Mechanical considerations in fracture...

$: Mechanical considerations in fracture fixationeprints.qut.edu.au/51002/1/Pushpanjali_Krishnakanth...Fracture fixation devices should provide a favourable mechanical and biological$
Mechanical considerations

in fracture fixation

Thesis submitted by

Pushpanjali Krishnakanth

B.E., MSc

This thesis is submitted in fulfillment of the requirements for

the degree of Doctor of Philosophy

Institute of Health and Biomedical Innovation

School of Engineering Systems

Faculty of Built Environment and Engineering

Queensland University of Technology

Brisbane, Australia

2012

Abstract

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Abstract

Bone’s capacity to repair following trauma is both unique and astounding.

However, fractures sometimes fail to heal. Hence, the goal of fracture treatment is

the restoration of bone’s structure, composition and function. Fracture fixation

devices should provide a favourable mechanical and biological environment for

healing to occur.

The use of internal fixation is increasing as these devices may be applied with less

invasive techniques. Recent studies suggest however that, internal fixation devices

may be overly stiff and suppresses callus formation. The degree of mechanical

stability influences the healing outcome. This is determined by the stiffness of the

fixation device and the degree of limb loading. This project aims to characterise the

fixation stability of an internal plate fixation device and the influence of

modifications to its configuration on implant stability. As there are no standardised

methods for the determination of fixation stiffness, the first part of this project

aims to compares different methodologies and determines the most appropriate

method to characterise the stiffness of internal plate fixators.

The stiffness of a fixation device also influences the physiological loads

experienced by the healing bone. Since bone adapts to this applied load by

undergoing changes through a remodelling process, undesirable changes could

occur during the period of treatment with an implant. The second part of this

project aims to develop a methodology to quantify remodelling changes. This

quantification is expected to aid our understanding of the changes in pattern due

to implant related remodelling and on the factors driving the remodelling process.

Abstract

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Knowledge gained in this project is useful to understand how the configuration of

internal fixation devices can promote timely healing and prevent undesirable bone

loss.

Keywords

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Keywords

Bone healing

Bone density

Bone geometry

Bone remodelling

Contra-lateral bone

Fixation stability

Internal fixation

Fixator configuration

Table of Contents

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Table of Contents Abstract .............................................................................................................................................. iii

Keywords ............................................................................................................................................. v

List of figures .................................................................................................................................. xii

List of tables .................................................................................................................................. xvii

Abbreviations ............................................................................................................................. xviii

Authorship ....................................................................................................................................... xx

1.1 Background .......................................................................................................................... 2

1.2 Problem description ......................................................................................................... 2

1.3 Research question and scope ........................................................................................ 4

1.3.1 Research question ..................................................................................................... 4

1.3.2 Scope .............................................................................................................................. 4

1.4 Thesis outline ...................................................................................................................... 5

Section 1: Fixation stability and healing ....................................................................... 5

Section 2: Fixation stability and remodelling ............................................................. 6

2.1 Bone ......................................................................................................................................... 8

2.1.1 Function of a bone ..................................................................................................... 9

2.1.2 Structure, type and composition of bone ......................................................... 9

2.1.3 Bone growth and development .......................................................................... 13

2.1.4 Bone modelling and remodelling ...................................................................... 15

2.2 Bone fractures ................................................................................................................... 16

2.2.1 Fracture healing process ...................................................................................... 18

Primary fracture healing .................................................................................................. 18

Secondary fracture healing .............................................................................................. 18

2.2.2 Factors influencing fracture healing process ............................................... 20

Mechanical factors (fixation stability) and blood supply influencing fracture

healing process .......................................................................................................................... 20

2.3 Fracture treatment ...................................................................................................... 22

2.3.1 Principles of fracture fixation ......................................................................... 23

2.3.2 Types of fracture fixation devices................................................................. 27

2.4 Influence of fixation stability on healing and remodelling .......................... 30

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

2. Literature review.............................................................................................................................. 7

Table of Contents

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2.4.1 Fixation stability and healing ......................................................................... 31

2.4.2 Fixation stability and remodelling ............................................................... 32

2.5 Finite Element Analysis (FEA) ............................................................................... 33

2.6 Computed Tomography (CT) of bones ................................................................ 34

2.7 Animal (ovine) models in orthopaedic research............................................. 35

Introduction .................................................................................................................................... 37

Problem description .................................................................................................................... 39

Goal ..................................................................................................................................................... 42

Structure .......................................................................................................................................... 42

3.1 Introduction ....................................................................................................................... 44

3.2 Materials and methods .................................................................................................. 48

3.2.1 Internal fixator ......................................................................................................... 48

3.2.2 Implant-Cylinder construct ................................................................................. 49

3.2.3 Implant-Bone construct........................................................................................ 49

3.2.4 Creation of Finite Element (FE) model ........................................................... 50

3.2.5 Boundary Conditions ............................................................................................. 51

3.2.6 Analysis ....................................................................................................................... 55

3.3 Results .................................................................................................................................. 56

3.4 Discussion ........................................................................................................................... 59

3.4.1 Method of stiffness calculation .......................................................................... 60

3.4.2 Boundary Conditions for stiffness determination ..................................... 61

3.4.3 Bone contoured geometry versus simple cylinder .................................... 64

3.5 Conclusion .......................................................................................................................... 66

4.1 Introduction ....................................................................................................................... 68

4.2 Materials and methods: ................................................................................................. 71

4.2.1 Internal fixator ......................................................................................................... 71

4.2.2 Implant-Bone analogue construct .................................................................... 71

4.2.3 Finite element model ............................................................................................. 72

4.2.4 Stiffness determination ........................................................................................ 73

4.2.5 Configurations .......................................................................................................... 74

4.3 Results .................................................................................................................................. 76

Section 1 Fixation stability and healing ................................................................................... 37

3 Development of a method to determine internal plate fixator stiffness .................. 43

4 Investigation of the influence of fixator configuration on fixation stiffness ........... 67

Table of Contents

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4.3.1 Standard configuration ......................................................................................... 76

4.3.2 Internal fixator material properties ................................................................. 77

4.3.3 Internal fixator offset ............................................................................................. 77

4.3.4 Internal fixator inclination ................................................................................... 78

4.3.5 Screw configuration ............................................................................................... 79

4.3.6 Far cortical locking ................................................................................................. 80

4.4 Discussion ........................................................................................................................... 80

Introduction .................................................................................................................................... 87

Problem description..................................................................................................................... 88

Goal ..................................................................................................................................................... 90

Structure ........................................................................................................................................... 90

5.1 Introduction ....................................................................................................................... 92

5.1.1 Previous bone-remodelling quantification methods ................................. 93

5.1.2 Use of contra-lateral ovine tibia as a pre-operative control in bone

remodelling analysis ................................................................................................................ 94

Contra-lateral bone ............................................................................................................. 94

Ovine tibia .............................................................................................................................. 95

5.1.3 Goal ............................................................................................................................... 96

5.1.4 Validation of bone-remodelling algorithms .................................................. 96

5.2 Material and methods..................................................................................................... 97

5.2.1 Intact left and right tibia comparison .............................................................. 97

Geometry comparison ....................................................................................................... 99

Bone density comparison .............................................................................................. 100

5.2.2 Comparison of operated and intact contra-lateral tibia: (Empty defect

group) 104

5.3 Results ............................................................................................................................... 106

5.3.1 Intact left and right tibia comparison ........................................................... 106

Geometry comparison .................................................................................................... 106

Density comparison ......................................................................................................... 108

5.3.2 Comparison of operated and intact contra-lateral tibia: Empty defect

(3 months post-operative) ................................................................................................. 111

Section 2 Fixation stability and remodelling ........................................................................ 87

5 Development of a method to quantify remodelling changes ....................................... 91

Table of Contents

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5.4 Discussion ......................................................................................................................... 114

5.4.1 Intact left and right tibia comparison ........................................................... 114

5.4.2 Operated and intact contra-lateral tibia comparison: Empty Defect

(defect was left untreated) (3 months post-operative) ........................................... 118

5.5 Conclusion ........................................................................................................................ 119

6.1 Introduction ..................................................................................................................... 122

6.2 Materials and methods ................................................................................................ 125

6.3 Results ................................................................................................................................ 126

6.3.1 Density changes within the cortical region ................................................ 126

Density changes at 3 months ........................................................................................ 128

Density changes at 12 months ..................................................................................... 129

6.4 Discussion ......................................................................................................................... 129

6.4.1 Density changes within the cortical region ................................................ 129

Density changes at 3 months ........................................................................................ 129

Density changes at 12 months ..................................................................................... 131

6.5 Conclusion ........................................................................................................................ 132

7.1 Discussion ......................................................................................................................... 134

Section 1: Fixation stability and healing ........................................................................ 134

Section 2: Fixation stability and remodelling .............................................................. 142

7.2 Conclusion ........................................................................................................................ 145

Appendix A: Determination of IFM (Inter-Fragmentary Movement) ................ 147

Calculation of rotational inter-fragmentary movements ........................................ 148

Defining LCS (Local Coordinate System): ................................................................ 148

Calculation of rotation matrix ...................................................................................... 150

Calculation of Euler angles from rotation matrix ................................................. 150

Appendix B: Sensitivity analysis ...................................................................................... 152

Material property of cortical bone: ................................................................................. 152

Analysis: ............................................................................................................................... 152

Conclusion: .......................................................................................................................... 153

6 Validation of bone remodelling quantification method ............................................... 121

7 Overall discussion and conclusion ....................................................................................... 133

Table of Contents

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Appendix C: Comparison of Finite Element Analysis (FEA) results against

mechanical or in-vitro tests ................................................................................................... 154

FE model comparison: Cylinder-fixator model .......................................................... 154

Mechanical testing: .......................................................................................................... 155

Testing equipment in use: ............................................................................................. 155

Set up of tracking system .............................................................................................. 156

Testing .................................................................................................................................. 156

FE analysis: ......................................................................................................................... 156

Transformation of 3D model into mechanical testing coordinate system: 157

Analysis: ............................................................................................................................... 159

Conclusion:.......................................................................................................................... 160

Appendix D: Journal Paper: Can the contra-lateral limb be used as a control

with respect to analyses of bone remodelling? (Published) ..................................... 161

References ....................................................................................................................................................167

List of figures

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List of figures

Figure 1 Shows the surface of a sheep tibia reconstructed from computed

tomography (CT) data using AMIRA software (Visage Imaging GmbH, Berlin,

Germany) used for illustration of the three regions of a tibia. ........................................ 10

Figure 2 Cross sectional view of a long bone.. ...................................................................... 11

Figure 3 Cross sectional view illustrating types of bone.. ................................................ 11

Figure 4 Schematic representation showing types of bone cells.. ................................ 12

Figure 5 Demonstrates skeletal development of long bone growth through

endochondral ossification.............................................................................................................. 14

Figure 6 Illustrates types of fracture lines.. ........................................................................... 17

Figure 7 Shows an X-Ray image of a fracture.. ...................................................................... 17

Figure 8 Shows schematic of a section through an intact long bone.. ......................... 19

Figure 9 Illustrates fracture healing stages: (a) inflammation phase; (b) callus

differentiation phase, (c) endochondral ossification phase and (d) Restoration of

original geometry of bone. ............................................................................................................. 19

Figure 10 Müllers plate design achieves inter-fragmentary compression by

tightening a tensioner that is temporarily anchored to the bone and the plate.. ..... 24

Figure 11 Illustrates tension band principle.. ....................................................................... 25

Figure 12 Shows an X-ray illustrating bridging osteosynthesis.. .................................. 27

Figure 13 Hoffman external fixator.. ........................................................................................ 27

Figure 14 Ilizarov external fixator.. .......................................................................................... 28

Figure 15 Plaster cast.. ................................................................................................................... 28

Figure 16 Intramedullary nail and screws.. ........................................................................... 29

List of figures

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Figure 17 Generic locking plate (modified from standard 4.5mm Locking

Compression Plate). .......................................................................................................................... 31

Figure 18 Callus histology after 6 weeks of healing.. ......................................................... 33

Figure 19 Shows the generic internal fixator attached to a cylinder. The outermost

screw holes were left empty to replicate the behaviour of a 7-hole plate with a

working of length of one empty hole spanning the fracture gap. The plate is offset

from the outer surface of cylinder by 1 mm............................................................................ 49

Figure 20 Shows the generic internal fixator attached to an ovine tibia. ................... 50

Figure 21 This close-up view of the plate-cylinder construct shows the relative

mesh densities for the components, the finest mesh was applied to the plate and

screws. The plate is offset from the outer surface of cylinder by 1 mm. ..................... 51

Figure 22 Schematic shows the MPC boundary condition. (DoFs = Degrees of

Freedom). ............................................................................................................................................. 53

Figure 23 Schematic shows the boundary conditions employed in each of the load

cases as defined by Kassi et al and Augat et al as well as the for the application of

loads via MPC. ..................................................................................................................................... 54

Figure 24 Shows the stiffness components determined for each of the three

investigated boundary conditions using implant-cylinder construct. .......................... 58

Figure 25 Shows the stiffness components determined for the internal fixator

affixed at an offset distance of 3 mm to a hollow cylinder and a bone contoured

geometry using MPC boundary condition. .............................................................................. 59

Figure 26 Shows the axial compressional stiffness value determined via stiffness

matrix method for different axial IFM’s (-0.69 mm - -0.73 mm) for the medial-

lateral bending load case. ............................................................................................................... 61

Figure 27 Internal fixator and bone cylinder construct in the standard

configuration (0xxx0xxx0) for an effective plate length of 7-hole with three screws

on either side of the osteotomy gap. .......................................................................................... 72

List of figures

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Figure 28 Illustration of calculation of axial component of IFM (Inter Fragmentary

Movement) using MPC (Multi Point Constraint) BC (Boundary Condition). ............. 74

Figure 29 Schematic representation of the screw configurations investigated.

(Notation: e.g. Top left 0XXX0XXX0, Top right X0XX0XX0X). .......................................... 75

Figure 30 Shows a generic locking plate (modified from 9 hole, 4.5 mm standard

Locking Compression Plate) with three screws on either side of the fracture gap

leaving the middle screw hole empty. ....................................................................................... 75

Figure 31 Schematic (plan/top view) represents principal of FCL in FE analysis. 76

Figure 32 Shows the division of an intact tibia into regions (proximal, diaphyseal

and distal). ......................................................................................................................................... 100

Figure 33 A colour map display of HU values across the cortex (illustrating

gradient in HU near the boundary). ......................................................................................... 102

Figure 34 The CT data was divided into four quarters (medial, lateral, anterior and

posterior) for determination of density differences. ........................................................ 104

Figure 35 shown here are transverse cross-sections of CT data of intact (figure on

left) and operated (figure on right) tibia divided into four quarters (medial, lateral,

anterior and posterior). A compression plate was affixed medially with bi-cortical

screws. ................................................................................................................................................. 105

Figure 36 (a): Shows the shell-to-shell deviation of an intact tibia pair (left and

right). Grey regions indicate a deviation of less than 1mm. The average shell-to-

shell deviation along the whole tibial length for this pair is 0.32 mm. (b): Shows the

regional (proximal, diaphyseal/shaft and distal regions) deviation. The average

shell-to-shell deviation in this case is 0.29 mm for the proximal, 0.41 mm for the

distal and 0.19 mm for the diaphyseal/shaft region. Grey regions indicate a

deviation of less than 0.5 mm. .................................................................................................... 108

Figure 37 Shows a density difference (%) histogram for intact left and right tibiae

pairs for the quarter volumes analysed (n =8). ................................................................... 109

Figure 38 Shows the density difference (left vs. right) in percentage in each of the

four (medial, lateral, anterior and posterior) quarters for a sheep tibia .................. 110

List of figures

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Figure 39 Shows the bone loss, as percentage change in density in each of the four

(medial, lateral, anterior and posterior) quarters for a sheep tibia with segmental

defect (SD) treated with a compression plate 3 months after surgery. .................... 112

Figure 40 Shows the peak density difference (%) in all quarters around the screw

holes and the segmental defect (SD) between the operated and intact contra-lateral

tibia at 3 months. ............................................................................................................................ 113


pairs (dark grey) and operated and contra-lateral tibiae pairs (light grey) for the

quarter volumes analysed (n =8). ............................................................................................ 114

Figure 42 Shows the percentage density difference between adjacent CT slices of a

tibia in the medial quarter for one tibia pair. The lateral, anterior and posterior

quarters also showed density differences of < 2% between adjacent transverse

slices along the diaphyseal region of the tibia..................................................................... 117

Figure 43 Representative 3D CT reconstructions of critical segment bone defects,

which were left untreated (A), reconstructed with a mPCL-TCP scaffold (B) and a

mPCL-TCP scaffold combined with rhBMP-7 (C).. ............................................................. 123

Figure 44 Demonstrates the differences in load transmission path between empty

defect and groups with PCL-TCP scaffold. ............................................................................ 124

Figure 45 Shows the change in density (%) at 3 months for the medial (a) and

lateral (b) aspects of the tibia for the empty defect (Black), scaffold (Light Grey)

and scaffold with BMP (Dark Grey) groups (mean ± standard deviation).

SD=Segmental Defect. ................................................................................................................... 127


lateral (b) aspects of the tibia for the scaffold (Light Grey) and scaffold with BMP

(Dark Grey) groups (mean ± standard deviation). SD=Segmental Defect. ............... 128

Figure 47 Illustrates calculation of translational inter-fragmentary movements.

................................................................................................................................................................ 147

List of figures

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Figure 48 Illustration of calculation procedure for unit vectors that forms the LCS

and the Rotation Transformation Matrix (RTM). (ULCSO = Upper Local Coordinate

System at time zero). ..................................................................................................................... 149

Figure 49 shows the axial compressional stiffness value determined for the chosen

Young’s modulus (14 GPa – 24 GPa) using implant-PVC construct. ............................ 153

List of tables

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List of tables

Table 1 Lists the inter-fragmentary movements for the six load cases and the

stiffness components determined from either the stiffness matrix (Km) or the

individual stiffness (Ki) for the implant-bone construct. .................................................. 57

Table 2 The effect of implant material properties on the stability of internal plate

fixation. .................................................................................................................................................. 77

Table 3 The effect of implant offset to the bone on the stability of internal plate

fixation. .................................................................................................................................................. 77

Table 4 The effect of implant inclination to the bone on the stability of internal

plate fixation. ....................................................................................................................................... 78

Table 5 The effect of working length on the stability of internal plate fixation. ...... 79

Table 6 The effect of working length on the stability of internal plate fixation. ...... 79

Table 7 The effect of bi-cortical versus far cortical locking on the stability of

internal plate fixation. ...................................................................................................................... 80

Table 8 Contains the average distance between the outer surfaces (shell/shell

deviation) for each tibia pair (intact left and right tibia) for the whole tibia and for

the proximal, distal and diaphyseal regions separately. Additionally, the

percentage of measured points within a 1 mm tolerance is given in brackets. ..... 106

Table 9 Lists the displacement of the proximal cup determined for the axial

compressional and torsional load cases for both the FE simulation and mechanical

tests (‘X’ represents a filled screw hole and ‘0’ represents an empty screw hole).

................................................................................................................................................................ 159

Abbreviations

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Abbreviations

FEA - Finite Element Analysis

IFM - Inter-fragmentary Movement

FCL Far Cortical Locking

LCP - Locking Compression Plate

CT - Computed Tomography

AP - Anterior-Posterior

ML - Medial-Lateral

MPC - Multi Point Constraint

3D - 3 Dimensional

BC - Boundary Condition

DoFs - Degrees of Freedom

BMD - Bone Mineral Density

HU - Hounsfield Unit

EFP - European Forearm Phantom

DICOM Digital Imaging and Communications in Medicine

PVE - Partial Volume Effect

BMP - Bone Mineral Protein

SD - Segmental Defect

Abbreviations

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LCS - Local Coordinate System

ULCS - Upper Local Coordinate System

LLCS - Lower Local Coordinate System

GCS - Global Coordinate System

Authorship

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Authorship

I declare that the work contained in this thesis has not been previously submitted

to meet the requirements for an award at this or any other higher education

institution. To the best of my knowledge and belief, the thesis contains no

materials previously published or written by another person except where due

references is made in the text.

……………………………………..

Pushpanjali Krishnakanth Date:……………………

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1 Introduction

In this introductory section, the goals of the thesis will be listed. Finally, a thesis

outline presents the structure of the thesis.

Chapter 1 Introduction

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1.1 Background

Bone is a vital skeletal tissue whose primary role is to provide support for the

body, protect the internal organs and enable in locomotion. Fractures occur when

bone fails to withstand the external force exerted upon them. The self-regenerating

capability of the bony skeleton helps bone fractures to heal without any surgical

intervention. However, sometimes, they fail to heal in a timely way without

treatment. Hence the goal of any fracture treatment is to restore bone’s structure,

composition and shape by providing a favourable mechanical and biological

environment necessary for successful and timely healing.

1.2 Problem description

There are many different kinds of fixation devices available for fracture treatment.

Regardless of the choice of fixation device, fixation stability is known to have an

influence on healing outcome and the degree of stability is determined by the

stiffness of the fixator. Fixation devices used to treat fractures are broadly

classified under (i) external and (ii) internal fixators. Recent developments in both

design and surgical techniques have led to rapid adoption of internal fixation

technology. Internal fixation technique is expected to provide sufficient stability

for healing to occur whilst allowing certain amount of inter-fragmentary

movements (flexible fixation) stimulating callus formation. On the contrary, there

have been recent reports regarding the internal fixators being too rigid (Kubiak et

al., 2006; Bottlang et al., 2010; Lujan et al., 2010; Bottlang and Feist, 2011) thus

hindering fracture healing due to insufficient callus formation. There is lack of

report in terms of stiffness requirements of internal fixation devices for timely and

efficient healing. Stability of fixation is assessed by determining the stiffness of the


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fixation device. Investigation of the influence of internal fixator configuration on

implant stability requires a suitable fixation stiffness determination method. Many

stiffness determination methods have been reported that differ in the manner and

orientation in which loads are applied and the manner in which displacements are

measured and stiffness calculated (Törnkvist and Hearn TC, 1996; Kassi et al.,

2001; Stoffel et al., 2003; Epari et al., 2007). In conclusion, the stiffness

requirements of these devices (internal fixation devices) are not well understood

and furthermore it is still unclear, how the configuration of the internal fixator

influences fixation stability. Additionally, there is no universal method for the

assessment of fixation stability which makes it harder to choose a particular

method in the characterisation of internal fixation devices.

Secondly, fixation stability is also known to influence the loading experienced by

the bone. Bone’s adaptation of its mass and structure to changes in its mechanical

loading through a process of remodelling is well documented. Undesirable

changes, such as bone loss, can occur due to changes in the load distribution

caused by the introduction of an implant. In the case of fracture fixation, such

reduction in mechanical competence of the bone (bone loss) can lead to implant

loosening and ultimately osteosynthesis failure. The implant chosen for fracture

treatment should prevent such undesirable bone loss leading to implant failure. In

order to understand the mechanism behind implant related bone remodelling,

quantifications of implant related changes in bone density due to remodelling is

necessary.


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1.3 Research question and scope

1.3.1 Research question

In view of the above mentioned research problem, the research question which

needs to be addressed is;

Can an internal plate fixation device be configured such that

a) It promotes healing

b) Does not produce undesirable bone loss through remodelling

The specific goals of this PhD project will be firstly, (i) to develop a method to

characterise the stiffness of an internal plate fixation device. The developed

tool will then be used to investigate the influence of modifications to its

configuration on implant stability. The knowledge thus gained can be used in

future in the configuration of internal fixation devices for better healing. Secondly,

(ii) to develop a method to quantify changes due to implant related bone

remodelling. The developed method will then be used to investigate the pattern of

remodelling for different treatment groups and at different post-operative time

points. The developed remodelling quantification method can be used to validate

bone remodelling algorithms which are used to predict remodelling changes

around an implant. Then, the validated remodelling algorithms can aid in the

configuration of internal fixation devices that does not produce bone loss through

remodelling.

1.3.2 Scope

Mechanical considerations in fracture fixation include investigation of the

influence of fixation stability on; healing, implant related changes due to bone


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remodelling and implant survival. This project investigates the influence of

fixation stability on healing and remodelling.

1.4 Thesis outline

This thesis investigates the importance of fixation stability on both healing and

implant induced bone remodelling. The chart below shows how these two

elements, discussed in two sections are linked together in this thesis.

Section 1: Fixation stability and healing

The prime aim of this section of the project is to understand how fixator

configuration (internal plate fixator) influences stiffness. In accomplishing this,

there are several sub aims, which will be addressed in Chapters 3 and 4

individually.

Chapter 1: Project Goals

Chapter 2: Literature Review

Section 1

Fixation stability and healing

Chapter 3

Chapter 4

Section 2

Fixation stability and remodelling

Chapter 5

Chapter 6

Chapter 7: Overall discussion and conclusion


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Chapter 3: Development of a method to determine internal plate fixator

stiffness

Chapter 4: Investigation of the influence of fixator configuration on fixation

stiffness

Section 2: Fixation stability and remodelling

After having investigated the influence of fixator configuration on implant stability,

the next task is to investigate the influence of the fixator stiffness on implant

related remodelling changes. In doing so, firstly, the mechanisms that regulate

implant related bone-remodelling process has to be understood. Hence,

quantification of bone-remodelling in experimental situations is necessary and

is realised in Chapter 5 of this PhD thesis.

Chapter 5: Development of a method to quantify changes due to remodelling

Chapter 6: Further validation of the bone remodelling quantification method

Chapter 7: Overall discussion and conclusion

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2. Literature review

This chapter provides a review of relevant literature. This chapter begins with an

introduction to basic anatomy of bone, including its functional adaptation. This is

then followed by a description of fractures, fracture healing mechanisms,

mechanical factors influencing the healing process along with an introduction of

fracture fixation devices. Finally discussion of the influence of fixator configuration

on its stiffness and in turn its influence on bone-remodelling concludes the

chapter.

Chapter 2 Literature review

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2.1 Bone

Bone is a highly complex skeletal tissue accounting for approximately 14% of body

weight in an average person (Steele, 1990). The adult skeleton consists of 206

distinct bones divided as follows (Gray, 1918).

Axial skeleton

o Vertebral column – 26

o Skull – 22

o Hyoid bone – 1

o Ribs and sternum – 25

Appendicular skeleton

o Upper extremities – 64

o Lower extremities – 62

o Auditory ossicles – 6

The above mentioned 206 bones fall in any one of the four broad classes (Bartel,

2006).

Long bones, which are long in one direction with tubular cross sections in the

central shaft (diaphysis), such as femur, the tibia, and the humerus.

Short bones, which are bones or portions of bones, which have same

dimensions in all directions, such as bones of the wrist and ankle.

Flat bones or tabular bones, which are smaller in one dimension than in the

others, and make up portions of skull, the scapula, the pelvis and the transverse

processes of vertebrae.

Irregular bones are the ones which do not fall in any of the above three

categories, such as vertebral bodies and the posterior elements.


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2.1.1 Function of a bone

Bone’s primary role is to provide support for the body and help in locomotion by

providing a strong supportive and mechanically optimal structure for the soft

tissues and muscles (Webb and Tricker, 2000; Bartel, 2006). Bone’s surfaces are

the attachment sites and lever arms for muscles, tendons and ligaments that aid in

posture and move the body parts (Steele, 1990).

In order to perform its primary role, bone should be stiff and strong as well as light

in weight. The strength and stiffness of a bone is determined by the architecture

(shape and dimensions) and mechanical quality of the bone material. Strength and

stiffness of the bone change with bone mass and structure, with noticeable changes

during its growth, remains in more or less constant in adulthood and deteriorates

in the elder. The mechanical loading environment is known to have an influence on

bone’s mass and structure (Mow, 2005). Hence bone is an adaptive tissue.

2.1.2 Structure, type and composition of bone

As shown in Figure 1, long bones, are divided into three identifiable regions

namely; Epiphysis, metaphysis and diaphysis. The cortex forms a tube surrounding

a hollow medullary cavity. Spongy or cancellous bone is found towards the ends of

the bones and near the internal cortex surface. From inside as well as outside,

bones are surrounded by connective tissue and membranes; Periosteum covers the

bone externally. While cartilage covers the articular surfaces and the internal

marrow cavities are lined by endosteum. Both endosteum and periosteum contain

bone manufacturing cells. Red marrow which forms blood cells exists within the

medullary cavity and inter-trabecular spaces in the cancellous bone (Steele, 1990).


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Figure 1 Shows the surface of a sheep tibia reconstructed from computed

tomography (CT) data using AMIRA software (Visage Imaging GmbH, Berlin,

Germany) used for illustration of the three regions of a tibia.

Primarily, there are three types of bone:

Woven bone (not illustrated in Figure 2) formed during embryonic development

or during fracture healing (callus) (Fredric, 2002) is composed of randomly

arranged collagen bundles and irregularly shaped vascular spaces lined with

osteoblasts. Woven bone is eventually replaced with cortical or cancellous bone

(Kalfas, 2001). Woven bone, due to its loose structure is mechanically inferior to

cortical bone (Currey, 2003).

Cortical or compact bone whose primary structural unit is an osteon is remodelled

from woven bone by means of vascular channels that invade the embryonic bone

from its periosteal and endosteal surfaces. Its mechanical strength depends on

how well osteons are tightly packed (Kalfas, 2001). Cortical bone comprises the

diaphysis of long bones and the thin shells that surround the metaphysis.

Proximal epiphysis

Metaphysis

Diaphysis

Distal epiphysis


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Figure 2 Cross sectional view of a long bone (modified from1).

Figure 3 Cross sectional view illustrating types of bone (modified from2).

1 http://www.web-books.com/eLibrary/Medicine/Physiology/Skeletal/Skeletal.html (accessed on 12/09/2011) 2 http://www.iofbonehealth.org/health-professionals/about-osteoporosis/basic-bone-biology.html (accessed on 12/05/2009


P a g e | 12

Cancellous or trabecular bone is less dense than cortical bone (Figure 3). The

classification of bone tissue as cortical or trabecular is based on relative density.

Trabecular bone in the metaphysis and epiphysis is continuous within the inner

surface of the metaphyseal shell and exists as a three-dimensional interconnected

network of trabecular rods and plates (Mow, 2005).

Bone is comprised of three distinctly different cell types as shown in Figure 4,

namely;

Osteoblasts or bone forming cells: Osteoblasts are the cells that lay down the

extracellular matrix and regulate its mineralization (Sommerfeldt and Rubin,

2001). They secrete osteoid; un-mineralised organic matrix which subsequently

undergoes mineralization, giving the bone its strength and rigidity. Some

osteoblasts are converted to osteocytes nearing the completion of their bone

forming activity, while others remain as lining cells on the periosteal or endosteal

surfaces of bone. Osteoblasts also play a role in activating bone resorption by

osteoclasts.

Figure 4 Schematic representation showing types of bone cells (reproduced from3).

Osteocytes or bone maintaining cells: These are mature osteoblasts trapped within

the bone matrix which are involved in the control of extracellular concentration of

3 http://www.iofbonehealth.org/health-professionals/about-osteoporosis/basic-bone-biology.html (accessed on 12/09/2011)


P a g e | 13

calcium and phosphorous. They are also involved in adaptive remodelling

behaviour via cell-to-cell interactions in response to local environment.

Osteoclasts or bone-resorbing cells: These cells are multinucleated bone resorbing

cells which function in groups termed “cutting cones” that attach to bare bone

surfaces, release hydrolytic enzymes, dissolves the inorganic and organic matrices

of bone and calcified cartilage (Kalfas, 2001).

2.1.3 Bone growth and development

Bone growth occurs by two different mechanisms; while bones of skull and some

irregular bones are formed through intramembranous ossification where sheet-like

connective tissue membranes are replaced with bony tissue; most bones are

formed through endochondral ossification where hyaline cartilage is replaced by

bony tissue (National Cancer Institute, 2011). Bone resorption by osteoclasts

followed by new bone deposition by osteoblasts is a continuous process which

occurs during growth and throughout life. Bone formed by this process is called

secondary bone. Primary bone or first bone is formed through endochondral

ossification-mineralization of cartilage (as illustrated in Figure 5) or direct sub-

periosteal deposition. Around the diaphysis, osteoblasts form a collar of compact

bone. Simultaneously, cartilage at the centre of diaphysis begins to disintegrate.

Osteoblasts penetrate the disintegrating cartilage and replaces it with spongy or

trabecular bone forming primary ossification centre. Further ossification continues

extending from the ossification centre towards the bone ends. Later osteoclasts

break down the newly formed spongy bone in the diaphysis to open up a

medullary cavity. Due to the continuous growth of cartilage in epiphysis,

developing bone increases in length. After birth, ossification continues with the

formation of secondary ossification centres formed in the epiphysis. Ossification in


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epiphysis differs from diaphysis ossification only by retaining spongy bone instead

of being broken down to form a medullary cavity. Hyaline cartilage is totally

replaced by bone at the completion of secondary ossification except over the

epiphysis surface where it remains as articular cartilage and as an epiphyseal plate

between epiphysis and diaphysis. The cartilage continues to grow in regions of

epiphyseal plate and next to the diaphysis. Chondrocytes next to the diaphysis age

and degenerate. Osteoblasts move in and ossify the matrix to form bone and

become trapped in the matrix as osteocytes. Other osteoblasts close off the bone

surface as lining cells (Mow, 2005). Until cartilage growth slows down and finally

stops, this process of bone growth continues throughout childhood and adolescent

years.

Figure 5 Demonstrates skeletal development of long bone growth through

endochondral ossification (modified from4).

With the increase in bone’s length with the individual’s age, the bone must increase

its diameter. This occurs through intramembranous ossification that does not

involve prior cartilage formation. The increase in diameter is called appositional 4 http://learnsomescience.com/anatomy/microscopic-structure-of-the-skeletal-system-what-makes-our-bones-strong/ (accessed on 12/09/2011)


P a g e | 15

growth. Osteoblasts in the periosteum form compact bone around the external

bone surface. At the same time, osteoclasts in the endosteum break down bone on

the internal bone surface, around the medullary cavity. These two processes

together increase the diameter of the bone while preventing bone from becoming

too bulky (National Cancer Institute, 2011).

2.1.4 Bone modelling and remodelling

Bone modelling can be defined as a process whereby bone is laid down onto

surfaces without necessarily being preceded by resorption. After ossification, bone

differentiation continues within the tissue (Mow, 2005). According to Frost

(Goodfellow and O’Connor, 1978), modelling is defined as growth and

development of the cortical and trabecular structure and later morphological

adaptation as it occurs in growth or reactions to reduced and increased external

loads.

Bone remodelling is the ongoing process of replacement of old bone by new bone.

During the remodelling process, bone is formed in places where it is needed and

removed from places where it is no longer needed .Hence it is related to removal

or maintenance of bone matrix and expressed by bone-resorbing osteoclasts and

bone forming osteoblasts, collectively known as “Basic multicellular units” or

BMU’s. Bone remodelling starts with the appearance of osteoclasts at the quiescent

bone surface which attach to the bone tissue matrix and form a ruffled border at

the bone /osteoclast interface that is completely surrounded by a “sealing zone”,

thus forming an isolated micro-environment, Osteoclasts acidify this

microenvironment and dissolve the organic and inorganic compounds of bone.

After this bone resorption stops, osteoblasts derived from mesenchymal stem cells,

periosteum and soft tissues appear at the same surface site, deposit osteoid, thus


P a g e | 16

mineralizing it to form new bone. Some osteoblasts get encapsulated in this

osteoid matrix, further differentiating to osteocytes. While others continue to

synthesize bone until they transform to form quiescent lining cells covering newly

formed bone surface. Since osteoblasts and osteoclasts together are responsible

for the remodelling process, it is believed that there exist a coupling mechanism

between formation and resorption. In cortical bone a BMU forms a cylindrical

canal. In its tip on the order of ten osteoclasts dig a circular tunnel (cutting cone)

which are followed by several thousands of osteoblasts that fill the tunnel (closing

cone), thus producing a secondary osteon of renewed bone. The remodelling

process in the trabecular bone is believed to be a surface event (Mow, 2005).

2.2 Bone fractures

Bone fractures occur when bone fails to withstand the external force exerted upon

them. Hence fractures occur as a consequence of mechanical overload whose

configuration is influenced by the material properties of the bone, the type and

magnitude of force and loading rate (Schatzker and Houlton, 1999). Bone fractures

represent a structural failure of the primary load-carrying apparatus of the body.

The uniquely biological aspect of a skeletal structure is its capability to repair

itself; bone fractures can heal without any external intervention. On the other hand

they sometimes fail to heal successfully in a timely way, without treatment. The

primary purpose of fracture treatment devices is to provide the initial structural

reinforcement and a favourable mechanical and biological environment that is

necessary for the healing to occur as quickly and uneventfully as possible (Bartel,

2006). Figure 6 illustrates different kinds of fractures and Figure 7 shows a

fracture line as seen in an X ray.


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Figure 6 Illustrates types of fracture lines (reproduced from5).

Figure 7 Shows an X-Ray image of a fracture (reproduced from6).

5 http://www.merckmanuals.com/professional/sec22/ch329/ch329b.html (accessed on 12/09/2011) 6 http://analabamalawyer.blogspot.com/2011/07/fda-warning-atypical-femur-fractures.html (accessed on 12/09/2011)

Fracture


P a g e | 18

2.2.1 Fracture healing process

A fracture results in a series of tissue responses that are designed to remove tissue

debris, re-establish the vascular supply, and produce new skeletal matrices

(Simmons, 1985).

Fracture healing is divided into; a) Primary fracture healing and b) secondary

fracture healing.

Primary fracture healing

Primary fracture healing or direct bone healing requires anatomical reduction,

stabilization and compression of fracture which is seen in cases of negligible gap

size and extreme stability (Webb and Tricker, 2000; Bailón-Plaza and van der

Meulen, 2001). According to the AO group, this situation is often seen only after

open reduction and rigid internal fixation. Here, fracture tissue appears at the

fracture site, bridges the fracture site by direct Haversian remodelling (Brighton,

1985) or direct cortical modelling by the formation of cutting cones. The

osteoclasts lead the way by tunnelling across the fracture. Thus the new blood

vessels along with osteoblasts directly model the cortical bone into a Haversian

structure (Webb and Tricker, 2000). Bone on one side of the cortex unites with

bone on the other side thus re-establishing mechanical continuity (Einhorn, 1998).

Secondary fracture healing

The majority of bone fractures undergo secondary fracture healing, which requires

some motion at the fracture site. This can be achieved either by non-operative

treatment or with the aid of a surgical procedure which allows some mobility at

the fracture site (Webb and Tricker, 2000). Secondary fracture healing involves a

combination of intramembranous and endochondral ossification process which

participates in fracture healing at different stages of healing. These stages of


P a g e | 19

healing (as shown in Figure 9) is comprised of an initial stage of hematoma

formation leading to the occurrence of inflammation, a subsequent stage of

angiogenesis development and cartilage formation, further leading to three

successive stages of cartilage calcification, cartilage removal and bone formation

and ultimately leading to bone remodelling (Einhorn, 1998).

Figure 8 Shows schematic of a section through an intact long bone-(reproduced

from7).

Figure 9 Illustrates fracture healing stages: (a) inflammation phase; (b) callus

differentiation phase, (c) endochondral ossification phase and (d) Restoration of

original geometry of bone (reproduced from 8).

7 (Goodfellow and O’Connor, 1978) 8 (Goodfellow and O’Connor, 1978)


P a g e | 20

2.2.2 Factors influencing fracture healing process

The factors that influence fracture healing can be broadly divided into two

categories;

Systemic factors: Age, hormones (Cruess and Dumont, 1975), nutritional status of

patients (Webb and Tricker, 2000), Pharmacological factors like smoking,

pregnancy, diabetes and etc., are some of the systemic factors which influences

fracture healing.

Local factors: Local factors influencing fracture healing are; degree of local trauma

experienced by bone and surrounding tissue, the amount of bone loss, the type of

bone affected, degree of immobilization, state of local blood supply to the fracture

area, degree of vascularity, bioelectric factors, mechanical factors governed by the

type of fracture treatment and fixation device used, and local pathological

conditions (infection, radiation, chemical burns) (Cruess and Dumont, 1975;

Brighton, 1985).

In clinical practice it is believed that local factors affecting fracture healing are far

more important than systemic factors in most of the patients (Brighton, 1985).

Mechanical factors (fixation stability) and blood supply influencing

fracture healing process

Fracture healing has two major prerequisites; mechanical stability and sufficient

blood supply among the local factors. Influence of mechanical environment with

reference to fracture healing depends on the type of fracture fixation device used

to treat a particular fracture among other factors. The degree of mechanical

stability of a bony fracture is determined by the stiffness of a fracture fixation

device (White et al., 1977; Goodship and Kenwright, 1985; Goodship et al., 1993;


P a g e | 21

Probst et al., 1999) and is expressed in terms of inter-fragmentary strain or inter-

fragmentary movement at the fracture site. Since blood supply is equally necessary

for the nutrition of healing zone, an insufficient blood supply can cause a delayed

union or even atrophic non union (Mow, 2005). Apart from other factors

responsible for diminished blood supply, a different pattern of vascularisation can

be seen under stable and unstable fixation. However even a well vascularised

fracture healing zone will lead to a hyper-trophic non-union if the mechanical

stability is insufficient (Claes et al., 2002). Hence, both inter-fragmentary

movement or inter-fragmentary strain and amount of blood supply are equally

important for successful and uneventful healing. Few previous studies have

investigated the relationship between the degree of instability (expressed as IFM

or IFS) and amount of blood supply found in various tissues in relation to fracture

healing.

Dahlkvist et al.(1982) speculated constant rupture of capillaries required for

osseous repair, resulting in the development of fibro cartilaginous tissue, thus

delaying fracture healing under unstable fixation (Dahlkvist et al., 1982).

Bell et al (1998) quantified correlation between vascularisation and tissue

formation under well defined biomechanical conditions(Bell et al., 1998). This

study showed that greater inter-fragmentary movements in a 2-mm osteotomy gap

of the sheep metatarsal led to significantly more fibro cartilage, less bone

formation, large hydrostatic pressures which may cause blood vessels to collapse

(Mow, 2005) and a small number of vessels close to the periosteum than under

small inter-fragmentary movements.

Among the mechanical factors, fracture gap size is another factor which influences

healing (Claes et al., 1998). Claes et al (1997) showed how small gap sizes promote


P a g e | 22

fracture healing in a fast and successful manner while large gap sizes impede

fracture healing process (Claes et al., 1997).Therefore, inter-fragmentary

movement and fracture gap size seem to be the two important mechanical factors

which influence the fracture healing process. Furthermore, the sensitivity of bone

healing to initial mechanical conditions has been shown both biomechanically and

histologically (Klein et al., 2003). Since the initial mechanical environment may

have lasting implications on the course of fracture healing, a detailed

understanding of the influence of fixation stability on the mechanical conditions

within the callus is believed to improve fracture treatment.

2.3 Fracture treatment

The goal of fracture treatment is the restoration of bone’s structure, composition

and function (Bartel, 2006). Fracture treatment is mainly to achieve an anatomical

alignment of broken bone fragments, to relive pain as well as stabilize the

fragments in order to initiate bony union (Mow, 2005). Unlike other tissues, bone

has a uniquely distinct property which helps it to regenerate itself by restoring the

properties of pre-existing tissue. Most fractures are either left untreated or are

treated with a form of surgical management that results in some degree of motion

(sling immobilization, cast immobilisation, external fixation, intramedullary

fixation) (Einhorn, 1998). For fractures which are inherently stable, little

additional effort is needed to maintain a minimal amount of IFM (Inter-

Fragmentary Movement). In such cases, cast or braces is sufficient to treat such

fractures where fractures heal by secondary fracture healing involving

intramembraneous and endochondral ossification. Until twentieth century,

fracture treatment was performed by external splinting. Today, even though

majority of fractures are treated with plaster casts or braces, complex fractures,


P a g e | 23

fractures with extensive soft tissue damage; open as well as infected fractures

cannot always be treated successfully with plaster cast stabilization. Hence, the

operative treatment of fractures with new fixation systems and implants came into

existence (Mow, 2005).

From a biomechanical point of view, fracture fixation must possess sufficient

stability, which means it has to reduce inter-fragmentary movement occurring due

to external loading and muscle activity to such an extent that it promotes timely

and successful fracture healing.

2.3.1 Principles of fracture fixation

Primarily there are two main principles of fracture fixation and all the fixation

devices used to treat fractures uses any one of these two principles;

Inter-fragmentary compression stabilisation:

Under absolutely stable conditions, bone heals by a process of direct bone healing

with no or minimal callus formation (Schatzker and Houlton, 1999). This absolute

stability can be achieved when compression over the whole cross section of a

fracture is sufficiently high such that all forces and moments acting at the fracture

site are neutralised. Under such conditions, there exists no inter-fragmentary

movement between the two fracture fragments (Mow, 2005). Such an inter-

fragmentary compression can be achieved by lag screws, compression plates, and

tension band systems (Delp et al., 1990).

o Compression plate

First the fixation plate is fixed with screws on one of the bone fragments. Then

a tension device placed on the second fragment which moves the plate axially,

is used temporarily to pull both the fragments together, thus creating an inter-


P a g e | 24

fragmentary compression (Figure 10). Later the second fragment is fixed to the

plate with additional screws. Compression between two fragments can also be

achieved with plates having a tapered screw hole upon which the screw head

slides (Delp et al., 1990).When the screw is inserted into the bone, it moves

towards the bone cortex, since the slope of the screw hole is pushed axially. The

compression achieved with the help of compression plates does not change

with changing loads and muscle activity and hence static in nature (static

compression) (Mow, 2005).

Figure 10 Müllers plate design achieves inter-fragmentary compression by

tightening a tensioner that is temporarily anchored to the bone and the plate

(reproduced from 9).

o Inter-fragmentary compression by tension band principle

Bones are not always loaded by axial force alone. According to Pauwels

(Pauwels, 1958) observation, certain long bones are eccentrically loaded

which results in bending. Pauwels postulated that apart from gravity and

muscle activity, the net loading on such bones, would create a compressive

9 (Uhthoff et al., 2006)


P a g e | 25

force on side closer to loading and a tensile force on the opposite side.

Compressive forces due to body weight, bending and pure axial forces

results in inter-fragmentary compression without the need for an additional

fixator. However the tensile force created due to bending has to be

neutralized to order to prevent dislocation of fragments. This neutralisation

can be achieved by placing the implant on the tension side of the bone

(Figure 11) which is commonly known as tension band principle (Schatzker

and Houlton, 1999). Compression thus achieved change dynamically,

depending on external loads and muscle activity (Mow, 2005).

Figure 11 Illustrates tension band principle (modified from 10).

Non compressive stabilisation

As the name suggests, the fracture fragments are not pulled against each other

with any external application of compressive force. Stabilization of fragments is

obtained by attaching an implant which holds the two fragments together with the

help of screws. The healing of a bony fracture follows the course of secondary

10 (Rüedi, 2007)


P a g e | 26

healing. Fracture healing under inter-fragmentary movement occurs by callus

formation that mechanically unites the bony fragments (Mow, 2005)

o Bridging osteosynthesis with bridging plates

The fundamental principle is to leave the fracture fragments undisturbed as

shown in Figure 12. This technique relies upon the soft tissue envelope to

reconstruct an approximate cylinder of bone fragments, while the major,

proximal and distal fragments are distracted and pulled out to length. Hence

the fracture fragments are neither immobilized nor realigned; thereby leaving

tenuous soft tissue attachments left undisturbed. Bridging osteosynthesis can

be achieved by a number of techniques. A conventional plate can be used to

bridge two fracture fragments with three of four screws anchored proximally

and distally in the intact parts of the fractured bone. Two advantages have been

identified with this technique;

Since the plate extends to a sufficient length along the fracture zone,

the load on the underside of the plate not fixed to the bone can be

distributed over an extended distance thus reducing sudden increase

in stress which could lead to fatigue failure in certain areas.

As the plate is applied at a distance to the bone, it permits better

vascular supply (Schatzker and Houlton, 1999).


P a g e | 27

Figure 12 Shows an X-ray illustrating bridging osteosynthesis (modified from11).

2.3.2 Types of fracture fixation devices

There is a wide range of fracture fixation devices (as shown in, Figure 13-Figure

16) available to treat fractures which could be broadly divided under two main

categories depending on whether the device is positioned entirely inside the skin

(Internal fixator) or is partially inside the skin for bracing purposes only while the

major part of fixator remains outside the skin surface (External fixators).

External fixator: Plaster Cast and Brace; for inherently stable fractures to enhance

natural healing, unilateral frames, bilateral frames, triangular frames.

Internal fixator: Intramedullary rod or nail (reamed nail and un-reamed nail),

screws (angle stable screws and lag screws), internal fixation plates (Locking

plates with angle stable screws).

Figure 13 Hoffman external fixator (reproduced from12).

11 (Rüedi, 2007) 12 http://www.rch.org.au/limbrecon/prof.cfm?doc_id=4873 (accessed on 12/09/2011)


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Figure 14 Ilizarov external fixator (reproduced from13).

Figure 15 Plaster cast (reproduced from14).

13 http://teamofmonkeys.com/html/leg.html (accessed on 12/09/2011) 14http://www.theinjurylawyers.co.uk/injury-lawyers-blog/2009/10/14/plaster-of-paris-burns-teenager/ (accessed on 12/09/2011)


P a g e | 29

Figure 16 Intramedullary nail and screws (modified from15).

In this proposed study, focus will be placed only on internal plate fixation device.

Internal fixation plates

Internal fixation plates are fixed to the bone like an external fixator but underneath

the skin to hold the two bone fragments together (Claes, 1998). Internal plate

fixators are believed to reduce the vascular disturbance resulting from the

implants (Claes, 2011) by providing a lower or no plate-bone contact. Some of the

most commonly used internal plate fixation devices used today are Locking

Compression Plates (LCP, Synthes AG, Switzerland), and Less Invasive Stabilisation

System (LISS, Synthes AG, Switzerland) plates.

15 http://www.ringthebellsofpeace.com/2010/02/fracture-of-shaft-of-femur.html (accessed on 12/09/2011)


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2.4 Influence of fixation stability on healing and remodelling

Fixation devices are used to treat fractures in order to stabilise the fracture

fragments until it heals. The mechanical stability of the bony fracture is known to

influence the healing outcome. This stability is determined by the stiffness of the

fixation device. Hence, fixation stiffness is known to influence healing. For

fractures which follow the course of secondary healing, mechanical stability is

known to be crucial for healing. Furthermore, the progressive maturation of the

fracture callus from woven to lamellar bone is known to be dependent on this

stability (Giannoudis et al., 2007). Surgical interventions such as the application of

systems of internal or external stabilisation are designed to improve stability of

fixation and thereby enhance healing. Additionally, the stiffness of the fixation

device determines the physiological loading environment of the affected limb.

Since bone is known to adapt its shape and structure to changes in loading

condition placed on it, through the remodelling process (Wolff et al., 1986),

fixation stiffness also influences remodelling.

The use of external fixators has certain disadvantages such as, the pin sites where

the metal work enters the skin and goes into the bone can sometimes be a source

of infection, the pins and rods extruding outside the skin demands extra care from

the wearer and wearing external fixators can sometimes become a social issue

with stares on street. These disadvantages can be overcome to an extent by the use

of internal fixation devices where the fixators are placed under the skin and

muscle. Also, internal fixators have gained popularity over the recent years as they

can be applied with less invasive surgical techniques. However there is still lack of

report with reference to stiffness requirements of these devices for better healing

outcome as well as restoration of bone’s structure and composition in terms of


P a g e | 31

remodelling. Therefore, this project focuses on internal plate fixators. A generic

locking plate representing a standard 9 hole 4.5 mm osteosynthesis plate and

screws commercially available from implant manufacturers was used in the

analysis (Figure 17).

Figure 17 Generic locking plate (modified from standard 4.5mm Locking

Compression Plate).

2.4.1 Fixation stability and healing

Minimal surgical technique while preserving fracture vascularity has led to rapid

adoption of internal fixation technology over the recent years. Locked internal

plates are aimed to provide elastic fixation that allows sufficient inter-fragmentary

movements (IFM) such that healing occurs via secondary bone healing with

external callus formation. This callus is then replaced by bone thus restoring the

mechanical strength and structure of the bone. The callus thus formed is known to

influence healing by providing the provisional stability (through its mass) and

strength (through its geometry) to ensure healing may progress (LaStayo et al.,

2003). The mechanical environment within the healing callus is determined by the

inter-fragmentary movements which in turn are a function of fixation stability and

limb loading. These IFM’s can be broken down into three translational and three

rotational components. However, the IFM’s during the initial healing phase have

been shown to be mainly composed of shear and axial movements (Schell et al.,

2005). While moderate axial movements are shown to be stimulatory to healing

(Claes et al., 1997), excessive shear movements are known to be detrimental to

healing (Yamagishi and Yoshimura, 1955).


P a g e | 32

These IFM’s vary inversely with fixation stability (more stable the fixator, less

IFM’s occur leading to less callus formation). The difference between beneficial

motion in the fracture gap which induces callus formation and too much motion

which leads to non-union is fairly bleak (Brennwald, 1996) Hence, it is difficult to

find the right balance between reducing the risk of plate failure (very flexible plate

leading to too much IFM) and providing optimal IFM (sufficiently flexible plate

with right amounts of IFM) to stimulate callus formation for successful healing.

Therefore, it is challenging to configure fixation devices of sufficient stability that

promotes better healing outcome.

2.4.2 Fixation stability and remodelling

The goal of fracture healing is the restoration of the mechanical properties such as

strength and stiffness of the fractured bone. Fixation devices which provide

sufficient stability to the bony fragments until it heals are chosen to treat fractures.

It is known that the load distribution on the affected limb in the presence of an

implant is determined by the stability of the fixation device used to treat fractures.

Regulation of load induced bone remodelling is well documented (Wolff et al.,

1986; Mori and Burr, 1993). Since bone adapts to changes in external loading by

undergoing changes in its shape and structure through remodelling process,

implant stability is believed to in turn influence remodelling changes.

Complications with fracture healing have been reported due to re-fractures

following stress protection by plates (Allgöwer et al., 1969). Stress protection is a

reduction in the mechanical competence of the bone in the presence of a fixator.

Figure 18 shows bone loss around an implant. By definition stress protection is a

way the implant protects the healing bone against loads that it may be temporarily

unable to sustain. Such unloading of the bone in the presence of a fixator is a result


P a g e | 33

of bone stresses being transmitted through the plate and not through the bone.

This unloading leads to bone atrophy since bone adapts to changes in its

mechanical loading and subsequently poses the threat of re-fracture after implant

removal. Hence the osteosynthesis device used to treat fractures should not only

provide sufficient stability for successful and timely healing but also should not be

too stiff to induce stress protection.

Figure 18 Callus histology after 6 weeks of healing (reproduced from16).

2.5 Finite Element Analysis (FEA)

FEA is a numerical tool used to solve complex engineering problems. When faced

with the task of solving complex engineering problems, it is often useful to

represent this complex system in terms of a simplified system or model of a system

by extracting the essential elements. This model can then be used to observe the

behaviour of the system to its response to altered input parameters or conditions.

Such modelling can be either physical modelling where real constructions are built

or mathematical modelling which uses conceptual representations. Finite element

16 (Epari, 2006)

Position of screw hole

Remodelling (bone loss) in regions adjacent to screw hole


P a g e | 34

models are numerical (rely on computers to find approximate solutions)

mathematical models (Prendergast, 1997). A system can be built by the addition of

structurally and mathematically defined finite elements, joined together by

commonly shared nodes. When the overall system is subjected to load, the

localised response of each element is calculated to form a solution to the system

load state, identifying the cause and effect relationship between loads placed on a

system and the resulting mechanical behaviour including stresses and strains. By

using this technique in an orthopaedic setting the actual mechanical environment

induced in a bone by application of a fixator can be measured and understood. FE

technique is used in orthopaedic research in many areas such as, analysis and

design of orthopaedic devices, analysis of tissue growth, remodelling and

degeneration and analysis of the skeleton. The first application of FEA in

orthopaedics was in 1972 (Brekelmans et al., 1972). Thereafter, its use in

orthopaedic research is increased with techniques and complexities increasing

rapidly in recent years. One of the prime advantages of using FE would be that it

overcomes the variability and repeatability issues encountered in

experimentation. However, any model is an attempt made to represent reality.

During such a representation, not all variables governing the process can be

considered and thus a model is a mere reduction of the complex reality. Due to the

many assumptions and simplifications involved in the development of FE model,

experimental approach (physical model e.g. mechanical testing) needs to precede

finite element analysis in an attempt to validate the FE model.

2.6 Computed Tomography (CT) of bones

Like X-Ray images, CT determines the radiographic density (RD) of an object,

which rather than being a true density is the relative attenuation of x-rays by the


P a g e | 35

tissue. In CT, a computer stores x-ray attenuation of data and generates a matrix of

picture elements termed pixels. This x-ray attenuation of data of each pixel is

represented as a shade of grey which is assigned a CT number in Hounsfield Units

(HU). The viewed CT image is thus composed of a series of pixel forming the

matrix. Since CT acquires tomographic images, each pixel in fact represents a small

volume of tissue (3D), a voxel (Saunders and Louis, 2002). CT scanning an object of

interest (bone) alongside an object of known density of a similar material (bone

phantom) allows conversion of intensity values (HU) to Bone Mineral Density

(BMD).

Most commonly the geometry of a bone model is derived from CT scans of the bone

in question. This technique yields a 3D model with a high degree of accuracy and

has been used frequently to create human bone models (Keyak and Falkinstein,

2003; Keyak et al., 2005; Taddei et al., 2006; Kim et al., 2007; Yosibash et al., 2007;

Gray et al., 2008). CT technique is also used to determine density of bones.

2.7 Animal (ovine) models in orthopaedic research

The use of animal models such as sheep/ovine model is commonplace in

experimental orthopaedic research. The hind leg of the sheep has broadly similar

anatomy to that of a human, with a femur and tibia only slightly shorter than

average length human bones. Additionally, data from human volunteers or

cadaveric bones are not always readily available. Because of this, both femoral and

tibial implants can be tested on them (ovine) with only minor modifications to

sizing. These analogues allow researchers to gather more information on healing

processes. Furthermore, experiments using animal models form an essential part

of pre-clinical testing.

P a g e | 37

Section 1 Fixation stability and healing

In this section, focus is placed on gaining an understanding of the influence of

fixator (internal plate fixation device) configuration on its stiffness.

Introduction

Bone has a remarkable capability to repair itself following a fracture. In some

instances external intervention in the form of cast or surgery is necessary for

timely and efficient healing. The choice of osteosynthesis device to treat fractures

may vary depending on the location, type of fracture and the extent of soft tissue

damage. The wide range of fracture fixation devices used to treat fractures can

broadly be divided into two categories; (i) external (ii) and internal fixators.

Nevertheless, the mechanical fixation stability of the fixation system is known to

influence the healing of long bone fractures (Yamagishi and Yoshimura, 1955;

Terjesen and Johnson, 1986; Chao et al., 1989) and this stability is determined by

the stiffness of the fixation device and the degree of limb loading.

The realisation that comminuted fractures should be treated without further

devascularisation of the fragments led to biological osteosynthesis where the

fractures were treated without perfect alignment or inter-fragmentary

compression (Claes, 2011). This led to development of flexible fixation plates.

Under flexible fixation conditions, that allow inter-fragmentary movement (IFM),

long bone fractures heal through secondary healing with the formation of an

external callus (Willenegger et al., 1971). Previous studies (Goodship et al., 1993;

Claes et al., 1997, 1998; Webb and Tricker, 2000; Perren, 2002; Augat et al., 2003;

Klein et al., 2004) conducted on investigating the influence of fixation stability and

initial mechanical conditions in the fracture gap on the callus formation have


P a g e | 38

shown that the size of external callus depends on the magnitude and frequency of

IFM (Goodship et al., 1993; Hente et al., 2004).

IFM’s are a reflection of fixation stability and varies inversely with it. In some

animal studies conducted previously, during the initial healing phase IFM’s are

shown to be higher initially (one week postoperatively and remain constant for a

period of first three to four weeks) and later on decreases with the increase in

callus formation (Klein et al., 2003, 2004; Schell et al., 2005). Earlier studies have

shown IFM during the initial healing phase to be mainly composed of axial and

shear components (Schell et al., 2005) with shear movements greater than axial

and sometimes exceeding by a factor of two (Duda et al., 2003). While it is believed

that moderate axial IFM of the order of 0.2 -1 mm for a fracture gap size of 3 mm

produces best healing results in sheep (Sturmer, 1996; Claes et al., 1997), the

influence of inter-fragmentary shear movements on healing is still a controversial

discussion. It is long been believed that inter-fragmentary shear is detrimental to

healing (Yamagishi and Yoshimura, 1955). Contrary to this belief is the study by

Klein et al., 2003, where high levels of inter-fragmentary shear during the early

healing phase were not found to be detrimental to bone healing (Klein et al., 2003).

Additionally, IFM greater than 2 mm is shown to have led to poor healing results

both in animal experiments (Kenwright and Goodship, 1989a, 1989b)and in the

clinic (Noordeen et al., 1995).

The most important parameters which influences fixator stiffness are its material

properties, geometry of the fixator , fixator position relative to bending direction

(plate fixator), number and position of screws, screw type, arrangement of screws,

the offset distance from the underside of the fixator to the bone surface (internal


P a g e | 39

plate fixator), side bar separation (external fixator), number of frames (external

fixator) (Willie et al., 2009).

Some previous parametric studies conducted on the influence of fixator

configurations on stiffness suggest that, for large fracture gaps, by having the

innermost screw very close to the fracture gap increases the axial compressional

stability (Ahmad et al., 2007), as well as widespread arrangement of screws along

the length of the fixator, increases its torsional strength (Törnkvist and Hearn TC,

1996). Spacing and omission of screws in certain defined symmetric patterns was

found to increase yield strength of the fixator coupled with better bone

remodelling results (Field et al., 1999). Additionally more than three screws per

fragment was shown not to further increase axial stability of the construct (Stoffel

et al., 2003).

Problem description

Bridging osteosynthesis using internal plate fixation devices, follows the course of

secondary bone healing through callus formation. Locked plating constructs

(internal plate fixators) are believed to heal fractures by following the course of

secondary bone healing via external callus formation. On the contrary, recent

studies have shown that these devices may be overly stiff when compared to

external fixation devices suppressing the amount of callus formation sufficient to

promote successful secondary healing (Kubiak et al., 2006; Bottlang et al., 2010;

Lujan et al., 2010; Bottlang and Feist, 2011). The amount of callus formation is

shown to be dependent on the local mechanical conditions among other factors

(Aro and Chao, 1993). The local mechanical condition, especially the IFM has a

decisive effect on callus formation during the early phases of healing (Claes et al.,


P a g e | 40

1998). Sufficient IFM are expected to stimulate callus formation. It is known that

the IFM’s are a reflection of fixation stability.

Fixation stability is a measure of stiffness of the fixation device which in turn is a

function of applied force and the resulting IFM. Various stiffness determination

methods have been reported in literature which varies in the manner and

orientation in which loads and boundary conditions are applied and the manner in

which displacement and stiffness values are calculated. Therefore, it is evident that

there is no standardised method of fixation stiffness determination.

Since finite element technique is not a new idea it was also one of the earlier

options adopted to quantify fixation stiffness. While most of the fracture fixation

stiffness characterisation studies reported in literature have investigated external

fixators (Drijber et al., 1992; Oni et al., 1993; Prat et al., 1994; Wehner et al., 2006)

using FE technique, reports on internal plate fixation stiffness characterisation

using computers of FE methods is very limited.

One of the FE studies on internal plate fixation stiffness published in literature was

conducted by Duda et al., 2002. This goal of this paper was to assess the suitability

of a newly developed internal fixator (fixator with locking screws using the

standard Less Invasive Stabilisation System (LISS) plate) under physiological-like

loading conditions. Both in-vitro mechanical stiffness testing and FE analysis were

conducted. Although this study illustrated the appropriateness of the new implant

design in treating proximal tibial defects, the FE model used was validated only for

simple axial compression loading against results from mechanical testing and not

for physiological-like loading (Duda et al., 2002a).


P a g e | 41

The use of internal fixation plates to treat fractures has increased since its

introduction in the late 1900’s due to the recent developments in both design and

surgical technique (Henderson et al., 2011). Yet, the stiffness characteristics of

these devices are not well understood and furthermore, it is unclear how fixator

configuration influences the fixation stability. The most important parameters

which influence internal fixator stiffness are the material properties, the cross-

section of the fixator, effective plate length, the offset distance from the underside

of the fixator to the bone surface, number and position of screws, and the screw

type. Therefore, it is not known to what extent each of these factors influence

implant stability.

Stoffel et al, 2003, provides us with a nice summary of the influence of some of the

fixator configurations on implant stability. The tests were performed for a bone

analogue-implant (Locking Compression Plate (LCP)) system. Results from FEA

were compared with in-vitro or mechanical tests. However, only axial compression

and torsional tests were performed during fixator stiffness characterisation

(Stoffel et al., 2003).

Although Krishna et al., 2008 included a much greater range of tests with axial,

torsion and bending loads investigated individually, the behaviour of the fixation

system under shear load was not investigated. FEA was conducted to demonstrate

the appropriateness of the use of Hemi Helical Plate (HHP) to treat spiral fractures.

Here, the slope of the load deflection curve determined fixation stiffness (Krishna

et al., 2008).

In summary, there exists no universal method to characterise fixation stiffness of

internal fixation devices. Additionally, it is still unclear how fixator configuration

influences implant stability.


P a g e | 42

Goal

The goal of this section of the project is to characterise the fixation stiffness of an

internal fixation device. Firstly, an appropriate method to determine the stiffness

characteristics of an internal plate fixation device is developed. Secondly, the

developed method will be used to investigate the influence of modifying fixator

configuration on the stiffness components of internal fixation device.

Structure

The prime aim of this section of the project is to understand how internal plate

fixator configuration affects its stiffness. This is accomplished in each of the

Chapters 3 and 4 individually.

Chapter 3: Development of a method to determine internal plate fixator

stiffness

Chapter 4: Investigation of the influence of fixator configuration on fixation

stiffness

P a g e | 43

3 Development of a method to determine

internal plate fixator stiffness

The prime aim of this part of the thesis is to define an appropriate stiffness

determination set up. This chapter begins with a review of the literature pertaining

to fixation stability and existing methods to assess fixation stability. Comparison

between different stiffness determination methods is then performed to determine

an appropriate method to characterise internal plate fixation stiffness.

Chapter 3 Development of a method to determine internal plate fixator stiffness

P a g e | 44

3.1 Introduction

The importance of fixation stability in healing outcome is well understood and

therefore assessing fixation stability is an important task. Fixation stability is

typically assessed by measuring the stiffness of the fixation. The stiffness of

fixation defines the relationship between applied force and the resulting

displacement. Although measurement of fixation stiffness has been reported for

various fracture fixation devices there are no standardised methods for the

assessment of fixation stability.

The methods reported in the literature vary in the stiffness components

investigated, whether the individual stiffness component or the 3D stiffness is

reported, how the boundary conditions are applied, how the displacements are

measured and the bone or bone analogue to which the fixation device is attached.

Most commonly the stiffness in a single load direction being either axial

compression, torsion (Törnkvist and Hearn TC, 1996; Field et al., 1999) or angular

(bending) (Florin et al., 2005) is investigated while assessing fixation stability. It is

known however that fixation systems create complex loading situations resulting

in a mixture of axial compression, translational shear, bending and axial torsion

(Gardner et al., 1996; Duda et al., 2002b, 2003; Epari et al., 2007). Due to their

highly non-linear nature and the complex in-vivo loading, it has been suggested

that a complete description of the 3D stiffness of fixation devices is necessary

(Duda et al., 1997). Methods to characterise the 3D stiffness of fixation devices

have been reported by Kassi et al (2001) and Augat et al (2008) (Kassi et al., 2001)

(Augat et al., 2008) in-vitro. Although both methods propose a similar set of six

independent load cases to determine the 3D stiffness, there are distinct differences

in the boundary conditions and the fixation stiffness calculation methods utilised.


P a g e | 45

The variability is not confined to the types of load cases selected to characterise

stiffness. Even with a single load case i.e. axial compression, the manner in which

the test is conducted varies in the point of load application, the boundary

conditions and the methods used to measure displacement. Loads are typically

applied at the top end of the implant-bone construct and fixed at the base (Kassi et

al., 2001) (Duda et al., 1998; Ahmad et al., 2007; Epari et al., 2007). Even within

this set-up, some authors have performed axial compression and confined lateral

displacements (confined compression) (Kassi et al., 2001), whilst other authors

have used a combination of ball or universal joints to dissipate out of plane

reaction forces (Penzkofer et al., 2009). The application of a shear load at the top

end of the bone-implant construct to determine the shear stiffness has the

unwanted affect of creating a significant bending moment in addition to a shear

force at the fracture gap. More recently methods have been introduced that apply

the shear loads as close to the fracture gap as possible to minimise the bending

moment (Gardner and Weemaes, 1999; Meleddu et al., 2007; Augat and Claes,

2008; Penzkofer et al., 2009).

Displacement is the other variable required to determine stiffness and a review of

the literature reveals that studies vary in the position at which displacements are

measured. Some studies conveniently use the displacement of the materials testing

machine’s cross-head which is readily available (Beaupre et al., 1983) However, it

is the displacements at the fracture gap that are critical for healing outcome.

Fracture gap displacements can be measured by determining the inter-

fragmentary (relative movement of one bone fragment with respect to the other)

movements. The measurement of inter-fragmentary movement requires

sophisticated measuring systems such as goniometers with spatial linkage (Wilke


P a g e | 46

et al., 1994; Duda et al., 1998; Gardner and Weemaes, 1999), or optical tracing

systems (Klein et al., 2003). Due to the complex deformation behaviour,

displacements of the cross-head may not be equivalent to measured inter-

fragmentary movements.

While the majority of studies (Törnkvist and Hearn TC, 1996; Stoffel et al., 2003;

Ahmad et al., 2007) determined fixation stiffness by simply equating the applied

loads to the IFM (Inter-fragmentary Movement) in the direction of load application

(individual stiffness), a few studies reported a 3D stiffness determination method

via a 6x6 stiffness matrix (Duda et al., 1998; Gardner and Weemaes, 1999) or

compliance matrix (Meleddu et al., 2007) which takes into account a full set of IFM

in 6 directions.

Determination of fixation stiffness is typically performed on a bone-implant

construct; the implant under investigation is attached to a bone or bone analogue.

The use of synthetic bones is common (Briggs and Chao, 1982; Gardner and Evans,

1992; Törnkvist and Hearn TC, 1996; Stoffel et al., 2003, 2004; Ahmad et al., 2007)

due to their low inter-specimen variability. Studies in the literature are also

divided between those that used cylindrical bone substitutes (Ahmad et al., 2007)

and those that used anatomically contoured specimens (Milek et al., 1996;

Kanchanomai et al., 2010). The influence this has on the stiffness determined has

not been evaluated.

While many of the stiffness determination methods reported in literature have

adopted in-vitro or mechanical tests, use of FEA (Finite Element Analysis) in

assessing the fixation stability is not uncommon in orthopaedic research (Drijber

et al., 1992; Prat et al., 1994). While mechanical tests gives a more realistic

environment such as bone-implant interaction, which in most cases is over


P a g e | 47

simplified in FE analysis, performing tests in-vitro can be extremely time

consuming and may not be considered feasible especially when trying to

investigate the influence of design parameters on fixation stability which requires

much number of tests during parameter analysis. Hence, where suitable, Finite

Element (FE) simulations are gaining importance over in-vitro tests.

It is evident from the literature that there exists no standardised method for

characterising fixator stiffness. The lack of a standard approach hinders

comparison of results between different studies. In recent years two different

approaches to characterise the 3D stiffness of fixation devices have been reported

((Kassi et al., 2001) and (Augat et al., 2008)). In both the methods, six individual

load cases were investigated (axial compression and rotation, shear and bending in

medial-lateral and anterior-posterior directions).

Methods suggested by Kassi et al (2001) involved investigation of the 3D stiffness

of different Ilizarov fixator configurations in-vitro where the fixator construct was

fixed firmly in all DoFs at its distal end and loads (forces and moments) were

applied to proximal end. Also, the mechanical device used in these tests restricted

the proximal fragment from rotational and lateral movements thus creating both a

confined axial compression and confined axial rotation (Kassi et al., 2001).

Augat et al (2008) investigated the stiffness characteristics of a tibial shaft fracture

fixed using a intramedullary nail. The distal fragment was fixed in all DoFs while

loads were applied to the proximal fragment (except for bending and shear loads)

which was free from any movement restrictions. However, shear loads were

applied as close to the fracture fragment as possible while the distal fragment was

held firm close to the fracture gap. Also, bending tests performed utilised four

point bending boundary condition (Augat et al., 2008).


P a g e | 48

However, only external fixator (Ilizarov fixator) (Kassi et al., 2001) and tibial nail

(Augat et al., 2008) were investigated in these studies in-vitro. Hence, it was not

clear whether can these methods be automatically adopted to characterise internal

plate fixation stiffness. Also, the effect these boundary conditions would have on

internal fixator stiffness characterisation was uncertain. Therefore, the aim of this

chapter is to evaluate the different methods (Kassi et al., 2001; Augat et al.,

2008) of fixation stiffness determination and define an appropriate method to

determine the stiffness characteristics of internal plate fixation device. To

minimise differences attributable to variability in construct assembly and

measurement error, the different stiffness determination protocols were

investigated using a finite element model. Analysis will be run in simulation

software ANSYS where loads (three forces and three moments) and boundary

conditions are applied and outputs from the analysis gathered for further stiffness

determination. Fixation stiffness will be determined using stiffness matrix and

individual stiffness calculation methods which are described in the following

sections.

3.2 Materials and methods

3.2.1 Internal fixator

A generic internal plate fixator was created (Solidworks 2010, Dassault Systèmes,

Massachusetts, USA) to represent a standard 9-hole 4.5 mm osteosynthesis plates

and screws that are commercially available from several manufacturers. The plate

was 170 mm long, 13.5 mm wide and 4.5 mm thick.


P a g e | 49

3.2.2 Implant-Cylinder construct

Assembly of the implant constructs was performed in Solidworks. A solid model of

a hollow cylinder 300 mm long with a 20 mm outer diameter and 3 mm wall

thickness was created as a bone analogue. The model of the 9-hole internal fixator

was attached to the hollow cylinder with an offset of 1 mm to form the implant-

cylinder construct. An extruded cut was performed to simulate a 3 mm osteotomy.

The fixator was affixed with three screws placed on either side of the fracture gap

occupying the three nearest screw holes nearest the gap as shown in Figure 19.

Figure 19 Shows the generic internal fixator attached to a cylinder. The outermost

screw holes were left empty to replicate the behaviour of a 7-hole plate with a

working of length of one empty hole spanning the fracture gap. The plate is offset

from the outer surface of cylinder by 1 mm.

3.2.3 Implant-Bone construct

A 3D solid bone model was created from computed tomography (CT) scans of an

ovine tibia according to the procedure described by Messmer et al. (Messmer et al.,

2007). The model of the 9-hole internal fixator was attached to the medial side of


P a g e | 50

the bone model at an offset of 3 mm to form the implant-bone construct (Figure

20). An extruded cut was performed to simulate a 3 mm mid diaphysis osteotomy.

The fixator was affixed with three screws placed on either side of the fracture gap

occupying the three screw holes nearest the gap.

Figure 20 Shows the generic internal fixator attached to an ovine tibia.

3.2.4 Creation of Finite Element (FE) model

A 3D finite element model was created for both the implant-cylinder and implant-

bone constructs (ANSYS Workbench 13, ANSYS, Inc, PA, USA). All structures were

described by linear elastic isotropic material properties. The implant material

(plate and locking screws) were made of stainless steel (E = 200 GPa, ν = 0.3).

Unlike implants which are made up of materials such as steel and have definite and

homogenous material properties throughout, living tissue such as bone are non-

homogenous and non-isotropic. Hence assigning material properties to bone is

more challenging. In the literature for such applications, assigning a single value


P a g e | 51

for Young’s modulus of is commonplace. However, the sensitivity analysis for a

range (16 GPa-20 GPa) (Spatz et al., 1996) of material properties of cortical bone

reported in literature was investigated and the results demonstrated variations of

less than 1% (for a complete description of sensitivity analysis refer to Appendix

B). Hence, for the cortical bone, a Young’s modulus of Ecort = 16,000 MPa and

Poisson’s ratio of νcort = 0.3 was used (Simon, 2003). All contacts between the

structures were modelled with surface-to-surface contact elements. The contacts

between the locking screws and the plate, as well as between the screws and the

bone were defined as bonded in all degrees of freedom (Stoffel et al., 2003; Wehner

et al., 2011).

All structures were meshed with 10-node tetrahedral elements. Convergence of

the solution occurred with a 5% allowable change in the total deformation with

163905 nodes and 105895 elements.

Figure 21 This close-up view of the plate-cylinder construct shows the relative mesh

densities for the components, the finest mesh was applied to the plate and screws. The

plate is offset from the outer surface of cylinder by 1 mm.

3.2.5 Boundary Conditions

Six independent load cases are required to determine the 3D stiffness

characteristics. The simulated load cases under partial postoperative weight

bearing (Duda et al., 1998; Taylor et al., 2006; Ebert et al., 2008) were axial


P a g e | 52

compression (400 N), torsion (5 Nm/degree), as well as bending (20 Nm/degree)

and shear (50 N) in both anterior-posterior and medial-lateral directions. The six

load cases were applied according to the boundary conditions described in

mechanical testing by both Kassi (Kassi et al., 2001)and Augat. (Augat et al., 2008)

in order to determine the effect of different boundary conditions reported in the

literature on the stiffness values calculated. In both the boundary conditions

suggested by Kassi and Augat, the distal/lower bone fragment was fixed firmly in

all DoFs (Degrees of Freedom). However, methods suggested by Kassi restricted

the lateral and rotational movements of the proximal/upper bone fragment, thus

creating both a confined axial compression and confined axial rotation.

Furthermore, while Augat applied four point bending, Kassi applied bending

moments to the top end of the proximal fragment. Also, shear loads were applied

as close to the fracture gap as possible using the BC (Boundary Condition)

suggested by Augat while Kassi applied shear force to the top end of the proximal

fragment. A third set of boundary conditions, referred to as the MPC (Multi Point

Constraint) boundary condition (Figure 22), was applied using a technique

specific to the finite element method that permitted the forces to be applied to

fracture fragments at the centre of the fracture gap using remote points rigidly

fixed to the upper and lower bone fragments. The boundary conditions

investigated are summarised in Figure 23.

To compare the stiffness values with the implant affixed to an anatomically

contoured bone and a simple cylinder model, the load cases were applied to both

constructs using the MPC boundary conditions described above. The individual

stiffness values in each of the six directions were compared.


P a g e | 53

Figure 22 Schematic shows the MPC boundary condition. (DoFs = Degrees of

Freedom).


P a g e | 54

Figure 23 Schematic shows the boundary conditions employed in each of the load

cases as defined by Kassi et al and Augat et al as well as the for the application of

loads via MPC ( or represents DoFs fixed in all 6 directions and represents

restricted lateral and rotational movements).


P a g e | 55

3.2.6 Analysis

The translational inter-fragmentary movements were determined from the

displacement of a node positioned at the centre of the fracture gap attached to the

upper fragment relative to a coincident node attached to the lower fragment. The

rotational inter-fragmentary movements were calculated using matrix algebra. For

a complete description of the inter-fragmentary movements calculation procedure,

refer to Appendix A. The orientation of each bone fragment was defined by a local

coordinate system defined by three nodes on each body (proximal and distal

fragments). The rotational transformation from one fragment into the other was

then calculated and decomposed into angles about the three coordinate axes.

The individual stiffness for each of the six load cases was determined by equating

the applied load to the IFM in the direction of load application.

x

xx

U

F=K , where x denotes the direction of load application

A complete 6 by 6 stiffness matrix (below) was calculated by relating the three

forces (Fx, Fy, Fz, forces in the x, y and z directions) and three moments (Mx, My, Mz,

moments about the x, y and z axes) applied in each of the six independent load

cases and the resulting inter-fragmentary movements (ux, uy, uz translations in x, y,

and z and α, β, γ rotations about x, y, and z) as described by Duda et al., 1998 (Duda

et al., 1997).

The diagonal values of the stiffness matrix (S11, S22..., S66) correspond to the

stiffness in the principal directions (i.e. S11 = anterior-posterior shear, S22 = medial-

lateral shear, S33 = axial compression, S44 = medial-lateral bending, S55 = anterior-

posterior bending, S66 = axial torsion).


P a g e | 56

z

y

x

z

y

x

M

M

M

F

F

F

666564636261

565554535251

464544434241

363534333231

262524232221

161514131211

SSSSSS

SSSSSS

SSSSSS

SSSSSS

SSSSSS

SSSSSS

*

z

y

x

U

U

U

3.3 Results

The inter-fragmentary movements and values for each of the six stiffness

components are listed in Table 1 for the different boundary conditions

investigated. The stiffness values calculated were varied depending on the method

of calculation; stiffness matrix versus individual and with the boundary conditions

applied.

The stiffness matrix method determined substantially different stiffness values for

axial compression, torsion, anterior-posterior and medial-lateral bending and

anterior-posterior shear. There was no difference in the medial-lateral shear

between the two methods (Augat and Kassi). Values determined via the stiffness

matrix method tended to be higher, in some cases many orders of magnitude

higher (axial compression stiffness determined using Kassi boundary conditions

equals 147000 versus 4444 N/mm) than the values determined using individual

stiffness calculation method. This trend was observed with all three sets of

boundary conditions.


P a g e | 57

Table 1 Lists the inter-fragmentary movements for the six load cases and the

stiffness components determined from either the stiffness matrix (Km) or the

individual stiffness (Ki) for the implant-bone construct.

The axial compression boundary conditions defined by Kassi and Augat produced

substantially different axial compression and shear stiffness values. Confined axial

compression (Kassi) more than doubled the axial stiffness as compared with

unconfined compression (Augat, MPC). Applying the shear load at the top end of

the proximal fragment (Kassi) also substantially increased the shear stiffness as

compared to applying the shear load in close proximity to the fracture gap (Augat,

MPC).

In bending and torsion there was to a lesser extent differences in the stiffness

values calculated from the three different boundary conditions. The most

significant difference occurred for the AP (Anterior-Posterior) bending component

Kassi Fx Fy Fz Mx My Mz ux uy uz α β γ Km Ki

Axial 0 0 -400 0 0 0 0 0 -0.09 0.4 0 0 147000 4444

Torsion 0 0 0 0 0 5 0.2 0 0 0 0 1.1 18 4.5

Bend AP 0 0 0 0 20 0 -0.01 0 0 0 1.5 0 150 13

Bend ML 0 0 0 20 0 0 0 0 -0.96 4.4 0 0 13 4.5

Shear AP 50 0 0 0 7.5 0 0.03 0 0 0 0.57 0.14 5990 1667

Shear ML 0 -50 0 7.5 0 0 0 -0.03 -0.35 -1.7 0 0 1667 1667

Augat Fx Fy Fz Mx My Mz ux uy uz α β γ Km Ki

Axial 0 0 -400 0 0 0 0 0 -0.24 1.1 0 0 50000 1667

Torsion 0 0 0 0 0 5 0.22 0 0 0 0 1.2 6.6 4.2

Bend AP 0 0 0 0 20 0 0 0 0 0 1.3 0 137 15

Bend ML 0 0 0 20 0 0 0 0 -0.95 4.5 0 0 15 4.4

Shear AP 50 0 0 0 3.8 0 0.05 0 0 0 0.2 0.1 1580 1000

Shear ML 0 -50 0 3.8 0 0 0 -0.04 -0.18 -0.9 0 0 1250 1250

MPC Fx Fy Fz Mx My Mz ux uy uz α β γ Km Ki

Axial 0 0 -400 0 0 0 0 0 -0.25 1.1 0 0 10400 1600

Torsion 0 0 0 0 0 5 0.24 0 0 0 0 1.4 6.9 3.6

Bend AP 0 0 0 0 20 0 0 0 0 0 0.6 0 34 33

Bend ML 0 0 0 20 0 0 0 0 -1 5.2 0 0 25 3.8

Shear AP 50 0 0 0 0 0 0.05 0 0 0 0 0.14 1900 1000

Shear ML 0 -50 0 0 0 0 0 -0.04 0 0 0 0 1250 1250


P a g e | 58

calculated from the MPC boundary condition. The MPC boundary condition led to a

significantly higher AP bending stiffness than both the Kassi and Augat BCs.

Figure 24 Shows the stiffness components determined for each of the three

investigated boundary conditions using implant-cylinder construct.

The stiffness characterisation of fixation devices may be performed with the

fixation construct attached to a bone or bone substitute such as a hollow cylinder

of artificial material. Comparing the stiffness values obtained, it was found that the

geometry of the bone analogue influenced axial stiffness the most.

0

10

20

30

40

0

1000

2000

3000

4000

5000

Sti

ffn

ess

(N

m/

de

g)

Sti

ffn

ess

(N

/m

m)

Kassi Augat MPC


P a g e | 59

Figure 25 Shows the stiffness components determined for the internal fixator affixed

at an offset distance of 3 mm to a hollow cylinder and a bone contoured geometry

using MPC boundary condition.

3.4 Discussion

A review of the literature exposes several different methods used in determining

the stiffness of fracture fixation devices. Kassi et al (2001) reported the

development of a loading apparatus to conveniently apply six independent load

cases to a fixation construct to determine the 3D stiffness matrix without the need

for multiple testing rigs. In the characterisation of an intramedullary nail (Kassi et

al., 2001). Augat et al (2008). reported contrasting methods of applying the loads

to the construct (Augat et al., 2008). With no clearly defined standard procedure

for characterising the stiffness of fracture fixation devices, it is unclear to what

extent stiffness values can be compared from different studies and as to how

future testing should be performed given no two fixation devices behave similarly.

The aim of this study was therefore to evaluate existing methods for characterising

0

10

20

30

40

0

1000

2000

3000

4000

5000

Sti

ffn

ess

(N

m/

de

g)

Sti

ffn

ess

(N

/m

m)

Cylinder Bone


P a g e | 60

the stiffness of fracture fixation devices and define an appropriate protocol for

evaluating the stiffness of an internal fixator.

3.4.1 Method of stiffness calculation

Stiffness is the relationship between force and displacement. For any single

direction, i.e. axial compression, the stiffness can be calculated by relating the

displacement in the direction of loading to the applied force. A three-dimensional

stiffness matrix can also be calculated to represent the stiffness behaviour of a

body or construct. A significant discrepancy was found for the stiffness values for

an internal fixator using the two different methods. The differences appear

attributable to the fact that the internal fixator does not undergo six unique

displacement modes under the six load cases. The deformation behaviour under an

axial compressive load and ML (Medial-Lateral) bending load are very similar, both

result in axial compression and ML bending at the fracture gap. Similarly, axial

torsion and anterior-posterior shear resulted in similar IFM’s. Because of the

position of the fixator relative to the long axis of the bone, eccentric loading is

created and asymmetric deformation results. For example, AP shear loading not

only produces an IFM in the AP direction but also results in an axial torsion

moment about the fixator it produces additional torsional deformation. As these

additional moments are not accounted for in the force matrix, this leads to errors

in the calculation of the stiffness components.

Moreover, when investigated in detail, it was surprising to know that even a slight

change to IFM’s of the order of 0.01 mm (especially in axial inter-fragmentary

movement for the ML bending load case) resulted in a huge difference in stiffness

value. The Figure 26 highlights the sensitivity of stiffness values to slight changes

in certain IFM’s. Hence, it was concluded that the stiffness matrix is highly


P a g e | 61

sensitive and even small amounts of error in determination of IFM of the order of

0.01 of a millimetre would result in huge differences in the calculated fixation

stiffness value.

Figure 26 Shows the axial compressional stiffness value determined via stiffness

matrix method for different axial IFM’s (-0.69 mm - -0.73 mm) for the medial-lateral

bending load case.

Therefore, the stiffness components in each direction were determined by relating

the applied force in each direction to the resulting displacement in that direction

(individual stiffness calculation method).

3.4.2 Boundary Conditions for stiffness determination

In both the boundary conditions adopted by Augat and Kassi for the determination

of axial compressive stiffness and torsional stiffness, the bone fixator construct

was held fixed at the bottom and load applied to the top end of the proximal

fragment. The BC’s did differ however in the constraints applied to the upper

fragment. The testing-rig proposed by Kassi restricts horizontal motion and

rotation of the upper fragment and so creates both a confined axial compression


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and confined axial torsion. Augat on the other hand employed a universal/cardan

joint to enable free rotation of the construct at the upper support. Determination of

the axial stiffness under confined compression led to significantly higher values

than under unconfined compression. Due to the position of the internal fixator

relative to the loading axis, this eccentric loading results primarily in a ML bending

deformation mode rather than a uniform axial compression. Because the confined

compression restricts the bending of the construct, the IFM is restricted and hence

higher stiffness results. In this study, the effect of confining the upper fragment

was less prevalent on the torsional stiffness. However, for more complicated

geometries, i.e. where stiffness determination is performed on a fixator attached to

a contoured bone, a more complicated deformation pattern may result and

stiffening occur due to restriction of movement.

In respect to the application of shear loads, there are also substantial differences

between the BC’s applied by Kassi and Augat. Kassi’s rig uses the rotation of biaxial

materials testing machine to apply a lateral load to top of the construct, whereas

Augat firmly grips both fragments, one is fixed and the other is attached to the

actuator of the materials testing machine. In applying the shear load to the top of

the construct, which is weakest in the middle section, the deformation mode is

more akin to bending rather than shear. The shear stiffness is also overestimated

relative to the situation where the loads are applied closer to the fracture gap

because, as the fragment bends relative to lower fragment, a fracture gap

displacement occurs in the opposite direction to loading. The resulting shear IFM

is thus equal to the shear IFM less the IFM in the opposite direction due to bending.

Applying the loads closer to the fracture gap reduces the lever arm of the load and

hence the moment and ultimately the bending.


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Despite differences in the shear stiffness determined applying the different BCs

(Boundary Conditions); the shear movements themselves were very small, of the

order of less than 0.05 mm. This is both attributable to the BCs themselves with

induced bending rather than pure shear, but also the nature of the internal fixation

device itself, that through its close proximity to the bone permits very little shear

movement. In this study, a relatively stiff internal fixator configuration was tested

with a short working length of one hole. Shear movements may be greater with

differently configured plates and the influence of internal fixator configuration on

the stiffness components is subject of a separate study (refer to Chapter 4).

The application of BC for the case of bending loads varied between the different

BC’s investigated. While Kassi held the bone-fixator construct fixed at the bottom

and applied bending moments to the top end of the upper fragment, Augat applied

4 point bending (Figure 23). On the other hand, using MPC BC, bending moments

were applied to the node forming centre of fracture gap connected to the proximal

fragment while a coincident node connected to the distal fragment was fixed in all

DoFs. Investigation of the effect of BC on bending stiffness showed that the

bending stiffness in anterior-posterior direction determined using MPC BC was

double the stiffness value determined using either Kassi or Augat BC’s. Since the

centre node connected to the distal fragment is fixed in all DoFs, it is restricted

from bending and hence a higher bending stiffness of the construct. Although

applying BC as suggested by Augat (four point bending) resulted in a more uniform

bending of the construct, applying four point bending to a bone-implant construct

may not be feasible due to the complex geometry of the bone. Hence, for purposes

of parameter analysis, the use of MPC BC may be appropriate while investigating

the effect of bending loads on implant stability.


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3.4.3 Bone contoured geometry versus simple cylinder

Methods of stiffness determination also vary in the use of bone analogues. Whilst

some studies used cadaveric bones, others used artificial bones or hollow cylinders

to represent bone. In this study, the influence of contoured bone geometry versus a

simple cylinder was investigated. The geometry of the bone analogue did influence

the stiffness components and to varying degrees, in this case, axial stiffness was

affected the most. Using the finite element method, all other variables (material

properties, interface properties, etc) were held constant. Therefore, the differences

determined here can be attributed to the effect of geometry alone. The reason for

the differences can be attributed to differences in offset between fixator and the

bone; the contoured bone shape dictates the plate be placed a greater distance

from the bone, the bone axis is also curved which gives rise to differences In some

cases, the use of a bone contoured geometry may be dictated by the question

addressed in a particular study, however a simple cylindrical geometry can be used

for stiffness determination and enhance comparison between the results of

different studies.

This study has few limitations and assumptions which should be discussed. The

cortical bone was simplified and described as a homogenic material with linear

elastic and isotropic material properties. Due to the presence of segmental defect,

it is expected that most of the load transfer happens through the fixator and the

bone acts very similar to a rigid body. Hence, we believe assigning a single value

for material property would not alter the fixation stiffness value determined.

However, sensitivity analysis performed demonstrated that the variations to the

value of young’s modulus of the cortical ovine tibia in the range 14 GPa- 24 GPa

(Spatz et al., 1996) reported in literature led to differences in calculated axial


P a g e | 65

compressional stiffness value of up to a maximum of 1 % (refer to Appendix B).

Hence, the simplified description of the bone material was assumed to be

uncritical.

In the model created for this project, forces were applied to an artificially

constructed conical extension to the bone within the fracture gap (imaginary point

representing the centre of the fracture gap connected to the fracture fragments

(proximal and distal) via rigid beam elements (Multi-Point Constraint (MPC))).

Hence, the deformation at the osteosynthesis and thus the determined stiffness

matrix will also be influenced by the local deformation of the bone fragments and

of the conical extension (rigid beam) apart from the deformations of the fixator.

However, the results showed that the deformation of the bone and the rigid beams

were less than 0.01 mm suggesting that they behaved very similar to a rigid body.

Therefore, the application of forces to this conical extension was assumed not to

alter the determined fixation stiffness.

In this study, the perfectly modelled screw-bone and screw-plate interface could

over estimate the stiffness values determined. However, the FE model was

compared with results from mechanical testing (For a complete description of the

FEA model comparison process, refer to Appendix C). Although there were

differences in absolute values between FEA and mechanical testing results, similar

deformation behaviour was observed between FEA and mechanical tests for the

two fixator screw configurations investigated which to an extent verifies the FE

model. Besides, since relative comparison (effect of different boundary conditions

on fixation stiffness) is performed in this study, determination of absolute values is

not essential. Hence, the assumption of perfectly modelled screw-bone or screw-

plate interface was assumed to be not critical.


P a g e | 66

3.5 Conclusion

In summary, this study highlighted the importance of input parameters such as

boundary conditions and method of stiffness calculation on fixation stiffness. After

having analysed different methods previously used in literature, it was concluded

that the method of applying loads to the centre of fracture gap as explained in MPC

BC to be a convenient method to determine internal plate fixation stiffness using

FE technique. In addition, owing to the highly sensitive nature of stiffness matrix, a

decision to use the individual stiffness calculation method for internal fixation

stiffness determination was made.

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4 Investigation of the influence of fixator

configuration on fixation stiffness

This chapter focuses on determining the influence of fixator configuration on

fixation stability using methods developed in Chapter 3 of this thesis.

Chapter 4 Investigation of the influence of fixator configuration on fixation stiffness

P a g e | 68

4.1 Introduction

The influence of mechanics on the healing outcome of bone fractures is well

documented. The local mechanical conditions are determined by limb-loading and

the stability of fixation. A range of fixation devices are available for the treatment

of bone fractures and choice depends on the location and the severity of the

fracture.

Locked plating constructs also referred to as internal fixation devices have been

developed with the goal of biologic fixation in mind. Used as a bridging construct,

internal fixation devices are intended to provide flexible fixation to support repair

via the secondary bone healing pathway with callus formation. The locking screws

allow the fragments to be stabilised without compressing the fixator onto the bone

surface, thereby preserving the peripheral blood supply to the bone. Recent

developments in surgical techniques have also enabled these devices to be applied

in a minimally-invasive approach causing less disruption to the injured tissues.

Internal fixation devices have also been shown to provide improved fixation

strength in osteoporotic bone (Henderson et al., 2011). These benefits of internal

plate fixation have led to rapid adoption of this technology.

Recent biomechanical studies suggest however, that internal fixation devices

(Locking plates) may be overly stiff when compared to external fixators and

suppress inter-fragmentary motion to a level that may be insufficient to reliably

promote secondary bone healing (Bottlang et al., 2010; Bottlang and Feist, 2011).

Due to the proximity of the plate to the cortex, movements at the near cortex are

again a fraction of those at the far cortex raising further concern that excessive

stiffness may prevent stimulation of callus formation. Recent clinical studies


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confirm that the inherently high construct stiffness of locked-plate constructs

suppresses callus formation (Bottlang et al., 2010; Bottlang and Feist, 2011).

There are no clear guidelines as to the stiffness requirements for fixation devices

because all fractures are not created equal. Therefore for the same fixation

stiffness, the inter-fragmentary motion in the fracture gap will vary depending on

limb loading and the size of the fracture gap. Furthermore, fixation devices are

highly non-linear in the sense that axial load does not translate purely into axial

inter-fragmentary motion but rather a combination of axial, shear and bending

displacements. Studies investigating the influence of micro-motion on healing have

demonstrated that axial inter-fragmentary movements of the order of 0.2 – 1 mm

in a 3 mm osteotomy gap provide best healing outcome in sheep where simple

diaphyseal long bone fracture stabilised with a custom made external ring fixator

was investigated (Claes et al., 1998). Furthermore, fixation devices that provide a

high resistance to shear and torsional movements but enable a moderate amount

of axial inter-fragmentary movement have been shown to provide timely healing

with callus formation in animal studies (Epari et al., 2007).

There is no single one way to configure an internal fixation device. Choices

available to the surgeon include the length and size of the plate, the material, the

number and configuration of the screws. The parameters which influence internal

fixator stiffness are the material properties, the cross-section or shape of the

fixator, effective plate length, the offset distance from the underside of the fixator

to the bone surface, number and position of screws, and the screw type. However,

it is unclear how all these different parameters affect the fixation stability and

whether they can be manipulated to optimise the mechanical conditions for

healing. Therefore, the purpose of this study is to characterise the fixation


P a g e | 70

stability of an internal plate fixation device and the influence of modifications

to its configuration on implant stability.

While the motivation of the study is configuration of internal plate fixation devices

for optimal stability (moderate axial inter-fragmentary movements with high

resistance to shear and torsional movements), the hypothesis of the study is that

the internal fixation devices are inherently too stiff so as to promote sufficient

callus formation for better healing outcome. In this study, characterisation of

fixation stiffness of internal plate fixator will be performed using MPC (Multi Point

Constraint) boundary condition where loads and boundary conditions will be

applied to the node forming the centre of fracture gap in FE. Simplified bone

geometry (cylinder) with a 3 mm mid shaft osteotomy on to which a generic 9 hole

locking plate is attached will be used in the analysis. Specifically, the current study

is designed to investigate the influence of modifications to fixator configurations

on implant stability. The fixator configurations chosen for analysis are fixator

material properties (Stainless Steel and Titanium), fixator offset (1 and 3 mm),

fixator inclination (+ and -0.75 degrees), screw configuration (Working length

(distance between the inner most screws), screw spacing, number of screws and

effective plate length). The fixator configuration in terms of material of the fixator

was dictated by the material of the commercially available implants.

The knowledge gained through this analysis is expected to prove useful in

providing a guideline in the configuration of internal plate fixators that allow

moderate axial IFM at the fracture site for sufficient callus formation.


P a g e | 71

4.2 Materials and methods:

4.2.1 Internal fixator

A generic locked plating implant was created (Solidworks 2010, Dassault

Systèmes, Massachusetts, USA) to closely represent a standard 9-hole 4.5 mm

osteosynthesis plates and screws that are commercially available from several

manufacturers. The plate was 170 mm long, 13.5 mm wide and 4.5 mm thick.

4.2.2 Implant-Bone analogue construct

In the standard configuration the plate was attached to a hollow cylinder with an

outer diameter of 20 mm and wall thickness of 3 mm that represented cortical

bone in diaphysis of a long bone (tibia). Six screws, three in each fragment, were

used to attach the plate to the bone utilising the three innermost screw holes on

each side of the simulated osteotomy (0xxx0xxx0, where empty screw holes are

represent by a “0” and filled holes by a “x”). The standard screw configuration is

shown in Figure 27.


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Figure 27 Internal fixator and bone cylinder construct in the standard configuration

(0xxx0xxx0) for an effective plate length of 7-hole with three screws on either side of

the osteotomy gap.

4.2.3 Finite element model

A finite element model of the implant-bone construct was generated in ANSYS 13,

(ANSYS, Inc., Canonsburg, PA, USA) by importing a parasolid file of the implant-

bone solid model.

All structures were meshed with 10-node tetrahedral elements with an assigned

element size for each component.

All structures were described by linear elastic isotropic material properties. For

the cortical bone, a Young’s modulus of Ecort = 16,000 MPa and Poisson’s ratio of

νcort = 0.3 was used. The implant material (plate and locking screws) were made of


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either stainless steel (SS) (Ess = 200,000 MPa, νss = 0.3) or titanium alloy (Ti) (ETi =

110,000 MPa, νTi = 0.33).

All contacts between the structures were modelled with surface-to-surface contact

elements. The contacts between the locking screws and the plate, as well as

between the screws and the bone were defined as bonded in all degrees of freedom

(DoFs).

For the application of boundary conditions, two coincident nodes were modelled in

the middle of the fracture gap, which were connected to the outer ends of the bone

fragments at the fracture site using rigid beam elements. The node connected to

the distal bone fragment was fixed in all six DoFs. At the proximal node the loads

for the different load cases used in the stiffness determination were applied.

4.2.4 Stiffness determination

The stiffness of the constructs was determined in all six directions (axial

compression and axial torsion, medial-lateral (ML) bending and anterior-posterior

(AP) bending and ML and AP shear). The loads applied in each direction were axial

compression (400 N), axial torsion (5 N/m), medial-lateral and anterior-posterior

bending (20 N/m) and medial-lateral and anterior-posterior shear (50 N). The

inter-fragmentary movements (IFM) (all three translations) were determined from

the node at the centre of the fracture gap and additionally the axial IFM at the near

and far cortex to the plate were determined from nodal displacements (Figure

28). The bending and rotational displacement components were from

displacement of the proximal fragment using matrix algebra. The detailed

description of the calculation procedure can be found in Appendix A.


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Figure 28 Illustration of calculation of axial component of IFM (Inter Fragmentary Movement)

using MPC (Multi Point Constraint) BC (Boundary Condition).

4.2.5 Configurations

To determine those parameters that have the greatest influence on internal plate

fixation stability a number of different configurations were investigated. The

material properties of the plate and screws were simulated as Stainless Steel or

Titanium (internal plate fixators are generally available in these two materials).

The distance between the plate and the bone (plate offset) was varied between 1

and 3 mm, the inclination of the plate was varied between +0.75 and -0.75 degrees

(maximum inclination achieved before plate contacted the bone surface for a 1 mm

offset distance between plate and bone) to the bone. Screw configuration was

altered varying the working length (distance between innermost screws), the

effective plate length, the screw spacing and the screw number. The screw


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configurations investigated are detailed in Figure 29. Finally, the effect of bi-

cortical and far cortical screw anchorage was examined. Far-cortical locking

(Figure 31) was simulated in the finite element model by removing the contact

surfaces on the near cortex. No inhibition of movement by the near cortex was

permitted, allowing determination of stiffness of fixation prior to screw contact

with the screw-hole wall on the near cortex.

Figure 29 Schematic representation of the screw configurations investigated.

(Notation: e.g. Top left 0XXX0XXX0, Top right X0XX0XX0X).

Figure 30 Shows a generic locking plate (modified from 9 hole, 4.5 mm standard

Locking Compression Plate) with three screws on either side of the fracture gap

leaving the middle screw hole empty.


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Figure 31 Schematic (plan/top view) represents principal of FCL in FE analysis.

4.3 Results

4.3.1 Standard configuration

The load cases investigated (under partial post-operative weight bearing) (Duda et

al., 1998; Taylor et al., 2006; Ebert et al., 2008) were axial compression (400 N)

and torsion (5 Nm/degree), bending (20 Nm/degree) and shear (50 N) in medial-

lateral and anterior-posterior directions. The standard internal plate fixator

configuration, with three screws on either side of the osteotomy gap resulted in an

axial compressive stiffness of 1600 N/mm and axial IFM of 0.25 mm at the centre

of the gap and 0.14 and 0.34 mm at the near and far cortices respectively. The

stiffness in axial torsion was 3.8 Nm/deg with a torque of 5 Nm resulting in a 1.3

degree displacement. The ML and AP shear stiffness components were similar and

of the order of 1000 N/mm. The stiffness in AP bending was approximately five

times the stiffness in ML bending.


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4.3.2 Internal fixator material properties

Table 2 The effect of implant material properties on the stability of internal plate

fixation.

0xxx0xxx0 (SS) 0xxx0xxx0 (Ti)

%

reduction

in stiffness

Stiffness IFM (mm) Stiffness IFM (mm)

Axial (N/mm) 1600 0.25 (0.14-0.34) 900 0.44 (0.26-0.61) 44

Torsion (Nm/deg) 3.8 1.3 2.3 2.2 36

Bend AP (Nm/deg) 33 0.6 20 1.0 39

Bend ML (Nm/deg) 4.0 5.0 2.4 8.4 40

Shear AP (N/mm) 1000 0.05 715 0.07 29

Shear ML (N/mm) 1250 0.04 830 0.06 34

Changing the implant material from stainless steel to titanium led to a 29 - 44%

reduction in the stiffness components, the greatest reduction occurred in the axial

direction (44%).

4.3.3 Internal fixator offset

Table 3 The effect of implant offset to the bone on the stability of internal plate

fixation.

0xxx0xxx0 1mm offset 0xxx0xxx0 3mm offset

% reduction

in stiffness


Axial (N/mm) 1600 0.25 (0.14-0.34) 1210 0.33 (0.10-0.56) 24

Torsion (Nm/deg) 3.6 1.4 3.1 1.6 14

Bend AP (Nm/deg) 33 0.6 28 0.7 15

Bend ML (Nm/deg) 4.0 5.0 4.0 5.0 0

Shear AP (N/mm) 1000 0.05 830 0.06 17

Shear ML (N/mm) 1250 0.04 1250 0.04 0


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Increasing the offset between the internal fixator and the bone resulted in a

decrease in construct stiffness, however not all stiffness components were affected

equally. No significant changes (see IFMs) were determined in either the ML or AP

bending or shear components. The greatest reduction occurred in the axial

direction (24%).

4.3.4 Internal fixator inclination

Table 4 The effect of implant inclination to the bone on the stability of internal plate

fixation.

0xxx0xxx0 0xxx0xxx0 +/- incl

% reduction

in stiffness


Axial (N/mm) 1600 0.25 (0.14-0.34) 1540 0.26 (0.07-0.44) 4

Torsion (Nm/deg) 3.8 1.3 5 1 -32

Bend AP (Nm/deg) 33 0.6 40 0.5 -21

Bend ML (Nm/deg) 4 5 4.9 4.1 -23

Shear AP (N/mm) 1000 0.05 1670 0.03 -67

Shear ML (N/mm) 1250 0.04 1670 0.03 -34

Placing the internal fixator at either a positive or negative inclination to the axis of

the bone and hence the loading direction had no significant effect on the axial IFM

at the centre of the gap and hence the axial stiffness. However the axial IFM at the

far cortex was increased by 29% and at the near cortex it decreased by 50%.

Contrary to the axial stiffness, the remaining stiffness components increased by

between 20 - 65% with AP shear most affected. There was no difference between

either the positive or negative inclination.


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4.3.5 Screw configuration

Table 5 The effect of working length on the stability of internal plate fixation.

0xxx0xxx0 xxx000xxx

%

reduction

in stiffness


Axial (N/mm) 1600 0.25 (0.14-0.34) 850 0.47 (0.10-0.83) 47

Torsion (Nm/deg) 3.6 1.4 2.3 2.2 36

Bend AP (Nm/deg) 33 0.6 20 1.0 39

Bend ML (Nm/deg) 4 5 2.2 9.2 45

Shear AP (N/mm) 1000 0.05 415 0.12 59

Shear ML (N/mm) 1250 0.04 225 0.22 82

Increasing the working length and the effective plate length, but keeping the

number of screws per fragment constant, resulted in a significant decrease in all

stiffness components (>40%). The largest decrease in stiffness occurred in the ML

shear direction (82%). Changing the working length by one empty screw hole i.e.

from xxx0xxx to xxx00xxxx decreased the axial stiffness by 30% when compared to

by two holes which decreased the stiffness by 47%.

Table 6 The effect of working length on the stability of internal plate fixation.

0xxx0xxx0 xx0x0x0xx

% reduction

in stiffness


Axial (N/mm) 1600 0.25 (0.14-0.34) 1600 0.25 (0.06-0.46) 0

Torsion (Nm/deg) 3.6 1.4 3.3 1.5 13

Bend AP (Nm/deg) 33 0.6 33 0.6 0

Bend ML (Nm/deg) 4 5 3.7 5.4 8

Shear AP (N/mm) 1000 0.05 1000 0.05 0

Shear ML (N/mm) 1250 0.04 1250 0.04 0


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Increasing the plate length but keeping the working length the same had little

effect on the stiffness of the construct. Similarly, altering the spacing of the screws

from xx0x0x0xx to x0xx0xx0x and xx0x0x0xx to xxxx0xxxx had only minor effects

on the stiffness of the construct.

4.3.6 Far cortical locking

Table 7 The effect of bi-cortical versus far cortical locking on the stability of internal

plate fixation.

0xxx0xxx0 0xxx0xxx0 FCL

%

reduction

in stiffness


Axial (N/mm) 1600 0.25 (0.14-0.34) 1170 0.34 (0.15-0.53) 27

Torsion (Nm/deg) 3.8 1.3 1.9 2.6 50

Bend AP (Nm/deg) 33 0.6 10 2.0 70

Bend ML (Nm/deg) 4 5 3.6 5.5 10

Shear AP (N/mm) 1000 0.05 450 0.11 55

Shear ML (N/mm) 1250 0.04 1000 0.05 20

Far cortical locking has been proposed as a new design to conventional internal

plate fixation devices to reduce construct stiffness. Far cortical locking led to a

27% reduction in axial stiffness but also over 50% reductions in torsion and AP

shear and bending stiffness. In contrast, to modifications to the working length

which decreased motion at the near cortex, far cortical locking increased axial IFM

at both the near and far cortex (Compare Table 5 and Table 7).

4.4 Discussion

Recent clinical and biomechanical studies have suggested that internal fixation

devices may be too stiff to reliably stimulate callus formation. Furthermore, timely


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healing has been shown to require a moderate axial stiffness and high stiffness in

the shear and torsional directions. In this study, a 3D finite element model was

used to characterise the stiffness of an internal plate fixator. An internal fixator

configured with an offset of 1 mm to the bone surface and three screws on either

side of the fixator made of stainless steel was found to exhibit high stiffness,

particularly against shear. The axial IFM at the near cortex under a load equivalent

to partial weight bearing was extremely low (0.05 mm). Modifications to the model

were then made to investigate the influence of changes to internal plate fixation

configuration on its stiffness components to determine the most appropriate

method to increase the flexibility of fixation and to control the axial IFM.

Internal plate fixation devices are available from most manufacturers in either

stainless steel or titanium. As expected, a change in material property from

stainless steel to titanium resulted in a decrease in stiffness by almost 50%,

equivalent to the difference in elastic modulus between the two materials. Due to

the complex non-linear nature of the bone fixator construct the change in material

properties did not influence all stiffness components equally. The change

influenced the axial, ML bending and torsional stiffness components to the greatest

extent. Although a 30% decrease in shear stiffness was determined, the shear

movements with both steel and titanium plates were insignificant (less than 0.1

mm). The axial IFM at the near cortex increased substantially from 0.14 to 0.26

mm (86%).

In the case of external fixation devices the distance between the plate and the bone

has a considerable influence on the overall construct stability. In contrast to

external fixation, the free bending length of the screws is considerably less with

internal fixation as the internal fixator is placed in close proximity to the bone


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under the muscle/skin. In internal fixation the plate should be held at a distance

slightly away from the bone to preserve the peripheral blood supply to the bone. In

this study we investigated influence of offset by increasing the offset between the

plate and the bone from 1 mm up to a conceivable 3 mm. Increasing plate offset by

2 mm reduced axial and torsional stiffness by approximately 20-25%, however

there was no influence on the bending stiffness and the magnitude of the shear

movements remained insignificant. The irregular geometry of the bone may also

dictate that the plate is placed at an inclination to the long axis and hence the

direction of loading. In this study, placing the plate at an inclination to the bone

had almost no effect on the axial stiffness but surprisingly increased the remaining

stiffness components. The change in stiffness was the same whether the plate was

inclined positively or negatively from the bone axis.

The screw configuration is known to influence not only the stability of internal

fixation but also the stresses within the plate and likelihood of plate failure. In a

previous study the influence of screw configuration on the axial and torsional

stiffness was investigated with the finding that the working length, the distance

between the innermost screws on either side of the fracture gap, is the greatest

determinant of construct stiffness and that more than three screws per fragment

did little to further increase stability (Stoffel et al., 2004). Increasing the working

length from one to three empty holes (and in doing so increasing plate length)

reduced the axial stiffness by approximately 50%, doubling the axial motion at

both the near and far cortices. Changing the working length also reduced the shear

stiffness considerably; the change in the ML direction was over 80%. Increasing

the plate length (7-hole to 9-hole) whilst maintaining a working length of one

empty hole, with at least three screws per fragment, had little effect on the stability

of the construct regardless of the spacing of the screws.


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Far cortical locking is a fixation principle whereby an internal fixator is anchored

only at the far cortex. This is achieved by either narrowing the screw diameter or

enlarging the size of the screw hole at the near cortex. In the finite element model

used in this study, far cortical locking was modelled by removing the contact

constraint on the near cortex. In doing so, no changes were made to the actual

geometries of the internal plate fixator or the screws. Far cortical locking

essentially increases the bending length of the screw, to be more comparable with

external fixation although the screw is anchored in only one cortex. In this study

far cortical locking resulted in a reduction in axial stiffness by 27%. Whilst the

increase in the inter-fragmentary movement in the centre of the gap was only 36%,

the increases at the near and far cortices were 200% and 55%. As opposed to other

modifications made to the configuration of the internal fixator, far cortical locking

substantially increased the axial IFM at the near cortex. Interestingly, far cortical

locking decreased the stiffness of the construct by over 50% in both the AP

bending and shear direction and also in axial torsion. However, as the internal

fixator is relatively stiff in these orientations, the reduced stiffness is unlikely to be

of great concern.

Using the finite element method, alterations to the configuration of the construct

were possible without altering the relative positions of the components to one

another, thereby eliminating the inter-individual variability inherent to in-vitro

testing. This provided the sensitivity needed to determine if subtle variations in

the construct such as the offset or the inclination of the plate to the bone expected

to occur in clinics had a significant impact on the construct stiffness. The in-silico

(computer) methods applied here provide an efficient way to investigate the

parameters that influence fixation stiffness. The knowledge gained here will aid in

the configuration of fixation stiffness for optimal healing conditions.


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In construction of the finite element model, assumptions and simplifications have

been made. While finite element models of each of the components has been

validated individually, simplifications made in modelling such as the interfaces

between the screw head and the plate and the screw and the bone may over-

estimate the actual stiffness of the construct. Comparison of results from FEA with

mechanical testing demonstrated a maximum of 70% over estimation of confined

axial torsional stiffness value in FE (refer to Appendix C). In spite of this, the finite

element method is a useful tool at the engineer’s disposal and enables the influence

of large number of parameters to be investigated in a timely fashion, allowing

identification of those parameters likely to be critical in determining internal plate

fixation stability. Determination of the absolute stiffness of the final constructs

should therefore still be assessed using conventional in-vitro methods.

In this study, modifications to the configuration of an internal plate fixation device

were investigated to reduce construct stiffness to create axial IFM at both the near

and far cortices to support bone healing via callus formation. Simply changing the

material property from stainless steel to titanium was effective in doubling the

axial IFM at the far cortex and by an order of magnitude at the near cortex. It did

however also decrease the bending and torsional stiffness by approximately 40%.

Increasing plate offset from 1 mm to 3 mm increased axial IFM but to a lesser

extent than material property. Movement in the other directions were hardly

affected. Modifying the screw configuration to increase the working length

increased axial IFM but also decreased torsional stability by a similar amount and

as well as up to an 80% reduction in shear stiffness. Far cortical locking also

increased the axial IFM at both the near and far cortices, but with an even greater

loss of torsional stability and the influence on shear was less significant. Large

torsional moments in far cortical locking can be controlled by the diameter


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difference between the screw and the hole at the near cortex. In this study, using a

generic 7-hole plate (effective plate length) with three screws or either side of the

fracture gap, changing the material property from steel to titanium was equally

effective in increasing micro-motion as far cortical locking. Specialised FCL

constructs may be able to achieve benefits over and beyond those determined in

this study.

Primarily, this study was focused on investigating the influence of modifications to

internal plate fixator configurations on implant stability and not on implant

survival. In order to investigate influence of fixator configuration on implant

survival, additional research in terms of analysis of system under dynamic or cyclic

loads which may significantly affect its fatigue life is required. Also, the model used

in this study assumes no load transfer across the fracture gap i.e. callus was not

incorporated in the FE model as the IFM during the initial healing phase that

stimulates callus formation was of focus in this study.

Results from this study are expected to provide guidelines for implant design and

is not intended to represent the clinical situation. Hence, results cannot be

extrapolated to the clinical setting as the cylinder geometry (cortical ovine bone

material properties) used in this current study cannot replace real bone and the in-

vivo situation is far more complex. However, the tests conducted on homogenous

cylinders exclude high variation in geometry of real bone and hence increases the

reproducibility of these results.

In conclusion, internal plate fixators were found to be comparatively stiff fracture

fixation devices (IFM less than 0.05 mm in shear and less than 0.3 mm in axial

directions for the fixator configurations investigated in this study). A number of

modifications can be made to increase the axial micro-motion in order to stimulate


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callus formation, however some of those modification come at a cost of both the

torsional and shear stiffness attributes, which should be maintained in order to

ensure timely healing.

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Section 2 Fixation stability and remodelling

In this section, focus is placed on developing a method to quantify implant related

changes due to remodelling.

Introduction

Bone has the capacity to adapt to changes in its mechanical loading through a

process termed bone remodelling (Wolff et al., 1986). Bone remodelling is a

lifelong process where old bone is replaced by new bone (Hadjidakis and

Androulakis, 2006). The onset of bone remodelling occurs when the bone senses

the stimulus for remodelling originating from the change in external loads. Mori

and Burr (Mori and Burr, 1993) showed remodelling as a response to damage

(presence of micro cracks). The lack of blood supply following a fracture could also

result in bone resorption and hence could be one of the reasons for remodelling

(Melnyk et al., 2008). In adults, approximately 18% of the bony skeleton is

replaced annually through the remodelling process (Donald, 2003). Several studies

have been conducted in the past which supports the aforementioned functional

adaptation of bone. Fhyrie and Carter postulated (Fyhrie and Carter, 1986) that

bone adaptively changes its structure and density in response to its stress and

strain rate (Jang et al., 2009). Since bone is a living adaptive tissue, it responds to

applied loading by altering its micro-structure over a period of few days or weeks

(Jacobs et al., 1997). Remodelling leads to both changes in the density and

structure of the bone (Jang et al., 2009). Only remodelling as a response to fracture

fixation, i.e. implant related remodelling changes will be discussed in this thesis.

Influence of fixation stability on the local mechanical loading environment

experienced by the healing bone is well documented. Hence fixator stiffness not


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only influences fracture healing, but also bone remodelling. In response to this

local mechanical environment induced by the fixation system, bone accordingly

adapts by undergoing changes in its structure and density. This local mechanical

condition is interpreted in terms of stresses and strains. While Huiskes (Huiskes et

al., 1987) postulated his bone remodelling theory assuming strain energy density

to act as a stimulus, Fyhrie and Carter (Fyhrie and Carter, 1986) developed a

remodelling theory which relates both the orientation and density changes of

cancellous bone in its stress and strain state.

Physical exercise is also known to cause changes in structure of the bone (Woitge

et al., 1998). For example, increased bone mass may be seen in the dominant arm

of a tennis player (Kannus et al., 1995). In this case, remodelling may be

considered positive as it enables the individual to withstand greater limb loading.

However in instances such as fracture fixation, load-sharing with an implant may

lead to unloading of the bone, a phenomenon known as stress shielding, and can

result in undesirable bone loss (Hernandez and Keaveny, 2006). This bone loss

may lead to further complications such as screw loosening leading to implant

failure or even re-fracture (Augat and Claes, 2008). In order to predict bone

remodelling related to a particular treatment or implant, it is necessary to

understand the underlying mechanism of remodelling.

Problem description

With the introduction of newer implants into the market, preclinical testing of

these implants has become necessary before its use on patients. Functional

adaptation of bone’s structure and mass to changes in its mechanical environment

around orthopaedic implants is well documented in literature. Such adaptation of

bone to changes in loading condition commonly known as bone remodelling can


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sometimes result in reduction in mechanical competence of the bone resulting in

refractures or implant failure. It is believed that this phenomenon is induced by

reduced stresses, which is due to the fact that the implant carries a portion of the

load. Apart from many other factors, successful fracture healing depends on

implant survival. Presently there is a growing concern in clinic about the risks

involved when fixation fails due to loosening of screws caused by stress shielding

(Gefen, 2002). Studies have shown that remodelling around an implant results in

loss of cortical or dense bone in localised regions around the implant (Pilliar et al.,

1979; Tomita and Kutsuna, 1987). Although a significant number of cases of screw

loosening due to remodelling have been reported (Heller et al., 1995; Lowery and

McDonough, 1998; McGlumphy et al., 1998; Goodacre et al., 1999), the reason

behind screw loosening due to remodelling is still controversial. While studies by

Perren (1988) argue that the lack of blood supply in the presence of a fixator to be

the main reason for reduction in bone density of cortical bone (Perren et al., 1988),

Uthoff (2006) has shown that changes in loading condition due to the fixator to be

the main reason for cortical bone loss and consequent screw loosening (Uhthoff et

al., 2006). In order to solve this controversy, bone remodelling quantification data

has to be generated which are more localised.

There has been substantial research into remodelling around compression plates

however, less with respect to internal fixation devices. One of the limitations of

previous studies is the methods used to quantify remodelling have been restricted

to either histology or is not sensitive enough to quantify highly localised

remodelling changes around plate fixation devices. Furthermore, previous studies

have assumed contra-lateral limb to be a suitable control for remodelling analysis.

Hence, the suitability of contra-lateral limb as a suitable control has to be

investigated. There is a need for a method to quantify throughout the entire bone


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in 3D the density changes as a result of both short-term and long-term bone

remodelling processes.

Goal

The goal of this section of the project is “to develop a method to quantify changes

due to implant related remodelling using experimental CT data”.

Structure

To better understand the mechanisms that regulate bone-remodelling process,

quantification of bone-remodelling in experimental situations is necessary. To do

this, changes in the loading conditions of the bone must be related to remodelling

changes and relationships formulated. Therefore, the prime aim of this section of

the project is to quantify implant (internal plate fixation device) related changes

due to remodelling. This is accomplished in each of the Chapters 5-6 individually.

Chapter 5: Development of a method to quantify remodelling changes.

Chapter 6: Further validation of bone remodelling quantification method.

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5 Development of a method to quantify

remodelling changes

In this chapter, firstly, an exclusive review of literature pertaining to bone

remodelling algorithms and existing methods to quantify changes due to

remodelling are discussed. After identifying the knowledge gap, the specific goals

addressed in this chapter are stated. Development of a method to quantify implant

related changes due to bone remodelling follows on.

Chapter 5 Development of a method to quantify remodeling changes

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5.1 Introduction

It is known from the literature that the fixation device used to treat fractures

influences the physiological loading environment of the healing bone and hence

the pattern of bone remodelling (Wolff et al., 1986; Mori and Burr, 1993; Jacobs et

al., 1997). With the introduction of newer implants into the market, preclinical

testing of these implants has become necessary before being used on patients. In

order to predict or evaluate the bone remodelling changes related to a particular

treatment or implant, it is necessary to understand the mechanism of remodelling.

To better understand the mechanisms that regulate implant related bone-

remodelling processes, quantification of bone-remodelling in experimental

situations is necessary. To do this, changes in the loading conditions of the bone

must be related to remodelling changes and relationships formulated.

Alternatively, several bone remodelling algorithms are available which can also be

used to predict implant related remodelling changes.

More than three decades of research has been conducted in the area of bone

remodelling simulations and validation of results through experimental

remodelling quantifications. From Cowin and Hegedeus (Cowin and Hegedus,

1976) early work in 1976 continuing through to recent works by Lian (Lian et al.,

2010) in 2010 and still many more underway, several bone-remodelling theories

have been developed in an attempt to accurately simulate the physiological bone-

remodelling process thus avoiding time intensive preclinical testing with animal

experiments as well as unsafe use of these implants.

Cowin and Hegedus (1976) proposed the first quantitative bone-remodelling

equations based on continuum mechanics (Cowin and Hegedus, 1976). Fyhrie and

Chapter 5 Development of a method to quantify remodelling changes

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Carter (1986) developed a theory which relates both the orientation and density

changes of cancellous bone to responses in its stress and strain state (Fyhrie and

Carter, 1986). Huiskes et al. (1987) assumed the strain energy density (SED), to act

as a stimulus to bone adaptive activity in his bone-remodelling theory (Huiskes et

al., 1987). There are still many remodelling theories which were developed

afterwards (Beaupre et al., 1990; Weinans et al., 1992; Mullender et al., 1994;

Jacobs et al., 1995; Bagge, 2000).

5.1.1 Previous bone-remodelling quantification methods

Herrera et al (2007) (Herrera et al., 2007), and Turner et al (2005) (Turner et al.,

2005), compared the finite element simulation results of a strain adaptive bone

remodelling algorithm following a cement-less total hip arthroplasty (THA) with

BMD (Bone Mineral Density) values obtained from DEXA (Dual energy X-ray

absorptiometry). Seven Gruen (Gruen et al., 1979) zones were identified and the

BMD values from DEXA were compared with finite element simulation results for

each of these zones. However, such a zonal comparison of BMD values may be

useful only for THA where the remodelling takes place in distinct areas which may

not be the case with plate fixation where density changes though localised, needs

to be quantified on a smaller and smaller scale which demands for a higher

resolution of BMD comparison. Additionally, DEXA being a projectional technique

provides only an area mineral density (in two dimensions) and not complete

circumferential information (in three dimensions).

Similar zonal comparison of BMD values following a peri prosthetic hip

arthroplasty was conducted by Lengsfeld et al (2002) where CT data (in 3

dimensions) collected during a two year post operative follow up was compared

with data from contra-lateral hip which served as a pre-operative control


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(Lengsfeld et al., 2002). Though the above study allows for a three dimensional

comparison of BMD values, the zonal comparison where the bone is divided into a

few regions of interest (ROI); seven ROI in this case, may not be suitable to study

the effects of plate fixation on bone remodelling since remodelling changes around

internal plate fixators are expected to be more localised, a scenario that is

demanding for comparison of regions smaller than zones.

Other articles in the area of bone remodelling quantifications were published by

Augat et al (1997) (Augat et al., 1997), Wachter et al (2001) (Wachter et al., 2001).

These papers used pQCT (peripheral quantitative computed tomography)

technique to assess the fracture callus material properties. Since pQCT techniques

allow for a volumetric density assessment, they could potentially be also used to

assess BMD changes due to remodelling. However, the need for remodelling

quantifications in relation to internal plate fixator may demand quantifications to

be performed in more than a few regions of interest and is expected to be more

localised (due to the pattern of load transfer around plate fixation). Such

quantifications may not be viable when conducted using pQCT techniques.

5.1.2 Use of contra-lateral ovine tibia as a pre-operative control in

bone remodelling analysis

Contra-lateral bone

Although the contra lateral limb has been used previously for some applications as

a pre-operative control for quantifying bone density changes (Engh et al., 1992;

Van Rietbergen et al., 1993; Weinans et al., 1993; Kerner et al., 1999; Lengsfeld et

al., 2002), it may not be automatically assumed that the contra-lateral bone

represents the pre-operative condition of the operated bone as this approach has

not yet been validated. There may be differences in geometry and density between


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left and right which would make such an assumption invalid, particularly as

density changes are quantified on a smaller scale. The use of the contra lateral

bone as a pre-operative control has therefore to be validated before any

comparison is made.

Calculating the changes due to remodelling requires bone density distributions to

be quantified prior to intervention and at a subsequent time-point providing

sufficient time for remodelling changes to occur. Quantitative bone density

distributions can be determined from computed tomography (CT) scans calibrated

with a bone phantom (Langton and Njeh, 2004). Since a CT scan exposes the

subject to ionising radiation, performing CT scan on humans is considered only

when it is essential to form a diagnosis. Additionally, metal implants can cause

substantial artefacts rendering CT data unusable for quantitative analysis of bone

remodelling. Thus the possibility of obtaining data before and after intervention

from human volunteers for the purpose of bone remodelling quantifications is

excluded.

Ovine tibia

Alternatively, large animals (such as sheep) are commonly used in orthopaedic

research (Hallfeldt et al., 1995; Viljanen et al., 1996; An, 1999) and obtaining post-

mortem CT scans of dissected bones with implants removed is commonplace.

Therefore, large animals may be considered a suitable model to study implant

related changes in the bone due to remodelling. However, obtaining pre-operative

CT scans of live animals is often not possible due to the limited availability of CT

scanners outside the clinical environment. An alternative approach to using a pre-

operative scan of the same limb is may be to use the contra-lateral limb.


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5.1.3 Goal

The current bone remodelling quantification methods using DEXA and CT based

zonal comparison methods may not be sufficient to assess changes in BMD due to

plate fixation. Furthermore, the use of contra-lateral bone as a pre-operative

control has to be validated before any comparison is made. Therefore, this section

of the project (Section 2) aims at quantifying implant related changes due to

remodelling. Hence, the goal of this chapter was to develop a method to quantify

changes in BMD due to implant related remodelling using CT data.

Aim: Determine whether the contra-lateral bone can be used as a pre-operative

control with respect to analyses of bone remodelling

Determine the extent of geometric similarity between left and right matched

tibia pairs

Determine the extent of similarity in density between left and right matched

tibia pairs

Validate the use of contra-lateral limb as a pre-operative control to analyse

changes due to remodelling

5.1.4 Validation of bone-remodelling algorithms

It is known that any model is an attempt made to represent reality. During such a

representation, not all variables governing the process may be considered and thus

a model is a mere simplification of the complex reality. Due to the many

assumptions and simplifications involved in the development of the

aforementioned bone-remodelling algorithms, validation of these models is

necessary. Only after validation can these models/algorithms aid our

understanding of the remodelling process and provide predictive insights into

implant behaviour. Hence, in an attempt to validate these bone remodelling


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algorithms, the first step in this approach is to quantify the remodelling changes

experimentally.

Although the combination of bone remodelling theories with finite element

simulations is highly developed and might predict BMD changes due to fixation,

there still persists a lack of validation due to the unavailability of quantitative data

for comparison. Hence, the developed method can further be used to generate data

to validate the bone remodelling algorithms.

5.2 Material and methods

5.2.1 Intact left and right tibia comparison

Eight pairs of healthy ovine tibia were used to determine the inherent geometric

and density differences between left and right bones. The mean age of the sheep

was 5.7 years (ranging from 4 years to 7 years) while the mean weight was 39.6 kg.

Specimens were obtained from sheep that had undergone a procedure on their

right femur (multi-fragmentary fracture and severe soft-tissue injury in the distal

third of the femur diaphysis stabilised with an internal plate fixation device). 4

weeks after the procedure, animals were sacrificed and the left and right tibiae

harvested and CT scanned after removing the implant from the bone.

The tibiae (both left and right placed end-to-end) were scanned using a Philips

Brilliance 64 CT scanner with 120 kvp and a slice spacing of 0.67 mm resulting in a

voxel size of 0.41×0.41×0.67 mm. The long axis of the tibiae was visually aligned

with the long axis of the CT scanner. The bones were scanned together with a bone

phantom (European Forearm Phantom (EFP), QRM GmbH, Moehrendorf,

Germany) to enable conversion of Hounsfield Units (HU) to Bone Mineral Density

(BMD). The images were reconstructed using a sharp convolution kernel and saved


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in the DICOM (Digital Imaging and Communications in Medicine) format for

further processing which is explained below in 4 steps.

Step 1: The DICOM files of each bone pair were read into AMIRA software

environment (Visage Imaging GmbH, Berlin, Germany) where the left and right

bones were cropped and saved separately as new DICOM files.

Step 2: In order to analyse the geometry and density differences between the left

and the corresponding right tibia, at first, the right tibia was mirrored. Mirroring a

tibia was performed by flipping the data stacks with respect to the global x, y or z

direction. Mathematically, flipping an image stack with respect to the desired axis

is obtained by multiplying an image matrix with the transformation matrix on its

right side. For e.g. transformation matrix

100

01-0

001

is used to flip along the y

coordinates.

Step 3: Then, surface (polygon) models of the outer contour of the tibia pairs were

created using a single intensity threshold (200 HU) followed by manual

segmentation in order to smooth the edges of the outer contour. The intra-

observer variability associated with manual segmentation was quantified to be less

than 1%. Following segmentation, the process of conversion from DICOM CT slices

to a three-dimensional solid model is an automatic process in AMIRA where

triangular surface mesh 3D model was generated which represents the outer

contour of the imaged bone. The reconstructed data was saved in STL

(steriolethography) file format for further processing.

Step 4: The surfaces of the paired tibiae were then positioned in the same

orientation by registering the surfaces of both bones (left and right (mirrored))


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with a reference bone in the desired orientation using RAPIDFORM (INUS

Technology, Seoul, Korea) (N.B. It is necessary to have all bones in the same

orientation for the division into anatomical quarters required for the density

comparison). The re-alignment was performed in two steps. Firstly, a gross

alignment was performed by manually selecting five corresponding points on

distinct anatomical features. This was followed by a fine alignment using the

Iterative Closest Point (ICP) algorithm which uses an automatic selection of points

during the registration process (Lee et al., 2008).

Geometry comparison

Following alignment (left and right tibiae), the distance of the outer surface of one

tibia from the other (shell-to-shell deviation) was measured in RAPIDFORM. In this

procedure, the difference between the two surfaces was quantified on a point-to-

point basis. The average shell-to-shell deviation was determined for the whole

bone model and for the three anatomical regions; proximal, distal and diaphysis

region separately as shown in Figure 32. The diaphyseal/shaft region was

determined according to the AO principles of Fracture Management (Rüedi, 2007)

that defines the proximal and distal end segments as a square whose sides are the

same length as the widest part of the epiphysis and the diaphysis forms the

remainder.


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Figure 32 Shows the division of an intact tibia into regions (proximal, diaphyseal

and distal).

Bone density comparison

The transformation matrix calculated to align the two tibial surfaces previously

was then applied to align the original DICOM data for the left and right tibia pairs.

This transformation re-oriented the bones in the desired orientation. As a result of

the transformation, the orientation of the CT slices was not perpendicular to the

long axis of the bone. Therefore, re-slicing of the DICOM data was necessary before

comparison. The density comparison was then performed using a MATLAB (The

Mathworks, Inc, USA) program developed in-house. Only BMD values

corresponding to cortical bone, with an intensity value greater than 600 HU were

considered in the analysis (Rathnayaka et al., 2010). As the bones were scanned

together with a bone phantom (EFP), a conversion of HU values to bone mineral

density was performed using a relationship between the HU values and apparent

density of hydroxyapatite determined from the bone phantom.

Two methods of density value comparison were proposed;

(i) High resolution, voxel to voxel comparison and

(ii) Lower resolution, volume comparison.


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Voxel to voxel comparison of HU values of the two image data sets was expected to

yield results of highest resolution. The distribution of the HU values across the

cortex of the bone was not uniform and showed a significant gradient in its

distribution near the boundaries i.e., at the image boundary, a voxel had a

difference of up to 800 HU when compared to its immediate neighbour as shown in

Figure 33. Due to shape and geometry differences between left and right tibia, it

was not possible to attain perfect alignment of the two bones. It was evident that

even a very small misalignment, could result in comparison between a voxel from

one bone, with its neighbouring voxel in the other during voxel to voxel

comparison. This could potentially give rise to very high differences in density all

along the boundary of the image, due to high gradient in density near the

boundaries. In this study such an effect was termed as an “edge effect” and the

differences were not the true difference in density between the left and right tibia.

Hence, a less resolution, volume comparison was also proposed.


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Figure 33 A colour map display of HU values across the cortex (illustrating gradient

in HU near the boundary).

voxel to voxel comparison

After aligning a tibia with its contra-lateral pair, a MATLAB program developed in-

house was used to read DICOM files of the tibiae pair and perform voxel to voxel

subtraction. A DICOM file was stored in MatLab in the form of a matrix. With each

voxel value being stored in its rows and columns, subtraction between two

matrices resulted in a voxel to voxel subtraction. The percentage difference in

density between the corresponding voxels of left and right tibia pairs was

computed. As explained in the previous section, high gradient in intensity values at

the boundary due to bone-soft tissue interface, led to large differences in intensity

between left and right tibia which.

2600

1800

1400

1000

500

-700


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Voxel to voxel comparison with introduction of filters

Median filter

In order to overcome the edge effect problem associated with voxel to voxel

comparison, an attempt was made to simply smooth the HU values which had high

gradient all along the boundary of the image data by applying a median filter to the

data sets before the comparison was made. For this purpose, a program was

written in MATLAB which worked by sorting pixels covered by N×N×N mask

(N=3,). An odd value for n was required. The centre voxel was then replaced by the

median of these voxels, i.e., the middle entry of the sorted list and the results saved

in a new DICOM file.

Average filter

Another attempt to overcome the edge effect was made by introducing an average

filter prior to actual voxel to voxel comparison of HU values. Even here, the voxels

with a HU > 600HU (investigated to be cortical region of the tibia were sorted and

covered by N×N×N mask (N=3, 5, 9, 13) (An odd value for n is required) A

condition; if (centre_pixel_value > 600HU) introduced, checked whether the centre

voxel was bone. If the condition was TRUE, then the centre value was replaced by

the average value of the assorted list, else it was replaced by a zero value.

Following smoothing of the HU values using either “Median or Average filters”, the

image data sets were then compared using voxel to voxel comparison method and

the percentage difference in density between the corresponding voxels of left and

right tibia pairs determined.


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Volume comparison

Under volume comparison, The DICOM data in the diaphyseal region of each bone

was first divided into discrete volumes, defined by a quarter (i.e. medial, lateral,

anterior, and posterior) of a transverse slice (Figure 34) using the customised

MATLAB program. The average BMD in each volume was then calculated and the

percentage difference between corresponding volumes of the left and right tibia

pairs computed.

Figure 34 The CT data was divided into four quarters (medial, lateral, anterior and

posterior) for determination of density differences.

5.2.2 Comparison of operated and intact contra-lateral tibia: (Empty

defect group)

Having investigated the anatomical similarity between the left and right ovine tibia

pairs, the next task was to validate the use of contra-lateral tibia as a pre-operative

control with respect to analyses of bone remodelling. The technique used to

investigate the similarity in density between intact left and right tibial pairs was

then extended to quantify the magnitude of implant related bone-remodelling in


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order to determine the usability of contra-lateral ovine tibia as a suitable pre-

operative control.

Figure 35 shown here are transverse cross-sections of CT data of intact (figure on

left) and operated (figure on right) tibia divided into four quarters (medial, lateral,

anterior and posterior). A compression plate was affixed medially with bi-cortical

screws.

Specimens were obtained from a parallel study which is only briefly described

here. Eight sheep underwent a mid-diaphysis osteotomy of the right tibia to create

a critical size defect (3 centimetres). The defect was stabilised with a compression

plate (7-hole DCP (Dynamic Compression Plate), Synthes AG, Switzerland) but the

defect itself was left empty (termed “empty defect group” in this project). Animals

were sacrificed 3 months after surgery and the fractured and intact contra-lateral

tibia were CT scanned together with a bone phantom (EFP). A density comparison

between the fractured and intact pairs (n=8) was performed following the

procedures described above (refer; Volume comparison). Newly formed bone as

part of the healing process (i.e. callus) was not considered in the analysis. Hence,


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density comparison is restricted to changes within cortical bone region. In order to

quantify localised bone density changes, the peak (maximum) percentage density

difference in regions in close proximity to screw holes and the segmental defect

was calculated.

5.3 Results

Results are reported as mean (minimum – maximum) unless otherwise specified.


Geometry comparison

The differences from the outer surface of one tibia to the other, for the whole tibia

and the different regions separately, are listed in Table 8 for all tibial pairs. Seven

out of eight pairs had a difference of less than 1 mm for over 90% of the measured

points and in the diaphyseal region six out of eight pairs had a difference of less

than 1 mm for all of the measured points.

Table 8 Contains the average distance between the outer surfaces

(shell/shell deviation) for each tibia pair (intact left and right tibia) for the whole

tibia and for the proximal, distal and diaphyseal regions separately. Additionally, the

percentage of measured points within a 1 mm tolerance is given in brackets.

Sheep Whole tibia (mm) Proximal (mm) Distal (mm) Diaphyseal (mm)

1 0.32 (91%) 0.29 (99%) 0.62 (78%) 0.19 (100%)

2 0.37 (95%) 0.34 (99%) 0.62 (81%) 0.27 (100%)

3 0.48 (93%) 0.36 (99%) 1.11 (61%) 0.34 (100%)

4 0.29 (97%) 0.35 (97%) 0.38 (92%) 0.16 (100%)

5 0.31 (97%) 0.30 (98%) 0.54 (86%) 0.22 (100%)

6 0.36 (97%) 0.38 (95%) 0.40 (81%) 0.37 (98%)

7 0.48 (88%) 0.43 (93%) 0.78 (69%) 0.37 (92%)

8 0.34 (97%) 0.46 (92%) 0.32 (98%) 0.26 (100%)


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The average geometric deviation (shell/shell deviation) between the whole outer

surfaces of the tibia was determined to be 0.37 (0.29 – 0.48) mm. The average

deviation for the diaphyseal region alone was 0.27 (0.16 – 0.37) mm, whereas the

distal and proximal ends showed higher values than the diaphyseal region with

0.57 (0.32 – 1.11) mm and 0.36 (0.29 – 0.46) mm respectively. Figure 36, shows

the deviation between the outer surfaces of left and right intact tibiae for one of the

pairs.


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Figure 36 (a): Shows the shell-to-shell deviation of an intact tibia pair (left and

right). Grey regions indicate a deviation of less than 1mm. The average shell-to-shell

deviation along the whole tibial length for this pair is 0.32 mm. (b): Shows the

regional (proximal, diaphyseal/shaft and distal regions) deviation. The average shell-

to-shell deviation in this case is 0.29 mm for the proximal, 0.41 mm for the distal and

0.19 mm for the diaphyseal/shaft region. Grey regions indicate a deviation of less

than 0.5 mm.

Density comparison

The left and right density differences [mean (max)] in the diaphyseal region of the

tibiae were 2.26% (8.21) medially, 3.71% (8.25) posteriorly, 2.67% (10.77)

anteriorly and 2.75% (7.57) laterally for all eight pairs. Whilst the maximum

density difference between a left and corresponding right quarter was 10.77%, the

majority (over 90% of investigated quarters) had density differences of less than

Figure 36 a

Figure 36 b


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5% (Figure 37). Figure 38 shows the average difference in density between intact

left and right tibia for one out of the eight tibia pairs.


pairs for the quarter volumes analysed (n =8).


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Figure 38 Shows the density difference (left vs. right) in percentage in each of the

four (medial, lateral, anterior and posterior) quarters for a sheep tibia


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5.3.2 Comparison of operated and intact contra-lateral tibia: Empty

defect (3 months post-operative)

The percentage density difference between an operated and intact pair for each of

the four quarters along the length of the diaphysis is shown in Figure 39. The

density differences were not uniformly distributed but rather in close proximity to

the segmental defect and the location of screw holes from the implant. The

maximum density differences (up to -50%) occurred in close proximity to the

segmental defect and in regions in close proximity to the screw holes (up to -30%).

The negative sign indicates a reduction in density value. However, in regions

farther from screw holes and the segmental defect, differences were less than ±5%

in all the four quarters analysed and in all 8 pairs. The peak density differences

adjacent to the segmental defect and the screw holes are shown in Figure 40.


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Figure 39 Shows the bone loss, as percentage change in density in each of the four

(medial, lateral, anterior and posterior) quarters for a sheep tibia with segmental

defect (SD) treated with a compression plate 3 months after surgery.


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Figure 40 Shows the peak density difference (%) in all quarters around the screw

holes and the segmental defect (SD) between the operated and intact contra-lateral

tibia at 3 months.


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pairs (dark grey) and operated and contra-lateral tibiae pairs (light grey) for the

quarter volumes analysed (n =8).

5.4 Discussion

The prime aim of this part was to determine whether the contra-lateral bone may

be used as a pre-operative control with respect to analyses of implant induced

bone remodelling in sheep. To address this question, firstly the extent of

anatomical similarity between left and right ovine tibias was investigated. As a

next step in this study, the magnitude of implant related bone-remodelling was

quantified to demonstrate that it is an order of magnitude greater than the

inherent contra-lateral differences and thus demonstrate the capability to use the

contra-lateral limb as a suitable control bone to determine patterns of bone

remodelling.


The investigation of anatomical similarity began with an examination of the

geometric similarity. The geometric similarity between the pairs of intact bones

was not consistent across the three regions examined. While the diaphyseal and

proximal regions showed good similarity with average (n=8) differences less than


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0.5mm, the distal regions of the bone showed average differences of up to 1 mm.

The similarity for each of the different regions is partly explained by the alignment

procedure used. Because of the larger surface area of the proximal region, this

results in a larger number of points from this region that are used in the ICP

algorithm for alignment. Therefore, there is an alignment bias towards the

proximal end. Much of the disparity between the surfaces at the distal end can be

attributed to length differences between left and right tibia. Since the focus in this

study, was on the diaphyseal region of the tibia, in which 99 (92 – 100)% of the

region (measured points) had ≤1 mm surface deviation, the left and right tibial

surface can be considered to have good similarity in the diaphysis.

A density comparison of the paired tibiae was then conducted by dividing the

diaphyseal of the bone into quarters (Medial, Posterior, Anterior and Lateral), one

slice thick. The majority of these regions/quarters (90%) displayed density

differences of <5% (Figure 37). The remaining regions were divided between a 5-

10% difference range (<10% of regions) and a 10-15% range (<1% of regions).

The locations of the larger differences in density did not appear to show any

recurring pattern for the bone pairs compared.

Interestingly, the density analysis of the left and right bones found that the right

tibiae in all cases tended to have lower (1.78 ± 0.371%) density values than the left

tibiae (result is reported as average ± standard deviation, n=8). It is possible that

the lower bone density in the right tibia could be the result of a surgical procedure

(multi-fragmentary fracture and soft-tissue injury) that had been performed on the

right femur four weeks prior sacrifice. Though loading was not monitored in these

animals, it is plausible that the operated limbs were subjected to reduced weight

bearing. Thus, the density comparison of left and right tibia pairs incorporates


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potential density changes due to reduced weight bearing and subsequent

remodelling as well as the inherent bone differences. It is however unlikely that

the reduced weight bearing resulted in significant bone loss in the affected limb for

two reasons. Firstly, due to the relatively short time period of four weeks and

secondly, while the animals may have reduced weight bearing during normal gait

through limping, the bones were not completely unloaded as the animals

continued normal activities such as running, jumping, standing up and lying down,

all activities that can produce high loads on the tibia. Therefore, in a worst-case

where there may be some short-term effects of remodelling; the left and right

density differences are of the order of 5%.

The methods applied in this study are subject to limitations. The comparison of

bone density in corresponding quarters is subject to the accuracy of alignment of

left and right bones. Despite the very good alignment, evident in the low geometric

differences as described above, alignment between the two tibiae is not perfect

primarily due to differences in tibial length. Because the height of the quarters

compared (1 slice thickness = 0.67 mm) is less than the length differences (2-3

mm), the possibility exists that the compared quarters where slightly offset from

one another. Analysis of the variation in bone density between neighbouring slices

revealed average differences of 0.30 % ± 0.03 with a maximum difference from all

eight pairs of 1.9%. As the difference between adjacent quarters (approx 0.5%) is

an order of magnitude lower than the left and right differences (approx 5%), any

axial misalignment of one or two slices is unlikely to yield observable differences.

Figure 42 shows the percentage difference in density between adjacent slices of a

tibia for the length of the diaphysis.


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Figure 42 Shows the percentage density difference between adjacent CT slices of a

tibia in the medial quarter for one tibia pair. The lateral, anterior and posterior

quarters also showed density differences of < 2% between adjacent transverse slices

along the diaphyseal region of the tibia.

The method to align the tibia in the same orientation requires a transformation

followed by re-slicing. The re-slicing requires an interpolation of the DICOM data

to determine values for voxels in the re-sliced data that are located between the

original voxel positions. Since there is a high degree of similarity in density

between adjacent slices, the effects of this interpolation are expected to be

minimal.

Segmentation of the CT data to define the outer and inner surfaces of the cortex of

the tibia is subject to selection of an appropriate threshold value. Due to partial

volume effects (PVE) in CT datasets, which occur predominantly in border regions

where bone and soft tissue interface, a voxel spanning this region contains a

mixture of tissue types (Jiri, 2006) and the Hounsfield Unit (HU) stored in that

voxel is an average of the included tissues. This makes a clear determination of the

bone boundary difficult. While this artefact cannot be eliminated, by scanning both

paired tibiae in a single CT scan and then creating models from these scans with

the same intensity threshold, the two bones are treated equally and the effects of


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over or under-estimating the cortical boundary cancel out in both the geometric

and density comparison.

Statistical tests were not conducted in this study. Given a very small sample size

(n=8) and the complexity of design (8 tibia pairs with each tibia divided into 4

regions and data analysed at more than 200 slices for each pair); the appropriate

statistical test would be a multi level mixed model with random intercepts. When

the aforementioned statistical test was conducted, differences between left and

right tibiae were statistically significant (p<0.05). However, the mean estimated

difference was still < 3%. Although, the differences between left and right are

statistically significant (p<0.05), they are not scientifically significant when

considered that implant related bone remodelling changes (bone loss) are of the

order of (10-40%).

5.4.2 Operated and intact contra-lateral tibia comparison: Empty

Defect (defect was left untreated) (3 months post-operative)

Thus far this study has demonstrated that left and right tibial pairs have a high

degree of geometric similarity and comparable density distributions. For the

contra-lateral bone to be considered an appropriate control to quantify bone

remodelling, it must second be demonstrated that the density changes as a result

of remodelling are substantially greater than any left-right differences. A

comparison of operated (3 months post-surgery) and intact contra-lateral tibia

showed substantially larger density differences compared to those determined in

the left-right comparison.

As would be expected, operated (3 months after surgery) and intact contra-lateral

tibia comparison showed much larger differences in density than were seen in the

intact tibia pair comparison. The greatest density changes (bone loss) as a result of


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the osteotomy and plate fixation were seen in close proximity to the segmental

defect (10-50 %) and the screw holes (10-30%). The magnitude of the differences

observed where substantially larger than the differences between the left and right

matched pairs (5%). The location of the observed density differences between the

operated and the intact contra-lateral tibia were in regions influenced by the

defect and plate fixation. As the plate was affixed to the medial aspect of the tibia

the orientation of the screws was mostly in the medial-lateral plane. Accordingly,

the bone loss adjacent to the screw holes occurred predominantly in the medial

and lateral quarters.

The finding of bone loss around the screw holes is in agreement with qualitative

studies (Jiri, 2006; Sumitomo et al., 2008; Rathnayaka et al., 2010; Claes, 2011)

examining changes around fracture fixation implants, in which histological and

radiolographic techniques were used to assess bone density changes due to

remodelling. Although CT data has been previously used to quantify changes due to

remodelling (Engh et al., 1992), the comparison was performed using significantly

larger regions (i.e. Gruen zones; divided medially and laterally and each region

many slices thick) as compared to those in the present study (medial, lateral,

anterior, posterior, 1 slice thick). The techniques applied in this study have further

refined CT based evaluation methods by increasing their resolution which will be

useful in quantifying highly localized remodelling changes such as those occurring

as a result of fracture fixation. The methods developed here were capable to detect

bone remodelling changes associated with fracture fixation.

5.5 Conclusion

In summary, left and right ovine tibiae were found to have a high degree of

geometric similarity with differences of less than 1.0 mm in surface deviation and


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density difference of less than 5% in the diaphyseal region (N.B. The similarity

between an ovine tibia and its contra-lateral pair is been accepted to be published

in Medical Engineering and Physics Journal (Krishnakanth et al., 2011) (refer to

Appendix D) The density differences occurring as a result of implant related bone

remodelling (10-40%) were well above the observed contra-lateral differences.

Although recent studies in small animal models have produced conflicting results

as to whether remodelling effects are confined to the bone subjected to external

loading or whether the contra-lateral is affected through systemic neuronal

pathway (Sample et al., 2008; Sugiyama et al., 2010), in this study localised implant

related remodelling produced substantial differences with respect to the contra-

lateral bone.

Hence, it can be concluded that for the purposes of implant related bone

remodelling investigations in sheep, the intact contra-lateral tibia may be

considered an alternative to a pre-operative control, provided that the changes in

density due to remodelling yield differences greater than 5% and including a

margin of safety, only changes greater than 10% should be considered as a result

of remodelling. Although limited to the diaphyseal region and only to the cortical

bone, this method may be used to quantify the pattern of bone remodelling in

experimental situations. The quantified patterns of bone remodelling may then

serve to validate the predictions of numerical algorithms simulating bone

remodelling.

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6 Validation of bone remodelling quantification

method

In this chapter, the bone remodelling quantification method developed in Chapter

5 is further validated by comparing changes between an intact and an

osteotomised contra-lateral tibia stabilised with three different type of therapeutic

approach (Empty defect; defects left untreated, defects reconstructed with a

cylindrical mPCL-TCP (polycaprolactone tricalcium) scaffold with or without

rhBMP-7 (Bone Mineral Protein) and at different time points after the surgery (3

and 12 months). The above three treatment groups were chosen because; the

differences in healing pattern between these groups due to differences in loading

were expected to ultimately result in differences in remodelling changes.

Chapter 6 Validation of bone remodelling quantification method

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6.1 Introduction

In chapter 5 density changes due to implant related remodelling was quantified

and the results demonstrated that the implant related remodelling changes in

terms of bone loss are well above the inherent contra-lateral differences. In this

Chapter, further validation of the developed CT based remodelling quantification

method was performed by comparing remodelling changes between three

different therapeutic approaches and at two different post-operative time points

after surgery.

CT data of ovine tibias stabilised with three different therapeutic approaches;

Empty defect (defects left un-treated), defects reconstructed with mPCL-TCP

(polycaprolactone tricalcium phosphate) scaffold and mPCL-TCP scaffold coated

with rhBMP-7 (Bone Mineral Protein) at 3 and 12 months after surgery obtained

from a parallel study was used for investigation.

It is believed that remodelling changes are influenced by the type of fixation device

or the treatment method adopted to stabilise fractures owing to differences in the

loading environment created by the implant or the treatment approach adopted.

Since bone adapts to changes in loading environment through the process of

remodelling, it was expected that there would be differences in remodelling from

one group to the other. As mentioned earlier, CT data of ovine tibiae were obtained

from a parallel study within the research group which was designed to investigate

the effect of these three different treatment approaches on the mechanical

properties of the newly formed bone in the defect region (Reichert et al., 2010).

Here, it was demonstrated that there were differences in the volume of newly

formed bone in the defect area for the groups investigated (Figure 43). Due to this,

we expect differences in loading environment of the healing bone and hence

Chapter 6 Validation of bone remodeling quantification method

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remodelling differences between the groups. Figure 44 shows the path of load

transmission for the groups where defect was left untreated (empty defect) and

defect reconstructed with a mPCL-TCP scaffold with and without rhBMP-7.

Figure 43 Representative 3D CT reconstructions of critical segment bone defects,

which were left untreated (A), reconstructed with a mPCL-TCP scaffold (B) and a

mPCL-TCP scaffold combined with rhBMP-7 (C).(modified from 17).

Additionally, given sufficient time for remodelling to occur, data obtained at

different time points (3 and 12 months after surgery) are also expected to show

differences in remodelling.

17 (Reichert et al., 2010)


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Figure 44 Demonstrates the differences in load transmission path between empty

defect and groups with PCL-TCP scaffold.

In order to understand the remodelling pattern induced by any particular type of

fixator, changes due to remodelling need to be quantified. Therefore, the purpose

of this study was to further investigate the pattern of remodelling changes

observed not only between different treatment groups but also at different

time points. The knowledge thus gained will aid our understanding of the factors

driving the implant related remodelling changes.

In this study contra-lateral limb is used as a pre-operative control. The use of

contra-lateral limb to enable changes due to remodelling to be discerned is verified

in Chapter 5 (refer to 5.1.3 Use of contra-lateral ovine tibia as a pre-operative

control in bone remodelling analysis) of this thesis.


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6.2 Materials and methods

Specimens were obtained from a parallel study. CT scans of forty pairs of tibia from

three different therapeutic approaches at 3 and 12 months after surgery were used

to determine changes due to remodelling. In all the three groups, sheep underwent

a mid-diaphyseal osteotomy of the right tibia to create a 3 cm defect which was

stabilized with a compression plate (7-hole DCP (Dynamic Compression Plate),

Synthes AG, Switzerland). In the first group the defects were left un-treated and

the defect was reconstructed with a cylindrical mPCL-TCP scaffold in the second

group. In the third group the scaffold in the defect region was coated with rhBMP-

7. CT data for empty defect group was available only for the 3 months post-

operative period.

The procedure described in chapter 5 (refer to Chapter 5: Volume comparison)

was used to compare density changes due to remodelling between different groups

(operated and intact contra-lateral tibia pairs) in this part of the thesis and hence

only briefly explained in the following paragraph.

As noted above, animals were sacrificed 3 (n=8) and 12 (n=8) months after

surgery and the fractured and intact contra-lateral tibia after removal of implant

were CT scanned together with a bone phantom (EFP) for comparison. A single

intensity threshold (200 HU) was used to create surface models of the tibia from

the CT data. The surfaces of the paired tibiae were then positioned in the same

orientation thus aligning the original CT data for matched tibia pairs before any

comparison. The density differences were determined between the operated and

the intact contra-lateral bone by dividing the CT data in the diaphyseal region into

discrete volumes, defined by a quarter of a transverse CT slice. As the bones were

scanned together with a bone phantom (EFP), a relationship between the HU


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values and apparent density of Hydroxyapatite in each of the phantom’s chambers

was established allowing conversion of HU values to bone mineral density (BMD).

The averaged density difference between corresponding volumes was computed.

Localized changes in BMD in regions in close proximity to the screw holes and the

segmental defect (SD) were determined by averaging the percentage density

differences over adjacent slices. Only BMD values corresponding to cortical bone,

with an intensity value greater than 600 HU (Rathnayaka et al., 2010) were

considered in the analysis.

6.3 Results

6.3.1 Density changes within the cortical region

Reductions in average density in the cortical bone of up to 50% were seen at 3 and

up to 60% at 12 months after surgery in regions in close proximity to the

segmental defect in the three groups analysed. The peak differences in density in

regions in close proximity to screw holes and the segmental defect (SD) between

the three treatment groups at 3 and 12 months are as shown in Figure 45 and

Figure 46 respectively for medial and lateral regions.

Figure 45 a


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lateral (b) aspects of the tibia for the empty defect (Black), scaffold (Light Grey) and

scaffold with BMP (Dark Grey) groups (mean ± standard deviation). SD=Segmental

Defect.

Figure 45 b

Figure 46 a


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lateral (b) aspects of the tibia for the scaffold (Light Grey) and scaffold with BMP

(Dark Grey) groups (mean ± standard deviation). SD=Segmental Defect.

Density changes at 3 months

The pattern of reduction in average density in the cortical bone was similar in all

three treatment groups and across all four regions analysed with reductions of up

to 50% in regions in close proximity to the segmental defect and the regions

adjacent to it. Also, greater density reductions in density (bone loss) were

observed in regions in close proximity to screw holes and SD as opposed to regions

further from it. Furthermore, the medial and lateral regions showed greater

reductions (bone loss) of up to 50% in close proximity to screw holes while

differences in anterior and posterior regions were up to 20%. However, the empty

defect group showed lesser reductions in density of up to 30% (segmental defect

and the adjacent regions) than the groups with scaffold and scaffold with BMP

where differences were up to 50%.

Figure 46 b


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Similar reductions (bone loss) in density was observed at 12 months where more

pronounced changes (up to 60%) was observed for lateral and medial regions in

both PCL TCP scaffold and PCL TCP scaffold coated with BMP groups, while

reductions of up to 30% was observed for anterior and posterior regions. However

the magnitude of differences in density in close proximity to the segmental defect

and the adjacent regions was greater (60%) than that observed in close proximity

to screw holes (50%) (Figure 46).

6.4 Discussion

6.4.1 Density changes within the cortical region

In this study the magnitude of implant related bone remodelling was quantified for

different treatment groups and at different time points to investigate possible

differences between the groups owing to differences in loading patterns and time

periods. As to be expected, the greatest density reductions occurred in close

proximity to the segmental defect and the screw holes, in particular the innermost

screws. In addition, there was a pattern of observed reductions in density which

was similar between all three treatment groups and at both time points i.e., the

reductions in density was more pronounced in the plane of fixation (medial and

lateral planes) and in regions influenced by the fixator (screw holes) and the defect

itself than the anterior and posterior planes (density differences < 10%).


The pattern of bone remodelling in the empty defect group was similar to the

group treated additionally with a rigid mPCL-TCP scaffold and PCL-TCP scaffold

coated with rhBMP-7. Greater reductions in density in regions adjacent to defect


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were reasoned to be the result of stress shielding effect (refer to Stress shielding;

2.4.2 Fixation stability and remodelling) in the presence of an implant. Since

most of the load gets transferred through the fixator, the bone predominantly in

the defect region is unloaded during initial stages of healing (before callus

formation) and thus, this unloading leads to bone loss or atrophy due to functional

adaptation of bone to changes in mechanical loading.

Although the reductions in density between operated and intact contra-lateral

tibial pairs were more in the regions adjacent to screw holes and the segmental

defect than the regions farther from the fixator, it was expected that the magnitude

of changes due to remodelling varies between different treatment groups. Less

bone loss was expected to occur in the groups reconstructed with scaffold than the

empty defect group, in particular, in the defect region, due to the continuous path

of load transmission maintained by the scaffold (Figure 44). However, contrary to

our expectation, bone loss tended to be greater in the groups reconstructed with a

scaffold relative to the empty defect group. It was reasoned that greater bone loss

observed in regions around the defect in the scaffold groups could be the result of

biological integration of the scaffold onto the bone material. Introduction of

scaffold in the defect region could have initiated such bone loss in defect region

during the process of integration of scaffold material on to already denser cortical

bone.

In addition, there was no significant difference in density changes between the

scaffold and scaffold coated with rhBMP-7 groups. Also, reductions in density

observed in regions in close proximity to screw holes farther from the segmental

defect were less (15%) than that observed in regions in close proximity to


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segmental defect (up to 45%) and such bone loss could be the result of implant

insertion process (drilling of screw holes).


Contrary to our expectation the magnitude of density differences (bone loss)

observed at 12 months was greater than that observed at 3 months (remodelling

or bone formation over time). However, reductions in density observed in regions

in close proximity to screw holes farther from the segmental defect at 12 months

was found to be of the around the same magnitude as observed at 3 months and

was seen across both treatment groups (scaffold and scaffold with BMP) and for all

four regions analysed. In such a case, the changes due to remodelling could be

related to trauma and the type of treatment rather than changes in loading pattern

in the presence of an implant. However, it was evident from the results that there

was a considerable increase in the percentage of reduction in density in the

regions in close proximity to the defect at 12 months than at 3 months. It is

possible that such a reduction could be the combined effect of integration of the

scaffold and BMP material onto the regions adjacent to the segmental defect as

well as stress protection. This combined effect was also seen to be spilled over to

regions of screw holes adjacent to the defect.

This study is subject to a few limitations. From the results of this analysis we

recognise that the treatment groups (empty defect, PCL-TCP scaffold and PCL-TCP

scaffold with BMP) chosen for the analysis might not be suitable in discerning

changes in remodelling due to changes in loading pattern alone. However, with

intent to reduce the number of animals used for experiments, we obtained

specimens (CT data) from a previous study which was readily and timely available.

Furthermore, owing to differences in loading patterns between the treatment


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groups, we believed the specimens would be adequate to demonstrate changes in

remodelling pattern due to changes in loading conditions between them.

6.5 Conclusion

As there was no considerable difference in density changes at different time points,

and that the data for the groups where the defect was left untreated was available

only at 3 months, the bone remodelling changes observed might be related to both

the initial trauma or the type of treatment (scaffold and/scaffold coated with BMP)

as well as adaptation to the changed loading condition. Also, contrary to the belief

that remodelling is stimulated by changes in loading conditions, empty defect

treatment group showed less bone loss than the other two groups where scaffold

was introduced at the segmental defect region. It is believed that data from

different treatment groups or from longer post-operative time periods might result

in significant remodelling changes between them, thus providing further insight in

to the factors driving the remodelling changes (such as changes in loading

patterns).

In conclusion, although the groups investigated might not be suitable to produce

significant differences in bone remodelling in response to changes in loading

conditions, the presented method to quantify remodelling across the entire

diaphyseal region (cortical bone) of the bone enabled changes around localised

features, such as plane of fixation, screw holes and segmental defect to be

discerned. Hence, the developed bone remodelling quantification method can be

considered suitable in quantifying changes due to implant related remodelling.

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7 Overall discussion and conclusion

This project focussed on characterising fixation stiffness of internal plate fixation

devices. Furthermore, a CT based implant related remodelling quantification

method was also developed. Knowledge gained in this project will be useful in

configuration and design of internal plate fixation devices which not only promotes

healing but also prevents undesirable bone loss through remodelling. This Chapter

discusses the main findings of this PhD project along with a mention of future

directions.

Chapter 7 Overall discussion and conclusion

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7.1 Discussion

Section 1: Fixation stability and healing

The objective of the first section of this project was to characterise the stiffness

of an internal plate fracture fixation device. In-silico or computer methods were

used to evaluate the different fixation stiffness determination methods and an

appropriate method to determine the stiffness characteristics of an internal plate

fixation device using Finite Element Analysis (FEA) was defined. The developed

method was then used in the characterisation of internal plate fixation stiffness

where the influence of modifications to fixator configurations on implant stability

was investigated.

The mechanical conditions in the fracture gap are thought to play a decisive role

not only in the overall healing outcomes of the bone but also in the remodelling of

the adjacent bone fragments. In fact with a good blood supply, the course of

fracture healing has been reported to be primarily influenced by the inter-

fragmentary motion, which in turn is determined by the applied load and the

stability of fixation device. Such mechanical conditions which each fixator creates

however are poorly understood. Experimental tests in animal models have studied

the effects of various fixators on healing and remodelling. The outputs of these

tests however – histology, mechanical testing etc, provide only a brief summary of

the results rather than a detailed understanding of the mechanism.

Finite Element (FE) modelling of the bone-fixator construct can be used to

simulate the conditions in the fracture gap. If these conditions are known then

their resultant effects on healing and remodelling can be studied and adaptations

made to the designs to improve outcomes.


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Comparison of boundary conditions demonstrated that applying loads closer to the

Fracture Gap (FG) reduces the unwanted indirect moments. A convenient way to

do so in FE is by using MPC (Multi Point Constraint) boundary conditions. The

developed in-silico method (MPC boundary condition and individual stiffness

calculation methods) of fixation stiffness determination provides a convenient way

to investigate the influence of modifications to fixator configurations on implant

stability.

Previous studies have evaluated the 3D stiffness (stiffness in 6 directions) of

external fixators and tibial nail in-vitro (Kassi et al., 2001; Epari et al., 2007; Augat

et al., 2008). This study represents one of the first attempts to characterise 3D

internal fixation stiffness (Locking plate) using computer model/FE. Although

during the past years several fracture fixation stiffness determination methods

have been reported in literature, there exists no universal stiffness determination

method which can be adopted owing to differences in functioning of fixation

devices. The deformation behaviour of all fracture fixation devices is not similar.

For example, unlike external ring fixators, the primary deformation mode of

internal plate fixators under axial load is more akin to bending. Due to the short

bending length of the screws, the whole construct results in bending, while the

longer bending length of the screws in external fixation devices allows the

construct to undergo more axial movement and less bending under axial loads. The

present study offers comparison between different methods and investigates the

influence of these methods on the implant stability. The purpose of this study was

not to show superiority of any particular method but rather to demonstrate

appropriateness of these methods to characterise internal plate fixator stiffness.


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The investigations showed that factors such as simulated boundary conditions, the

point of load application and the manner in which fixation stiffness is calculated

ultimately influences the value of fixation stiffness determined and that some

methods may not be suitable in characterisation of fixation stiffness of some of the

fracture fixation devices.

This study investigated two methods of applying loads (axial compression and

rotation) to the proximal part of the bone-fixator construct; Kassi (confined lateral

and rotational movements of the proximal fragment) and Augat (unconfined

lateral and rotational movements of the proximal fragment). For the case of

internal plate fracture fixation devices, due to the shorter length of the screws and

closer placement of the plate to the bone’s surface, the construct is more akin to

bending. By confining the movement of the proximal fragment, the main mode of

movement (bending in medial-lateral direction) associated with unilateral internal

fixation devices is restricted and hence makes the system overly stiff. Therefore,

such a boundary condition although suitable for external fixators may not be

appropriate to simulate the load-displacement behaviour of internal fracture

fixation devices. Moreover, confined compression or rotation does not represent

in-vivo deformation behaviour since in physiology the bone-implant system is not

restricted of lateral or rotational movements of the proximal fragment.

Likewise, investigation of shear fixation stiffness when the shear load was applied

to the top end of the proximal fragment (Kassi) suggested that it produces more

bending of the construct at the fracture gap due to the relative position of the

fixator in relation to the long axis of the bone. This undesirable effect due to

excessive bending at the fracture site was reduced when loads were applied close

to the fracture gap.


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Moreover, the study highlights the problems associated with the use of stiffness

matrix for calculation of fixation stiffness. The neutral axis of composite plate-bone

structures is located very close to the external surface of the bone or even inside

the plate because the elastic modulus of the plate (200 GPa) is much greater than

that of the bone (16 GPa) as well as due to discontinuity in bone (segmental

defect). Due to this, the system produces asymmetric deformation behaviour due

to eccentric loading conditions. Example, shear in anterior-posterior direction and

axial torsion resulted in similar IFM’s. Shear load in anterior-posterior direction

not only resulted in shear IFM (Inter-fragmentary movement), but also resulted in

a torsional moment about the fracture gap. Due to the shift of neutral axis, it is

quite complex to determine the position of the neutral axis of the combined

structure (osteotomised tibia stabilised with internal plate fixator) which will help

in realising this rotational moment. Since the stiffness matrix did not account for

the indirect axial rotation moment caused by this shear force about the fracture

gap, it resulted in errors in stiffness calculation and very high stiffness values.

Therefore, the suggestion to use the individual stiffness calculation method for

internal fixation stiffness calculation was made.

If the aim of any study is to compare fixation stiffness for different fixator

configurations in FE where relative and not absolute values are important, this

study suggests the use of MPC boundary condition and individual stiffness

calculation method as it reduces the unwanted effect due to indirect and

unaccountable out of plane forces which are hard to determine.

Primarily, this project aimed at investigating the influence of modifications to

fixator configurations on implant stability by making alterations to fixator

configurations such as material property, fixator axis inclination with respect to


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the long axis of bone, offset distance between fixator and bone surface, distance

between inner most screws (Working Length), position, spacing and number of

screws and use of FCL (Far Cortical Locking) screws.

Investigation of the influence of modification to fixator configurations on implant

stability suggests that there is more than one way to alter fixation stiffness to meet

better healing requirements. However, the choice also depends on type, location

and severity of the fracture among other factors.

The hypothesis that the internal fixation devices (locked plates) are invariably stiff

was supported by the observed axial IFM which was <0.14 mm at the near and

<0.34 mm at the far cortex for the standard (three screws on either side of the

fracture gap leaving the middle three screws holes empty) fixator configuration.

Shear IFM were also invariably small (<0.05 mm) for the fixator configurations

investigated making the fixation device stiffer against shear loading. The current

state of the art in creating models of bone-fixator systems is to model the

interfaces (bone-screw and screw-plate) as fixed. It is believed that the FE results

will be overestimated due to such perfectly modelled interface and FE model

comparison conducted has shown that the results from FEA are over estimated up

to a maximum of 70% (refer to Appendix C) when compared with results from in-

vitro. Hence, even with 70% over estimation, for the fixator configurations

investigated in this study, it is believed that the axial and shear IFM are still very

small and hence it can be concluded that these devices are inherently stiff fixation

devices.

The motivation of this study was that, fixators that allow moderate axial IFM but

provide higher resistance to shear and torsional movements to be better for


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successful and timely healing. Although the standard fixator configuration

(0XXX0XXX0) was invariably stiffer than the published stiffness values for external

fixators in-vitro (Epari et al., 2007)so as to allow moderate axial IFM, this study has

shown that by making certain modifications to fixator configurations in terms of

fixator material (Ti), offset distance (3 mm), working length (three screw hole

width) and introduction of Far Cortical Locking (FCL) screws the axial micro

motion can be increased to stimulate callus formation for healing. However, some

of these modifications resulted in reducing shear and torsional stiffness attributes

when compared to standard configuration (0XXX0XXX0), which should be

maintained in order to stimulate callus formation for timely healing. Since, shear

IFM for all the fixator configurations investigated was less than 0.1 mm, it can be

considered that the internal fixation devices are stiff against shear loading even

with the above modifications to configurations.

Of the suggested modifications to increase axial IFM, the use of FCL screws was one

of the options to stimulate callus formation towards better healing outcome.

However, the use of FCL screws in clinics may pose certain complications which

have not yet been investigated. Firstly, these FCL screws lock into the plate and

onto the far cortex of the diaphysis. This allows for elastic flexion of the screw

under the application of loads at the near cortex thus enabling parallel IFM. All

loads are directly transferred from the plate to the far cortex through flexible

shafts (screw shaft). While this may permit IFM stimulatory to healing, particularly

at the near cortex, the effect the flexion of FCL screws has against bone’s surface in

areas particularly adjacent to screw holes is not yet been investigated. It is

expected that such an arrangement might result in bone resorption in regions

around screw holes at the near cortex. Further investigations are required to

determine the effect of FCL screws on fracture healing and remodelling.


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There are a number of issues that were not addressed in the current study as the

primary focus of this study was characterisation of fixation stiffness and hence the

study did not include investigations related to implant survival. In future studies

addressing implant survival, it would be interesting to investigate the stresses

experienced by the construct as they are particularly important in deciding the life

of the implant, multifaceted and physiological loading conditions and fatigue tests.

In addition, results of this study are limited to investigation of single mid-

diaphyseal osteotomy. Behaviour of the bone-implant system may be different for

fractures with large fracture gaps and multiple fractures.

The current state of the art in creating models of bone –fixator constructs is to

model the interfaces as being fixed. Little mention is actually made in the literature

as to the appropriateness of this technique This assumption (fixator-bone

interfaces modelled as fixed in all DoFs) made during the creation of finite element

model about the screw-bone and plate-screw interface) might over estimate the

fixation stiffness. However, the FE model used in this study is been compared

against results from in-vitro tests Since the investigation of the influence of

modifications to fixator configuration on its stiffness is based on relative

comparison, absolute values are not important. Therefore, the simulated perfect

screw-bone or plate-screw interface was assumed to be uncritical

It should be pointed out that studies such as this were not intended to represent

clinical situation and therefore cannot accurately predict complex in-vivo

behaviour. However, they do provide useful information to the surgeon on the

influence of fixator configuration on implant stability. At present due to the

minimal invasive surgical techniques, certain factors that affect fixation stiffness

are sometimes beyond surgeon’s control. Example, the limited visibility of the


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fracture site and sliding of the plate from a cut made at a distance from the fracture

zone may result in some amount of inclination between the plate and bone axis.

The parameter investigation suggests that such slight inclination of the plate axis

with the bone does not affect axial compressional stiffness. Additionally, since

working length was shown to be the greatest determinant of fixation stiffness and

the spacing and position of screws had only minor influence, it gives the surgeon a

wide range of options (screw configuration) especially in situations where certain

screw spacing cannot be avoided.

The in-silico methods developed in this project enabled investigation of

parameters that influence fixation stiffness. The parameter analysis conducted in

this section has strengthened our knowledge about the influence of fixator

configuration on its stiffness characteristics and may further be used to suggest

modifications to screw configuration which results in optimal stiffness conditions.

The knowledge gained here will aid in the configuration of fixation stiffness for

optimal healing conditions via in-vitro tests. As mentioned earlier, results from this

study demands further research investigating the influence of FCL screws on

adverse effects of bone remodelling of the surrounding bone fragments.

In conclusion, the investigation of fixator configuration on implant stability using

developed in-silico methods is an effective way to investigate the influence of

fixator configurations on implant stability. However configuration of optimal

fixator configurations of final constructs for better healing should include in-vitro

tests (FE results are over estimated due to perfectly modelled interfaces). Hence,

further in-vitro studies are required in the assessment of stiffness of final

constructs and the results from this parametric evaluation may only be used as a

guideline for implant design.


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Section 2: Fixation stability and remodelling

In the second section of this project, a CT based bone remodelling

quantification technique was developed. In the process of the development of

this quantification method, the use of contra-lateral ovine tibia as a suitable pre-

operative control with respect to the analysis of changes due to implant induced

bone remodelling was validated. The developed remodelling quantification

method was then used to quantify implant related remodelling changes between

different treatment groups (Empty defect, PCL-TCP scaffold and PCL-TCP scaffold

with BMP) and at two different time periods (at 3 and 12 months post operative).

The presented CT based bone remodelling quantification method was able to

identify changes due to remodelling around the fixator, especially in the plane of

fixation and in regions near screw holes and segmental defects.

Previously, studies have assumed the use of contra-lateral limb to serve as a

suitable control in remodelling analysis. In this study, for the first time, the use of

contra-lateral ovine tibia as a pre-operative control in analysis of changes due to

remodelling is validated. Since the differences in geometry was < 3% and density

differences were < 5% between intact left and right tibiae and differences between

operated and intact were of the order of 40% (bone loss) in regions of screw holes

and segmental defect, it was concluded that contra-lateral bone can be used as a

suitable pre-operative control. In this study, all the intact tibiae were extracted

from animals which underwent a previous surgery on their right femur. It was

expected that the differences between left and right would also include differences

due to reduced weight bearing on the right limb which was justified by higher

density values found for left tibiae in all 8 pairs analysed. Hence, this validation

study accounts for the reduced weight bearing of the operated limb.


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Quantification of implant related remodelling changes between different

therapeutic approaches and at different post-operative time periods showed that

bone atrophy especially in the defect region is unavoidable. Interestingly, the

results showed that the magnitude of bone loss in regions in close proximity to

screw holes did not worsen at 12 months as compared to data at 3 months and

such bone loss (15%) could be more related to implant insertion procedure

(drilling of screw holes) rather than changes due to loading conditions. In the

regions adjacent to defect and inner most screws, the bone loss data (50%) was

due to combined effect of stress protection and biologic integration of scaffold

material on to the surrounding cortical bone and such an effect was found to

increase at 12 month post-operative. It was expected that at 12 months, there

would be less bone loss than at 3 months due to changes in loading (more load is

expected to pass through the callus at 12 months thus resulting in new bone

formation around the defect). Hence, the question is, should the implant be

removed since it is causing bone loss due to stress protection? Investigation of

implant related bone remodelling changes for longer post-operative periods may

be necessary before making a decision on implant removal.

The treatment groups chosen for comparison was readily and timely available

from a parallel study and not handpicked to demonstrate distinguishing changes in

remodelling patterns between the groups. Changes in loading pattern between the

different treatment groups, was believed to result in differences in the magnitude

of changes due to remodelling between these groups. However, realisation of

changes in remodelling due to difference in loading patterns as expected between

different treatment groups and at different time points was not identifiable using

the developed quantification method. Therefore, it is assumed that there may be

other factors driving the remodelling process apart from the changes in loading


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patterns and data from longer time periods (> 12 months) might be required to

discern changes in remodelling between different treatment groups. Also, it is

expected that comparison of density data when performed on volumes smaller

than a quarter of a transverse slice may help identify the localised changes in

remodelling (smaller regions may aid in better identification of localised

remodelling changes which otherwise might be compromised due to averaging of

density values when larger volumes are analysed) between different treatment

groups (changes in remodelling due to change in loading pattern) to be discerned

and can be a focus of future studies.

The study is subject to a few limitations. Post-processing of CT data (segmentation

and transformation) led to changes in original CT data by around 2%. However,

such alterations are un-avoidable. Hence we concluded that density changes >10%

(twice the density difference observed between left and right intact tibiae) can be

considered as changes due to implant related remodelling thereby accounting for

post-processing errors.

The developed CT based bone remodelling quantification technique (refer to

Chapter 5; Volume comparison) has enabled quantification of changes due to

implant induced remodelling. The remodelling quantification tool can now be used

to quantify changes due to implant related remodelling which are more localised.

This will aid our understanding of how much remodelling occurs around implants

and will help clinicians decide whether the amount of remodelling which occurs

around orthopaedic implants; internal fixation plates in this case, is a threat to

implant survival? Furthermore, this quantification method can also be used to

validate existing bone remodelling simulation algorithms which can predict

implant related remodelling changes.


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Further improvements can be made to the existing quantification method such that

comparison of smaller volumes (smaller than quarter of a transverse slice) is

possible which may enable identification of highly localised remodelling changes

between different treatment groups.

The introduction of dual energy CT scanners (Gemini PET-CT scanner; Philips

Medical Systems, Discovery CT 750 HD; GE Healthcare) is been effective in

reducing metal artefacts caused by orthopaedic implants due to better image

quality. However, it is still to be investigated whether these scanners may make

possible the possibility of performing quantifications in human bones with

implants.

7.2 Conclusion

In conclusion, this study has shown that it is possible to achieve moderate axial

stiffness so as to promote better healing by making certain modifications to fixator

configurations; however some of these modifications could also result in lowering

shear and torsional stiffness which should be maintained in order to promote

better healing outcome. Additionally, internal plate fixation devices were found to

be comparatively stiff fixation devices.

In this study it was shown that the contra-lateral limb can be considered to

represent the pre-operative state of the operated ovine tibia for remodelling

analyses. In addition, the fact that we were able to quantify highly localised

remodelling changes in the plane of fixation and in regions around fixator screws

illustrates the sensitivity of this CT based bone remodelling quantification method.

This PhD project can be furthered by creating an FE model for one of the treatment

groups for which changes due to implant related remodelling has been already


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quantified in Section 2 of this project (e.g. Empty defect, PCL-TCP scaffold or PCL-

TCP scaffold with BMP). Then, conducting subsequent FE simulations using the

developed in-silico methods (Section 1) will help establish a relationship between

fixation stiffness and/or initial IFM and the amount of remodelling changes for the

fixator chosen. It is believed that such an analysis will aid in the configuration of

internal plate fixator not only for better healing but also for better remodelling

(reduction in bone atrophy).

Overall, this project has delivered and aided our understanding of the influence of

fixator configurations (internal fixation plates) on its stiffness characteristics

which, in turn influences the fracture healing process and the remodelling of the

adjacent bone fragments. Knowledge gained in this study will be useful to further

our understanding in the configuration and design of internal fixation devices

which not only promotes timely healing but also prevents undesirable bone loss.

Appendix A

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Appendix A: Determination of IFM (Inter-Fragmentary

Movement)

The translational Inter-fragmentary movements were determined from the

displacement of a node positioned at the centre of the fracture gap attached to the

upper fragment relative to a coincident node attached to the lower fragment as

shown in Figure 47.

Figure 47 Illustrates calculation of translational inter-fragmentary movements.

The rotational inter-fragmentary movements were calculated using matrix algebra

which is explained in the following paragraphs.

Proximal fragment

Distal fragment

Appendix A

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Calculation of rotational inter-fragmentary movements

Defining LCS (Local Coordinate System): Firstly a local coordinate system (LCS)

was set up for each bone fragment. A LCS is a reference system that is fixed within

a body or a segment and moves along with it. The global coordinate system (GCS)

also called as the reference coordinate system is the fixed coordinate system from

which all positions are ultimately derived. It is a right handed orthogonal

coordinate system. In this analysis, GCS was defined by X axis pointing posterior-

anterior direction, Y axis medial-lateral, and Z axis pointing distal-proximal

direction as shown in Figure 48. The unit vectors for the GCS are→

i ,→

j and→

k

respectively. The unit vectors are the vectors of unit length along each axis

representing the coordinate system and were represented by,→

i ,→

j and→

k along X, Y,

Z axis respectively. The LCS was oriented such that x axis of the LCS points

posterior-anterially, y axis medial-laterally and z axis distal-proximally. The

orientation of the LCS with respect to GCS defines the orientation of the body in 3D

space and it changes as the body moves in space.

Three non-collinear points/nodes were chosen on each bone fragment and the LCS

was set up using equations from matrix algebra which are listed below. The

selection of three points is as shown in Figure 48. First subtracting the position of

point UA from UB, and by dividing by the norm of the vector created by (UB-UA),

gave rise to a unit vector which has its origin at UA and pointing towards UB, i.e., in

→

j direction, lateral-medial axis of the segment. Now the →

i axis, the posterior-

anterior axis was determined in two steps. Again, subtracting (UB-UA) created a

vector originating from UA and pointing towards UB. Next, subtracting (UC-UA)

gave a vector originating from UA and pointing towards UC. By performing a cross

product and dividing by the norm as shown in equation, the result was a unit

Appendix A

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vector, →

i in the posterior-anterior direction. The third axis of the LCS,→

k , the

distal-proximal axis, was determined by the cross product of the two unit

vectors, →

i ×.→

j The order of vectors in the cross product was determined by the

right hand rule.

Figure 48 Illustration of calculation procedure for unit vectors that forms the LCS

and the Rotation Transformation Matrix (RTM). (ULCSO = Upper Local Coordinate

System at time zero).

At first, ULCS (Upper Local Coordinate System), LLCS (Lower Local Coordinate

System) were defined in a matrix form, in which the rows represent the 3D

coordinates of,→

i ,→

j and →

k unit vectors of the LCS of the two bone fragments.

Appendix A

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ULCS =

kkk

jjj

iii

zyx

zyx

zyx

'''

'''

'''

, LLCS =

kkk

jjj

iii

zyx

zyx

zyx

''''''

''''''

''''''

Calculation of rotation matrix

The RTM (Rotation Transformation Matrix) was determined by performing the dot

product of a unit vector matrix from one coordinate system and the unit vector of

another coordinate system.

RTM = LLCS ULCS T

Calculation of Euler angles from rotation matrix

The orientation of an object in 3D space can be determined by performing

analogous operations. Hence, one way to do so is to perform rotations about all

three axes. A common rotation sequence often used in biomechanics is an Xyz

sequence. Here, the angles for the Xyz sequence were designated as α (alpha) for

the first rotation, β (beta) for the second rotation and γ (gamma) for the third

rotation. The rotation matrix for the Xyz sequence can then be described as

R = Rz R

y R

x

Rx=

cossin0

sincos0

001

, Ry=

cos0sin

010

sin0cos

, Rz=

100

0cossin

0sincos

The rotations were then expressed as the successive rotations of these matrices to

produce the combined rotation matrix.

R =

coscossincossin

sincoscossinsinsinsinsincoscoscossin

cossincossinsincossinsinsincoscoscos

Appendix A

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The angles alpha, beta and gamma are then deduced by solving the equation for the

combined rotation matrix.

Appendix B

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Appendix B: Sensitivity analysis

A sensitivity analysis was performed to quantify the influence of uncertainty of the

input data (material property of cortical bone) on fixation stiffnesses calculated.

Material property of cortical bone: The assignment of material properties to

the elements is a vital component of the FE model creation. Both elastic or Young’s

modulus and a Poisson’s ratio need to be assigned to each material identified in the

model. While it is much simpler to assign material properties to materials made of

steel as they are homogenous and isotropic, assigning material properties to living

tissue such as bone is more challenging as they are non-homogenous and non-

isotropic in nature. In such cases, it is ideal to obtain material properties through

CT scan. However, obtaining material properties from CT data is both time

consuming and beyond the scope of this study/thesis.

In literature assigning a single value for Young’s modulus is commonplace and the

range used for cortical bone of ovine tibia varies between16 GPa – 20 GPa (Spatz et

al., 1996). Also, the ovine tibia samples used in the second section of this thesis

(bone-remodelling quantifications) also revealed the young’s modulus of cortical

bone to be in the range 14 GPa – 24 G Pa. In order to assess the sensitivity of the

analysis against material property of cortical bone five simulations with axial

compression load of 235 N were performed for modulus of elasticity values; 14, 16,

18, 20 and 24 GPa and the stiffness value determined were compared.

Analysis: Results are expressed as (Average ± Standard Deviation) unless

otherwise specified. Evaluation of the effect of the Young’s modulus value on

fixation stiffness (axial compressional stiffness) was tested for the range of values

reported in literature (14 GPa to 24 GPa). The results demonstrated that the

Appendix B

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calculated axial compressional stiffness value might vary up to a maximum of 1.05

% due to uncertainties of the input parameter, i.e., modulus of elasticity of bone.

The axial compressional stiffness determined for different modulus of elasticity

values of bone are as shown in Figure 49.

Figure 49 shows the axial compressional stiffness value determined for the chosen

Young’s modulus (14 GPa – 24 GPa) using implant-PVC construct.

Conclusion: Since the maximum difference in stiffness values for the chosen

material property of the cortical ovine tibia (Young’s Modulus ranged between

14.3 GPa to 24 GPa) was only 1%, a single value of Young’s Modulus (e.g. 16 GPa

(Simon, 2003)) as reported in literature can be considered during analysis.

1000

1010

1020

1030

1040

1050

14 16 18 20 24

Ax

ial

Sti

ffn

ess

(N

/m

m²)

Young's Modulus (Gpa)

1.05%

Appendix C

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Appendix C: Comparison of Finite Element Analysis (FEA)

results against mechanical or in-vitro tests

FE model comparison: Cylinder-fixator model

Cylinder-fixator FE model results for two of the fixator screw configurations were

compared with results from in-vitro testing. This was performed through

comparison of difference in results between the screw configurations (XXX000XXX

and X0X000X0X) (the filled screw holes are represented by an “X” and the empty

ones with “0”) tested in-vitro with the FE simulation results using simple PVC-

fixator model. By using a cylinder (PVC) the variation in response caused by bone

factors – complex geometry and/or inhomogeneous material properties was

nullified. As mentioned earlier, each of the fixation systems (mechanical testing

and FE simulations) was examined in a cylinder/PVC material. Examination of

results will help determine whether closer examination of the boundary conditions

is required or if the current modelling techniques already represent the behaviour

with sufficient accuracy. Testing comprised of two load cases – axial compression

and torsion. Each of these load cases was replicated in the model and the outputs

(displacement of the proximal cup) were compared.

Movements in prime direction (direction of load application) determined at the

proximal cup were compared with the results from mechanical testing. The focus

of this comparison study is however not to determine the slack or difference in

outputs between the in-vitro and FE analysis, but rather the difference in the

behaviour of changes observed in-vitro and in FE analysis for any two models

(XXX000XXX and X0X000X0X) tested.

Appendix C

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Mechanical testing: Mechanical testing was conducted on the construct where

fixator was implanted onto a cylinder/PVC material and will provide information

required to complete and compare FE models.

Testing equipment in use: Testing of the cylinder-implant system was conducted

in an Instron 30kN universal testing apparatus (Instron Pty Ltd, Illinois Tool

Works, USA). The IFM was calculated by tracking the 6D (three translational and

three rotational) movement of the bone-implant system using an NDI Opto-track

position sensor system which has;

a) 2 x rigid bodies incorporating 8 infrared strobing markers (one on the proximal

and one on the distal fragment)

b) 3 cameras which track the movement of the rigid bodies in 6 dimensions (3 x

translations and 3 x rotations)

Specimens were prepared from PVC tube precision cut to desired length

(measured length of intact tibia) using a circular saw. Testing of the PVC-fixator

construct was conducted in an Instron 30kN universal testing machine using a

custom built rig and the desired tests (axial compression and axial rotation)

performed. Attachment of the PVC ends to the rig was through stainless steel cups

where the ends of PVC were embedded in bone cement (polymethylmethacrylate)

poured in between PVC and steel cups. A custom built alignment jig was used to

ensure proper alignment of PVC ends in the steel cups.

Upon alignment of PVC ends in steel cups; the PVC-fixator construct was secured in

the testing rig, a 3 mm mid-shaft osteotomy representing the fracture gap created,

a 9 hole LCP (Locking Compression Plate, Synthes, Switzerland) attached on to its

side with the required number of screws (XXX000XXX and X0X000X0X) and the

Appendix C

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coordinate system of the FARO arm and Optotrack was set up as explained in the

following paragraph

Set up of tracking system (Optotrack coordinate system, Digitising 6 points to get

Fracture Gap position): Rigid bodies were attached to the PVC’s surface at desired

locations for tracking purposes. Certain positional measurements such as relative

positions of the rig, PVC, rigid bodies, point of load application, and steel cups was

captured using the FARO arm 6D digitiser (Faro Technologies Inc, Florida, USA)

throughout the testing. In order to determine the centre of the fracture gap,

positional measurements of 6 points on the edge of osteotomy (3 point pairs

representing maximum and minimum in each of the 3 coordinate directions) were

recorded. This resulted in the generation of a relevant testing coordinate system

which aided in the determination of IFM.

Testing (Load magnitudes, BC and specifications): Testing was conducted on an

Instron dual-axis universal testing machine by applying desired loads individually

(confined axial compression and torsion). Data from the Instron testing apparatus

(load magnitudes, displacement, and rotation) as well as rigid body positions from

Optotrack system were recorded simultaneously during the test.

While, the FARO arm data gathered during the test was used in building the FE

model, the data from Instron and Optotrack (displacement data) was used to

compare results from modelling.

FE analysis: Modelling software SOLIDWORKS was used to create 3D model of

PVC-fixator constructs. While 3D model of the fixator was created from the

manufacturers drawing, 3D model of PVC was built to replicate the mechanical

testing model dimensions. The constructed PVC-fixator model was then

Appendix C

P a g e | 157

transformed into testing coordinate system using the procedure explained in the

following paragraph.

Transformation of 3D model into mechanical testing coordinate system: The

positional measurements recorded using FARO arm was used to create virtual

surfaces of PVC which was used in creation of FE model in testing coordinate

system. During mechanical testing, the FARO arm was used to take positional

measurements such as relative positions of different components which make up

the PVC-fixator construct. The surfaces of the PVC were also recorded using a

streaming mode with a sample distance of 0.5 mm. Several locations which form

the proximal and distal ends of PVC were also recorded. The measurements on the

surface of PVC were imported as a point cloud into RAPIDFORM software where

triangulated surfaces of PVC were built based on this point cloud. These

triangulated surfaces were further processed in RAPIDOFORM where they were

converted into non uniform rational B-spline surfaces. In the next step, the outer

surface of PVC was converted to a shell and smoothed to fill any holes. The result

was the outer shell of PVC in the testing coordinate system.

After the 3D models (XXX000XXX and X0X000X0X) of PVC built to match

mechanical testing model dimensions was created, it was imported as surface

model into RAPIDFORM where it was transformed into mechanical testing

coordinate system. At first, the imported surface model was converted into solid

which was further converted into shell representing the outer shell of PVC. In the

second step, the PVC shell created from 3D modelling was registered with PVC

surface generated from mechanical testing measurements. Firstly, a gross

alignment was performed by manually selecting at least four distinct

corresponding points on the surface. This was followed by a fine alignment using

Appendix C

P a g e | 158

the Iterative Closest Point (ICP) algorithm which uses an automatic selection of

points during the registration process. This results in the transformation of PVC

model into the mechanical testing coordinate system. The transformation matrix

responsible for this transformation was calculated using matrix algebra and was

then applied to the 3D PVC model in SOLIDWORKS. Further on, the fixator, steel

cups, cement were assembled on to the transformed PVC model with the aid of

relative positional measurements obtained from testing.

Once the model was transformed into the testing coordinate system, it was then

imported into ANSYS for simulation tests. The creation of FE model from 3D model

was conducted as explained in earlier sections of this chapter (for a complete

description, refer, 3.2.4 Creation of Finite Element (FE) model). While

elasticity modulus of 3.1 GPa was applied to PVC, 1.6 GPa was applied to cement

and 200 GPa applied to fixator plate and screws, a uniform poisons ratio of 0.3 was

chosen for all structures. The material properties (elasticity modulus) for PVC as

well as cement were obtained through material testing methods conducted as part

of a parallel study within the research program and hence not explained in this

project. Fixator components were meshed with a seed of 1.5 and a seed of 3 used

to mesh PVC, steel cups and cement. Ten node tetrahedral elements were used in

meshing all structures.

Loads and boundary conditions were applied to the model to replicate the

mechanical testing. In this case an axial compression and torsional tests were

conducted separately. Nodes at the location of distal cup were constrained in all six

degrees of freedom. While nodes at the location of proximal cup were constrained

in the x and y directions (confined lateral movements (axial compression and

torsional tests)), loads were applied to the proximal cup in z direction; proximal to

Appendix C

P a g e | 159

distal. The magnitude of load applied reflected the total load applied by the Instron

in the mechanical testing set up. This load was applied as a concentrated point load

to the node which was determined by FARO arm as closest to the mechanical

testing load point. All interactions such as, PVC-screw interface, cement-steel cups,

screw-plate, cement-PVC were modelled as “bonded” in all degrees of freedom.

A non-linear static analysis was run for a time period of one minute and outputs

from the model such as displacements, reaction forces and stresses were gathered

for further analysis.

Analysis: Although the value of the top cup displacement observed in axial

compression tests in FEA was similar (difference=0.02 mm) to that observed in-

vitro, in torsion, there was difference (up to 70%) between FE and in-vitro results.

However, the change in the value of top cup displacement with the change in screw

configuration (Axial compression=0.01mm and Axial torsion=0.6 degree) observed

in mechanical testing was comparable to that observed in FE simulations. The

displacement observed at the proximal cup in the direction of force application in

FE analysis and mechanical testing are as listed in the Table 9.

Table 9 Lists the displacement of the proximal cup determined for the axial

compressional and torsional load cases for both the FE simulation and mechanical

tests (‘X’ represents a filled screw hole and ‘0’ represents an empty screw hole).

Screw

Configuration

Displacement at the Proximal/top cup

FE simulation Mechanical testing

Axial Compression (207 N) XXX000XXX -0.13 mm -0.15 mm

Axial Torsion (7 Nm/deg) 4.3 deg 7.3 deg

Axial Compression (207 N) X0X000X0X -0.14 mm -0.16 mm

Axial Torsion (7 Nm/deg) 4.9 deg 7.9 deg

Appendix C

P a g e | 160

Conclusion:

Despite differences between FE and mechanical test results for the torsional

displacement value, the results for axial compression tests were comparable. Such

smaller variation in axial displacement results could be attributable to the

boundary condition which restricts the top of the proximal fragment from any

translational and rotational movements. Hence, the construct is overly stiff both in-

vitro and FEA thus restricting the construct from bending which is the primary

deformation mode for internal plate fixators constructs. The resulting axial

displacement from FEA is thus similar to the results from mechanical test. On the

other hand, torsional displacement in FEA was over estimated by 70% as opposed

to results from mechanical tests. It was reasoned that this difference in

displacement value could be the perfectly modelled interface in FEA which

restricts the rotational displacement thus making the FE model much stiffer than

in-vitro set up for torsional loads.

However, since the change in pattern of results between the two fixator

configurations tested in FE simulations are comparable with results from

mechanical testing, the FE model of PVC-fixator system can be considered to

represent the behaviour of the PVC-implant construct in-vitro while keeping in

mind that the FE results are an over estimation (up to 70% difference in torsion) of

mechanical testing.

Appendix D

P a g e | 161

Appendix D: Journal Paper: Can the contra-lateral limb be

used as a control with respect to analyses of bone remodelling?

(Published)

GModel

jJBE-1864: No.ofPages6

Medical Engineering & Physics xxx (2011 ) xxx-xxx

Contents lists available at ScienceDirect

Medical Engineering & Physics

EUifov iER jou r na I h omepage: www.elsevie r .co mllocate/ medeng phy

Can the contra-lateral limb be used as a control with respect to analyses of bone remodelling?

P. Krishnakanth, B. Schmutz, R. Steck, S. Mishra, M .A. Schiitz, D.R. Epari • Institute of Health and Biomedical Innovation. Queensland University of Technology. 60 Musk Ave. Kelvin Grove. 4059. Brisbane. Australia

A R TICLE I NFO ABSTRACT

Article history: Received 20 August 20 I 0 Received in revised form 24 March 2011 Accepted 24 March 2011

Keywords: Ovine Tibia Computed tomography Bone remodelling Contrd-ldteral bone ?re-operative control Image processing

Bone loss may result from remodell ing initiated by implant stress protection. Quantifying remodelling requires bone density distributions which can be obtained from computed tomography scans. Preoperative scans of large animals however are rarely possible. This study aimed to determine if the contra-lateral bone is a suitable control for the purpose of quantifying bone remodelling. CT scans of 8 pairs of ovine tibia were used to determine the likeness of left and right bones. The deviation between the outer surfaces of the bone pairs was used to quantify geometric similarity. The density differences were determined by dividing the bones into discrete volumes along the shaft of the tibia. Density differences were also determined for fractured and contra-lateral bone pairs to determine the magnitude of implant related remodelling. Left and right ovine tibiae were found to have a high degree of similarity with differences of less than 1.0 mm in the outer surface deviation and density difference of less than 5% in over 90% of the shaft region. The density differences (10-40%) as a result of implant related bone remodelling were greater than left-right differences. Therefore. for the purpose of quantifying bone remodelling in sheep. the contra-lateral tibia may be considered an alternative to a pre-operative control.

1. Introduction

Bone has the capability to adapt to changes in its mechanical loading through a process of remodelling (1). Bone remodelling is a lifelong process whereby old bone is replaced by new bone (2(. 1n adults, approximately 18%ofthe bony skeleton is replaced annually (3(. Remodelling leads to both changes in the density and structure of bone (4).

Physical exercise is known to cause changes in the structure of bone (5(. For example, increased bone mass may be seen in the dominant arm of a tennis player (6). In this case, the remodelling may be considered positive as it enables the individual to withstand greater limb loading. However, in instances such as fracture fixation. load-sharing with an implant may lead to unloading of the bone, a phenomenon known as stress protection, and result in undesirable bone loss (7). This bone loss may lead to complications such as screw loosening leading to implant failure or even re-fracture (8). In order to predict bone remodelling related to a particular treatment or implant, it is necessary to understand the mechanism of remodelling. To do this, changes in the loading conditions of the bone must be related to remodelling changes and

• Corresponding author. Tel.: +61 7 3138 0167. E-mail address: [email protected] (D.R. Ep<~ri~

<0 2011 I PE M. Published by Elsevier Ltd. All rights reserved.

relationships formulated. Thus. the first step in this approach is to quantify the remodelling changes.

Calculating the changes due to remodelling requires bone density distr ibutions to be quantified prior to intervention and at a subsequent time-point providing sufficient time for remodelling changes to occur. Quantitative bone density distributions can be determined from computed tomography (IT) scans calibrated with a bone phantom (9). Since a er scan exposes the subject to ionising radiation, performing a er scan on humans is considered only when it is deemed essential to form a diagnosis. Additionally, metal implants can cause artefacts rendering er data unusable for quantitative analysis. Therefore obtaining data from human volunteers for the purpose of quantifying bone remodelling is excluded. Alternatively. large animals (such as sheep) are commonly used in orthopaedic research )10- 12) and obtaining post-mortem er scans of bones with implants removed is commonplace. Therefore. large animals may be considered a suitable model to study implant related changes due to bone remodelling. However, obtaining preoperative er scans of l ive animals is often not possible due to the limited availability of er scanners outside the clinical environment. An alternative approach to using a pre-operative scan of the same limb may be to use the contra-lateral limb.

Although the contra-lateral limb has been used previously as a control for quantifying bone density changes (13-17), it may not be automatically assumed that the contra-lateral bone represents

13.50-4533/S- see front matter () 2011 IPEM. Published by Elsevier Ltd. All rights reserved. dol: I 0.10 16/j.medengphy.20 I 1.03.011

Please ci te this article in press as: Krishnakanth P. et al. Can the contra-lateral limb be used as a control w ith respect to analyses of bone remodelling? Med Eng Phys (2011 ), doi: 10.1 016/j.medengphy.20 11.03.01 1

halla

Due to copyright restrictions, the published version of this article is not available here. Please consult the hardcopy thesis available from QUT Library or view the author version online at: http://dx.doi.org/10.1016/j.medengphy.2011.03.011

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