected to result in higher safety factors. Lower hole-size

subtracted less material from the spheres, and same rule applies to them. This was true for both

4-hole and 6-hole designs.

In terms of interaction between design parameters, no compelling interaction was

observable for 4-hole design, but some interaction effects were observable for 6-hole design. In

44

general, it is desirable not to have any interactions between factors. If two independent variables

interact, the effect of one differs depending on the level of the other variable. As shown in Figure

4.11, lines of thickness – diameter and thickness – hole size were almost parallel, which meant

there was no interaction between them. Diameter – thickness lines can also be regarded as

parallel. In the 6-hole design, except thickness – hole size, an interaction effect was visible

among other variables.

In general, the 6-hole spheres were stronger than the corresponding 4-hole spheres. This

might be due to the loading regime that we used in this study. The load was applied to one end of

the spheres while the other end was fixed. Since the axes of the holes in 4-hole design were

located with an angle to the normal plane of the applied force, higher stress values were induced

to critical regions in 4-hole spheres. Solid spheres had the highest safety factors among all

designs. Perforated spheres were the second-best design in terms of safety factor.

For the 6-hole design, diameter was the most effective factor among other variables (β =

0.76). This indicates that changing the diameter had the most noticeable effect on the safety

factor. Hole-size was the second effective variable (β = -0.335). For the 4-hole design, thickness

was the most effective variable (β = 0.697) followed by diameter (β = 0.448).

The load carrying capacity of spheres was evaluated using the BCM failure criterion.

Safety factors below 1 are regarded as failure under load. Based on the result, only solid spheres

withstood the loading regime used in this study, and perforated spheres came close to it. In order

to evaluate the forces between spheres in real life, a simplified model of the radius with a flat top

surface was used. This represents the worst-case scenario, and in real life, the spheres may

withstand higher loads. However, the ratio of safety factors between different designs is

independent of the applied load (assumption of linear elasticity). Therefore, the presented results

can be used to evaluate the relative load carrying capacity of each design.

One limitation associated with the novel implant design is that in this design, a hole is

needed to be drilled proximal to the fracture, to insert the spheres and rods inside the bone. This

reduces the structural integrity of the bone. However, it is possible to patch the hole (e.g. with

Norian putty) after the implant is placed inside the bone. Another limitation associated with

finding the forces between spheres with this method was that the force was dependent on the

position of spheres inside the bone. In our study, a number of random layouts of spheres were

chosen. The results change with different layouts. The simplified radius model was also not a

45

real representation of the bone. Furthermore, the effects of bending loading, cyclic loading and

fatigue failure were not incorporated in the model. In addition, future studies should seek to

incorporate the drilled hole into the FE model for improved accuracy.

In conclusion, solid spheres out-performed other designs. Some cases of perforated

spheres, also, exhibited sufficient safety factors for further analysis. With careful design,

perforated spheres have potential to be used instead of solid spheres. 6-hole and 4-hole spheres

results were comparable. 6-hole spheres, however, had higher safety factors.

46

Chapter 5 Subject-specific FE modeling integrated with a bone adaptation

algorithm

5.1 Introduction

When bone is intact (i.e. not fractured), all external forces induced by daily activities are relayed

through bone. In cases where an external device (e.g. VLP or the novel surgical implant

presented here) is added, normal mechanical behavior of the bone will be affected. Specifically,

the presence of a stiff object will change internal load distribution of the bone.

The objective of this chapter was to evaluate the long-term effects of the two implants (the

novel surgical implant and the gold-standard VLP) by using subject-specific QCT-FE models

integrated with a bone adaptation algorithm.

5.2 Method

5.2.1 Specimen

One fresh-frozen human forearm specimen (female, age = 84 years old) was used to create the

subject-specific FE model of the radius.

5.2.2 Finite element modeling

5.2.2.1 Segmentation

The procedure is identical to section 4.4.2.1.2. In short, the outer contour of each 2D slice of a

different CT image was segmented using the HMH method with Analyze (Figure 5.1).

47

Figure 5.1. (A) CT image of the distal radius, and (B) segmented bone. Images show a transverse

reconstruction from the CT image volume.

5.2.2.2 Geometry

5.2.2.2.1 Bone

The procedure is identical to section 4.4.2.1.3. In short, after segmenting, the object file of the

3D polygonal of the outer surface was extracted and converted into a NURBS surface using

reverse-engineering software (GEOMAGICS). The geometrical complexity of the CAD model

was maintained by ensuring that the maximum smoothing distance was kept less than half of a

voxel size (0.25 mm).

In order to simulate a clinically relevant (unstable) fracture of the distal radius, a wedge

of bone was removed from the model (Figure 5.2), which was approximately 10 mm wide and

centered 20 mm proximal to the tip of the radial styloid [106]. This model has been widely used

in the literature and has been reported as a worst case DRF representation since it neutralizes all

load-bearing capabilities of the bone [106–112].

48

Figure 5.2. CAD model of the bone generated from the segmented CT image. The induced osteotomy was

approximately 10 mm wide and centered 20 mm proximal to the tip of the styloid.

5.2.2.2.2 Volar locking plate

VLP was sketched in SOLIDWORKS 2015 from an anatomical standard volar plate (Figure

5.3A) (Stryker, VariAx 2 Distal Radius Plate [113]) and was converted into a 3D volume. The

screws and pegs were angled to give a predetermined pattern in the distal block of the bone.

Screw/peg angles relative to the plate are shown in Figure 5.3B. This screw pattern is achieved

when an aiming block [used for inserting the pins and mounting the plate to the bone] is used.

49

Figure 5.3. Anatomical standard plate from Stryker (VariAx 2 Distal Radius) used to model the volar

locking plate. (B) Screw/peg angles relative to the plate, which is achieved when an aiming block is used

[113].

5.2.2.2.3 Novel surgical implant

The design procedure of the novel surgical implant is described in Chapter 4. The final CAD

model of the implant was obtained and imported into SOLIDWORKS to create the CAD

assembly model of the bone-implant system.

5.2.2.2.4 Assembly (osteotomized radius treated with implants)

Two assembly parts were generated using SOLIDWORKS: (1) osteotomized radius treated with

the VLP (bone-VLP) and (2) osteotomized radius treated with the novel implant.

To generate the bone-novel surgical implant system, spheres and rods were positioned

inside the bone, and were subtracted from the bone volume using CAVITY feature of

SOLIDWORKS (Figure 5.4 and Figure 5.5). To generate the bone-VLP model, the plate was

positioned on the volar surface of the radius, and pegs/screws were inserted inside the bone

through the plate holes. All pegs/screws were positioned at the center of the holes of the plate.

50

Figure 5.4. Generated 3D geometries of bone with (A) novel surgical implant, and (B) volar locking plate.

Figure 5.5. Dorsal view of the (A) novel surgical implant, and (B) volar locking plate. Plate is located at

the volar side.

51

5.2.2.3 Meshing

Due to geometrical complexities of bone and implant models, they were discretized using 10-

node quadratic tetrahedral elements. A convergence study was performed regarding maximum

von Mises stress of each part, and outputs did not change by more than 5% when smaller

elements used. The 5% threshold was determined as per prior research [114–118]. The global

element-edge length of 0.75 mm was determined as the converged mesh size, which resulted in

346322 elements and 505280 nodes for the bone-novel implant system, and 302628 elements and

441467 nodes for the bone-VLP model (Figure 5.6).

Figure 5.6. Discretized FE model meshed with tetrahedral 10-node elements: (A) bone-Novel implant

system, and (B) Meshed bone-VLP model.

5.2.2.4 Material mapping

In FE, material properties are needed at integration points to perform the Gaussian quadrature

[77]; hence, here, we assigned the material properties directly to each integration point. As the

number of integration points inside an element was more than one (the quadratic tetrahedral

52

element has four integration points), the 3D variation of material properties inside the elements

was accounted for in this study. The elastic modulus for each voxel was calculated and imported

into ABAQUS externally via “UEXTERNALDB” subroutine, which only runs at the beginning

of the analysis. Then, the elastic modulus was assigned to each integration point, based on which

voxel contains it, by using the “USDFLD” subroutine. The distribution of material properties in

bone is shown in Figure 5.7. In ABAQUS, material properties and density were linked together

via a lookup table. All subroutines were programmed in FORTRAN.

Figure 5.7. The initial distribution of material properties in bone with (A) the novel implant and (B) VLP.

Red regions indicate a density of 1.8 g/cm3 and blue regions indicate 0.02 g/cm3.

The elastic modulus of bone was calculated from the ash density, using the following

equation [119]:

𝐸 = 𝐼𝑂, 500𝜌𝑎𝑠ℎ2.29 (5.1)

where E is elastic modulus in MPa, and ρash is ash density expressed in g/cm3 [119]. In this

study, ρash was assumed to be equal to ρQCT. [120].

5.2.2.5 Bone remodeling algorithm

For this study, bone remodeling was implemented with FE modeling by adopting the strain-

energy based bone remodeling theory [50,56,89,90] (Eq. 2.2). Neuert et al. [53] studied

remodeling parameters for a strain-adaptive FE model, and reported that ω=150 μJ/g and δ=0.55

53

result in the most accurate results with least root-mean-square error (RMSE) values. Those

values were used in this study. C=1 was determined as per previous studies [53,121,122].

5.2.2.6 Numerical approach in bone remodeling simulation

As described in section 5.2.2.4, at the first step of the simulation, the material properties have

been assigned to each integration point. After obtaining a solution (results at the end of

increment 1), the SED value of each integration point was used to calculate the bone remodeling

stimulus of that point. These values were then used to update the density and advance the

simulation to the next increment. This approach was in contrast with the traditional, slower node-

based approach where density and SED values are interpolated/extrapolated between nodes and

integration points during the analysis. Euler’s forward scheme was implemented for numerical

integration of the bone remodeling equation [48,51,54,123,124]. The user-subroutine

“USDFLD” was used to solve the bone remodeling equation and update density.

5.2.2.7 Boundary conditions

To represent the loading applied to the radius, a 180 N quasi-static force representing the

scaphoid, and a 120 N quasi-static force representing the lunate was applied to the radius [60,98].

This was based on the assumption that the scaphoid and lunate bear 60% and 40% of the load

transmitted through the wrist to the radius [98,125]. The 300 N load was selected based on

achieving a radius periosteal strain of 1,000–2,000µ [126] which is consistent with the low-

magnitude mechanical loading of animal models [126,127]. Both forces were directed toward the

centroid of the proximal most 1 cm of the radius [60]. All degrees-of-freedoms of all the nodes

of the proximal most 1 cm were completely constrained (Figure 5.8) [60]. This loading protocol

is associated with modest improvements of bone mineral parameters [60,119,126]. As per prior

research [128–130], all contacts between the VLP and bone were assumed to be bonded. In the

novel implant model, the contact between the implant and bone was assumed to be “frictional’

and was modeled using tangential behavior of the ABAQUS package, with the “rough” friction

formulation.

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Figure 5.8. FE model of the osteotomized radius treated with the volar locking plate with boundary

conditions. The 180 N was applied at the location of the scaphoid and the 120 N was applied at the

location of the lunate. Both forces were directed towards the centroid of the constrained nodes.

5.2.2.8 FE outcomes

To examine the effects of stress shielding associated with each implant, the long-term changes of

bone density within cross-sections of radius were inspected. The regional density analysis

focused on three transverse cross-sections. The transverse cross-sections were positioned

proximal to the subchondral plate [bone beneath the cartilage], and were distanced 50, 57, and 64

mm from the subchondral endplate (Figure 5.9).

To assess whether each of the implants fails under external loads, the safety factors were

calculated for the novel implant and VLP. Since Norian is a brittle material, BCM failure

criterion was used for the novel implant. Since titanium is a ductile material, von Mises failure

criterion was used for the VLP.

55

Figure 5.9. Cross-sections examined in regional density analysis to obtain the long-term effects of

implants. Transverse cross-sections located 50, 57, and 64 mm from the subchondral plate.

In order to find the average FE-predicted density of each cross-section, after the model was

completely solved and the bone remodeling algorithm reached equilibrium, the desired cross-

section was identified by “Activate/Deactivate View Cut” command in ABAQUS. Then, the

density values of all the elements present in that cross-section were calculated at their centroid,

and were externally saved in a text file. The average of all density values was reported as the

density of each individual cross-section.

5.3 Results

Maximum and minimum principal stress distribution in the novel implant is shown in Figure

5.10A and Figure 5.10B, respectively. Von Mises stress distribution in the VLP is shown in

Figure 5.10C. Both implants did not fail during the analysis. The minimum safety factor

(calculated via BCM failure criterion) in spheres was 1.71. Volar and radial rods had a minimum

safety factor of 1.9 and 3.6 respectively. The minimum safety factor (calculated via von Mises

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failure criterion) for the VLP was 19.6. The Cross-sectional view of the von Mises stress

distribution in the bone is shown in Figure 5.11, for both the novel implant and VLP.

Figure 5.10. Stress distribution in the novel implant and VLP. (A) Maximum principal stress distribution

in the novel implant. (B) Minimum principal stress distribution in the novel implant. (C) Von Mises stress

distribution in the VLP.

Figure 5.11. Cross-sectional view of the von Mises stress distribution in bone for novel implant (left) and

volar locking plate (right).

57

Figure 5.12 shows the changes in bone density at different transverse cross-sections for

both the “novel implant” and “VLP”. In all cases, the bone started to resorb right after the

implant insertion (stress shielding) and was converged to a constant value after 75 time-

increments.

Figure 5.12. Bone density changes at different transverse cross-section for both “novel implant (NI)” and

“volar locking plate (VLP)”.

Figure 5.13 shows the resultant (after convergence) density distribution at different

transverse cross-sections for both the novel implant and VLP. For both implants, cortical bone

was reserved completely at the volar side. On the dorsal side, the cortical bone was completely

resorbed in the VLP model; however, the general shape of the cortical bone was reserved in the

novel implant model, especially in more proximal cross-sections (cross-sections B and C).

58

Figure 5.13. Resultant density distribution at different transverse cross-sections when the osteotomized

bone was stabilized with the novel implant (left) and volar locking plate (right). Red regions indicate a

density of 1.8 g/cm3 and blue regions indicate 0.02 g/cm3.

Figure 5.14 shows the converged density values averaged for each cross-section for both

implants. In all cross-sections the resultant density was appeared to be higher for the “novel

implant”. The difference between the two implants ranged from 33% (cross-section A) to 36%

59

(cross-section C) in favor of the “novel implant”. On average, the density values of the novel

implant were 34% higher (SD = 2%) in transverse cross-sections (A, B, and C).

Figure 5.14. Average resultant density values at different transverse cross-sections for both "novel

implant" and “volar locking plate".

5.4 Discussion

The objective of this study was to evaluate the effects of the “novel surgical implant” on density

distribution of the bone over a long period and compare findings to the gold-standard VLP. To

quantify the resultant density distribution, four transverse were determined and the average

density of those cross-sections were compared. Density values of the novel implant were higher,

which suggests that the novel implant may be superior to the VLP in terms of avoiding stress

shielding.

The main reason why the novel implant appeared to yield higher density values was the

material. It is well-known that using stiffer implants cause more bone resorption

[54,78,79,128,131–133]. The reported elastic modulus for Norian is 24 GPa [101], while the

elastic modulus of titanium is 110 GPa [79]. The higher elasticity of the VLP increased load

60

sharing of the plate, which in turn decreased the load distribution to bone. This caused bone

resorption. Although the elastic modulus of the Norian is still higher than bone (hence bone

resorption) it is still closer to the elastic modulus of the bone (20 GPa [134]); therefore, it

resulted in less bone resorption. It should be mentioned that various elastic moduli have been

reported for Norian in the literature due to its sensitivity to different conditions (as low as 674

MPa in [100]); in this study the highest value found (24 GPa reported in [101]) was chosen to

represent the worst-case scenario.

In all cross-sections, the resultant density of the novel implant appeared to be higher than

the plate. The highest difference was observed in the transverse cross-section C (most proximal

from the osteotomy). In addition to the material, the geometry of the implants could also have

played an important role in this difference. In this simulation, since the induced osteotomy

removed all load-carrying capacities of the bone (especially on the dorsal side) the mechanical

stimuli needed to be transferred through the implants from the distal regions to proximal regions.

In the novel implant model, the mechanical stimuli were transferred through both volar and

radial rods. Conversely, with the VLP, the mechanical stimuli only transferred through the VLP

which was located on the volar side. The fact that stress was transferred both volary and radially

in the novel implant might have helped the density distribution of the proximal regions, and

might be the reason why the cortical bone was reserved on the dorsal side.

One novelty of this study was constructing an efficient and accurate FE model which was

capable of demonstrating nuanced differences between both designs. Unlike similar studies

where material properties were assumed to be constant across each element, we accounted for

the variability inside element by initially mapping and consequently solving the bone remodeling

equation at integration points.

One of the limitations of this study was associated with the material properties of the

bone. although the heterogeneity of bone was considered, the material properties were assumed

to be isotropic for trabecular and cortical bone in the QCT-based FE model, while bone is known

to be orthotropic (transversely isotropic) [135]. Accounting for different mechanical behavior in

different directions at each integration point (orthotropic behavior) might improve the accuracy

of FE models; however, it was shown previously that neglecting orthotropic material properties

often has little effect on the FE predictions [136]. Therefore, assuming inhomogeneous isotropic

material properties for the bone is a reasonable simplification, since it simplifies and accelerates

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FE modeling, and makes it a better candidate for potential future clinical applications. Second, in

this study, FE models were assumed to be linearly elastic, which means the mechanical behavior

was independent of loading regime. However, bone is known to have viscoelastic properties, in

which the mechanical behavior changes under different loading rates. Third, in contrast with the

novel implant model, in the VLP mode, all contacts between the implant and bone were assumed

to be bonded, without allowing any relative movements at their interface. This is a common

approach in modeling implant-bone systems, and it has been shown that using bonded contact

merely affects the results, while remarkably decreasing the computational time [130]. However,

future work should seek to model contact at the bone-implant interface.

In summary, this study showed that the novel implant offers higher density distributions

compared to the VLP. Rationale for this difference is primarily because the material properties of

the novel implant are comparable with bone.

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Chapter 6 Mechanical testing of distal radius fractures treated with the

volar locking plate and novel implant

6.1 Introduction

The main goal of DRF treatment is to obtain and maintain an anatomical reduction while the

fracture heals [137]. Open reduction via surgery, specifically via internal fixation through a

fixed-angle VLP, has become standard for the treatment of a wide range of unstable DRFs.

However, several complications are associated with this treatment, such as incomplete reduction

[138], fracture re-displacement [139], screw loosening [140], tendon irritation, attrition and

rupture [141,142], and carpal tunnel syndrome [143] [a medical condition caused by pressure on

the median nerve]. The ideal fracture repair implant should address these limitations, not

interfere with the fracture healing, minimize soft tissue risk, and be technically easy to perform.

The objective of this chapter was to evaluate the novel implant and VLP’s resistance to

cyclic loading, which was measured by calculating the change in fracture-length during testing.

6.2 Method

6.2.1 Specimens

Seven (N=7) cadaveric human forearm specimen (all female, mean = 82.3 years, SD = 11.3

years) were examined during this study; all of which were acquired from people who had

donated their body to research. They were all fresh-frozen at -20°C to avoid any deterioration

prior to testing. All specimens had been used in a prior study related to DRF [144] and, as a

result, all had a DRF, each with a unique pattern.

6.2.2 Radiography

Since all specimens had induced DRFs, postero-anterior and lateral 2D radiographs were done to

confirm and characterize the DRF pattern (Figure 6.1). Only those specimens with DRFs that

reflected the typical “Colles” fracture pattern were used, while wrist dislocations and very

oblique fractures were excluded from the study.

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Figure 6.1. 2D radiographs of (A) posterior-anterior and (B) medial-lateral views. All specimens were

imaged prior to testing to confirm and characterize the distal radius fracture.

6.2.3 Specimen preparation

Specimens had been potted during the DRF inducing study using PMMA (Poly(methyl

methacrylate)) and Denstone (a gypsum-based potting material). The procedure is described in detail

in [144]. In short, the soft tissue surrounding the potting materials was removed from the intact arm,

and radius and ulna were positioned in a natural falling position.

The specimens were prepared for cyclic mechanical testing, isolating two distinct groups,

the finger/thumb flexors and the wrist flexors. A transverse incision was performed in the palm

of the hand to expose the flexor superficialis and profundus tendons. The superficialis tendons

were then delivered from the distal forearm to the palmar region, and sectioned at the level of

first annular pulley, overlying the metcarpal neck, and discarded. The profundus tendons were

also delivered from the forearm to the palm, and the attached lumbrical muscles were removed.

The surrounding soft tissues were mobilized and/or removed to provide an environment for the

unimpeded proximal movement of the profundus tendons, maintaining their intact connectivity

to fingers (Figure 6.2A).

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The wrist flexors (FCR and FCU) were individually mobilized distally to just beyond the

trapezium and pisiform, respectively. The palmaris longus tendon, when present, was discarded.

Care was taken to preserve the carpal tunnel to provide a natural channel close to the axis

of rotation of the wrist, through which the finger flexors would be subjected to the loading

conditions during the testing (Figure 6.2B).

Figure 6.2. (A) Flexor profundus tendons were identified and their surrounding soft tissues were

mobilized or removed, while maintaining their intact connectivity to fingers. (B) The carpal tunnel was

preserved for simulating natural loading condition

As for the flexor tendons, the extensor tendons were prepared into two distinct groups,

the finger and thumb extensors, and the wrist extensors (Figure 6.3). The finger tendons were

delivered from the distal forearm to the dorsum of the hand and mobilized independently to a

level just proximal to the extensor hoods of the metacarpophalangeal joints. The thumb extensor

was mobilized to a similar level.

Again care was taken to preserve the extensor retinaculum at the level of the wrist to

provide a natural channel close to the axis of rotation of the wrist, through which the finger

extensors would be subjected to the loading conditions during the testing.

The wrist extensor tendons (ECRL and ECRB, and ECU) were mobilized separately to

their insertions at the bases of the second, third, and fifth metacarpals, respectively. The

brachioradialis tendon and the tendons of the first extensor compartment (APL and EPB) were

discarded.

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Figure 6.3. Extensor tendons were mobilized or separated from the surrounding soft tissues while

maintaining their natural connectivity to fingers and preserving the extensor retinaculum.

The thumb and finger tendons, on both the flexor and extensor surfaces, were passed

through four holes of a 5-hole 3D printed connector frame and sutured to themselves or their

neighboring tendon (Figure 6.4). The tendons were sutured in such a way that when tension was

applied to the frame, the fingers would flex or extend in a normal cascading pattern.

Similarly, the wrist flexor and extensor tendons were secured to different, 3-hole

connector frame. On the flexor surface, the FCR and FCU were passed through separate holes.

They were sutured to secure them to the frame. On the extensor surface, the ECRL and ECRB

tendons were passed through the radial hole, the ECU through the ulnar hole. They, too, were

sutured in order to secure them to the frame. Again, the balance of the tendon suturing was done

to bring about central flexion or extension of the wrist when tension on the frame was applied.

For each specimen there were two flexor frames, and two extensor frames (Figure 6.5).

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Figure 6.4. 3D printed connecting frames for fingers flexors/extensors (left) and wrist flexors/extensors

(right).

Figure 6.5. Connecting frames sutured to (A) flexor wrist and finger tendons, and (B) extensor wrist and

finger tendons.

To each 3D printed polylactic Acid (PLA) connector frame a braided polyester rope was

tied. The rope attached to the finger frame on the flexor surface passed through the carpal tunnel,

the rope attached to the finger extensors on the extensor surface passed through the extensor

retinaculum. There were no natural channels available for either the wrist flexor or extensor

pairings. All four ropes were then connected to four separate constant springs (25 N each) so that

finger and wrist tendon groups were independent of one another. The surgical protocol was

developed and performed by Dr. G. Johnston, an orthopedic surgeon.

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DRFs are characterized by dorsal instability. As a result, the dorsal surface tends to

implode proximally post-fracture. This brings about the commonplace and unwanted residual

dorsal tilt of the distal radius following a fracture. To mimic this dorsal instability, a standardized

dorsal wedge of bone was removed just opposite from the fracture of the volar cortex. An

attempt to place the apex of the wedge at the site of the volar cortical fracture was made for each

specimen. The distance from the proximal and distal transverse osteotomies was 10 mm and was

positioned 20 mm proximal to the tip of the radial styloid, a protocol which has been widely

reported in the literature in similar mechanical testing systems [106–108,145–148]. When

performing the osteotomies, we made sure that a complete circumferential fracture was achieved,

either induced by previous DRF or by sawing through the volar cortex after removing the wedge

(Figure 6.6). The osteotomy removed all load-bearing capabilities of bone, equivalent to a worst-

case-scenario for DRF fixation [106].

Figure 6.6. Standardized osteotomy performed on all specimens. The osteotomy was 10 mm wide and

was positioned 20 mm proximal to the tip of the radial styloid

After performing the osteotomies, and prior to testing the implants, mechanical testing

with no fixation, then with agar (to simulate hematoma) was done, and in both cases prompt

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complete failure of the construct was observed. In other words, the agar did not provide any

fixation. The novel surgical implant was tested first, followed by the VLP.. All specimens were

tested with both the novel surgical implant and the VLP (Figure 6.7). In the case of the novel

implant, after introducing the implant into the intramedullary shell, the bone was filled with agar,

not only to mimic the gelatinous hematoma which immediately develops after a fracture, but also

to keep the spheres within the bone given the artificial nature of a dorsal bone defect (Figure

6.7B).

Figure 6.7. (A) Novel surgical implant inserted inside the osteotomized specimen, (B) Osteotomy filled

with agar around the novel surgical implant. Osteotomized specimen treated with VLP in (C) anterior and

(D) lateral views.

6.2.4 Mechanical testing setup

To mimic the natural loading applied to the arm, the specimens underwent cyclic mechanical

testing using a custom-built setup and a material testing system (MTS Bionix Servohydraulic Test

System, Model 370.02) while tension load was applied to tendons (Figure 6.8).

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Figure 6.8. Specimen placed inside a custom-built setup and MTS Bionix Servohydraulic Test System

Model 370.02

The specimens were placed inside the holder in a natural position (0° flexion/extension).

Ropes connected to the tendons were positioned inside a pulley guidance system, to keep the

loading in a natural direction. Each flexor/extensor rope was connected to a 25-N constant force

spring, which applied a total force of 100 N axial force on the arm during the testing [113]. A pin

was attached to the distal radius dorsally, and distal to the distal osteotomy. The pin was then

connected to a position tracking linear variable inductance transducer (LVIT) (OMEGA, High

Accuracy Displacement Transducer/Motion Sensors, LDI-119-025-A010A). The top view of the

testing system is shown in Figure 6.9. The LVIT probe was connected to the pin in a way which

allowed movement perpendicular to the axis of the radius. Therefore, only axial movement of the

distal segment of the osteotomy was captured by the LVIT. The LVIT captured the movement

from a distance from the bone surface; therefore, what LVIT measured was not bone

displacement, but it was linearly related to it. Hence, LVIT measures were multiplied by a

constant (between 2.5 and 3 for different specimens) to obtain the bone displacement. As the

proximal side of the osteotomy was completely fixed, this was equal to a change in the fracture-

length.

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Figure 6.9. The top view of the testing system.

Using the torsional capabilities of the MTS, the specimens were cycled between -30°/30°

flexion/extension, at 0.5 Hz, for 2000 cycles [107,149–151]. MTS and LVIT were connected to a

data acquisition system (DAQ, National Instruments PXIe-1078 chassis with a PXIe-4300

voltage measurement) which recorded actuator angular displacements and LVIT measurements

via a custom LABVIEW program.

6.2.5 Mechanical testing outcomes

Angular displacements, and LVIT measurements, which captured fracture-length changes, were

recorded. Change in fracture length, as a function of number of cycles, was used to assess

implant resistance to fatigue loading. At any point of testing, if the change in fracture-length

exceeded the osteotomy length of 10 mm (fracture completely collapsed), the testing stopped and

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number of cycles till failure was recorded. If the change in fracture-length remained under 10

mm, a custom MATLAB code was used to obtain the average change in fracture-length. With

this code, maximum and minimum LVIT measurements (corresponding to positions of the dorsal

side of osteotomy in extension and flexion, respectively) obtained in each cycle (Figure 6.10A).

The “change in fracture-length” was calculated for each cycle (Figure 6.10B). These values were

then averaged over all cycles, and one final value was calculated as the final output for each

implant.

Figure 6.10. (A) LVIT maximum and minimum positions. (B) Change in fracture length.

6.2.6 Statistics

Since the same specimens were used to test both implants, a paired, two-tailed student t-test was

performed using IBM® SPSS Statistics 24, to determine whether there was a significant

difference between the mean of two groups. The null hypothesis was that the mean difference

between the paired samples was zero. Level of significance was determined as 5% (p < 0.05).

6.3 Results

Changes in fracture fracture-length for both novel implant and VLP is shown in Table 6.1.

Additional figures showing the maximum/minimum position of the LVIT and changes in

fracture-length for all tests are shown in Appendix B. On average, the fracture-length changed by

1.3 mm (SD = 1.1 mm) for the novel implant, while it was 0.100 mm (SD = 0.11 mm) for the

VLP.

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Table 6.1. Changes in fracture-length (mm) when the osteotomized bone was treated with the novel

implant and the volar locking plate.

Specimen Novel implant Volar locking plate

1 2.8557 0.1875

2 1.011 0.3205

3 2.8813 0.0133

4 0.0112 0.028

5 0.37 0.0894

6 1.2004 0.0297

7 1.1076 0.0327

Mean 1.3482 0.1002

SD 1.1226 0.1144

A graphical representation of the means and standard deviations of the two groups is

displayed in Figure 6.11. The paired t-test indicated significant differences between the two

groups in terms of change in fracture length (p = 0.026). Thus, the null hypothesis was rejected.

Figure 6.11. Graphical representation of the means and standard deviation of the two data groups.

0

0.5

1

1.5

2

2.5

3

Novel implant Volar locking plate

Ch

an

ge

in f

ract

ure

-len

gth

(m

m)

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6.4 Discussion

The purpose of the mechanical testing study presented in this chapter was to compare the

resistance of the novel surgical implant and the VLP to fatigue loading. Our results showed the

novel implant was less resilient under cyclic fatigue loading compared to VLP, and a higher

change in fracture-length was observed.

High variance was found with the results of the novel implant (SD = 1.12 mm), and the

outcome ranged from very stable (change in fracture-length = 0.01) to highly un-stable (change

in fracture-length = 2.88 mm). We believe the reason for this variance, at least in part, originates

from the surgical procedure used during the testing. In this study, first, the rods were inserted

inside the bone by hand, then the empty space between the rods was filled with spheres by

putting as many spheres inside as possible. The novel implant was designed to provide stability

with the help of friction between rods and spheres, and, the provided stability is highly

dependent on the positions of the rods. For clinical use, special parts are needed to be designed to

easily and accurately place the rods on the desired locations. We believe this can notably

enhance the repeatability of the outcomes, since one very strong stabilization (change in fracture-

length = 0.01) and one acceptable stabilization (change in fracture-length = 0.37) was obtained in

this study.

Also, the standard osteotomy performed on all specimens removed a wedge of the bone.

Since the stability of the novel implant is established by the friction force between the bone and

rods, removing a piece of bone adversely affects its stability, while having no effect on the VLP.

Accordingly, in the real clinical case, a less severe fracture case would offer improved friction

and thus likely a smaller change in fracture length.

The clinical significance of the maximal measured change of fracture length (2.88 mm) in

the novel implant testing should be acknowledged. This would imply a loss of volar tilt of the

fracture fragment of approximately nine degrees. If the initial fracture reduction was satisfactory

(e.g. 10 degrees of volar tilt) then an isolated loss of nine degrees would still render a reduction

that would still be acceptable.

The main limitation associated with the mechanical testing was the number of specimens.

Only seven specimens were tested during this study, which resulted in relatively high standard

deviations for both groups. However, this study proves the potential clinical use of the novel

74

implant design, as a proof-of-concept, while acknowledging further research is needed before the

studied novel implant is ready for clinical use. Another limitation was associated with the

existent DRF on all samples. Specimens used in this study were previously fractured in a prior

related study [144] and consequently, all had a unique DRF pattern. Although a standardized

fracture was induced prior to testing on all specimens, the fracture still differed between

specimens. However, since same specimens were used to compare the two implants, the effect of

this should not be significant. Another limitation was related to the in-vitro wrist simulator used

in this study. A passive motion simulator was used to simulate flexion/extension. Although

passive motion simulators can adequately generate physiological load distribution in the radius

[95], active motion simulators provide a more realistic load distribution. Also, a constant load

was applied to the tendons. It can be argued that this approach is not the most realistic approach.

During the physiological wrist motion, flexor and extensor muscles are not activated

simultaneously. Therefore, it is more accurate to develop and implement individual time-

dependent tendon loading protocol for each tendon [95]. Another limitation was associated with

the material of the novel implant which tested in this study. The implant was designed to be

produced with Norian; however, due to the complicated production procedure of Norian, the

implants were 3D printed using PLA filaments. Since the mechanical strength of the PLA is

higher than the Norian, the results of the mechanical testing cannot be used to assess whether the

novel implant would fail under cyclic loading. However, the 3-D printed prototypes were

successfully used to investigate the geometrical features of the novel implant (different design

iterations) and to evaluate the effectiveness of the final design on stabalizing the fracture.

In conclusion, although there was a significant difference between the average of the

novel implant and VLP outcomes, this study proved the potential of the novel surgical implant as

a proof-of-concept.

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Chapter 7 Discussion

7.1 Overview of findings

The gold-standard VLP for DRF is not without complications. The aim of this research was to

evaluate the feasibility of a novel surgical implant for clinical treatment of DRFs. Since the novel

implant is intramedullary in its application there should be no risk of either flexor or extensor

tendon attritional rupture. The soft tissue dissection, carried out dorsally and proximal to the

extensor retinaculum, is minimal compared to a volar approach, presumably limiting the

potential for surgically-induced scarring and resulting limitation of restoration of wrist motion.

A key accomplishment of Chapter 4 was to present an optimal design for the novel surgical

implant in terms of load carrying capacity and ease of surgery. For the novel surgical design, our

research indicated that spheres were the weakest link (i.e., they will fail first). The porous or

perforated spheres promote bone in-growth but had inferior safety factors in relation to solid

spheres. An optimal design was investigated for spheres and rods, derived via various design

iterations by simulating the surgery process on cadaveric specimen to optimize the surgery

procedure. The final design presented as the novel implant consisted of 6 mm solid spheres and a

system of linked volar-radial rods.

A key accomplishment of Chapter 5 was to evaluate the long-term effects of the novel

implant vs the VLP by comparing the density distribution predicted when the osteotomized

radius was treated by each implant. The results showed that the novel implant resulted in 17%

higher density values (averaged of all investigated cross-sections) compared with the VLP,

which indicated that the novel implant was less susceptible to stress shielding. Another

accomplishment of Chapter 5 was to present a novel framework for evaluating the long-term

effects of bone fixation devices by integrating subject-specific FE modeling with a bone adaption

algorithm. The methodology presented here was also valuable regarding numerical analysis

methodology. Here, the variability of the elastic modulus had been accounted for by updating the

material properties at integration points, which was a novel approach among time-dependent

subject-specific FE studies. This methodology results in more accurate and efficient models

which can be used with higher confidence to predict the long-term effects of bone fixation

devices.

A key accomplishment of Chapter 6 was to present a mechanical testing framework capable

of simulating physiological loading conditions. The osteotomized specimens were treated by

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both implants individually, and the resistance of the implants to mechanical testing was

evaluated. The VLP almost completely stabilized the fracture in all tests (change in fracture-

length = 0.1 mm, on average), while the novel implant did not completely stabilize the fracture in

all cases (average change in fracture-length = 1.35 mm); however, complete stabilization was

achieved in one test (change in fracture-length = 0.0112 mm).

7.2 Study Strengths and Limitations

Optimal design of the novel implant was explored in this study. One strength related to this

analysis was that all different combinations of design factors were investigated via a full factorial

design of experiment. In this analysis, the effect of each factor on the response variable (safety

factor), as well as the effects of interactions between factors, were investigated. The main

limitation of this study was related to simplistic FE modeling. First, a simplified model of the

radius was used to derive the contact force between the spheres, and then, the calculated force

was applied to the spheres. Although a number of different sphere diameters and positions (how

spheres fill the space inside of the bone) were analyzed, and the maximum observed force was

used to evaluate the safety factors, this force changes under different settings (different sphere

positioning).

A main strength of the computer simulation was to use subject-specific FE modeling

derived from CT images for modeling the radius, as opposed to idealized geometries. In addition

to the geometry, the heterogeneity of material properties of the bone was also considered, using

material property-density equation, which has shown to improve the accuracy of QCT-based FE

predictions [136]. Second, in this study, the material properties of QCT-based FE models were

mapped to integration points, which increased the accuracy and decreased the computation time.

This is important as lesser computation time makes this technique a potential tool in clinical

practice. In addition, by considering material properties at the level of integration points (as

opposed to the level of elements, which assumes identical material properties for all integration

points of one element), the variability of material properties inside the elements was accounted

for, which increased the accuracy of QCT-FE based predictions. To the best of our knowledge,

this was the first study to incorporate element-based material mapping method to construct QCT-

FE models of the radius. Third, another novelty of this research was to propose an efficient and

accurate framework to predict the long-term effects of the bone fixation devices. In this study, a

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novel element-based numerical approach for implementing bone remodeling algorithm into FE

models was used, which significantly decreased the computational time while providing accurate

results. In this approach, the bone remodeling equation was solved and density values were

updated at integration points, as opposed to nodes in traditional, slower gold-standard numerical

implementations. The main limitation of this study was the assumption of isotropic and linearly

elastic material properties for bone. Bone, though, has been reported to be orthotropic

(transversely isotropic) [120]. In addition, the bone remodeling equation was solved using the

Euler’s forward integration scheme. Although this approach is widely used in the literature

[48,51,54,123,124], recent studies showed that a more advanced integration scheme (e.g. the

first-order Adams-Bashforth method [123]) can enhance the accuracy of the model and reduce

the computational cost. Another limitation was that the trabecular and cortical bones were not

separated in the QCT-FE model, and only one material property-density equation was used to

assign material properties to bone. It has been shown that separating the cortical and trabecular

bone (either by thresholding [152] or separate segmentation [153]) can improve the accuracy of

QCT-FE models.

We presented a robust mechanical testing platform for simulating physiological conditions

of the radius. This is important since the resistance of implants to fatigue loading plays an

important role to assess their effectiveness. In this platform, the hand was cycled through

flexion/extension while axial force was applied to the radius through tendons to mimic the

physiological conditions. One strength of this study was that the carpal tunnel and the extensor

retinaculum were preserved in specimens, and ropes connected to the tendons crossed through

these channels to provide a natural loading direction for tendons during the testing. Another

strength of this study was to create a standardized fracture pattern for all specimens. This was

accomplished by removing a dorsal wedge of the bone from the dorsal side of the radius. One

limitation associated with the mechanical testing setup was the material used for the novel

implant. Another limitation of this study was the limited range of motion. The specimens were

only cycled between -30°/30° flexion/extension.

7.3 Conclusions

1- Solid spheres and a composition of volar-radial rods linked together were showed to best

meet our design criteria.

78

2- By using subject-specific FE models integrated with a bone adaptation algorithm, the

investigated novel implant appeared to provide better density distribution in the bone

compared to the VLP.

3- The novel material mapping method and numerical implementation of the bone

remodeling algorithm proposed in this study showed to be an accurate and efficient

framework.

4- Except for 1 specimen, the novel implant was not able to match the mechanical stability

of the VLP during the mechanical testing. Future research is needed to design a

dependable and repeatable surgery procedure for securing the novel implant parts inside

the radius.

7.4 Future work

1- In this study, only trabecular-specific material property-density equation was used to

model material properties of the bone. In future studies, the cortical bone can be

separated from the trabecular bone by one of many common approaches (manual

threshold, manual segmentation, automatic segmentation, etc.) and cortical-specific and

trabecular-specific equation can be used to assign the material properties to the models.

2- In this study, isotropic material properties were assumed. It would be useful to model

trabecular anisotropy with future QCT-FE models of the distal radius.

3- In this study, only external forces of lunate and scaphoid were modeled, and the muscle

forces were ignored. In future studies, muscle forces should be included in the FE model

to predict a more accurate density distribution.

4- The mathematical bone adaptation algorithm used in this study was a simple bi-linear

strain energy-based theory. More advanced bone remodeling theories have been recently

proposed which can be incorporated into the QCT-FE model.

5- Currently, the surgery procedure determined for the insertion of the novel implant is to

drill a 6.5 mm hole on the proximal side of the radius and insert the implants through the

drilled hole. Since this reduces the mechanical integrity of the bone, alternative surgical

approaches can be explored to minimize the bone injury (e.g., minimally invasive surgery

techniques).

79

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Appendix A – Optimal Design of Spheres Raw Data

Table A. 1. Results of the 6-hole design.

Diameter (mm) Thickness (mm) Hole-size (mm) 6-hole Safety Factor

5 1 1.5 0.47274

5 1 2 0.373

5 1.5 1.5 0.504074

5 1.5 2 0.234363

5 2 1.5 0.540814

5 2 2 0.234363

5.5 1 1.5 0.522259

5.5 1 2 0.491518

5.5 1.5 1.5 0.587851

5.5 1.5 2 0.549629

5.5 2 1.5 0.607888

5.5 2 2 0.549925

6 1 1.5 0.573962

6 1 2 0.541962

6 1.5 1.5 0.639296

6 1.5 2 0.668999

6 2 1.5 0.66574

6 2 2 0.699444

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Table A. 2. ANOVA for 6-hole design.

Type III Sum of Squares df Mean Square F Sig.

Corrected Model .212a 3 .071 11.900 .000

Intercept .024 1 .024 3.962 .066

Diameter .170 1 .170 28.677 .000

Thickness .009 1 .009 1.461 .247

Hole-size .033 1 .033 5.563 .033

Error .083 14 .006

Total 5.265 18

Corrected Total .295 17

a. R Squared = .718 (Adjusted R Squared = .658)

99

Table A. 3. Results of the 4-hole design.

Diameter (mm) Thickness (mm) Hole-size (mm) 4-hole Safety Factor

5 1 1.5 0.372814442

5 1 2 0.344021878

5 1.5 1.5 0.477073597

5 1.5 2 0.406777371

5 2 1.5 0.500406907

5 2 2 0.406777371

5.5 1 1.5 0.450777327

5.5 1 2 0.305233028

5.5 1.5 1.5 0.470888418

5.5 1.5 2 0.481073593

5.5 2 1.5 0.542480939

5.5 2 2 0.470221752

6 1 1.5 0.433666233

6 1 2 0.373258886

6 1.5 1.5 0.570777207

6 1.5 2 0.482629147

6 2 1.5 0.582406825

6 2 2 0.582629047

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Table A. 4. ANOVA for 4-hole design.

Type III Sum of Squares df Mean Square F Sig.

Corrected Model .093a 3 .031 24.033 .000

Intercept 1.026E-6 1 1.026E-6 .001 .978

Diameter .022 1 .022 17.289 .001

Thickness .054 1 .054 41.852 .000

Hole-size .017 1 .017 12.957 .003

Error .018 14 .001

Total 3.896 18

Corrected Total .111 17

a. R Squared = .837 (Adjusted R Squared = .803)

101

Appendix B – Mechanical Testing Raw Data

7.4.1.1.1.1

Figure B. 1. LVIT maximum and minimum positions (left column) and change in fracture length (right

column) for the novel implant (top row) and volar locking plate (bottom row) for the specimen 15-

03022R (test 1).

102



02039R (test 2).

103

Figure B. 3. . LVIT maximum and minimum positions (left column) and change in fracture length (right


06029R (test 3).

104



06064R (test 4).

105



05068L (test 5).

106



08067R (test 6).

107



05024L (test 7).

comparison of a novel surgical implant with the volar

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