Fracture Resistance Behaviour of γ-Irradiation Sterilized Cortical Bone Protected with a Ribose Pre-Treatment

by

Carman Mitchell Woodside

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Materials Science and Engineering University of Toronto

© Copyright by Carman Mitchell Woodside 2015

ii

Fracture Resistance Behaviour of γ-Irradiation Sterilized Cortical

Bone Protected with a Ribose Pre-Treatment

Carman Mitchell Woodside

Master of Applied Science

Materials Science and Engineering

University of Toronto

2015

Abstract

Structural bone allograft reconstructions are often implemented to repair large skeletal defects.

To ensure the biological safety of the patient, allograft material is routinely sterilized with γ-

irradiation prior to implantation. The sterilization process damages the tissue, specifically the

collagen protein network, leading to severe losses in the mechanical properties of the bone. Our

lab has begun developing a ribose pre-treatment that can protect bone from these harmful effects.

The goals of the present study were to develop a method to measure the fracture toughness of

bone, an important clinical failure mode, and implement it to determine the effectiveness of the

ribose pre-treatment on fracture toughness. We have shown that the ribose pre-treatment is

successful at protecting some of the original fracture toughness of sterilized bone, and that the

connectivity of the collagen network is an important contributor to the fracture resistance of

bone.

iii

Acknowledgments

To Ena, for your love and support. None of this is possible without your endless and generous

contributions of time, energy, and self. I love you and thank you. To Mom and Dad, for your

friendship, and for your guidance and clarity on issues big and small, important and irrelevant.

Your discussion and critique has always been and always will be invaluable. To Andrew, for the

gentle reminder that there is no need to take anything too seriously. To Killian, for your

ceaseless entertaining reprisals from the routine. To the Ujić, Sweetman, and Rossall families

for your perpetual generosity, sustenance, and shelter. To Tom, for challenging my weaknesses

and exposing the fun in asking questions about our work. To John Barrett, for arming me with

the sharpest tools. To Nanny, Grampie, and Grammie, for your unwavering belief and humour.

To Jindra, Julia, Tarik, and Sam, for your technical contributions and for transforming our

workplace. To Marc Grynpas, for your willing donation of space, equipment, time, resourses,

and direction, without which this project would not exist.

iv

Table of Contents

Acknowledgments .......................................................................................................................... iii

Table of Contents ........................................................................................................................... iv

List of Tables ................................................................................................................................ vii

List of Figures ................................................................................................................................ ix

List of Appendices ....................................................................................................................... xiv

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

1.1 Clinical Motivation/Need .................................................................................................... 1

1.2 Clinical Use of Bone Allograft ........................................................................................... 3

1.3 Cortical Bone ...................................................................................................................... 5

1.3.1 Overall Structure ..................................................................................................... 6

1.3.2 Collagen Structure .................................................................................................. 8

1.4 Fracture in Bone .................................................................................................................. 9

1.4.1 Deformation Mechanisms ..................................................................................... 11

1.4.2 Crack Tip Shielding Mechanisms ......................................................................... 13

1.4.3 Role of Collagen in Fracture Toughness .............................................................. 14

1.5 Elastic-Plastic Fracture Mechanics ................................................................................... 15

1.5.1 Rising R Curve Behaviour .................................................................................... 18

1.5.2 J Measurement ...................................................................................................... 20

1.6 Effects of Irradiation ......................................................................................................... 23

1.7 Ribose Pre-Treatment Effects ........................................................................................... 25

Chapter 2 Objectives and Hypothesis ........................................................................................... 28

2.1 Objectives ......................................................................................................................... 28

2.2 Hypothesis ......................................................................................................................... 28

Chapter 3 Materials and Methods ................................................................................................. 29

v

3.1 Experimental & Treatment Design ................................................................................... 29

3.2 Single Edge Notched Bending Fracture ............................................................................ 31

3.2.1 Optical Crack Length Measurement ..................................................................... 34

3.2.2 Timing and Signalling Chip .................................................................................. 38

3.2.3 Calculating JR Curves and Fracture Toughness .................................................... 40

3.2.4 Modulus Screening ............................................................................................... 43

3.3 Machining ......................................................................................................................... 44

3.3.1 Crack Notching ..................................................................................................... 46

3.4 Hydrothermal Isometric Tension Testing ......................................................................... 48

3.5 Scanning Electron Microscopy ......................................................................................... 51

3.6 Statistical Data Analyses ................................................................................................... 52

3.6.1 Repeated Measures and Comparisons of Means .................................................. 52

3.6.2 Statistical Power Analysis ..................................................................................... 53

Chapter 4 Results .......................................................................................................................... 55

4.1 Bovine Study Results ........................................................................................................ 55

4.1.1 JR Curves & Crack Initiation Fracture Toughness: JIc-ASTM & JIc-Obs .................... 55

4.1.2 Tearing Modulus (Modulus of Toughness) .......................................................... 59

4.1.3 Collagen Characterization – HIT Testing ............................................................. 61

4.1.4 Scanning Electron Microscopy ............................................................................. 64

4.1.5 Power Analysis ..................................................................................................... 65

4.2 Human Study Results ........................................................................................................ 65

4.2.1 JR Curves & Crack Initiation Fracture Toughness: JIc ASTM & JIc Obs ..................... 65

4.2.2 Tearing Modulus (Modulus of Toughness) .......................................................... 70

4.2.3 Collagen Characterization – HIT Testing ............................................................. 72

4.2.4 Scanning Electron Microscopy ............................................................................. 75

4.2.5 Power Analysis ..................................................................................................... 75

vi

Chapter 5 Discussion, Conclusions, & Future Work .................................................................... 77

5.1 Discussion ......................................................................................................................... 77

5.1.1 Literature Comparison .......................................................................................... 77

5.1.2 Connectivity and Toughness ................................................................................. 78

5.1.3 Defining Crack Initiation ...................................................................................... 81

5.1.4 Ribose Treatment Protection of Intrinsic and Extrinsic Toughness ..................... 82

5.1.5 Testing Limitations ............................................................................................... 84

5.2 Error Analysis ................................................................................................................... 85

5.3 Conclusions ....................................................................................................................... 87

5.4 Future Work ...................................................................................................................... 89

References ..................................................................................................................................... 77

Appendix A: Bovine Data Tables ............................................................................................... 104

Appendix B: Human Data Tables ............................................................................................... 108

vii

List of Tables

Table 3.1 A general repeated measures ANOVA example [86] 52

Table 4.1 Summary of the bovine crack initiation fracture toughness results. Data is

presented as the mean ± standard deviation 58

Table 4.2 Summarized Bonferroni-adjusted p-values for the comparison of group

means for crack-initiation fracture toughness 58

Table 4.3 Summary of the tearing modulus data in bovine bone. The data is present

as the mean ± standard deviation 60

Table 4.4 Bonferroni-adjusted p-values for the multiple comparisons of group

means for bovine bone tearing modulus 61

Table 4.5 A summary of the bovine HIT results. Data is presented as the mean ±

standard deviation 62

Table 4.6 Summarized Bonferroni-adjusted p-values for the comparison of group

means for bovine HIT connectivity measures 63

Table 4.7 The calculated β and required sample sizes from the power analysis on

the bovine results. The required sample size is to achieve a statistical

power of 0.8 (β = 0.2) given the resulting effect size from each metric. 65

Table 4.8 Summary of the human crack initiation fracture toughness results. Data is

presented as the mean ± standard deviation. 69

Table 4.9 Summarized Bonferroni-adjusted p-values for the comparison of group

means for crack-initiation fracture toughness 70

Table 4.10 Summary of the tearing modulus data in human bone. The data is present

as the mean ± standard deviation 72

Table 4.11 Bonferroni-adjusted p-values for the multiple comparisons of group

means for human bone tearing modulus 72

viii

Table 4.12 A summary of the human HIT results. Data is presented as the mean ±

standard deviation 73

Table 4.13 Summarized Bonferroni-adjusted p-values for the comparison of group

means for human HIT connectivity measures 74

Table 4.14 The calculated β and required sample sizes from the power analysis on

the human results. The required sample size is to achieve a statistical

power of 0.8 (β = 0.2) given the resulting effect size from each metric. 76

Table 5.1 The errors for each basic measurement in the test method 86

Table 5.2 Summarized error for quantities used in the evaluation of the J-integral 87

Table A.1 Summary of the fracture data by specimen for the bovine study 104

Table A.2 Summary of the HIT data by specimen for the bovine study 105

Table B.1 Summary of the fracture data by specimen for the human study 108

Table B.2 Summary of the HIT data by specimen for the human study 109

ix

List of Figures

Figure 1.1 X-ray of a large segmental defect in a human femur [120] 1

Figure 1.2 X-ray image of a large structural allograft reconstruction [121] 2

Figure 1.3 Micrograph showing micro-cracks that have formed in human bone [12] 3

Figure 1.4 An outline of bone’s hierarchical structure [44] 5

Figure 1.5 The formation process of plexiform bone. The lettered arrows indicate

the same location in the bone at progressively later time points [19] 7

Figure 1.6 The triple helix of the tropocollagen molecule and approximate

dimensions [29] 8

Figure 1.7 Overview of the toughening mechanisms in bone and their respective

length scales [34] 11

Figure 1.8 The strain energy of the cross-hatched area above the yield stress must be

redistributed across a larger area, because the material yields to dissipate

that energy and cannot be stressed locally beyond the yield stress [26] 12

Figure 1.9 Stress strain curve behavior under unloading conditions for nonlinear

elastic and elastic-plastic materials [50] 16

Figure 1.10 Contour around the crack tip for the line integral evaluation of the

nonlinear energy release rate of a growing crack [35, 51] 17

Figure 1.11 Rising JR behaviour plotted against crack growth [50] 19

Figure 1.12 Schematic outline of the approach taken by Landes and Begley [57, 58]

to make early experimental J measurements [36] 21

Figure 1.13 Diagram depicting the damage irradiation does to the connectivity of the

collagen network 23

x

Figure 1.14 Fracture surface micrographs of cortical bone three point bending

specimens from Willett et al. [10]. N and I indicate non-irradiated and

irradiated tissues, respectively. 24

Figure 1.15 A summary of the protect results achieved to date using ribose pre-

treatment 26

Figure 1.16 Ribose pre-treatment may help protect connectivity by inducing the

formation of cross-links in irradiation-damaged bone collagen 27

Figure 3.1 Outline of the treatment and testing procedure for each treatment group 30

Figure 3.2 A summary of the a priori required sample size evaluation 31

Figure 3.3 SENB specimen geometry 32

Figure 3.4 A schematic of the optical crack length measurement layout 34

Figure 3.5 A typical force-displacement curve for fracture testing of metals using

unloading compliance to measure crack growth. The inset shows the

compliance taken during unloading steps [36]. 35

Figure 3.6 An example of photos taken during a fracture test with the low

magnification macro lens. Frame a) was captured as the test began and

frame b) was captured just prior to failure of the specimen. The arrows

highlight discernible crack mouth spreading 36

Figure 3.7 Demonstration of how crack length measurements are made. The white

arrow indicates the crack showing through the ink coating. a) The length

in pixels of the blue line divided by the specimen thickness sets the

measurement scale for the test b) The established scale is then used to

find the unbroken ligament length. 37

Figure 3.8 Circuit diagram of the timing chip and the Instron controller’s digital

output system. The digital output is set to ‘low’ to turn the output on. Vss

(5 volts) powers the timing chip when the output is on. 39

xi

Figure 3.9 A typical JR curve with a fitted power law and 0.2 mm offset construction

line. 42

Figure 3.10 a) The crack tip just prior to the occurrence of JIc-Obs, the encircled area

contains a small micro-cracking field b) The crack tip just after the

occurrence of JIc-Obs, the encircled area contains a small crack – crack

initiation has started 43

Figure 3.11 Dashed lines indicate the plane of a cut a) The diaphysis is sectioned

along its length b) The diaphysis sections are split into halves c) ‘slabs’

are cut from the cortex d) each slab is sectioned into beams 45

Figure 3.12 The chosen direction of fracture for this study 47

Figure 3.13 A close-up of the sharpened notch 48

Figure 3.14 HIT tester design 49

Figure 3.15 An example HIT curve depicting the denaturation temperature and

maximum slope metrics 50

Figure 3.16 An example G*Power output for a pseudo a priori required sample size

evaluation 53

Figure 3.17 An example G*Power output for a post-hoc statistical power evaluation 54

Figure 4.1 Force-displacement recordings from a matched set of bovine specimens 56

Figure 4.2 JR curves for the bovine N, I, and R groups from a representative

matched set 57

Figure 4.3 A comparison of the two different crack initiation fracture toughness

measures in bovine bone. The error bars represent the standard deviation

and an asterisk signifies a statistically significant difference between

groups (p < 0.05). 57

xii

Figure 4.4 Examples of the crack path in bovine bone before instability for each

group. White arrows indicate micro-cracking 59

Figure 4.5 The bovine bone tearing modulus means for each group. The error bars

represent the standard deviation and an asterisk signifies a statistically

significant difference between groups (p < 0.05 adjusted). 60

Figure 4.6 Representative HIT curves for decalcified bovine bone collagen from

each group 62

Figure 4.7 ASTM defined fracture toughness plotted against the HIT measures of

both denaturation temperature and maximum slope of isometric tension

for bovine bone. The error bars represent one standard deviation. 63

Figure 4.8 Representative SEM micrographs taken of the fracture surfaces of the

bovine test specimens 64

Figure 4.9 Force-displacement recordings from a matched set of human specimens 67

Figure 4.10 JR curves for the human N, I, and R groups from a representative

matched set 68

Figure 4.11 A comparison of the two different crack initiation fracture toughness

measures in human bone. The error bars represent the standard deviation

and an asterisk signifies a statistically significant difference between

groups (p<0.05). 69

Figure 4.12 Examples of the crack path in human bone for each group. White arrows

indicate micro-cracking 70

Figure 4.13 The human bone tearing modulus means for each group. The error bars

represent the standard deviation and an asterisk signifies a statistically

significant difference between groups (p<0.05). 71

Figure 4.14 Representative HIT curves for decalcified human bone collagen from

each group 73

xiii

Figure 4.15 ASTM defined fracture toughness plotted against the HIT measures of

both denaturation temperature and maximum slope of isometric tension

for human bone. The error bars represent one standard deviation. 74

Figure 4.16 SEM micrographs taken of the fracture surfaces of the human test

specimens 75

Figure 5.1 Bovine and human ASTM-defined fracture toughness values plotted as a

function of HIT connectivity measures. The error bars represent one

standard deviation 79

Figure 5.2 Bovine and human tearing modulus values plotted as a function of HIT

connectivity measures. The error bars represent one standard deviation. 81

Figure 5.3 The p-values of the repeated measures ANOVA for changing definitions

of crack initiation toughness. Lower p-values indicate greater effect size

detected between the groups 83

Figure 5.4 Test specimen cross-sections in the plane of the crack demonstrating two

different nonlinear crack front behaviours. The cross-hatched areas

represent the unbroken ligament 84

xiv

List of Appendices

Appendix A: Bovine Data Tables ............................................................................................... 104

Appendix B: Human Data Tables ............................................................................................... 108

1

Chapter 1 Introduction

1.1 Clinical Motivation/Need

The overarching clinical challenge motivating this work is the reconstruction of critically sized

skeletal defects. Critically sized defects, like the one shown in Figure 1.1 are those that present

too large of a gap or fracture for the body’s physiology to heal on its own. They can be caused by

incidences of cancer, trauma, infection, or revision arthroplasty, among others. In these

situations, some form of reconstruction is necessary to bridge the gap and restore structure and

function. Reconstruction of a critically sized segmental defect in a long

bone commonly involves the use of a large cortical bone allograft, shown

in Figure 1.2. A bone allograft is simply the transplantation of typically

dead bone tissue from a human donor to another human recipient. In the

United States and Canada, around 2 million allograft transplants are

performed each year [1, 2] of which an estimated 450,000 are cortical

bone allografts [3].

Under normal physiological loading conditions, micro-cracks will

accumulate in bone tissue [4]. This micro-cracking, shown in Figure 1.3,

is normal and the cells present in bone (osteoclasts and osteoblasts) will

remodel the damage accumulated by laying new bone in its place via

osteonal remodelling. Since allograft tissue is dead bone, the normal

mechanisms of remodelling are limited to the region close to the host-

graft junction, or do not take place at all [5]. The micro-cracks that

accumulate constitute flaws in the material and become stress

concentrations when the bone is loaded. High local stress can cause the

cracks to grow. If the stresses are high enough and the cracks are large

enough, the allograft will fail. Fracture toughness, or resistance to crack

growth, is essential to limit the propagation of micro-cracks. Graft

fracture is a clinically recognized failure mode and structural allograft reconstructions fail in this

manner an estimated 20 - 40% of the time [6-8].

Figure 1.1 – X-ray

of a large segmental

defect in a human

femur [120]

2

In order to ensure the biological safety of the recipient, any donated tissue must

be sterilized prior to implantation. Sterilization destroys or removes pathogens

that may be present in the tissue such as bacteria and viruses, and prevents them

from infecting the tissue recipient. For bone tissue, sterilization is often done

with a relatively large dose of γ-irradiation. A standard dose doesn’t exist, but

tissue banks often use doses in the range of ~20-30 kGy [6]. Unfortunately, in

addition to destroying pathogens, γ-irradiation sterilization also has severe

deleterious effects on the mechanical properties of bone [7, 8]. Bone that has

been irradiated is weaker, more brittle, and fractures more easily. Research has

shown that allograft reconstructions performed with γ-irradiation sterilized bone

fracture approximately twice as often as those performed with tissue that has not

been irradiated [9]. There is a real need for a sterilization process that can

retain or protect the mechanical integrity of the bone tissue without eliminating

the use of γ-irradiation.

Our lab has developed a treatment that protects the mechanical properties

of bone from the deleterious effects of the irradiation sterilization process

[10]. Although some preliminary testing has been performed, the effects of

the treatment on the fracture resistance of graft material have yet to be

fully characterized [10, 11]. As briefly touched upon above, fracture

toughness is an essential property of bone and bone allografts for resisting the growth of small

micro-cracks and preventing complete fractures. The effects of the treatment on the fracture

toughness of irradiation sterilized cortical bone need to be measured to determine the treatment’s

effectiveness.

Figure 1.2 – X-ray

image of a large

structural allograft

reconstruction [121]

3

Figure 1.3 – Micrograph showing micro-cracks that have formed in human bone [12]

1.2 Clinical Use of Bone Allograft

When using bone grafts to reconstruct skeletal defects, autografts, grafts where the patient’s

tissue is transferred from one location to another in their body, are considered the gold standard

[13]. Autograft reconstructions do not suffer from immunological rejection and have superior

osteoconductive and osteogenic properties [14, 15], meaning they are much more likely to

incorporate the graft material. When large or structural grafts must be performed, like the one in

Figure 1.2, allograft tissue has distinct advantages over an autograft. The availability in size and

shape of an allograft is far less limited and the acquisition of such a graft carries no risk of

damaging donor structures in the patient [13]. This damage is known as donor site morbidity,

and is a serious problem clinically. For allograft procedures, preventing the transmission of

pathogens to the recipient is of the utmost concern. To ensure patient safety sterilization of the

graft material is key.

Graft tissue is commonly sterilized with γ-irradiation for a number of reasons. Most importantly

γ-irradiation effectively kills bacteria, viruses and other pathogens [16]. The DNA and RNA of

these pathogens are severely damaged either directly by high energy gamma rays, or indirectly

by the radiolysis of water and the free radicals that it creates. Additionally, γ-irradiation can

easily penetrate the sterile packaging, preventing the need to reseal or repackage sterilized tissue

and risk re-contamination. It avoids the use of heat for sterilization which can cause damage to

the tissue. It can also penetrate thick tissue samples [16], reaching all corners of the graft, which

is a distinct advantage over other sterilization methods using chemical processing [17]. The

4

safety that γ-irradiation sterilization provides is essential. Even in light of the mechanical

degradation it causes, regulatory agencies (such as the Food and Drug Administration in the

USA) call for its use. For tissue banks, the mechanical degradation presents a product quality

issue, and for surgeons, it presents a clinical outcome concern [10].

5

1.3 Cortical Bone

Bone is a hierarchically-structured, protein-rich, and mineral-reinforced composite material. It

has many purposes in the body, its structural function being first and foremost. It provides a rigid

framework to house and mount the soft tissues of the body. This rigid framework is also

important for motion, as muscles need something rigid to pull against. It protects many important

organs from trauma or impact. It serves as

a reservoir for calcium, an important

substance for a variety of purposes in the

body. Its marrow houses production of stem

and blood cells. Many different organisms

have bone and bone-like material but for

this study, we will be concerned with

mammalian skeletal bone tissue, specifically

bovine and human bone.

Mammalian bone manifests itself in two

obviously different types: cortical (or

compact) and trabecular (or cancellous).

The main differentiating feature between

them is their porosity, with cortical bone

being the denser of the two. They are

largely comprised of the same material, but

it is their configuration at greater length

scales that distinguish them. Cortical bone is

a low porosity, compact formation of bone

tissue. It is found on the outside layer of

many bones in the body and comprises the

diaphysis of most long bones like the femur

or humerus. The relative density (total

mass/bulk volume/material density) of

cortical bone is 0.7 or greater. Cortical bone

Figure 1.4 – An outline of bone’s hierarchical

structure [44]

6

is much stronger, but much heavier than trabecular bone. Bone that has a relative density of less

than 0.7 can be classified as trabecular bone [18]. Trabecular bone is found in the metaphyses of

long bones and in vertebrae. Its structure is highly porous and usually has marrow occupying the

spaces in between the struts of material, or trabeculae.

1.3.1 Overall Structure

Bone is formed beginning with osteoid laid down by osteoblasts. The osteoid material consists

primarily of type I collagen (~90% along with some other non-collagenous proteins) arranged in

bundles of cross-linked tropocollagen molecules called microfibrils (see 1.3.2), and is free of the

mineral phase. Later it becomes infiltrated with hydroxyapatite mineral platelets. Mineral is

precipitated first in the regions between the molecule ends (the gap region), and slowly spreads

along the rest of the length of the fibril [19]. The mineral is laid down in thin, wide platelets,

about 5 x 40 x 100 nm in size [20, 21]. The mineral adds stiffness to the fibrils as well as

resistance to compressive forces [19]. Mineralized microfibrils are then bundled again to form

larger collagen fibrils about 0.1-3 µm in diameter [22].

Collagen fibrils group together into regions assuming the same orientation. These regions are

laid down in thin concentric layers (see Figure 1.4) around the long axis of the bone. These

layers, called lamellae form what known as lamellar bone [19]. Slight changes in the orientation

of the collagen fibrils between lamellae create a plywood-like structure [23]. Woven bone is a

bone structure whose collagen fibrils are short and arranged in varying orientations throughout

[22, 24]. Woven bone is also highly mineralized tissue [19]. Woven bone can be laid down much

more quickly than lamellar bone but is organized much less precisely [19].

Many large mammals, including bovines, exhibit an overall bone morphology known as

plexiform or fibrolamellar bone. Plexiform bone essentially grows a scaffold of woven bone with

interstitial regions where lamellar bone is laid down more slowly [19]. The formation process is

shown in Figure 1.5. The result is alternating regions of lamellar and woven bone.

7

Figure 1.5 – The formation process of plexiform bone. The lettered arrows indicate the

same location in the bone at progressively later time points [19]

Humans on the other hand, display a morphology known as Haversian bone. Haversian bone is

formed when osteoclasts cleave out hollow cylinders in the existing lamellar structure [25].

Theses hollow cylinders are then refilled with lamellar bone in concentric layers on the interior

surface to form osteons [19]. Osteons are left with a central cavity down its length known as a

Haversian canal. These canals can house blood vessels and nerves [26]. This process of osteon or

Haversian system creation is the result of bone remodeling [19]. The final overall morphology is

8

a bulk material of lamellar bone interspersed with cylindrical osteons, and is shown in cross

section in Figure 1.4.

1.3.2 Collagen Structure

As mentioned above, the organic matrix of cortical bone, called osteoid, when initially laid

down, is largely type I collagen (~90 %). Type I collagen molecules, known as tropocollagen

(see Figure 1.6), are actually triple helices formed from three long polypeptide α-chains.

Tropocollagen molecules stack together side by side, overlapping by approximately one quarter

of their length, and end to end, with small gaps between the end of each triple helix and the next

[27]. The stacks are cross-linked together by enzymatic and non-enzymatic cross-links

throughout to form microfibrils.

The chains in the triple helix typically follow a repeating glycine-proline-hydroxyproline amino

acid sequence. Sometimes the proline-hydroxyproline portion can be substituted with other

amino acids. Lysine and hydroxylysine are substitutions that enable cross-linking. Glycine is a

constant in the sequence and it enables the helical structure because it packs very neatly inside

the triple helix. Intramolecular hydrogen bonding adds stability to the network [28]. The

extremities of the tropocollagen molecule are non-triple helical and are termed telopeptide

regions.

Figure 1.6 – The triple helix of the tropocollagen molecule and approximate dimensions

[29]

9

Pyridinolines and pyrroles are enzymatic cross-links that are formed within the collagen

network. The formations of these cross-links are controlled by the expression of the enzyme

lysyl oxidase [30]. The action of lysyl oxidase converts ε-amino groups of lysine and

hydroxylysine of the telopeptide region in the aldehydes allysine and hydroxyallysine. Allysine

and hydroxyallysine react and condensate with residues of lysine and hydroxylysine in the helix

region of a neighbouring collagen molecule [31]. This reaction forms a divalent, or immature,

cross-link. Immature cross-links can stabilize to become trivalent, or mature, cross-links. The

mechanisms behind this stabilization are not fully understood [30], but some mechanisms

involved are believed to be an interaction with another nearby immature cross-link, or by

reaction with a free allysine or hydroxyallysine [35-38].

There are also non-enzymatic cross-links that can be formed in vivo. Oxidation of free-reducing

sugars can form cross-links, such as pentosidine and gluscosepane, at various locations along the

length of the collagen helices. While the origin of enzymatic cross-links are limited to the

telopeptide regions of tropocollagen, non-enzymatic cross-links are believed to be non-specific

and located throughout the length of tropocollagen structure [32]. Non-enzymatic cross-links are

formed when a reducing sugar in open chain form oxidizes and reacts with the ε-amino group of

a lysine, arginine, or hydroxylysine to form a Schiff base [40-42]. The Schiff base quickly

experiences Amadori rearrangement and the more stable Amadori product then reacts with free

ε-amino groups on the same amino acids in the neighbouring collagen molecules [40-42]. The

result is a stable non-enzymatic cross-link between collagen chains [33].

The general state of the collagen network can be described by its connectivity. Connectivity is a

somewhat abstract quantification of the degree to which the collagen network is linked together.

A function of main chain length and cross-link density, connectivity is increased by longer main

chains or adding crosslinks and decreased by main chain scission or losing cross-links.

1.4 Fracture in Bone

When bone fails, the predominant mode is fracture. Long bones fracture in vivo, and recognized

failure modes of grafts and graft material include fracture [6-8]. Bone’s capacity to accommodate

post yield deformation (~1% strain post-yield) while exhibiting a total strain to failure

somewhere in the range of 1.9-2% [13, 43-46] means that bone, although still brittle, does have

some plasticity to it. Because of its small scale structure and the way it’s formed as a living

10

tissue, bone inherently contains many flaws, defects, or other irregularities in structure. Among

existing flaws are channels for blood vessels, Haversian canals, osteocyte lacunae, and micro-

cracks. Flaws in a material serve as stress concentrations and nucleation sites for fracture, so

more traditional measures of strength may not be sufficient for predicting failure. Measures such

as yield stress, ultimate tensile strength, and elongation to failure are certainly meaningful

evaluations of bone, especially in compression [19], but in a material that fractures and contains

flaws, any strength measurement will be dependent on flaw size and distribution.

A material’s fracture toughness is the required energy for cracks to grow in that material.

Fracture toughness provides a measure of strength by determining a material’s resistance to the

growth or propagation of existing defects. The mechanisms that provide this resistance can be

grouped into two categories: intrinsic and extrinsic toughening mechanisms (see Figure 1.7).

Intrinsic toughening mechanisms act ahead of the tip of a growing crack. They reduce stresses at

the crack tip by widening the root radius and by redistributing stresses ahead of the crack tip and

dissipating energy with permanent deformation mechanisms [34, 35, 36]. Extrinsic mechanisms

shield the crack tip from external loads by providing closing tractions in the crack wake or

diverting the crack away from large crack-opening stresses (the direction of maximum driving

force) [34, 35, 36].

11

Figure 1.7 – Overview of the toughening mechanisms in bone and their respective length

scales [34]

1.4.1 Deformation Mechanisms

Intrinsic toughening mechanisms are those that act ahead of a growing crack front. They help

reduce the stress intensity in the vicinity of the crack by widening the crack tip root radius,

termed crack blunting, and redistributing the stresses in that region [36]. Crack blunting and

stress field redistribution are accomplished through localized permanent deformation, or

plasticity. Figure 1.8 shows how this localized plastic behaviour redistributes the stress intensity

field created around the tip of a crack. The same mechanisms that allow a material to deform past

12

the yield point, or deformation mechanisms, are also that material’s intrinsic toughening

mechanisms. As mentioned, bone sustains some plastic deformation, and therefore has a handful

of deformation mechanisms. The breaking of hydrogen bonds and molecular uncoiling of

tropocollagen molecules is proposed to be one of these mechanisms. The sliding of both

mineralized collagen fibrils and fiber arrays and micro-cracking are established contributors to

the plastic behaviour of bone [34].

Figure 1.8 – The strain energy of the cross-hatched area above the yield stress must be

redistributed across a larger area, because the material yields to dissipate that energy and

cannot be stressed locally beyond the yield stress [26]

It’s postulated that when tropocollagen is stretched beyond its elastic limit, the hydrogen bonds

holding the helix together break and the helix itself begins to uncoil and stretch. Numerically,

these processes have been shown to allow up to 50% tensile strain before breaking [49-53]. It

must be noted this is a somewhat reversible process as the helix strands remain in close enough

proximity for hydrogen bonds to reform after breaking [37, 38], but it contributes to larger scale

plasticity of the collagen network and bone material [34].

When yielded in tension, the bundled collagen fibril arrays experience sliding between the

individual mineralized fibrils, and against adjacent arrays. At the individual fibril level, slip

occurs at the tropocollagen-hydroxyapatite particle interface and between tropocollagen chains

13

themselves [39]. Evidence shows that the infusion of hydroxyapatite mineral in to the collagen

fibrils contributes greatly to the increases in energy required to undergo this sliding process [39].

The mineralization increases the stiffness [19], strength, and toughness of the fibrils [39]. The

longitudinal sliding of the fibril arrays against one another is enabled by the shearing of the thin

protein layer that separates them [56-59].

Micro-cracking, a non-catastrophic nucleation of small cracks, is the main mechanism of small

scale permanent deformation of bone structure [34]. Micro-cracking drives up the critical crack-

driving force by absorbing work that would otherwise go towards propagating the main crack by

releasing strain energy as they are formed [36]. In stress concentrated regions, they form a

diffuse field of cracks tens of micrometres in length separated by only a few micrometres [40].

1.4.2 Crack Tip Shielding Mechanisms

Extrinsic toughening mechanisms, sometimes called crack shielding mechanisms, act behind, or

in the wake of, the crack tip. They reduce the crack driving force at the crack front by absorbing

work energy, bearing or diverting external loads through the crack wake (closing tractions), and

by lowering the stress intensity at the crack tip [35]. Bone’s fracture resistance originates

primarily from its extrinsic toughening behaviour [41]. This toughening requires an increasing

crack driving force with longer crack lengths [42]. The crack shielding mechanisms in bone

initiate with micro-cracking and include crack bridging by collagen fibrils and unbroken

ligaments, and crack path deflection [34]. Micro-cracking has been shown to have a far greater

contribution intrinsically than extrinsically [43, 44]. It is however, an important precursor to

other, more noteworthy, extrinsic mechanisms [34].

Crack bridging occurs when unbroken material spans the crack wake. The unbroken material

alleviates the crack driving force by first bearing load, or exerting a closing traction on the crack

faces, and then by absorbing energy as it fails [35, 36]. In composites, bulk material or second

phase particles can be responsible for bridging crack wakes [35, 36]. Uncracked-ligament

bridging occurs in bone when nearby micro-cracks coalesce and advance the crack front while

still leaving unbroken portions of material in the wake [61, 63-66]. Collagen fibril bridging does

occur in bone but at much smaller scales. Micro-cracks, especially, split the mineral phase while

keeping the collagen fibrils in that region intact [45].

14

The direction a growing crack travels will generally be the path normal to the greatest crack-

opening force, or the path of least resistance. If in a material, there are regions where the

resistance to crack growth is lower than neighbouring regions, the crack will preferentially travel

along the weaker regions. The cement line interfaces between lamellae are weaker than the

surrounding bone material, so any micro-cracking fields and dominant cracks will deflect and

align themselves along the cement lines. If the fracture is transverse, this phenomenon can

deflect cracks nearly 90°. This deflection greatly blunts main cracks [34, 35], diverts main cracks

away from, and out of the plane of, the maximum driving force, and demands more energy to

realign the crack in its original direction if it is to continue through the material [35]. These

deflections create arduous paths for cracks to traverse, especially in the transverse direction [34].

1.4.3 Role of Collagen in Fracture Toughness

The composite nature of bone allows it to adopt properties from both of its individual

constituents – the stiff and strong hydroxyapatite mineral and the ductile and soft collagen

network. The mineral phase of bone is responsible for its stiff, elastic behaviour, affording it

rigidity and strength against applied loads. On the other hand, the collagen phase is responsible

for its post-yield and ductile behaviour, affording it the capacity for permanent deformation and

energy absorption [13, 43-46]. Bone owes its ability to tolerate deformation beyond the elastic

limit to its collagen matrix. A healthy collagen network enables bone to resist crack growth and

fracture, preventing bone from becoming brittle and susceptible to fracture failure.

The ductility permitted by the tough collagen matrix contributes to the fracture toughness of

bone [46] by allowing high local strain energies to be absorbed by permanent deformation.

Intrinsic toughening mechanisms such as molecular uncoiling and fibrillar sliding fundamentally

rely on the collagen structure [34]. Altering collagen structure would alter the action of these

mechanisms. Collagen is also thought to be an important part of the constrained micro-cracking

[47, 46] and fibril bridging [8, 7] displayed by bone during transverse fracture. Some diseases

that affect the health of bone collagen can have serious effects on bone toughness. Osteogenesis

imperfecta is a disease that causes small mutations to collagen molecules that lead to defects in

the structure of the network. As a result, people with osteogenesis imperfecta suffer from

extreme bone fragility [48]. Willet et al. [10] recently performed a study where both collagen

connectivity and fracture toughness were measured for untreated normal bone, and bone with a

15

collagen network damaged by irradiation. Results showed that greater collagen connectivity was

associated with greater fracture toughness. This is line with previous work demonstrating

positive correlations between fracture toughness and collagen network connectivity [70-72].

1.5 Elastic-Plastic Fracture Mechanics

Elastic-plastic fracture mechanics (EPFM) builds and extends upon linear elastic fracture

mechanics (LEFM). In the case of the latter, it is essential that for any specimen, material, or

design being analysed, plastic or permanent deformation is limited to a very small region just in

front of the crack tip. If there is more plasticity than that, the assumptions behind the approach

are violated. EPFM extends the regime of validity to material and specimens that exhibit

plasticity on a much larger scale. Materials that experience crack blunting, the development of a

process zone in front and in the wake of the crack, and global yielding are appropriate for the

application of the EPFM approach.

Bone contains many inherent flaws and defects that either are cracks, can act like cracks, or can

nucleate cracks. Additionally, clinical failure of bone is often by fracture. Many studies have

attempted to measure bone fracture toughness, and many have taken an LEFM approach to bone

fracture testing [73-76]. This approach provides a single point value for describing the resistance

to fracture. Bone however, exhibits substantial post yield deformation capability [13, 43-46],

exhibits a number of (extrinsic) fracture mechanisms that act in the wake of the crack (see

section 1.4.2), and develops a process zone that can be on the same size scale as the specimen

itself [44, 49]. These indicate large amounts of permanent deformation, and that toughening

occurs as a crack propagates, meaning fracture resistance is dependent on crack growth. In turn,

this suggests that a linear elastic approach is inappropriate and invalid. The LEFM approach to

bone fracture has been questioned while taking an elastic-plastic approach to assessing its

toughness [77-80]. Results clearly show there is too much plasticity and crack growth dependent

toughness for LEFM to be appropriate and that an EPFM approach to evaluating bone’s fracture

toughness is more appropriate.

16

Figure 1.9 – Stress strain curve behavior under unloading conditions for nonlinear elastic

and elastic-plastic materials [50]

Nonlinear elastic and elastic-plastic stress-strain responses are quite similar. The sole difference

between the two is their response to an instance of unloading. A nonlinear elastic material will

trace the loading curve back to a zero-stress, zero-strain condition, whereas an elastic plastic

material will trace a line back to the horizontal axis with a slope of Young's modulus. These

responses are demonstrated in Figure 1.9. Rice [51] developed a method for evaluating the

energy release rate for a growing crack in a nonlinear elastic material. This method could be

extended to elastic plastic materials simply by assuming that the elastic plastic material would

not experience any unloading and equating the two responses.

17

Figure 1.10 – Contour around the crack tip for the line integral evaluation of the nonlinear

energy release rate of a growing crack [35, 51]

Rice’s method involves a path-independent line integral around the crack tip, the contour of

which is shown in Figure 1.10. Called the J-integral, it is equivalent to the energy release rate,

and is given by

J = ∫ (Wdy − T⃑⃑

∂u⃑

∂xds)

C

( 1.1 )

Where

𝑊 = strain energy density

�⃑� = stress vector along C

�⃑� = displacement vector components

𝑑𝑠 = increment along C

Equation ( 1.1 ) is an energy balance. The first term, Wdy, represents the decrease in stored

strain energy for a unit increment in crack growth. The second term, T⃑⃑ ((∂u⃑ )/ ∂x)ds, represents

the work added via stresses for the same increment of crack growth. The difference equates to

the total release of energy for an increment of crack growth. For instances when the material

being tested or analyzed is linear elastic, the J-integral provides an energy release rate equivalent

to the LEFM approach [36]. This makes sense because the J-integral is simply an extension of

LEFM to a more general scenario. The J-integral is a complex formula, and is not trivial to

calculate. Although it is path-independent, detailed information on the stress-strain field is

18

required. Rice et al. [52] showed that there are some configurations for which J can be evaluated

with only the force displacement curve. For these situations, J can generally be expressed in the

following manner:

J =

ηU

Bb ( 1.2 )

Where

𝜂 = configuration dependent constant

𝑈 = area under the force-displacement curve

𝐵 = specimen thickness

𝑏 = unbroken ligament length

Here, η is a dimensionless constant that depends on the configuration of the specimen. For a

single edge notched specimen in bending, η=2 [53].

1.5.1 Rising R Curve Behaviour

When bone fractures, it allows some slow and stable crack growth [54]. This behaviour is in

large part due to the extrinsic toughening mechanisms present [54, 55, 56]. As a crack begins to

lengthen, the extrinsic mechanisms begin to engage, increasing resistance to further crack

growth. As the crack driving force increments, the crack will slowly overcome the increase in

resistance. Once it does, it will begin to grow further, more extrinsic toughening will become

recruited, and the resistance to crack growth will increase again. Mathematically, for a crack to

be stable, the rate of change of the crack driving force with respect to crack growth must be less

than that of the crack resistance [36].

dJ

da≤

dJRda

( 1.3 )

Where J is the crack driving force as discussed above, and JR is the resistance to crack growth or

the J resistance. It is easy to see how this prevents catastrophic failure. As the crack length

increments, so does fracture resistance, requiring the driving force to increase for further crack

propagation. As long as resistance is growing faster than the driving force, complete failure is

prevented. Eventually, if the crack driving force does not reach a limit, the toughening

19

mechanisms will reach their final capacity and dJ/da will exceed dJR/da. When this happens,

instability is reached and leads to final fracture.

Figure 1.11 – Rising JR behaviour plotted against crack growth [50]

This type of behaviour is characteristic of many materials and is termed rising R curve or JR

curve behaviour [36, 50]. Figure 1.11 shows a plot of J against crack growth for a fracture

specimen demonstrating rising JR curve behaviour. The curve can be separated into four regions.

Region one is that of crack blunting. In this phase the intrinsic mechanisms dominate and

ductility prevents the material ahead of the crack from failing [50]. Blunting the crack tip causes

the root radius to expand however, so some effective crack growth occurs [36]. Region two is the

onset of real crack growth [50]. This point is indicated JIC, the crack-initiation fracture

toughness. Region three is where stable tearing occurs. In this regime extrinsic mechanisms

dominate and continue to drive up crack growth resistance [50]. Finally if instability is not

reached and all toughening mechanisms reach a final capacity, steady-state crack growth occurs

in region four [50].

20

A JR curve is considered a full characterisation of an elastic-plastic material’s fracture behaviour.

The crack-initiation fracture toughness, JIC, is the most important point on the curve. Although

dependent on the overall shape of the curve, it is a useful scalar for describing overall elastic-

plastic fracture toughness [50]. Tearing modulus, or modulus of toughness, is the slope of the

crack growth resistance with respect to crack length, dJR/da [36]. This measure is indicative of a

material’s ability to engage and recruit toughening mechanisms as cracking proceeds.

1.5.2 J Measurement

Early experimental measurements of JR curves, as demonstrated by Landes and Begley, required

several specimens [57, 58]. They used several identical specimens except each was induced with

an initial notch of a different length. Their approach is outlined schematically in Figure 1.12.

They loaded each specimen and recorded load-displacement curves and U, the area under those

curves. At chosen fixed displacements, U could be plotted against crack length. Since J is the

energy release rate of the material, for a specimen of thickness B, the J-integral can be evaluated

as

J = −

1

B(∂U

∂a)∆ ( 1.4 )

where a is the crack length and Δ is displacement [36]. J can be taken as the slope of the curve in

Figure 1.12 (b).

21

Figure 1.12 – Schematic outline of the approach taken by Landes and Begley [57, 58] to

make early experimental J measurements [36]

The experimental analysis for an approach similar to what Landes and Begley performed is

complicated, and requires multiple specimens [59]. Multiple specimens increase variation and

material requirements, both of which are compounded when dealing with biological tissue.

Variation is already quite high between biological samples, and material availability is at a

premium. A single specimen approach would be highly advantageous. Also, Equation ( 1.2 ) is

not valid for a growing crack [36]. Adjustments must be made for a growing crack unfortunately,

if a single specimen is to be used to elucidate an accurate JR curve.

22

To begin a different approach, Equation ( 1.2 ) can be broken down into its elastic and plastic

components [53]:

JTotal = Jel + Jpl ( 1.5 )

with

Jel =

K2(1 − υ2)

E ( 1.6 )

where K is the stress intensity factor and ν is Poisson’s ratio.

The elastic portion, Jel, is accurate as long as the current crack length is used for calculating the

stress intensity, and helps maintain consistency between approaches when conditions are near

linear elastic [59]. The plastic portion of the calculation is more involved. In 1981, Ernst et al.

[60] developed an iterative calculation that corrects for crack growth on the J measurement for

the previous step and on the incremental work done between iterations. Building upon that

procedure, Kanninen and Popelar [61] applied the work to the plastic portion of the J-integral:

Jpl(i) = [Jpl(i−1) + (

ηpl(i−1)

b(i−1)) (

Apl(i) − Apl(i−1)

B)] [1 − γpl(i−1) (

a(i) − a(i−1)

b(i−1))] ( 1.7 )

Where

𝜂𝑝𝑙 = configuration dependent plastic constant

𝛾𝑝𝑙 = geometry factor related to ηpl

𝐴𝑝𝑙 = area under the force-plastic displacement curve

𝑎 = crack length

This evaluation for the elastic and plastic components of the J-integral is utilized by ASTM

Standard E1820, a common standard for evaluating the JR curves of metals. The standard

provides a reliable mathematical procedure for single specimen testing method. Measurements

for force, displacement, and crack length (or unbroken ligament length) are required for this

approach to work. The practical challenge comes with applying a crack length measurement

technique that is sufficiently accurate and precise. A common method for metals is to apply

small unloading cycles to the specimen at intervals throughout the test. The unloading

23

compliance can be discerned from the force-displacement curves, and from that, crack length by

using empirical formulas available in standards and textbooks [36, 53]. Although this violates the

assumption of no unloading used to generate the J-integral in the first place, practically, it is a

viable method for obtaining crack lengths in a single specimen test [36, 53].

1.6 Effects of Irradiation

It has been demonstrated extensively that exposure to γ-irradiation can have a severe deleterious

impact on the mechanical integrity of bone tissue [10, 11]. This is dose dependent, of course. The

post yield behaviour of bone is highly degraded as a result of the irradiation, leading to

embrittlement of tissue [7, 8, 62]. Losses are reported in ductility, toughness, fracture toughness,

fatigue resistance, and ultimate strength [7, 8, 10, 47, 46, 62, 63]. Elastic properties however,

such as stiffness and yield strength, do not seem to be affected [10, 47]. The detriments to the

mechanical properties occur in a dose dependent fashion. That is, the greater the dose of

irradiation, the more severe the losses to the various measures of mechanical integrity [7, 8]. All

evidence suggests that the root cause for the embrittlement of the bone is the degradation of the

collagen network [3, 47], shown in Figure 1.13. There is likely damage to the non-collagenous

proteins that create an interface between the collagen and mineral [64]. While free radicals are

known to form in the mineral phase, the effect of this damage is uncertain and likely minimal

due to the very small size of the mineral crystals [65]. This requires further study.

Figure 1.13 – Diagram depicting the damage irradiation does to the connectivity of the

collagen network

24

γ-Irradiation considerably compromises the connectivity of the collagen network. Akkus et al.

[3] used gel electrophoresis to show that the collagen in irradiated bone is greatly degraded when

compared to normal controls. The smearing shown in the gel staining indicated reduced

quantities of intact collagen molecules and extensive damage in the irradiated bone. Heightened

collagen solubility, another indication of degradation, has been shown to increase in collagen

samples exposed to conventional irradiation sterilization doses [3, 16]. Thermal stability of the

collagen network, determined by the denaturation or melting temperature, is reduced with

irradiation sterilization [10, 47], again indicating damage to the network [66]. Burton et al. [47]

and Willett et al. [10] have used hydrothermal isometric tension tests (see Section 3.4) to assess

connectivity in collagen. The loss of connectivity in decalcified bone collagen was appreciable

when the bone was exposed to conventional sterilization doses of γ-irradiation.

Figure 1.14 – Fracture surface micrographs of cortical bone three point bending specimens

from Willett et al. [10]. N and I indicate non-irradiated and irradiated tissues, respectively.

An intact collagen network is necessary for ductility and post-yield behaviour in bone. Strong

positive correlations have been found between the mechanical properties of bone and the

connectivity of its collagen network [10, 47]. Akkus et al. and Willett et al. [3, 10] examined

fracture surfaces of both control and irradiated bone specimens under high magnification. Both

studies found the fracture surfaces of the non-irradiated bone showed arduous or tortuous crack

paths through the material, indicating high levels of energy were required to fail the material.

Fracture surface micrographs are shown in Figure 1.14. Irradiated bone exhibited relatively flat

25

fracture surfaces, indicating a far easier path to failure. Section 1.4.3 also discusses the role of

collagen in post-yield and energy absorbing processes.

1.7 Ribose Pre-Treatment Effects

We hypothesized that soaking the bone in a ribose solution prior to irradiation would protect the

collagen network from the damaging effects of irradiation and therefore improve the mechanical

properties of the graft. Ribose is a free-reducing sugar which when in open chain form, reacts to

form cross-links in collagen (see 1.3.2). Since oxidation of the free-reducing sugar is pivotal in

driving the reaction [67] and irradiation causes oxidation [11], the intended cross-linking during

sterilization could theoretically be advanced. There are other reducing sugars besides ribose,

glucose and fructose for example. The formation of cross-links requires the reducing sugars be in

an open chain, not their typical ring structure, and ribose more readily takes this form [68].

Additionally, at less than 300 Da, ribose is small enough to diffuse into the compact structure of

cortical bone [69]. It is not a dangerous substance, nor is it toxic. The cytocompatibility of

collagen that has been cross-linked with ribose is also good [70, 71]. Investigation by Burton

[11] found high temperature incubation of bone in a ribose solution effectively protects the

collagen connectivity and some of the mechanical properties of γ-irradiation sterilized bone.

Also confirmed was its superiority to the use of other sugars and treatment at room temperature.

26

Figure 1.15 – A summary of the protect results achieved to date using ribose pre-treatment

Some very encouraging results have been achieved using this treatment. In bovine bone,

protection has been observed in a wide array of mechanical properties. Complete protection was

observed for ultimate strength, 52% protection for ductility, 57% for work-to-fracture, 32% for

fracture toughness, and 75% and 100% protection for thermal stability and connectivity of the

collagen network, respectively, was achieved [10]. The protection levels for bovine bone metrics

are summarized in Figure 1.15. In human bone, many of the same properties have been protected

as well, save for fracture toughness, which has not yet been tested. Complete protection was

again observed for ultimate strength, 60% protection for ductility, 76% for work-to-fracture, and

100% protection for both the thermal stability and connectivity of the collagen network [10].

These results are summarized in Figure 1.15. The data from the collagen network analysis helps

to explain the origin of this protective effect. It is widely believed that the collagen network is a

large contributor to the post-yield performance of bone. The protection of the stability and

27

connectivity of the collagen network are understood to be an effect of cross-linking induced by

the ribose pre-treatment and perhaps during the irradiation process [10, 11]. Thus protection of

the collagen network is understood to be the driver for the protection of the bulk post-yield

mechanical properties [10, 11].

Figure 1.16 – Ribose pre-treatment may help protect connectivity by inducing the

formation of cross-links in irradiation-damaged bone collagen

Treatment of the tissue with a cross-linking agent prior to sterilization may prove to help

maintain net connectivity in the collagen network. Although additional cross-linking in normal

tissue can lead to brittleness [99-103], in tissue that has already been damaged however, the

added cross-links may link up main chain regions that were separated by irradiation and help

maintain a more continuous network [10, 11] (see Figure 1.16). Of course whatever the

treatment, sterility must be maintained, which means that irradiation of the tissue must be the

final step in the process. Breaking the seal on the sterilized tissue to treat it prior to implantation

would void the sterilization process and make any graft material unsafe.

28

Chapter 2 Objectives and Hypothesis

2.1 Objectives

The main objective of this study was to develop a method to measure the elastic-plastic fracture

toughness of cortical bone and use this method to evaluate the effects of the ribose pre-treatment

on the fracture toughness of irradiation sterilized bone. A secondary objective was to evaluate

bone collagen network connectivity and observe the consequences it has on fracture toughness.

Previous work by Willett et al. 2015 and Burton et al. 2014 [10, 47] showed that gamma-

irradiation and ribose pre-treatment along with gamma-irradiation results in weakened and

protected mechanical properties, respectively. Also shown was that bone collagen networks were

less connected overall in irradiated bone than normal bone material. The goal of this work was to

investigate in more detail the property of fracture toughness in bone and probe possible

relationships between it and the structure of the associated collagen network. There were four

objectives for this study:

1. Develop a method for measuring the JR curve behaviour for cortical bone material

2. Compare the fracture toughness of ribose pre-treated, irradiation sterilized bovine bone to

untreated normal and irradiated only controls.

3. Repeat an identical comparison on human bone

4. Evaluate the connectivity of the bone collagen and its impact on fracture toughness.

2.2 Hypothesis

We hypothesized that the fracture toughness of cortical bone would be greatly reduced by

irradiation and that ribose pre-treatment would protect some, but not all, of that loss with respect

to untreated normal bone. This is the same pattern that has been observed in previous work with

other mechanical properties using the same treatment. We also hypothesized that collagen overall

connectivity will correlate positively with fracture toughness, with high connectivity resulting in

more fracture resistant bone and degraded collagen resulting in bone that is less fracture resistant.

29

Chapter 3 Materials and Methods

Intact long bone diaphyses (bovine tibiae, and human femora) were machined into matched sets

of three nominally sized 50 x 4 x 4 mm rectangular beams. A matched set is a group of (3)

beams cut from directly adjacent material. All members of a set originate from the same location

(i.e. distal-anterior femoral diaphysis) in the same donor. Each beam in a set was randomly

assigned to one of three treatment groups: un-irradiated normal controls, the ‘N’ group, γ-

irradiation sterilized controls, the ‘I’ group, and a ribose-treated and irradiated group, denoted

‘R’. After treatment, the beams were non-destructively screened for their elastic modulus, and

notched to form single edge notched bending (SENB) fracture testing specimens. The beams

were fractured with a method that adheres closely to the method described by ASTM Standard

E1820 [53], with some adjustments made for this unique material. After the specimens were

fractured, the fracture surfaces were carefully removed for fractography and imaged with

scanning electron microscopy (SEM). One of the remaining fracture halves was decalcified in an

ethylenediaminetetraacetic acid (EDTA) solution to get decalcified bone collagen specimens.

The bone collagen was then characterized for its stability and connectivity using hydrothermal

isometric tension (HIT) testing.

3.1 Experimental & Treatment Design

The ribose pre-treatment consisted of soaking the bone graft materials in a ribose solution at high

temperature prior to irradiation. Optimal ribose treatment concentrations and conditions were

experimentally determined by Burton [11]. In the bovine study, the bone was soaked in 1.8 M

ribose. In the human study, the concentration was changed to a 1.2 M ribose solution. The

concentrations were the only difference in treatment between the two types of bone tissue.

After the machining process, the N group was simply kept frozen (-20°C) in saline soaked gauze

until testing. The R group was soaked in 10-15 ml of ribose solution of the appropriate

concentration in phosphate buffered saline (PBS) at 60°C for 24 hours. The I group underwent a

soak as well, in PBS only, also at 60°C for 24 hours. After the treatment, the R and I groups were

packed on dry ice and sent for irradiation. They were subjected to a 30 kGy dose (±10%) of

irradiation and returned within 24 hours of initial packaging. All groups were then kept at -20°C

30

until just prior to fracture testing. Figure 3.1 is a schematic depicting the treatment and testing

procedure

Figure 3.1 – Outline of the treatment and testing procedure for each treatment group

Prior to specimen preparation, data from Willett et al. [10] – a study that performed a fracture

study on irradiated and ribose-treated bovine bone – was used to estimate the required sample

size needed for acceptable statistical power. G*Power software (Heinrich-Heine-Universität-

Düsseldorf) [72] was used to perform the analysis. Even though the study used repeated

measures, the sample size calculation was done assuming un-paired data because the correlation

between treatments was not reported. This yielded a conservative estimate of the required sample

size. The inputs and outputs from the analysis with G*Power are shown in Figure 3.2. The effect

size field was determined with G*Power from the means and standard deviations of the two most

similar groups. Using a two-tailed t-test, the required power for the study was set to 0.8

(probability of type II error, β = 0.2). A type I error probability, α, of 0.05 was required, however

α = 0.0167 was used in the analysis because for this study p-values would be Bonferroni-

31

adjusted (see Section 3.6) for three multiple comparisons (α/3 = 0.0167). The required sample

size was determined to be 15.

Figure 3.2 – A summary of the a priori required sample size evaluation

For the bovine study, fifteen matched sets of three beams were used in accordance with the

analysis above. For the human study, a lack of tissue availability meant that only ten matched

sets were obtained. Bovine cortical bone was obtained from fresh tibia diaphyses of steers

approximately two years of age. Human bone was obtained from three cadaveric femora

originating from two donors, both male, aged 37 and 52 years.

3.2 Single Edge Notched Bending Fracture

Fracture testing for the present study was carried out with a single edge notched bending (SENB)

test specimen, a well understood and well characterised fracture testing geometry. The

dimensionless constants for evaluation of the J-integral are known for SENB, and it is a simple

test specimen to machine. For these reasons it was the chosen testing geometry. Shown in Figure

3.3, an SENB specimen is simply a three point bending specimen with a crack of known size

machined into the tension side of the beam. Dimension B is the width of the beam, W its height,

and a is the as-machined starting length of the crack. ASTM Standard E1820 [53] provides

detailed guidelines for the fracture testing of SENB specimens.

32

Figure 3.3 – SENB specimen geometry

ASTM Standards E1820 and D6068 [73] were followed as closely as possible for the testing

procedure. E1820 is a standard procedure for evaluating JR curves of metals with a single

specimen. Standard D6068 is based on Standard E1820 and provides guidelines for altering the

procedure to test polymers with multiple specimens. Obviously bone is neither a metal nor a

polymer, but combining suitable aspects of both standards yields a method that can be

appropriately applied to the testing of a strong ductile composite like bone. For example, D6068

calls for the sharpening of the starter crack with a razor blade, instead of fatiguing a starter crack

as found in E1820. In bone, fatigued starter cracks in the transverse direction tend to divert

perpendicular to the longitudinal direction [74]. In this case, the D6068 step of razor-notching

starter cracks (see Section 3.3.1) was adopted.

There were also some testing points that were not adopted from either E1820 or D6068. The

specification for the testing span in both standards is 4W, or four-fold the height of the test

specimen. Due to bone's composite nature, and its prominent anisotropy, a span of 10W was

used to avoid high shear stresses near the crack tip [75]. Additionally, because of equipment cost

and availability, traditional three point bending test hardware was used. The ASTM standards

call for the use of fracture bending jigs that use rollers for the outside supports. Bending jigs with

rollers were not available in our lab. The bone was wet when tested and the work lost due to

friction at the supports was assumed to be negligible. The recommended crack length

measurement technique was also altered, and is discussed below.

For consistency with preliminary point-value fracture testing performed in our lab [10], the

SENB configuration was kept identical to what was used previously. Although it is reasonable to

assume that crack initiation fracture toughness determined from a JR curve is a material property,

33

there is some geometry and size dependent variation reported [36]. The width and thickness of

the SENB specimens tested were both 4 mm, therefore the support span was 40 mm and the total

length of beams was roughly 50 mm. A nominal initial crack of 2 mm (a0 = 0.5W) was used, as

specified by standards and previous studies.

To evaluate JR curves, the force-displacement curve and a crack length measurement linked in

the time domain to the force displacement data are required. The fracture test was carried out

with an Instron Electropuls E1000 (Instron, Norwood, MA) mechanical testing device. The

SENB beams were loaded in displacement control at a rate of 0.2 mm/min. Force and load-line

displacement were recorded at every micron of crosshead travel with an Instron ±100 N load cell

(Model No. 2530-427). Displacement was tracked using the internal digital linear encoder

(±0.00041 mm) on the E1000 mechanical testing machine. Crack length was measured optically

using a Sony α SLT-A65V DSLR camera attached to a Micro Tech Labs LM 32x Macroscope

lens aimed at the crack tip. The optical crack length measurement technique is detailed in Section

3.2.1. The camera shutter was automatically fired throughout the test at 0.6 Hz with a timing

chip, detailed in Section 3.2.2. To ensure that the moment each photo was collected was recorded

in the test data file, the timing chip also sent a voltage signal to the Instron controller whenever

the camera shutter was open. High voltage signalled a closed shutter, and a voltage drop

signalled an open shutter. The testing setup is shown schematically in Figure 3.4.

34

Figure 3.4 – A schematic of the optical crack length measurement layout

3.2.1 Optical Crack Length Measurement

The recommended method for estimating crack length in the E1820 standard is to use the

unloading line compliance at regular intervals throughout the test. This technique involves

unloading the specimen by a small amount at pre-determined points in the test (see Figure 3.5).

The unloading slope, or unloading compliance, at these points is measured and can then be used

to determine crack length. Testing standards provide polynomial expressions for determining

crack length from compliance measurements [36, 53], but their appropriateness for testing bone

has been questioned [76]. Although the J-integral derivation assumes no unloading (see Section

1.5), in practice, these small unloading regimes do not greatly affect results in metals. Problems

arise when the material to be tested is visco-elastic. Visco-elasticity creates hysteresis loops, or

strain-rate dependent compliances, or both, in the force-displacement response during unloading,

rendering it very difficult to elicit the true compliance. Bone, particularly when notched, exhibits

visco-elastic behaviour [77] so testing was required to find an appropriate crack length

measurement method.

35

Figure 3.5 – A typical force-displacement curve for fracture testing of metals using

unloading compliance to measure crack growth. The inset shows the compliance taken

during unloading steps [36].

Preliminary fracture testing was conducted on eleven SENB specimens of the aforementioned

size. Each specimen was tested with two crack length measurement techniques employed. Both

unloading line compliance cycles and a preliminary optical technique were tried. The optical

technique was similar to the final one employed but used a much less powerful lens (Sony alpha

DT30mm F2.8 Macro). Upon examination, the unloading cycles exhibited large amounts of

hysteresis, non-linearity, and stress relaxation. The unloading slopes varied throughout the

loading and unloading cycles and the mean force decreased with each loading cycle. Taking

various representative slopes failed to yield reasonable or plausible crack length measurements.

The optical method also failed to yield usable crack length measurements. Using the macro lens,

the spatial resolution in the focus plane was ~4 μm per pixel. This resolution was not fine enough

to resolve small amounts of crack growth around crack initiation, but large amounts of crack

mouth spreading were detectable (see Figure 3.6). From these results, it was hypothesized that

more magnification could help resolve crack growth in fine enough detail.

36

Figure 3.6 – An example of photos taken during a fracture test with the low magnification

macro lens. Frame a) was captured as the test began and frame b) was captured just prior

to failure of the specimen. The arrows highlight discernible crack mouth spreading

Fracture tests were repeated without unloading cycles and with the lens upgraded to the Micro

Tech Labs 32x macroscope. An initial test with one specimen was conducted to see if crack

growth was at all resolvable. In the initial test, crack growth was certainly discernible, but the

exact location of the crack tip was ambiguous and contrasts between the crack and intact bone

material were low. Subsequent tests were then conducted one at a time while altering various

conditions to better resolve the growing crack in the captured images. Shutter speed, aperture,

lighting location and intensity, as well as dark ink coatings on the bone surface were all varied in

the proceeding tests. A setup of two 2-watt LED lamps (IKEA, Jansjö LED work lamp) in close

proximity to the crack tip, a shutter speed of 1/8th

of a second, aperture f-stop at 5.6, and a thin

coating of black ink on the bone surface was qualitatively best for optically detecting the crack.

The ink coating allowed for the pale bone material beneath the surface to show up in stark

contrast to the coated free surface when the crack began to grow even slightly (shown in Figure

3.7).

37

Figure 3.7 – Demonstration of how crack length measurements are made. The white arrow

indicates the crack showing through the ink coating. a) The length in pixels of the blue line

divided by the specimen thickness sets the measurement scale for the test b) The

established scale is then used to find the unbroken ligament length.

Crack length measurements using this method were done by first setting a scale with a feature of

known length in the photo, and then by using the scale to calculate the unbroken ligament length.

Each specimen’s W dimension was measured with a micrometer (Mitutoyo, 0-1” digital

micrometer, 0.001 mm resolution) at the location of the starter notch prior to testing. Shown in

Figure 3.7 a), this known length was then used to set the measurement scale for the test.

Measurement scales were generally in the range of 1325-1345 pixels/mm, providing a spatial

resolution of around 0.75 μm per pixel. After the measurement scale was set, unbroken ligament

lengths were measured using ImageJ software (US National Institutes of Health) [78] by

38

manually drawing a line from the crack tip to the upper free surface of the specimen (shown in

Figure 3.7 b)). The lengths were automatically calculated based on the resolution of the

measurement scale for each specimen and recorded. Each photo that had visible crack growth

from the previous frame and a discernible crack tip had a measurement taken.

3.2.2 Timing and Signalling Chip

To link each photo to the precise moment during the test in which it was taken, the Instron

controller was provided with a signal when the camera shutter was opened. This was

accomplished by using a Fairchild Semiconductor LM555 Single Timer chip. The chip was

activated by the Instron controller at the beginning of the fracture test by programming the

Instron digital output to turn on when the test began. When powered, the chip sent identical

square wave voltage signals to the camera shutter and the Instron data acquisition system. A

voltage drop (high to low) triggered the camera shutter and a baseline (low) voltage recording in

the test readout signified an open shutter.

39

Figure 3.8 – Circuit diagram of the timing chip and the Instron controller’s digital output

system. The digital output is set to ‘low’ to turn the output on. Vss (5 volts) powers the

timing chip when the output is on.

The timing chip and camera setup are shown in Figure 3.8. The resistors, RA and RB, and

capacitor, C1, determine the characteristics of the square wave generated by the LM555 Single

Timer. Capacitor, C2, is required for the circuit, but does not impact the output signal. From the

technical documentation [79] provided by Fairchild Semiconductor, the frequency of the timer

output is determined by the following equation:

f =

1.44

(RA + 2RB)C1 ( 3.1 )

with the time spent at low voltage determined by:

tL = 0.693RBC1 ( 3.2 )

40

Experimenting with frequencies beginning at 2 Hz and decrementing slowly by switching the

resistors in the circuit, a frequency of 0.6 Hz was found to be as fast as the camera could open

the shutter, record the image, and prepare to shoot again. Frequencies faster than 0.6 Hz resulted

in the timing chip signalling that a photo had been taken with an unprepared camera failing to

actually record an image. To obtain a signalling frequency of 0.6 Hz, a 5.0 kΩ resistor was used

for RA, two 4.7 kΩ resistors in series were used for RB, and two 100 μF capacitors were used for

C1 and C2.

3.2.3 Calculating JR Curves and Fracture Toughness

The final JR curves were generated using Equations ( 1.5 ), ( 1.6 ), and ( 1.7 ) and the force,

displacement, and crack length data. Each subsequent crack length measurement served as

another iteration point in the calculation of J. Poisson’s ratio was assumed to be 0.3 [10, 11], and

the elastic modulus for each individual specimen was screened prior to notching using a non-

destructive three-point bend test (see Section 3.2.4). The stress intensity factor, K, was calculated

as follows:

Ki = [

PiS

BW32

] f (ai

W) ( 3.3 )

where:

f (ai

W) =

3(ai

W)

12[1.99 − (

ai

W)(1 −ai

W)(2.15 − 3.93 (ai

W) + 2.7 (ai

W)2

)]

2 (1 + 2ai

W)(1 −ai

W)

32

( 3.4 )

and

𝑆 = test span

𝑃 = load

Equations ( 3.3 ) and ( 3.4 ) are a given in ASTM Standard E1820. The value of J at each

iteration was plotted against the measured crack growth at that point. Using nonlinear least

squares curve fitting in MatLab, the data was then fitted to power law of the form:

41

J = C1(Δa)C2 ( 3.5 )

where Δa is the measured change in crack length from a0, and C1 and C2 are the power law fit

coefficients. A typical JR curve and fit are shown in Figure 3.9. In addition to the complete curve

describing the fracture behaviour of the material, three point-measures were pulled from the data.

JIc-ASTM (shown in Figure 3.9), or the ASTM-defined crack initiation fracture toughness, was

calculated as described by ASTM Standard E1820, that is, the intersection of the power law fit

with a 0.2 mm offset construction line with a slope of twice the flow stress, σy, of the material.

Flow stress is defined as the average of a material’s yield and ultimate strength [53]. The flow

stresses for the normal, irradiated, and ribose-treated groups were assumed from the data

gathered using the same treatments in Willett et al. [10]. JIc-Obs, or the observed crack initiation

fracture toughness, was calculated differently. The first photo where any real crack growth was

discernible was deemed crack initiation. The value of the J-integral at this point in the test was

then taken as JIc-Obs. Figure 3.10 shows an example of how JIc-Obs was determined. Figure 3.10 a)

shows the starter notch just prior to crack initiation and Figure 3.10 b) shows the starter notch

just after. A small micro-cracking field can be seen in Figure 3.10 a) and in Figure 3.10 b) it has

appeared to coalesce into real crack growth. This was a more subjective measurement of JIc and

crack initiation but was useful for comparison with the ASTM definitions.

42

Figure 3.9 – A typical JR curve with a fitted power law and 0.2 mm offset construction line.

The final measure taken for evaluating fracture resistance was the tearing modulus, TR, or

modulus of toughness. The modulus of toughness is the slope of the JR curve and is usually

represented as a dimensionless quantity, tearing modulus [36]:

TR =

E

σ02

dJ

da ( 3.6 )

E is the elastic modulus of the material and σ0 is a representative stress, typically and in this case,

the yield stress was used [36]. The tearing modulus describes a material’s ability to engage

fracture toughness mechanisms near, and beyond, crack initiation. The modulus of toughness

was evaluated by the slope of a linear least squares fit to all of the data points on the JR curve

falling above 0.15 mm of crack extension, and then normalized with Equation ( 3.6 ). This

method of determining the modulus of toughness was chosen because it quantifies the overall

trend of JR curve from the region very close to crack initiation to the end of the fracture test.

43

Figure 3.10 – a) The crack tip just prior to the occurrence of JIc-Obs, the encircled area

contains a small micro-cracking field b) The crack tip just after the occurrence of JIc-Obs,

the encircled area contains a small crack – crack initiation has started

3.2.4 Modulus Screening

After machining (Section 3.3) and before notching (Section 3.3.1), each specimen was screened

for its elastic modulus. Due to the variation in bone properties with donor and location in the

body, an accurate elastic modulus measurement for each specimen helped eliminate variability in

fracture toughness measurements. Prior to notching, each specimen was non-destructively loaded

in three-point bending to half of the yield stress of irradiated bone (obtained from Willett et al.

[10]). The yield stress of irradiated bone was used because it is lower than normal bone, and is

therefore more conservative. A more conservative approach to mechanical loads on specimens

prior to actual testing reduces the risk of the screening process affecting results by incurring

damage of any kind. The loading slope of the screening test was taken as the bending modulus

and then used to determine the specimen’s elastic modulus with the following relationship:

Emeas =

MS3

4BW3 ( 3.7 )

where,

Emeas = measured elastic modulus

44

M = bending modulus or three-point bending loading slope

S= test span

The elastic modulus was then corrected for the compliance of the load string of the mechanical

testing device (Instron Electropuls E1000). The specimen and load string were treated as springs

in series, and the measured bending modulus as the total equivalent stiffness. The stiffness of the

load string of the three-point bend setup was tested by sliding the supports together (span of

zero) to support just the crosshead. The load string had a measured stiffness of 1.26 kN/mm. The

true elastic modulus could be then be determined by multiplying Emeas (Equation ( 3.7 )) by a

factor:

Etrue

Emeas=

1

1 −kLS

M

( 3.8 )

where,

kLS = load string stiffness

Etrue = true elastic modulus

3.3 Machining

All cortical bone specimens were cut from the diaphysis of bovine tibiae or human femora. In

each case, the specimen machining procedure was identical. Throughout the procedure, the bone

was kept irrigated with saline to prevent it from drying. All cutting was performed at room

temperature with thawed bone material, except for the rough cuts with the band saw, which were

performed while the bone was still frozen.

Beginning with an entire, frozen long bone and using a band saw (C.I.I. 14” wood cutting

bandsaw), both metaphyses were removed and the remaining diaphysis was mounted to a v-

block on a tenoning jig (General International). Shown in Figure 3.11 a), the diapysis was cut

into lengths of the desired specimen length, with a little bit of added material (~60 mm). With

the bovine tibiae, there was only enough diaphysis length for a single section. With the human

femora, there was enough diaphysis length for at least two, sometimes three sections. Again

using the band saw, the diaphysis sections were then split in half along the long axis of the bone.

The marrow was allowed to thaw and was removed, leaving two semi-cylindrical shells for each

45

diaphysis section, shown in Figure 3.11 b). The rough cuts on the diaphyses were performed in

this manner to yield raw material pieces small enough to handle in the subsequent machining

steps.

Figure 3.11 – Dashed lines indicate the plane of a cut a) The diaphysis is sectioned along its

length b) The diaphysis sections are split into halves c) ‘slabs’ are cut from the cortex d)

each slab is sectioned into beams

A Buehler Isomet 1000 metallurgical saw (Buehler, Lake Bluff, IL) with a diamond wafering

blade (Series 20 HC diamond, Buehler, Lake Bluff, IL) was then used in conjunction with a

bespoke work piece chuck to hold and remove 4 mm thick 'slabs' from the half-diaphyses. The

slabs are show in Figure 3.11 c) and d). Each 'slab' was cut from the straightest, thickest, and

flattest portion of the cortex available to ensure they yielded the most samples possible. To cut a

slab, a half-diaphysis was held by the chuck with the ideal part of the cortex parallel with the saw

blade. The work piece was fed until the blade lined up with the innermost portion of available

46

material, and the position was zeroed. The blade was then moved 4.8 to 5.0 mm towards the

periosteal face, depending on the amount of material available. The nominal thickness was 4

mm, and the excess 0.8 to 1.0 mm was to allow for polishing (0.1-0.3 mm) and blade thickness

(0.7 mm). Less available material required a thinner slab to be cut, while thicker cortices

provided more of a margin for error. The lid was shut and the work piece was allowed to meet

the running blade under gravity to machine the periosteal face of the slab. When the cut was

complete, the position of the work piece was returned to zero and the cutting process was

repeated to machine the endosteal face, parallel to the periosteal one.

Once the slab was completed, a diamond wire saw (Model 3241, Well) was used to cut parallel

beams from the slab. Using the same chuck, the slab was mounted so cuts were made orthogonal

to the machined faces, and along the original long axis of the bone (see Figure 3.11 d)). The slab

was fed so that the cutting wire lined up with the outermost available material, and the work

piece position was zeroed. After the first cut was made, the slab was indexed 4.4 mm (4 mm

nominal thickness, 0.1 mm of error allowance, and 0.3 mm thick diamond wire) and the next cut

was made. This left rectangular beams with a nominally 4 mm x 4 mm cross section about 50-60

mm in length. The beams were now ready for polishing, modulus screening (see Section 3.2.4),

and notching.

After machining, the faces of the beams were polished, to remove stress concentrations, in four

progressively finer steps. Each step was done by hand, for ten seconds, on each face of the beam

using wide circular motions and applying light pressure as evenly as possible across the

specimen. The first two steps were done with wet metallurgical polishing paper (BuelerMet2

abrasive paper, Buehler, Lake Bluff, IL) with grit ratings of 400 and 600, respectively. The final

two steps were done the same way, with a 5 μm and then a 1 μm, diamond suspension slurry

(MetaDi supreme, polycrystalline diamond suspension, Buehler, Lake Bluff, IL).

3.3.1 Crack Notching

The notching process for the SENB starter crack was divided into two steps, macro-notching and

micro-notching. The macro-notching process used a diamond wire saw (Model 3241, Well) to

machine a groove 1.8 mm in depth at the mid-span of the specimen in the circumferential

direction on the transverse (radial-circumferential) plane (see Figure 3.12). The micro-notching

process involved sharpening the tip of the groove with an ultra-sharp razor blade. This ensured

47

that the crack root-radius was as fine as possible. In ASTM Standard E1820 the crack sharpening

is done by cyclically loading the specimen to induce a starter crack through fatigue. Due to the

anisotropy of bone, attempts to create a starter crack in this fashion result in cracks that

propagate orthogonally to the direction of the groove [74]. This violates the conditions required

for the SENB geometry and would create inaccuracies in the equations used to calculate J for this

type of specimen. The solution to this problem was to use the aforementioned razor sharpening

technique [7, 10, 75]. The crack may not be as sharp as in metals tests, but it is as sharp as

practically possible for bone material.

Figure 3.12 – The chosen direction of fracture for this study

To perform the macro notching, the cutting wire of the saw was aligned to the mid-span of the

specimen machined in Section 3.3. The beam was held so that the cutting direction of the saw

was perpendicular to its long axis, and the wire was ensured to be as parallel as possible to the

beam face normal to the circumferential direction of the original bone. The beam was fed

towards the wire until the wire was observed, under a magnifying glass, to begin to contact the

surface. The work piece position was zeroed, the saw turned on, and the beam fed to a position

of 1.8 mm. This left a 1.8 mm long groove in the circumferentially transverse direction in the

beam.

48

Figure 3.13 – A close-up of the sharpened notch

Once the groove was machined, the beam was moved to the micro-notching jig. The micro-

notching jig was attached to the base of an Instron E1000 mechanical testing machine. The jig

held the beam with the groove opening towards the crosshead of the Instron machine. Mounted

on the crosshead was an ultra-sharp razor blade (American Line, Extra Keen Single Edge

Blades). Using a pipette, 1-3 drops of 1 μm diamond suspension slurry were allowed to flow into

the groove. The razor blade was guided down through the center of the groove until it contacted

the end. A load of 10-15 N was applied and the displacement reading on the mechanical testing

device was zeroed. The beam was then reciprocated, sliding back and forth along the length of

the razor. As the notch sharpened, the load decreased. After several passes, the 10-15 N load was

reapplied, the displacement was checked, and the procedure repeated. When the displacement

readout was 0.2 mm, the nominal crack length of 2 mm was reached, and the notch sufficiently

sharpened (see Figure 3.13).

3.4 Hydrothermal Isometric Tension Testing

After testing, one half of the fracture specimen, with the fracture surface removed, was placed in

a 0.5 M EDTA solution for decalcification. The specimens remained in solution at room

temperature while agitated using an orbital shaker table (Vision Scientific Co. Ltd.) for three

weeks. The solution was changed every second day during that time span. After three weeks, the

EDTA solution was checked for trace amounts of calcium to ensure that the specimens were

completely decalcified. Equal parts of the EDTA solution, ammonium hydroxide, and

49

ammonium oxylate were mixed together in a test tube. Turbidity in the mixture indicates the

presence of calcium. Since the mixture was totally transparent, the fracture halves were deemed

fully decalcified. After decalcification, the bone collagen was trimmed with a razor blade to

dimensions of roughly 1.5 x 1.5 x 20 millimetres.

Figure 3.14 – HIT tester design

50

The decalcified specimens were then tested with a custom-built hydrothermal isometric tension

tester. The device, shown in Figure 3.14, is based on a design profiled by Lee et al. [80] and

measures the thermo-mechanical behaviour of collagen under isometric constraints. The tissue

sample was held at a fixed length while attached to the load cell (Interface MB-5, Durham

Instruments, Pickering, ON). While held, the tissue was then placed in a bath of distilled water

heated from approximately 35°C to 90°C at a rate of around 1.5°C per minute. When heat is

slowly applied to collagen it will reach a temperature where it changes structure from a highly

crystalline triple helix to a random amorphous coil [81]. This structural change occurs when the

collagen begins to denature and induces shrinkage in the tissue [82, 83], or if it is held at a fixed

length, induces it to produces a contractile force [80, 84]. This contractile force was monitored

throughout the test by the load cell. A typical response of bone collagen is shown in Figure 3.15.

Both the rate of contraction and temperature at the onset of shrinkage are indicators of the

condition of the cross-links and the connectivity of the collagen network [66, 85], and are

characterized by the maximum slope of the contractile force response, simply termed maximum

slope, and the temperature at the onset of denaturation, or denaturation temperature, Td. More

cross-linking and greater connectivity in the collagen sample result in a greater maximum slope

[66, 80]. A greater denaturation temperature is indicative of a more thermally stable collagen

network and is also driven up by greater degrees of cross-linking in the tissue [66].

Figure 3.15 – An example HIT curve depicting the denaturation temperature and

maximum slope metrics

51

The force and temperature signals were recorded at a sampling rate of 2 Hz. The signal was

digitally filtered to remove noise and the force response was normalized by the initial cross-

sectional area of the tissue sample to generate an isometric (fixed length) stress. The slope of the

curve was determined with an eleven-point moving average of the gradient of the filtered and

normalized signal. The maximum slope was taken as the peak value of the moving average of the

gradient and is reported in units of MPa/°C. Denaturation temperature is not impacted by sample

geometry and is reported in degrees Celsius. It was calculated as the intersection between a

horizontal line through the minimum recorded isometric stress and a line tangent to the curve at

the location of the maximum slope.

3.5 Scanning Electron Microscopy

The fracture surfaces were carefully removed from the specimen halves using a diamond wire

saw (Model 3241, Well) and fixed, rinsed, and dehydrated in preparation for scanning electron

microscopy (SEM). For fixation, the surfaces were placed in a 2% glutaraldeyde solution in 0.1

M sodium cacodylate buffer (pH 7.3) for two hours. Then they were placed in a 0.1 M sodium

cacodylate buffer with 0.2 M sucrose (pH 7.3) for twenty minutes. Dehydration consisted of five

twenty-minute soaks in 70%, 90%, and three consecutive 100% ethanol solutions. Between each

soak, the surfaces were allowed to dry quickly in air, and then moved to the next solution. Once

the ethanol drying was finished, the fracture surfaces underwent critical point drying (Bal-Tec

CPD 030 Critical Point Dryer), were mounted to aluminium stubs with carbon tape (Leit-C Plast,

Plano GMBH, Wetzlar, Germany), and were sputter coated with gold for 90 seconds (Denton

Vacuum Desk II; Moorestown, NJ, USA). The imaging was performed with a scanning electron

microscope (XL30 ESEM; Philips, USA) with the accelerating voltage set to 20 kV and a spot

size of 4.

The regions of the fracture surfaces near the starter notch, the regions of stable tearing, were

imaged to look for signs, or lack thereof, of ductility and toughness mechanisms on the fracture

surface. Roughness created by crack deflection, and collagen fibril pullout and tearing are

indicators of ductile tearing [10, 11, 47], and their absence indicates these mechanisms were not

active. Observations from SEM provided qualitative data on small scale toughening mechanisms

supplemental to the fracture toughness measurements.

52

3.6 Statistical Data Analyses

3.6.1 Repeated Measures and Comparisons of Means

Test specimens were prepared in matched sets to facilitate the use of repeated measures statistics.

A matched set of three specimens is treated as a single test subject upon which three treatments

(normal control, irradiated control, and ribose-treatment) were applied. Repeated measures

statistics control for the variation between donor sites by eliminating the between-subject

variation, and comparing the variation due to the treatment to the residual within-subject

variation when performing a repeated measures analysis of variance (RM-ANOVA) [86]. An

example RM-ANOVA with m treatments and n subjects is shown in Table 3.1. Sum of squares is

shorthand for sum of squared deviations from the mean. The variables 𝑆�̅�, �̅�𝑗, and �̅� represent the

means for each subject, each treatment, and the entire data set, respectively, while 𝑋𝑖𝑗 denotes

the measurement for the ith

subject with the jth

treatment. The sum of squares divided by degrees

of freedom is known as the mean square, denoted MS.

Variation Source Sum of Squares Degrees of Freedom

Between-Subjects 𝑆𝑆𝐵−𝑇 = 𝑚∑ (𝑆�̅� − �̅�)2𝑛

𝑖=1

𝐷𝐹𝐵−𝑇 = 𝑛 − 1

Within Subjects 𝑆𝑆𝑊−𝑆 = ∑ ∑ (𝑋𝑖𝑗 − �̅�)2𝑚

𝑗=1

𝑛

𝑖=1

𝐷𝐹𝑊−𝑆 = 𝑛(𝑚 − 1)

Treatment 𝑆𝑆𝑇 = 𝑛 ∑ (�̅�𝑗 − �̅�)2𝑚

𝑗=1

𝐷𝐹𝑇 = 𝑚 − 1

Residual 𝑆𝑆𝑊−𝑆 − 𝑆𝑆𝑇 𝐷𝐹𝑅 = (𝑛 − 1)(𝑚 − 1)

F =SSTDFR

SSRDFT=

MST

MSR

Table 3.1 – A general repeated measures ANOVA example [86]

A confidence level of 95% (α = 0.05) was used to establish significance. The null hypothesis of

equal treatment means was rejected when the F-statistic corresponded to p-values less than 0.05.

Post-hoc comparisons of treatment means was conducted with paired t-tests and Bonferroni-

53

adjusted p-values (critical p-value = α/m) to determine which groups were detectably different

from one another. The Bonferroni correction was applied in this case because of the small

number of treatments. Typically Bonferroni is highly conservative, and when many treatments

are used this conservatism may make real differences difficult to detect [86]. The effect is

minimized with fewer treatments, and was deemed appropriately conservative for this study.

The group means were used to determine percent loss from irradiation and percent protection

from the ribose treatment for each metric. Percent loss is calculated as (XN-XI)/XN x 100 and

percent protection as (XR-XI)/(XN-XI) x 100. The mean for each group, specified by the

subscripts, is represented Xi.

3.6.2 Statistical Power Analysis

In instances where post-hoc analyses did not detect differences in the treatment means, a

statistical power analysis was conducted to assess whether reasonably more subjects would have

aided in detecting differences. G*Power software (Heinrich-Heine-Universität-Düsseldorf) [72]

was used to calculate statistical power post-hoc and the required sample size to obtain a

statistical power of 0.8 (β = 0.2), given the size of the treatment effect. The statistical power was

calculated for a comparison of means with a two-tailed paired t-test. Effect size was input as the

mean difference between treatments divided by the standard deviation of the difference. A

sample input for both the post-hoc evaluation of statistical power and the pseudo a priori

evaluation of required sample size in Figure 3.16 and Figure 3.17.

Figure 3.16 – An example G*Power output for a pseudo a priori required sample size

evaluation

54

Figure 3.17 – An example G*Power output for a post-hoc statistical power evaluation

55

Chapter 4 Results

4.1 Bovine Study Results

4.1.1 JR Curves & Crack Initiation Fracture Toughness: JIc-ASTM & JIc-Obs

A sample set of force-displacement curves are displayed in Figure 4.1. The specimen from the R

group experienced instability before reaching a force plateau, but not before reaching 0.2 mm of

crack growth. A representative set of JR curves from a single matched set are shown in Figure

4.2. The fracture responses were as hypothesized, with the irradiated (I) group showing less

toughness and less rising J behaviour (lower modulus of toughness; a flatter curve) than the other

two groups. The normal (N) group, as hypothesized, was the toughest, and the ribose-treated and

irradiated (R) group showed intermediate toughness. This hierarchy of N > R > I was maintained

for all values of crack growth. The means for both JIc-ASTM and JIc-Obs followed the same

hierarchy. For JIc-ASTM, statistical significance was seen across all groups. The loss of fracture

toughness resulting from γ-irradiation sterilization was 64% (p < 0.0001), and the ribose pre-

treatment protected the fracture toughness by 42% (p < 0.0001) (see Table 4.1 and Table 4.2).

For JIc-Obs, although the means maintained the hierarchy, there was no statistically detectable

difference between I and R suggesting no proof of protection of crack initiation toughness. The

sterilization process resulted in a statistically detectable 47% reduction (p = 0.0024) in fracture

toughness measured in this fashion. The JIc results are summarized graphically in Figure 4.3. The

group means, standard deviations, and repeated measures ANOVA p-values are displayed in

Table 4.1. The results of the post-hoc Bonferroni-adjusted p-values are summarized in Table 4.2.

The mean and standard deviation of the adjusted coefficient of determination for the power law

fits was r2=0.96 ±0.04. Data for individual tests is available in Table A.1.

Figure 4.4 contains images of the crack path, obtained with the macroscope during testing,

immediately prior to instability. The normal bone has several instances of crack path deflection

and branching, more than the irradiated or ribose-treated bone. It also forces the crack tip to

greater distances from the maximum driving force (a vertical plane passing through the center

plane of the initial notch) than the other two treatment group examples. The crack path in the

56

irradiated specimen undergoes fewer large deflections and remains close to the maximum driving

force. In the ribose-treated specimen, the crack tip is forced away from the maximum driving

force, but experiences only a few, relatively small, deflections. In the both the irradiated and

ribose-treated cases, micro-cracking (designated by white arrows) is limited.

Figure 4.1 – Force-displacement recordings from a matched set of bovine specimens

57

Figure 4.2 – JR curves for the bovine N, I, and R groups from a representative matched set

Figure 4.3 – A comparison of the two different crack initiation fracture toughness measures

in bovine bone. The error bars represent the standard deviation and an asterisk signifies a

statistically significant difference between groups (p < 0.05).

58

Treatment JIc-ASTM [mJ/mm2] Result JIc-Obs [mJ/mm2] Result

N 9.25 ±3.8 N/A 3.19 ±1.1 N/A

I 3.53 ±1.2 62% loss 1.70 ±0.58 47% loss

R 6.21 ±1.6 47% protection 2.12 ±0.91 None detected

RM-ANOVA p < 0.0001 p < 0.0005

Table 4.1 – Summary of the bovine crack initiation fracture toughness results. Data is

presented as the mean ± standard deviation

Comparison JIc-ASTM JIc-Obs

N v. I 1.5·10-5

0.0024

N v. R 0.0093 0.029

R v. I 5.5·10-5

0.52

Table 4.2 – Summarized Bonferroni-adjusted p-values for the comparison of group means

for crack-initiation fracture toughness

59

Figure 4.4 – Examples of the crack path in bovine bone before instability for each group.

White arrows indicate micro-cracking

4.1.2 Tearing Modulus (Modulus of Toughness)

The tearing modulus data also displayed the hypothesized hierarchy of N>R>I. Statistical

significance was seen across all three groups (p<10-5

). The complete data is presented in Figure

4.5 and Table 4.3. Irradiation resulted in an 80% reduction in tearing modulus (p<0.001) and the

ribose pre-treatment protected the tearing modulus by 27% (p<0.002). The post-hoc multiple

comparisons of means p-values are presented in Table 4.4. The p-values are Bonferroni-

corrected. Data for individual tests is available in Table A.1.

60

Figure 4.5 – The bovine bone tearing modulus means for each group. The error bars

represent the standard deviation and an asterisk signifies a statistically significant

difference between groups (p < 0.05 adjusted).

Treatment TR [-] Result

N 0.0389 ±0.024 N/A

I 0.0076 ±0.0042 80% loss

R 0.0160 ±0.0086 27% protection

RM-ANOVA p < 10-5

Table 4.3 – Summary of the tearing modulus data in bovine bone. The data is present as

the mean ± standard deviation

61

Comparison TR

N v. I 0.00069

N v. R 0.010

R v. I 0.00031

Table 4.4 – Bonferroni-adjusted p-values for the multiple comparisons of group means for

bovine bone tearing modulus

4.1.3 Collagen Characterization – HIT Testing

The connectivity metrics for the irradiated controls were statistically different from the N and R

groups (p<0.0001). Denaturation temperature, Td, and the maximum slope of the hydrothermal

isometric tension with respect to temperature of the decalcified collagen network were degraded

by 22% and 62%, respectively, due to irradiation sterilization. The N and R groups were not

statistically distinguishable for both of these measures. This shows high levels of protection for

both denaturation temperature and maximum slope with the ribose pre-treatment, at 90% and

97%, respectively. Characteristic test responses are show in Figure 4.6. Notice the low

temperature at which the contractile behaviour begins in the irradiated group, and the low rate of

isometric tension development that accompanies it. The group means, standard deviations, and

repeated measures ANOVA p-values are displayed in Table 4.5. The results of the post-hoc

Bonferroni-adjusted p-values are summarized in Table 4.6. Data for individual tests is available

in Table A.2.

62

Figure 4.6 – Representative HIT curves for decalcified bovine bone collagen from each

group

Treatment Td [°C] Result Max. Slope [kPa/°C] Result

N 71.8 ±3.4 N/A 67.2 ±20 N/A

I 52.6 ±1.2 27% loss 25.6 ±7.4 62% loss

R 69.9 ±3.5 90% protection 66.1 ±19 97% protection

RM-ANOVA p < 0.0001 p < 0.0001

Table 4.5 – A summary of the bovine HIT results. Data is presented as the mean ± standard

deviation

63

Comparison Td Max. Slope

N v. I 1.4·10-11

2.77·10-7

N v. R 0.11 1.0

R v. I 9.9·10-11

2.73·10-7

Table 4.6 – Summarized Bonferroni-adjusted p-values for the comparison of group means

for bovine HIT connectivity measures

The HIT results were also compared to the fracture toughness results. Plots of JIc-ASTM against Td

and maximum slope are shown in Figure 4.7. The comparison showed a general trend of greater

fracture toughness accompanying increases in both HIT measures. Even with full protection of

connectivity in the R group, there remained a deficit in the fracture toughness values.

Figure 4.7 – ASTM defined fracture toughness plotted against the HIT measures of both

denaturation temperature and maximum slope of isometric tension for bovine bone. The

error bars represent one standard deviation.

64

4.1.4 Scanning Electron Microscopy

Figure 4.8 – Representative SEM micrographs taken of the fracture surfaces of the bovine

test specimens

Representative SEM micrographs taken of the fracture test specimens are shown in Figure 4.8.

The irradiated surface is flatter than that of the normal and ribose pre-treated ones. It’s

comparatively featureless as well. The surface from the normal group displays more overall

depth of roughness (larger peaks and valleys – indicated by black arrows). The surface from the

ribose pre-treated specimen strikes a balance between the features of the other two groups. There

is substantial roughness similar to normal bone, but there are also some amorphous or flat

characteristics (indicated by white arrows).

65

4.1.5 Power Analysis

Table 4.7 contains the post-hoc computed values for β and the required sample size to achieve a

statistical power of 0.8 given the effect sizes from the results detailed above. Only instances

where there was failure to detect a statistically significant difference were examined. The

calculated β is high (indicating very low statistical power) for the undetectable differences in the

JIc-Obs and maximum slope measures. With the Td measurement, the statistical power was

intermediate for the comparison between the N and R groups, resulting in a required sample size

greater than twice as large as the current study (N = 15). The other two required sample sizes are

not feasible at 79 and 1428 for JIc-Obs and maximum slope, respectively.

JIc-Obs Max. Slope Td

Comparison β N0.8 β N0.8 β N0.8

N v. I - - - - - -

N v. R - - 0.98 1428 0.62 32

R v. I 0.86 79 - - - -

Table 4.7 – The calculated β and required sample sizes from the power analysis on the

bovine results. The required sample size is to achieve a statistical power of 0.8 (β = 0.2)

given the resulting effect size from each metric.

4.2 Human Study Results

4.2.1 JR Curves & Crack Initiation Fracture Toughness: JIc ASTM & JIc Obs

A sample set of force-displacement curves are displayed in Figure 4.9. The human specimens

had lower maximum loads and experiences long decreasing load regimes. The JR curves for the

human bone were also as hypothesized with the normal bone being the toughest and the

irradiated bone being the least tough. However in this experiment, the effect of irradiation was

much smaller and the ribose-treatment provided much more relative protection. The ribose-

treated JR curve is far less distinguishable from that of N group when compared with the bovine

study. A representative set from the experiment is shown in Figure 4.10. At longer crack growth

values, the curves display the N > R > I hierarchy. As hypothesized, the crack initiation fracture

66

toughness was greatest in the normal control group and least in the irradiated group for the

ASTM-defined crack initiation toughness. All of the crack initiation fracture toughness values

are summarized in Figure 4.11. The treatment effects are summarized in Table 4.8. The γ-

irradiation sterilization significantly reduced the JIc-ASTM by 48% (p = 0.0031). The effect of the

ribose-treatment was significant (p < 0.001 R relative to I) and protection was large enough that

the N and R groups were statistically indistinguishable. For JIc-ASTM, the ribose pre-treatment led

to 75% protection. The observed crack initiation toughness, JIc-Obs, group means displayed the

hypothesized hierarchy (see Figure 4.11), although none of them differed significantly from one

another (p = 0.12 – repeated measures ANOVA). The irradiation process and ribose pre-

treatment both had no statistically detectable effect on this metric. The post-hoc Bonferroni-

adjusted p-values for comparison of the group means are shown in Table 4.9. There was no post-

hoc analysis with JIc-Obs because the repeated measures ANOVA p-value was greater than 0.05.

The mean and standard deviation of the adjusted coefficient of determination for the power law

fits was r2=0.96 ±0.03. Data for individual tests is available in Table B.1.

Figure 4.12 shows images of the crack path obtained with the macroscope during testing. Since

the human bone did not often experience instability, see Section 5.1.2, the images were chosen at

advanced stages of crack growth. The normal bone experienced more frequent abrupt crack path

deflections than the irradiated bone. Although the crack path in the irradiated bone strays from

the maximum driving force, deflections are rare, small, and there is little evidence of micro-

cracking. The behaviour of the crack path in the ribose-treated group is more similar to the

normal group for human bone than bovine bone. There are frequent large deflections and a

similar extent of micro-cracking.

67

Figure 4.9 – Force-displacement recordings from a matched set of human specimens

68

Figure 4.10 – JR curves for the human N, I, and R groups from a representative matched

set

69

Figure 4.11 – A comparison of the two different crack initiation fracture toughness

measures in human bone. The error bars represent the standard deviation and an asterisk

signifies a statistically significant difference between groups (p<0.05).

Treatment JIc-ASTM [mJ/mm2] Result JIc-Obs [mJ/mm

2] Result

N 6.67 ±2.3 N/A 2.38 ±1.2 N/A

I 3.50 ±0.89 48% loss 1.40 ±0.94 None detected

R 5.88 ±1.1 75% protection 1.98 ±0.90 None detected

RM-ANOVA p < 0.0002 p = 0.12

Table 4.8 – Summary of the human crack initiation fracture toughness results. Data is

presented as the mean ± standard deviation.

70

Comparison JIc-ASTM

N v. I 0.0031

N v. R 0.84

R v. I 0.00067

Table 4.9 – Summarized Bonferroni-adjusted p-values for the comparison of group means

for crack-initiation fracture toughness

Figure 4.12 – Examples of the crack path in human bone for each group. White arrows

indicate micro-cracking

4.2.2 Tearing Modulus (Modulus of Toughness)

The tearing modulus of normal bone was approximately twice as great as that of both the I and R

groups. Despite the similarity between the means and standard deviation of the I and R groups,

only statistical significance was detected between the N and R groups (p = 0.038). The complete

data set is presented in Figure 4.13 and Table 4.10. Irradiation did not result in a statistically

detectable loss of tearing modulus (p = 0.16). The post-hoc multiple comparisons of means p-

71

values are presented in Table 4.11. The p-values are Bonferroni-corrected. Data for individual

tests is available in Table B.1.

Figure 4.13 – The human bone tearing modulus means for each group. The error bars

represent the standard deviation and an asterisk signifies a statistically significant

difference between groups (p<0.05).

72

Treatment TR [-] Result

N 0.0207 ±0.013 N/A

I 0.0101 ±0.0041 None detected

R 0.0101 ±0.0040 No protection

RM-ANOVA p < 0.02

Table 4.10 – Summary of the tearing modulus data in human bone. The data is present as

the mean ± standard deviation

Comparison TR

N v. I 0.16

N v. R 0.038

R v. I 1.0

Table 4.11 – Bonferroni-adjusted p-values for the multiple comparisons of group means for

human bone tearing modulus

4.2.3 Collagen Characterization – HIT Testing

Differences in denaturation temperature, Td, were statistically detectable across all groups, with a

16% decrease (p < 0.0001) due to irradiation and an 80% protection (p < 0.0005) due to the

ribose pre-treatment. Maximum slope also experienced a statistically detectable (p < 0.0002)

reduction due to irradiation of 41%. Again, connectivity was protected with the ribose pre-

treatment. The effect was such that the N and R groups were not detectably different (p ≈ 1) thus

protection of this measure was 100%. Characteristic HIT curves are shown in Figure 4.14.

Results as well as the treatment effects are summarized in Table 4.12. Table 4.13 contains the

Bonferroni-adjusted p-values for the post-hoc analysis comparing the group means. Data for

individual tests is available in Table B.2.

73

Figure 4.14 – Representative HIT curves for decalcified human bone collagen from each

group

Treatment Td [°C] Result Max. Slope [kPa/°C] Result

N 65.0 ±2.10 N/A 43.0 ±9.04 N/A

I 54.6 ±1.59 16% loss 25.5 ±4.00 41% loss

R 62.9 ±3.35 80% protection 41.8 ±6.71 93% protection

RM-ANOVA p < 0.0001 p < 0.0001

Table 4.12 – A summary of the human HIT results. Data is presented as the mean ±

standard deviation

74

Comparison Td Max. Slope

N v. I 5.6·10-6

0.00015

N v. R 0.025 1.0

R v. I 0.00033 0.0014

Table 4.13 – Summarized Bonferroni-adjusted p-values for the comparison of group means

for human HIT connectivity measures

Relationships between the HIT metrics of Td and maximum slope of isometric tension and crack

initiation fracture toughness were explored. Figure 4.15 shows fracture toughness as a function

of both Td and maximum slope. The relationship is highly linear and, similar to the bovine

results, the connectivity is almost fully recovered while the fracture toughness deficit remains.

This result is more subtle here with human tissue, since there was a greater protection of fracture

toughness and less protection of connectivity. Notice how the human specimens do not reach the

maximum slope and fracture toughness values that the bovine specimens do.

Figure 4.15 – ASTM defined fracture toughness plotted against the HIT measures of both

denaturation temperature and maximum slope of isometric tension for human bone. The

error bars represent one standard deviation.

75

4.2.4 Scanning Electron Microscopy

Figure 4.16 – SEM micrographs taken of the fracture surfaces of the human test specimens

Figure 4.16 shows three representative SEM micrographs of the fracture surfaces from each of

the different treatment groups. The SEM image for the normal bone shows roughness and more

variable topography (indicated by the black arrows). The irradiated control on the other hand, has

a distinct lack of definition, and a more amorphous appearance (indicated by white arrows). The

lamellae are more difficult to pinpoint, and the surface has less depth, or is not as rough as its

normal bone counterpart. The fracture surface from the R group displays mostly characteristics

of normal bone, showing a lot of roughness and ridges.

4.2.5 Power Analysis

Table 4.14 contains the post-hoc computed values for β and the required sample size to achieve a

statistical power of 0.8 given the effect sizes from the results detailed above. Only instances

76

where there was failure to detect a statistically significant difference were examined. The

calculated β is greater than 0.9 (statistical power < 0.1) in all cases except for the comparisons

between the N and I groups, where β was more intermediate at around 0.7. The intermediate

values of the calculated β resulted in feasible required sample sizes for JIc-Obs and tearing

modulus of 21 and 23, respectively. The other required sample sizes (where β > 0.9) were all

unfeasibly high – the lowest was 69 and the highest surpassed a half-million.

JIc-Obs JIc-ASTM Max. Slope TR

Comparison β N0.8 β N0.8 β N0.8 β N0.8

N v. I 0.74 21 - - - - 0.67 23

N v. R 0.95 151 0.92 83 0.96 241 - -

R v. I 0.91 69 - - - - 0.98 6.6·105

Table 4.14 – The calculated β and required sample sizes from the power analysis on the

human results. The required sample size is to achieve a statistical power of 0.8 (β = 0.2)

given the resulting effect size from each metric.

77

Chapter 5 Discussion, Conclusions, & Future Work

5.1 Discussion

5.1.1 Literature Comparison

The fracture toughness results from this study align well with other elastic-plastic fracture testing

conducted on human and bovine cortical bone. Barth et al. [8] evaluated JR curves for normal and

irradiated (70 kGy dose) human bone. They reported KJc values of 13.3 and 7.4 MPa∙m1/2

for

normal and irradiated tissue. KJ is an equivalent stress intensity factor for any given J

measurement, and is defined in ASTM Standard E1820 [53] as:

KJ = √(E

1 − ν2) J ( 5.1 )

where

E = Young’s modulus

ν = Poisson’s ratio

J = measured J-integral

For comparison, the equivalent KJ values were calculated using the JIc-ASTM measurements for

human bone. Normal and irradiated bone had critical stress intensities of 11.0 and 7.7 MPa∙m1/2

,

respectively, showing good agreement with the values from Barth et al. They did not measure

elastic modulus and instead used a characteristic Young’s modulus of 20 GPa, which is around

20% greater than the mean Young’s modulus measured for human bone in the present study

(16.2 GPa). Repeating the J and KJ calculations for the current study with a characteristic

Young’s modulus of 20 GPa yielded new KJ values of 11.6 and 8.1 MPa∙m1/2

for the N and I

groups, respectively. This did little to improve the agreement between their study and the present

one. Barth et al. used beams that were at most half as thick (B = 1.5-2 mm) as ours, and a span of

7.5 mm. Although J is usually taken as a material property, variation does occur with testing

geometry. The difference in measured toughness may be due to typical variation in results. Yan

et al. [75] reported an elastic-plastic fracture toughness for non-irradiated bovine bone of 6.6

78

mJ/mm2. Willett et al. [10] reported elastic-plastic toughness values of 4.5, 2.3, and 3.0 mJ/mm

2

for normal, irradiated, and ribose-treated and irradiated bone under the same treatment conditions

of the present study. Both studies used a simpler evaluation of Jc, where the critical load was

taken as the maximum load (Pmax), and no corrections for a growing crack were made. Using the

raw data from the present study and applying their methods, the critical J values calculated for

the N, I, and R groups in the bovine study were 5.4, 2.9, and 4.3 mJ/mm2, respectively. The

toughness in the normal group falls in between those reported by Yan et al. and Willett et al. The

values for irradiated bone agree, however there is some disagreement in the two ribose-treated

toughness values. Overall, the cortical bone toughness reported in the present study for both

human and bovine bone achieve good agreement with the values already presented in literature.

5.1.2 Connectivity and Toughness

The ribose pre-treatment was successful in protecting the fracture toughness of both bovine

(47%) and human bone (75%). Characterization of the collagen network of these tissues suggests

that the toughening is a result of a less degraded and more connected collagen network. The

normal and ribose pre-treated and then irradiated groups which demonstrated greater fracture

toughness than the irradiated specimens also displayed less degradation and greater connectivity

during HIT testing. This result experimentally supports the theory of collagen as a major

contributor to bone fracture toughness. Collagen is essential for several toughening mechanisms

present in bone such as intrinsic fibrillar sliding, and micro-cracking, and extrinsic fibril

bridging, and crack ligament bridging [10, 34, 87] (see Section 1.4). Presumably, a degraded

collagen network cannot contribute to these mechanisms to the same extent as a healthy network.

A weakened collagen structure would be less capable of absorbing energy in deformation, and

would provide weaker traction forces (across main cracks and micro-cracks) through a smaller

range of crack opening in the crack wake. These effects impact the J-integral directly (both

during crack growth initiation and propagation) and result in decreased fracture toughness.

Cross-linking of collagen has been shown to drive bone tissue towards more brittle behaviour

[99-103], such as in the case of aged tissue with AGEs. The situation with γ-irradiation sterilized

tissue is different because the cross-linking is occurring in a tissue that is already highly

damaged. In healthy tissue the added cross-linking may serve to constrain plastic behaviour [88,

79

89, 90], but in damaged tissue it may serve to repair the connectivity losses before contributing

to the constraint of plastic behaviour.

Figure 5.1 – Bovine and human ASTM-defined fracture toughness values plotted as a

function of HIT connectivity measures. The error bars represent one standard deviation

During testing, the bovine normal and ribose-treated groups almost always experienced sudden

instability and catastrophic failure after some stable crack growth. The other four groups

(normal, irradiated, and ribose-treated from human, and the irradiated bovine bone) all

demonstrated slow stable crack growth all the way to the end of the test, resulting in a wide range

of crack extensions. The catastrophic instability shown by the bovine normal and ribose-treated

groups suggests exhaustion of extrinsic toughening mechanisms. Figure 5.1 is a plot of both

human and bovine fracture toughness, JIc-ASTM, against the connectivity measures from HIT

testing. Incidentally, the two most connected groups, normal and ribose-treated bovine bone,

experienced fracture instability and had the highest JIc values. This aligns with the idea that

increases in collagen cross-linking can lead to apparently brittle behaviour in bone, perhaps

through trading plasticity for strength in the organic phase. Tradeoffs between strength and

ductility are documented in many metals as well [35]. This embrittlement is not so severe that the

bone no longer exhibits a rising JR curve, and in the case of normal bovine bone, it still

contributes to tissue that possesses higher crack initiation fracture toughness. But in the case of

the ribose-treated bovine bone, the added connectivity does not appear to contribute to any extra

crack growth initiation toughening when it is compared with the ribose-treated human bone.

80

For both types of bone, the HIT measures of degradation and connectivity of the ribose-protected

bone are very near that of normal tissue but there remains a deficit in the fracture toughness

compared to normal controls (see Figure 5.1). This suggests that there is still something further –

other than connectivity – that contributes to fracture toughness; that protecting the original

connectivity of the collagen network (prior to irradiation) is not sufficient to protect all of the

original fracture toughness. This discrepancy could stem from possible configuration differences

between the collagen networks of ribose-treated and normal bone. Although the HIT testing

shows the connectivity of the two groups is similar, they likely achieve this connectivity in

differing fashions. The collagen in normal bone has longer, intact main chains whereas the

ribose-treated bone is still presumably broken along its main chains but is more highly cross-

linked. The contribution of the collagen network to fracture toughness may be more complex

than simply being a question of overall connectivity. Primary protein structure may play an

important role, with intact main chains being particularly important.

The ribose protection was more pronounced in human bone. Normal human bone collagen shows

less connectivity than normal bovine bone, and the accompanying lower fracture toughness

suggests a less robust network in human bone to start. This could be the reason that the

irradiation has less of an effect on human bone, and ribose pre-treatment has a greater protection

effect. It is interesting to note that the connectivity and toughness of the irradiated groups in both

bovine and human bone were quite similar. The irradiation effect on the less robust human

collagen network may be less severe because there is less initial connectivity available to deplete.

Therefore the difference between the normal and irradiated controls becomes less pronounced.

81

Figure 5.2 – Bovine and human tearing modulus values plotted as a function of HIT

connectivity measures. The error bars represent one standard deviation.

Figure 5.2 examines tearing modulus as function of HIT measures. The effect of connectivity on

TR is similar to the effect on JIc-ASTM: even though much of the connectivity is protected via the

ribose pre-treatment, there remains a significant portion of tearing modulus that is not. Again,

this suggests that there is more characterization of the material phases required, beyond bulk

connectivity measures, to fully understand how it impacts fracture resistance and toughness

mechanisms. The protection of tearing modulus with ribose pre-treatment was less pronounced

than for fracture toughness, and in human bone, there was no protection at all. A lot of variation

accompanied the tearing modulus data, and more points along the curve after crack initiation

may help reduce the variation

5.1.3 Defining Crack Initiation

Importantly, the JIc-ASTM values are heavily dependent on the definition of when crack initiation

occurs. The onset of stable crack growth is somewhat arbitrarily defined (similar to yield strength

in stress-strain curves) [36] by the intersection of the JR curve with a construction line. The 0.2

mm offset for the construction line in ASTM Standard E1820 was developed for the testing of

ductile metals. The appropriateness of this offset for bone material is not known, but many

metals are able to tolerate much more crack extension than bone [35], and exhibit true crack

blunting behaviour. For some of the specimens tested in this current study, the maximum load

was reached before the initial crack had extended 200 µm. This was confirmed using the digital

82

imaging. On the other hand, many other test specimens did not reach peak load until well after

200 µm of crack extension. Pmax is often accepted as a de facto instability point (it can be

difficult to measure) [10, 75] and ideally crack growth initiation by definition happens before the

peak load is reached. The offset construction line is in place because the onset of crack growth is

difficult to detect (optically or otherwise). This combined with the large variation in behaviour

between bone specimens makes it difficult to suggest a more appropriate construction line offset

to measure JIc in bone. Instead of suggesting a construction line offset that more appropriately

designates JIc for bone tissue, it’s hypothesized that bone has a range of possible material

behaviour. Depending on the structure of the collagen network, it may be more or less brittle and

experience Pmax before or after 200 µm of crack growth.

5.1.4 Ribose Treatment Protection of Intrinsic and Extrinsic Toughness

The extrinsic toughening mechanisms of bone may be affected more than the intrinsic ones by

irradiation and the ribose pre-treatment. The first hint at this is the greater distinction between

treatment groups in the fracture toughness defined by ASTM than the observed crack initiation

toughness measurement. The JIc-ASTM measurement is taken after some stable crack extension,

and the engagement of extrinsic toughening mechanisms. Most of the toughening that is

measured with JIc-Obs happens with very little crack growth, meaning extrinsic mechanisms do

not have much of a chance to engage and contribute to the outcome. The JIc-ASTM measurement is

biased towards extrinsic toughening and the JIc-Obs is biased towards intrinsic toughening. The

statistical difference between treatment groups increases in both bovine and human for fracture

toughness measured at increasing values of crack growth. If JIc is measured using construction

lines offset at 0.05, 0.1, 0.15, and 0.2 mm, the p-values for the repeated measures ANOVA

decrease with the greater offsets (see Figure 5.3). This shows that the effects of ribose-treatment

and irradiation are less pronounced at small values of crack growth, where intrinsic mechanisms

dominate.

83

Figure 5.3 – The p-values of the repeated measures ANOVA for changing definitions of

crack initiation toughness. Lower p-values indicate greater effect size detected between the

groups

The tearing modulus data in the bovine study suggests greater protection of extrinsic mechanisms

as well. The tearing modulus describes a material’s ability to continue to engage extrinsic

toughening mechanisms after crack initiation has begun, and a greater tearing modulus suggests

more robust extrinsic toughening mechanisms are present. The fractography results also support

this idea. The SEM micrographs of the fracture surfaces of normal and ribose-treated bone show

evidence of crack deflection and tearing of the collagen structure that is noticeably absent in the

less descript surfaces of the irradiated controls, more indication that there are extrinsic

mechanisms present in ribose-treated bone than in irradiated-only tissue. The idea that the ribose

pre-treatment has a greater effect on extrinsic toughening mechanisms is not supported by the

tearing modulus data from the human study. There was no protection at all from the ribose pre-

treatment. This is an unexpected result because of the protection seen in so many plasticity

related mechanical properties [10], and because the ribose treatment was so effective for JIc in the

human study. Further study is required on this issue.

84

5.1.5 Testing Limitations

The testing method and the optical crack measurement technique have some limitations. Firstly,

the optical method is only capable of measuring the length of the crack at one free surface.

Composite materials often exhibit crack fronts with a degree of nonlinearity or non-uniformity

through the thickness of the test specimen (see Figure 5.4). Under the assumption that crack front

nonlinearity remains small, the optical measurement can serve as an accurate approximation of

the average crack length. This is also assumed with other crack length measurements, such as the

standard unloading compliance method. They too become inaccurate with increasing crack front

nonlinearity [53]. In fact, ASTM standards require confirmation of crack length uniformity.

Figure 5.4 – Test specimen cross-sections in the plane of the crack demonstrating two

different nonlinear crack front behaviours. The cross-hatched areas represent the

unbroken ligament

With biological tissues there is a large degree of non-uniformity, heterogeneity, and variation in

structure and composition between donors and donor locations, resulting in variation in

properties as well. Repeated measures statistics was implemented to help account for the effects

of variation between donors, but it remains a hurdle for achieving statistically significant results,

requiring large sample sizes. A lot of work was spent on securing as many specimens that can be

matched as possible so that repeated measures could be used, and even then the achieved

statistical power was low.

85

The results from the statistical power analysis indicate that most of the undetected differences in

group means are far too small to feasibly detect. Sample sizes were in excess of 60, which for

three treatment groups requires 180 test specimens. Often required sample sizes were many-fold

this amount. Three effect sizes however, appeared small enough that extra statistical power may

have been able to detect a difference between treatments: the differences between the N and R

groups for Td in bovine bone, and the N and I groups for TR and JIc-Obs in human bone. This is

unsurprising because they were all statistically significant differences in the opposite species.

5.2 Error Analysis

An error analysis was carried out to assess the uncertainty involved with the measurement of J.

The error associated with the basic measurements of the test method such as force, displacement,

specimen dimensions, and crack length were either obtained from certified calibration reports or

measured. If an error had to be measured, ten measurements were performed with the device or

method in question on a known quantity (i.e. gauge blocks for the Mitutoyo micrometer). The

standard deviation of the mean was multiplied for the t-statistic corresponding to a 99%

confidence interval (see Equation ( 5.2 )) for 9 degrees of freedom (10 measurements, ν = n-1) to

get the uncertainty for that measurement [91].

um = t [∑ (xi − x̅)2n

i=1

n(n − 1)]

12

( 5.2 )

In the above equation 𝑥𝑖 is each individual measurement, �̅� is the mean or known quantity, and 𝑛

is the total number of measurements taken. This approach was taken for assessing the error

associated with the Mitutoyo micrometer and the optical measurement of crack length. The

errors for each basic measurement are given in Table 5.1 as well as how those errors were

determined.

86

Measurement/Device Error Determination Method

Load Cell ±0.1% Certified Calibration

Digital Encoder ±0.00041 mm Certified Calibration

Micrometer ±0.0038 mm Equation ( 5.2 )

Crack Length ±0.0089 mm Equation ( 5.2 )

Table 5.1 – The errors for each basic measurement in the test method

For a general function of k variables, 𝑌 = 𝑓(𝑋1, 𝑋2, … , 𝑋𝑘), each with associated errors,

𝑒1, 𝑒2, … , 𝑒𝑘, the total error, 𝐸𝑌, is give by Equation ( 5.3 ) [91]. The errors for each of the

constituent quantities of the J-integral were computed using Equation ( 5.3 ), and then the

process was repeated with the new cumulative error values to find the total error associated with

J. The total error was calculated assuming 22 iterations of J, the most points for any single JR

curve in the present study. The results are summarized in Table 5.2. The total error on J was

determined to be ±0.06 mJ/mm2. This amounts to less than 2% error on the smallest average

measurement of ASTM-defined JIc (irradiated human bone – 3.50 mJ/mm2).

EY = √∑ (∂Y

∂Xi)2

ei2

k

i=1 ( 5.3 )

87

Quantity Error

Elastic Modulus, E ±610 MPa

Dimensionless Quantity, 𝒇 (𝒂

𝑾) ±0.011

Stress Intensity, K ±0.97 MPa∙m1/2

Plastic Energy Absorbed, Apl ±0.039 mJ

Elastic J, Jel ±0.013 mJ/mm2

Plastic J, Jpl ±0.014 mJ/mm2 per iteration

Total J (22 iterations) ±0.06 mJ/mm2

Table 5.2 – Summarized error for quantities used in the evaluation of the J-integral

It is reasonable to assume that there is a small amount of crack growth that occurs before the

macroscope is able to detect any. Very close to the crack tip, the crack wake may not spread the

surface, and the ink coating, enough to show the bone beneath. This would result in a small

length of crack near the crack tip that remains undetectable throughout the test, leading to crack

length measurements that are shorter than the actual length of the crack. This introduces a bias in

the results, so two assumptions were made concerning the undetectable crack length. The first

was that it was very small, and the second was that the bias error was repeatable between

specimens. The extent of undetected crack growth is difficult to measure, and more study on this

topic is required to fully characterize the accuracy and error of the optical crack length

measurement described in the present study.

5.3 Conclusions

The γ-irradiation sterilization process has severe deleterious effects on the fracture toughness of

cortical bone allograft material. These effects arise as a result of the irradiation process damaging

the structure of the bone at very small scales and, for example, reducing the overall connectivity

of bone’s collagen network, which plays an important role in many of bone’s fracture toughness

mechanisms. The ribose pre-treatment was successful in protecting some of the fracture

88

toughness from these harmful effects. It is believed that the pre-treatment protects the collagen

by limiting the damage to the nativity and connectivity through the formation of non-enzymatic

cross-links, which maintain the connectivity within the broken down main chain network. This is

a proof-of-concept that is meaningful for both tissue banks and surgeons. For tissue banks, it

presents the possibility of a higher quality product without sacrificing the use of their most

effective sterilization method. The success of the ribose pre-treatment is of clinical significance

because it shows the possibility of a more structurally sound and longer lasting graft, reducing

fracture failure of allograft-based structural reconstructions, revision surgery for graft failures,

and a reduction in pain for patients as a result.

The single-specimen fracture testing method to generate JR curves for cortical bone was

effective. The optical crack length technique was able to resolve the crack tip and the small

increments of crack extension necessary for a quality power law fit. The resulting fracture

toughness measurement agreed well with previously published fracture data for cortical bone

measured using an elastic-plastic testing approach. It achieved the objective of quantifying the

effects of the ribose pre-treatment on γ-irradiation sterilized cortical bone graft material and

confirmed our hypothesis.

The elastic-plastic fracture testing procedure presented generates JR-curves from a single

specimen by using an optical crack length measurement technique. This method reduces noise

due to variability between specimens and increases potential statistical power by permitting more

tests for any given amount of raw material. The optical crack length measurement technique

allows for the generation of JR-curves from a single specimen by linking crack length data in the

time domain with force and displacement readouts from the fracture test. Additionally, the

optical technique permits the testing of hydrated specimens, and tests are short enough in

duration (< 10 min) that the specimens do not dry out by the end of the test. Measuring the crack

length in this way eliminates the effects of visco-elasticity on the crack length measurements by

dispensing with the need for loading cycles, like in the unloading compliance technique.

Determining an elastic modulus for each specimen prior to fracture further reduces noise and

improves accuracy by taking into account the natural variability of the elastic properties of bone.

89

5.4 Future Work

Work remains in improving the fracture testing method and understanding the precise

mechanisms behind the effects of the ribose pre-treatment. The conclusions reached in this study

regarding the state of the collagen network are based on overall measures of general thermo-

mechanical behaviour, deductions from what is known about cross-link structure and formation

in collagen, and previous work conducted on this topic in our lab. Further study is required to

gain more insight into the mechanism behind the observed protection from the ribose treatment.

The fracture testing method is effective, but the crack length measurement is coarse. Work

remains on fine-tuning the method so it can be used to its full potential. Further study beyond

static fracture, into cyclic loading conditions, would also be useful as bone in vivo is not

statically loaded. With these shortcomings in mind, and an overall objective of implementing the

ribose pre-treatment in clinical scenarios, we recommend some future work:

If the ribose pre-treatment is to be used clinically, more understanding of the mechanisms behind

the toughening effect is required. All the specific types of cross-links formed, and whether they

are formed both before and during irradiation remain unclear.

Work must be done towards scaling up the ribose treatment to perform properly on large graft

sizes; sizes that may actually be used in clinical applications such as large diaphysis segmental

defects. Ensuring the ribose can evenly diffuse though the full wall thickness of a sample of that

size is necessary to ensuring the properties throughout the graft are protected.

It is important to ensure that the treatment also has no effect on the remodelling capacity of the

graft material. Experiments on in vivo reconstructions using treated and traditional graft

materials can be conducted to compare the remodelling characteristics of each.

Further work on the fracture testing method can be done to improve the precision and resolution

of the optical crack measurement. Preliminary attempts were made at automating the crack

length measurement with graphical analysis tools. These attempts were not successful, with

image noise, specimen variation, and deviations from ideal conditions being the main

contributing factors. The manual crack measurement method was adequate, but automating the

measurement would make it more repeatable and less subjective. Testing under different lighting

conditions, along with a less reflective and more even coating method are possible measures to

90

help reduce noise in the captured images. Images with less noise and sharper contrasts would

allow for automated software methods to more easily and reliably detect the crack and the upper

free surface of the specimens, permitting consistent, precise, and accurate crack length

measurements.

The present study was confined to static fracture. In vivo bone is cyclically loaded, therefore its

fatigue fracture characteristics are also important. Subsequent fatigue fracture experiments using

the same treatments should be conducted to determine the effect of irradiation on fatigue

properties and assess the viability of the ribose pre-treatment for clinical use. Some of the

methodology described in the present study may prove useful for such experimentation.

91

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104

Appendix A Bovine Data Tables

Table A.1 – Summary of the fracture data by specimen for the bovine study

Set Group a0

[mm]

B

[mm]

W

[mm]

E

[MPa]

PMAX

[N]

C1

[N/mm(1+C2)

]

C2 JIc-ASTM

[mJ/mm2]

JIc-Obs

[mJ/mm2]

TR

1 I 2.112 4.089 4.066 18,700 30.8 3.7 0.06 3.43 2.32 0.00214

1 N 1.894 4.077 4.063 19,990 58.9 30.9 1.00 6.73 2.35 0.02152

1 R 1.958 4.056 4.069 20,053 51.8 19.6 0.64 7.45 1.11 0.01340

2 I 2.001 4.203 4.074 20,780 31.6 7.2 0.59 2.89 1.74 0.00531

2 N 1.956 4.186 4.146 20,443 53.7 4.1 0.13 3.10 2.58 0.00495

2 R 2.049 4.192 4.064 20,164 42.1 17.2 0.81 4.91 3.27 0.01136

3 I 2.099 4.172 4.106 19,068 28.9 10.7 1.00 2.22 0.93 0.00589

3 N 2.047 4.181 4.105 19,103 44.1 10.9 0.40 5.31 2.45 0.01141

3 R 2.182 4.164 4.075 19,104 35.1 15.0 0.80 4.29 1.81 0.01028

4 I 2.066 4.085 4.146 19,315 34.7 7.3 0.41 3.87 1.89 0.00584

4 N 2.030 4.095 4.057 20,396 58.2 23.9 0.45 9.33 4.01 0.08239

4 R 2.036 4.072 4.115 19,544 44.0 17.1 0.82 4.78 1.68 0.01081

5 I 2.065 4.081 4.021 20,665 36.8 11.0 0.49 5.19 1.44 0.00913

5 N 2.077 4.084 4.030 22,076 54.5 41.1 1.00 9.23 3.68 0.03963

5 R 2.038 4.076 4.096 21,844 52.7 11.7 0.39 6.40 3.17 0.00974

6 I 1.987 4.074 4.074 20,256 34.1 10.0 0.91 2.40 1.13 0.00805

6 N 2.127 4.033 4.113 20,963 44.5 15.2 0.46 5.09 2.72 0.07427

6 R 2.135 4.079 4.097 20,891 41.2 22.2 1.00 4.71 1.33 0.01716

7 I 2.128 3.756 4.145 21,105 27.0 5.3 0.45 2.62 1.46 0.00478

7 N 2.200 3.858 4.118 21,237 53.6 24.8 0.49 12.17 4.60 0.07080

7 R 2.046 4.005 4.164 20,847 52.6 12.1 0.33 7.30 3.35 0.01725

9 I 2.134 4.239 4.028 20,898 27.2 3.3 0.19 2.41 1.63 0.00059

9 N 2.113 4.243 4.115 20,504 56.3 29.5 0.85 8.21 2.68 0.03127

9 R 1.982 4.259 4.116 19,606 47.0 15.4 0.72 5.07 1.77 0.00914

10 I 2.113 4.237 4.059 21,329 39.6 22.6 0.78 6.32 2.49 0.01277

10 N 2.173 4.228 4.121 20,953 71.9 65.3 0.90 18.64 4.25 0.04824

10 R 2.116 4.246 4.158 21,366 60.9 28.9 1.00 6.25 0.33 0.02928

11 I 2.033 4.171 4.073 20,577 36.7 11.1 0.62 4.25 2.28 0.00972

11 N 1.943 4.165 4.243 20,484 84.6 43.2 0.88 11.94 2.86 0.02961

11 R 1.939 4.206 4.069 21,687 60.2 22.3 0.53 10.20 1.82 0.02224

12 I 1.999 4.184 4.048 20,001 40.2 7.7 0.36 4.40 2.40 0.01710

12 N 2.050 4.203 4.100 21,307 65.0 44.3 0.91 11.60 3.14 0.03262

12 R 2.016 4.199 4.372 21,745 80.0 24.7 0.74 8.08 3.46 0.04032

105

Set Group a0

[mm]

B

[mm]

W

[mm]

E

[MPa]

PMAX

[N]

C1

[N/mm(1+C2)

]

C2 JIc-ASTM

[mJ/mm2]

JIc-Obs

[mJ/mm2]

TR

13 I 1.909 4.108 4.097 19,609 36.6 9.1 0.79 2.64 1.98 0.00749

13 N 2.084 4.105 4.069 20,491 50.3 18.3 0.37 8.24 1.46 0.02193

13 R 2.005 4.103 4.078 22,211 54.7 16.4 0.68 5.79 1.96 0.01293

14 I 1.947 4.097 4.122 18,806 36.1 8.9 0.69 3.02 1.59 0.00717

14 N 1.999 4.103 4.039 20,739 47.8 14.9 0.56 6.33 2.58 0.01310

14 R 1.993 4.198 4.147 20,265 46.4 17.0 0.84 4.63 2.63 0.01136

15 I 2.036 4.492 4.113 18,819 37.6 8.1 0.40 4.36 1.77 0.00607

15 N 2.001 4.478 4.063 19,921 61.5 45.6 0.95 11.24 2.87 0.06700

15 R 1.934 4.512 4.117 21,588 53.9 16.5 0.68 5.83 2.28 0.01259

16 I 1.960 4.520 4.095 20,275 37.2 14.1 1.00 2.94 0.43 0.01213

16 N 1.933 4.530 4.330 21,628 109.6 45.4 0.93 11.56 5.58 0.03537

16 R 2.059 4.522 4.110 22,851 55.1 13.9 0.36 7.43 1.76 0.01235

Set = matched set ID

Group = treatment group

a0 = initial crack length

B = specimen width

W = specimen thickness

E = elastic modulus

PMAX = peak load

C1 = first power law fit constant

C2 = second power law fit constant

JIc-ASTM = ASTM-defined crack initiation fracture toughness

JIc-Obs = observed crack initiation fracture toughness

TR = tearing modulus

Table A.2 – Summary of the HIT data by specimen for the bovine study

Set Group Td

[°C]

Max.

Slope

[kPa/°C]

1 N 66.3 51.1

1 I 52.2 15.7

1 R 70.0 42.7

2 N 66.7 49.3

2 I 53.5 34.2

2 R 65.5 45.5

106

Set Group Td

[°C]

Max.

Slope

[kPa/°C]

3 N 68.0 38.1

3 I 51.0 12.8

3 R 70.9 50.9

4 N 70.6 54.6

4 I 53.1 17.0

4 R 67.4 54.8

5 N 70.7 57.1

5 I 53.5 19.0

5 R 63.1 45.6

6 N 70.0 49.2

6 I 52.0 24.9

6 R 69.9 55.1

7 N 70.7 62.1

7 I 51.8 26.6

7 R 64.6 57.8

8 N 67.0 54.9

8 I 51.2 27.8

8 R 62.6 49.8

9 N 76.1 75.3

9 I 50.9 29.0

9 R 72.9 65.1

10 N 74.8 109.0

10 I 52.8 39.5

10 R 71.2 80.1

11 N 73.1 91.0

11 I 50.7 24.8

11 R 68.4 71.3

12 N 74.7 77.8

12 I 52.9 31.8

12 R 72.8 104.6

13 N 71.1 59.5

13 I 54.1 23.1

13 R 71.0 65.0

14 N 71.4 55.7

14 I 53.4 25.8

14 R 72.6 73.0

15 N 77.1 84.2

15 I 54.7 25.1

15 R 74.1 90.7

107

Set Group Td

[°C]

Max.

Slope

[kPa/°C]

16 N 75.7 94.4

16 I 52.0 33.1

16 R 74.4 88.9

Set = matched set ID

Group = treatment group

Td = denaturation temperature

Max. Slope = peak slope reached

108

Appendix B Human Data Tables

Table B.1 – Summary of the fracture data by specimen for the human study

Set Group a0

[mm]

B

[mm]

W

[mm]

E

[MPa]

PMAX

[N]

C1

[N/mm(1+C2)

]

C2 JIc-ASTM

[mJ/mm2]

JIc-Obs

[mJ/mm2]

TR

1 I 2.150 4.203 3.922 15,610 21.4 8.5 0.79 2.47 0.67 0.00915

1 N 2.051 4.166 3.985 16,387 35.9 15.9 0.64 6.10 2.44 0.01922

1 R 2.203 4.077 3.992 16,716 27.2 7.4 0.24 5.09 3.06 0.00668

3 I 2.144 4.144 4.034 14,670 24.6 8.7 0.75 2.68 0.54 0.00987

3 N 2.136 4.182 4.040 14,510 28.6 10.1 0.57 4.20 1.42 0.00862

3 R 2.110 4.059 3.994 14,990 29.9 10.9 0.42 5.77 2.19 0.00901

5 I 2.180 4.125 4.110 16,728 30.5 10.5 0.65 3.83 0.59 0.01228

5 N 2.169 4.125 4.041 16,588 39.8 23.9 0.57 10.49 3.72 0.03563

5 R 1.985 4.113 4.048 17,245 38.0 14.2 0.65 5.22 0.32 0.01251

7 I 2.118 4.272 4.069 15,996 26.8 8.5 0.89 2.11 0.69 0.01234

7 N 2.244 4.236 4.061 17,405 34.3 16.7 0.55 7.42 1.59 0.01429

7 R 2.103 4.347 4.091 15,976 38.5 10.9 0.29 7.04 2.80 0.01258

8 I 2.038 4.265 4.117 15,831 29.9 6.9 0.49 3.24 1.60 0.00716

8 N 2.279 4.243 4.008 16,491 23.7 10.1 0.71 3.33 1.31 0.01112

8 R 2.057 4.238 4.060 17,968 34.1 12.2 0.65 4.48 1.75 0.00908

9 I 2.222 4.029 4.073 16,544 25.7 7.2 0.48 3.43 0.42 0.01976

9 N 1.992 4.030 4.102 17,001 41.2 13.9 0.59 5.70 1.98 0.01282

9 R 2.041 4.022 4.081 15,977 37.6 10.6 0.38 5.97 2.64 0.00735

10 I 2.090 4.392 4.000 15,323 27.9 8.9 0.47 4.30 2.79 0.00795

10 N 2.222 4.312 4.012 18,085 33.7 17.8 0.61 7.24 3.01 0.01934

10 R 2.003 4.306 3.944 16,557 28.2 7.6 0.33 4.59 2.28 0.00469

11 I 2.186 4.165 4.113 15,025 30.2 11.2 0.56 4.80 2.77 0.01010

11 N 1.944 4.141 4.099 16,082 46.2 20.7 0.76 6.68 3.17 0.02150

11 R 1.885 4.125 3.997 15,909 39.7 13.9 0.39 7.74 1.33 0.01223

12 I 2.088 4.273 4.108 14,022 26.9 7.5 0.45 3.71 1.87 0.00661

12 N 2.054 4.378 4.094 15,203 36.2 13.9 0.62 5.41 0.73 0.01207

12 R 2.070 4.401 4.121 15,974 35.1 10.6 0.42 5.61 0.82 0.00827

13 I 2.252 4.205 4.085 15,906 25.5 7.5 0.34 4.47 2.08 0.00562

13 N 2.241 4.265 4.022 17,208 37.8 43.1 1.00 10.16 4.40 0.05200

13 R 2.249 4.255 4.119 16,719 38.0 19.1 0.64 7.33 2.55 0.01868

Set = matched set ID

Group = treatment group

a0 = initial crack length

B = specimen width

109

W = specimen thickness

E = elastic modulus

PMAX = peak load

C1 = first power law fit constant

C2 = second power law fit constant

JIc-ASTM = ASTM-defined crack initiation fracture toughness

JIc-Obs = observed crack initiation fracture toughness

TR = tearing modulus

Table B.2 – Summary of the HIT data by specimen for the human study

Set Group Td

[°C]

Max.

Slope

[kPa/°C]

1 N 63.2 30.7

1 I 55.7 23.8

1 R 60.4 35.6

3 N 64.8 31.9

3 I 57.7 22.5

3 R 64.3 35.2

5 N 64.8 47.7

5 I 55.4 30.4

5 R 61.1 41.9

7 N 63.0 43.2

7 I 54.0 25.7

7 R 62.7 38.6

8 N 68.0 46.0

8 I 52.3 18.6

8 R 69.3 48.7

9 N 68.5 54.6

9 I 53.2 29.5

9 R 67.0 52.9

10 N 61.7 46.3

10 I 53.5 27.3

10 R 57.8 33.3

11 N 65.2 44.3

11 I 55.3 30.1

11 R 62.1 45.2

110

12 N 65.1 30.9

12 I 55.4 21.0

12 R 63.9 38.0

13 N 65.7 54.7

13 I 53.4 25.8

13 R 60.8 48.5

Set = matched set ID

Group = treatment group

Td = denaturation temperature

Max. Slope = peak slope reached