MECHANICAL PROPERTIES OF SPINAL CORD GREY

MATTER AND WHITE MATTER IN CONFINED

COMPRESSION

by

Justin Junehung Yu

B.A.Sc., University of Waterloo, 2015

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

in

THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES

(Biomedical Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA

(Vancouver)

December 2019

© Justin Junehung Yu, 2019

ii

The following individuals certify that they have read, and recommend to the Faculty of Graduate

and Postdoctoral Studies for acceptance, a thesis entitled:

Mechanical properties of spinal cord grey matter and white matter in confined compression

submitted by Justin Junehung Yu

in partial fulfillment of the requirements

for

the degree of Master of Applied Science

in Biomedical Engineering

Examining Committee:

Thomas Oxland, Department of Orthopaedics & Mechanical Engineering

Supervisor

Peter Cripton, Department of Biomedical Engineering & Mechanical Engineering

Supervisory Committee Member

David Wilson, Department of Orthopaedics & Mechanical Engineering

Supervisory Committee Member

iii

Abstract

To better understand the link between spinal cord impact and the resulting tissue damage,

computational models are often used. These models typically simulate the spinal cord as a

homogeneous and isotropic material. Recent research suggests that grey and white matter tissue

differences and directional differences, i.e. anisotropy, are important to predict spinal cord

damage. The objective of this research was to characterize the mechanical properties of spinal

cord grey and white matter tissue in confined compression.

Spinal cords (n=11) from the thoracic and cervical regions of pigs (Yorkshire and Yucatan) were

harvested immediately following euthanasia. The spinal cords were flash frozen (60 secs at -80

oC) and prepared into four types of test samples: grey matter axial, grey matter transverse, white

matter axial, white matter transverse. For each sample type, 2 mm diameter biopsy samples were

collected, thawed, and subsequently tested with a custom confined compression apparatus. This

was performed within 6 hours of euthanasia, minimizing time post-mortem effects. All samples

were compressed to 10% strain at a quasi-static strain rate (0.001/sec) and allowed to relax for

120 secs. A quasi-linear viscoelastic model combining a first-order exponential with a 1-term

Prony series was used to characterize the loading and relaxation responses respectively. The

effect of tissue type (grey matter vs. white matter), direction (axial vs. transverse), and their

interaction were evaluated with a two-way ANOVA (p<0.05) with peak stress, aggregate

modulus, and relaxation time as dependent variables.

The mechanical properties of spinal cord grey and white matter were found to be heterogeneous

and slightly anisotropic. For peak stress, the effect of tissue type showed that grey matter was 1.6

times stiffer than white matter. For aggregate modulus, the effect of tissue type showed that grey

matter was 2 times stiffer than white matter. The effect of direction showed that the transverse

direction was 1.3 times stiffer than the axial direction. For relaxation time, grey matter took 1.6

times longer to relax than white matter in the transverse direction. These findings emphasize the

importance of tissue type and to a lesser extent direction when studying SCI biomechanics using

computational models.

iv

Lay Summary

Spinal cord injury (SCI) is often studied using mathematical models. These models simulate

spinal cord deformation. The reliability of these models are dependent on underlying

assumptions about the material behaviour. The material properties describing the material

behaviour are controversial and sparse in the literature. Studying material properties will relate

spinal cord deformation to tissue damage and neurological deficits.

Spinal cord tissue was used to study material properties. The spinal cord was separated into

different specimens to analyze the effect of tissue (grey matter, white matter) and direction

(axial, transverse).

The specimens were placed under compression and their behaviour was measured. The model

showed spinal cord grey matter was stiffer than white matter, and the transverse direction was

slightly stiffer than the axial direction. This contributes new material properties for future SCI

mathematical models.

v

Preface

This thesis represents my own work under the guidance of Dr. Oxland. The study was designed

by me in collaboration with Dr. Tom Oxland. The experiments, data collection, and data analysis

were conducted by myself.

The mechanical design in Chapter 2 of the confined compression apparatus and biopsy punch

was designed by me with design input from Dr. Tom Oxland and Dr. Robin Coope. The

fabrication of this design was performed by the British Columbia Cancer Agency Machine Shop.

The pig spinal cord tissue was provided by Dr. Brian Kwon’s laboratory group. Harvesting of the

spinal cord from the pig and removal of the dura mater were performed by Neda Manouchehri

and Megan Webster. Animal ethics were not required since ex-vivo animal tissue was used for

this study.

vi

Table of Contents

Abstract .......................................................................................................................................... iii

Lay Summary ................................................................................................................................. iv

Preface............................................................................................................................................. v

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

List of Tables .................................................................................................................................. x

List of Figures ................................................................................................................................ xi

List of Abbreviations .................................................................................................................... xv

Acknowledgements ..................................................................................................................... xvii

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

1.1 Background & Motivation .................................................................................................... 1

1.2 Project Definition .................................................................................................................. 2

1.3 Anatomy of the Human Spine and Spinal Cord.................................................................... 2

1.3.1 The Spinal Column ........................................................................................................ 2

1.3.2 The Spinal Cord ............................................................................................................. 5

1.3.3 Grey Matter and White Matter ....................................................................................... 7

1.4 Overview of Spinal Cord Injury ......................................................................................... 11

1.4.1 Epidemiology and Etiology ......................................................................................... 11

1.4.2 Pathophysiology of Spinal Cord Injury ....................................................................... 12

1.5 Experimental Modeling of Spinal Cord Injury ................................................................... 12

1.5.1 Animal Models of SCI ................................................................................................. 13

1.5.2 Spinal Cord Injury Mechanisms .................................................................................. 15

1.5.3 Effect of Velocity, Depth, and Duration ...................................................................... 18

1.6 Spinal Cord Finite Element Model ..................................................................................... 20

1.6.1 Finite Element Modeling ............................................................................................. 20

1.6.2 Constitutive Models ..................................................................................................... 21

1.6.3 Spinal Cord Computational Models............................................................................. 24

1.7 Spinal Cord Mechanical Properties .................................................................................... 26

1.7.1 Loading Types ............................................................................................................. 27

1.7.2 Intact Spinal Cord Mechanical properties .................................................................... 29

1.7.3 Spinal Cord Grey Matter and White Matter Mechanical properties ............................ 33

vii

1.7.4 Spinal Cord Grey Matter and White Matter Anisotropy ............................................. 36

1.7.5 Gap in literature ........................................................................................................... 40

1.8 Thesis .................................................................................................................................. 40

1.8.1 Research Question ....................................................................................................... 40

1.8.2 Thesis Objectives ......................................................................................................... 40

1.8.3 Hypotheses ................................................................................................................... 41

1.8.4 Scope ............................................................................................................................ 41

Chapter 2: Methods ....................................................................................................................... 42

2.1 Mechanical Design of the Biopsy Punch & Confined Compression Apparatus ................ 42

2.1.1 Biopsy Punch Design ................................................................................................... 42

2.1.2 Confined Compression Apparatus Design ................................................................... 45

2.1.1.1 Confined Compression Apparatus Overview ....................................................... 46

2.1.1.2 Confined Compression Fixture ............................................................................. 47

2.1.1.3 Load Cell Sizing ................................................................................................... 48

2.1.1.4 Nonporous Indenter .............................................................................................. 49

2.1.1.5 Magnetic End Effector .......................................................................................... 51

2.1.1.6 Actuator................................................................................................................. 51

2.1.1.7 Design Feature #1: Connection between the Nonporous Indenter and the Magnetic

End Effector ...................................................................................................................... 52

2.1.1.8 Design Feature #2: Tissue Leakage Prevention .................................................... 53

2.1.2 Verification of the Load Cell Accuracy ....................................................................... 56

2.1.3 Verification of the Confined Compression Apparatus Repeatability .......................... 56

2.1.4 Pilot Test Validation for Mechanical Design ............................................................... 57

2.1.4.1 Porous Filter .......................................................................................................... 57

2.1.4.2 Measuring Time Independent and Dependent Properties of Spinal Cord Tissue . 58

2.2 Spinal Cord Sample Preparation ......................................................................................... 60

2.3 Confined Compression Testing Protocol ............................................................................ 64

2.3.1 Time Post-Mortem Criterion........................................................................................ 64

2.3.2 Test Order .................................................................................................................... 65

2.3.3 Sample Size .................................................................................................................. 66

2.4 Experimental Protocol ........................................................................................................ 67

2.5 Constitutive Modeling ........................................................................................................ 68

2.5.1 Parameter Optimization ............................................................................................... 69

viii

2.5.2 Outcome Variables....................................................................................................... 70

2.6 Statistical Methods .............................................................................................................. 70

2.6.1 Effect of Tissue Type and Direction ............................................................................ 70

2.6.2 Effect of Time Post-Mortem ........................................................................................ 71

2.7 Histological Methods .......................................................................................................... 71

2.7.1 White Matter Axon Direction Verification .................................................................. 72

2.7.2 Grey Matter Heterogeneity Verification ...................................................................... 75

Chapter 3: Results ......................................................................................................................... 76

3.1 Stress-Strain and Stress Relaxation Responses................................................................... 76

3.2 Constitutive Model Fit ........................................................................................................ 78

3.2.1 Outcome Variables....................................................................................................... 79

3.3 Statistical Results ................................................................................................................ 80

3.3.1 Verifying Two-way ANOVA Assumptions ................................................................ 80

3.3.2 Peak Stress Results ...................................................................................................... 81

3.3.3 Aggregate Modulus Results ......................................................................................... 82

3.3.4 Time Constant Results ................................................................................................. 83

3.3.5 Effect of Time Post-Mortem on Peak Stress Results ................................................... 85

3.4 Histology ............................................................................................................................. 86

Chapter 4: Discussion ................................................................................................................... 89

4.1 Overview ............................................................................................................................. 89

4.2 Mechanical Property Findings ............................................................................................ 89

4.2.1 Time Independent Mechanical Properties ................................................................... 89

4.2.2 Time Dependent Mechanical Properties ...................................................................... 91

4.2.2.1 Aggregate Modulus ............................................................................................... 92

4.2.2.2 Time Constant ....................................................................................................... 93

4.2.3 Effect of Time Post-Mortem on Peak Stress................................................................ 94

4.3 Comparison to Histological Parameters.............................................................................. 94

4.4 Clinical Relevance to SCI ................................................................................................... 97

4.4.1 The Effect of Time Independent Mechanical Properties on SCI ................................. 97

4.4.2 The Effect of Time Dependent Mechanical Properties on SCI ................................... 99

4.4.3 The Effect of Spinal Cord Tissue Bulk Moduli ........................................................... 99

4.4.4 Drug Delivery ............................................................................................................ 100

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4.5 Limitations ........................................................................................................................ 100

4.5.1 Heterogeneity of Samples .......................................................................................... 100

4.5.2 Strain Rate and Strain Sensitivity .............................................................................. 101

4.5.3 Loading Type ............................................................................................................. 102

4.5.4 Ex-Vivo Tissue .......................................................................................................... 102

Chapter 5: Conclusion................................................................................................................. 103

5.1 Conclusions ....................................................................................................................... 103

5.2 Contributions..................................................................................................................... 104

5.3 Recommendations for Future Work.................................................................................. 104

5.4 Concluding Statement ....................................................................................................... 105

References ................................................................................................................................... 106

Appendix A – Engineering Drawings ......................................................................................... 114

Appendix B – Pilot Test Data in Air ........................................................................................... 121

Appendix C – Load Cell Calibration .......................................................................................... 122

Appendix D – Repeatability Analysis of Confined Compression Apparatus ............................. 123

Appendix E – Specimen Testing Order ...................................................................................... 125

Appendix F – Power Analysis .................................................................................................... 126

Appendix G – Constitutive Modeling Hand Calculations .......................................................... 128

Appendix H – Constitutive Modeling Matlab Script .................................................................. 130

Appendix I – Staining Protocols ................................................................................................. 137

Appendix J – Raw Data: Stress-time curves, Constitutive Model Fit, Outcome Variables ....... 140

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List of Tables

Table 1-1: Material property combinations for modeling the spinal cord in finite element

simulations adapted from Jannesar et al. [8] ................................................................................. 25

Table 1-2: Key parameters used in the literature investigating intact spinal cord mechanical

properties [42]–[44], [65]–[67], [73]. The shaded cells indicate that the author(s) did not measure

that quantity. ................................................................................................................................. 31

Table 1-3: Key parameters used in the literature to compare grey and white matter properties

from the literature [11], [41], [47], [59], [60], [63]. The shaded cells indicate that the author(s)

did not measure that quantity. ....................................................................................................... 34

Table 1-4: Key parameters used in the literature to compare grey and white matter anisotropy

properties from the literature [11], [60]. ....................................................................................... 38

Table 1-5: Brain anisotropy ratio in the literature, categorized by loading type [56], [57], [71],

[85]. The shaded cells indicate that the author(s) did not measure that quantity.......................... 39

Table 2-1: Example specimen testing order in a six hour window ............................................... 65

Table 3-1: Material constants A, B, g, and ꞇ (mean ± SD) for GA, GT, WA, and WT specimens

....................................................................................................................................................... 79

Table 3-2: Peak stress, aggregate modulus, and time constant (mean ± SD) for GA, GT, WA, and

WT specimens ............................................................................................................................... 79

Table 3-3: Summary of Shapiro-Wilk scores for each specimen and dependent variable ........... 80

Table 3-4: Levene’s test score for homogeneity of variance for each dependent variable ........... 80

Table C-1: Load cell calibration using standard weights. The gain in the load cell was adjusted

based on the error ........................................................................................................................ 122

Table E-1: Specimen testing order for all pigs (n=11) ............................................................... 125

Table F-1: Power analysis (Part 1) calculation used to calculate minimum sample size for this

thesis. The study by Prange & Margulies, 2002 was used as reference [57] .............................. 126

Table F-2: Power analysis (Part 2) calculation used to calculate minimum sample size for this

thesis. The study by Prange & Margulies, 2002 was used as reference [57]. ............................. 127

Table J-1: Constitutive model material constants for GA, GT, WA, and WT specimens for all

pigs .............................................................................................................................................. 141

xi

List of Figures

Figure 1-1: The vertebral column. The spine consists of 24 articulating vertebrae and 5 distinct

regions: cervical, thoracic, lumbar, sacral, coccygeal. The image is adapted from:

https://opentextbc.ca/anatomyandphysiology/chapter/7-3-the-vertebral-column/ - CC by 4.0 ...... 3

Figure 1-2: Anatomy of typical vertebra. The image is from:

https://opentextbc.ca/anatomyandphysiology/chapter/7-3-the-vertebral-column/ - CC by 4.0 ...... 4

Figure 1-3: A mid-sagittal section (left) and a 3D isometric view (right) of the intervertebral disc.

The nucleus pulposus (NP) and annulus fibrosis (AF) along with the typical features are shown –

CC by 4.0 [9]................................................................................................................................... 4

Figure 1-4: Dermatome pattern indicating which spinal nerves innervate specific areas of the

body. The image is by Mikael Häggström, used with permission. ................................................. 6

Figure 1-5: The pia mater, arachnoid mater, and dura mater surround the spinal cord and are

known as the meninges. The image is by Mysid Inkscape – public domain. ................................. 7

Figure 1-6: Grey matter and white matter in the spinal cord. The image is from:

https://opentextbc.ca/anatomyandphysiology/chapter/13-2-the-central-nervous-system/ - CC by

4.0.................................................................................................................................................... 7

Figure 1-7: Anatomy of a neuron. Electrical impulses travel from the left hand side to the right

hand side. The image is from: https://opentextbc.ca/anatomyandphysiology/chapter/12-2-

nervous-tissue/ - CC by 4.0 ............................................................................................................. 8

Figure 1-8: Histological staining of grey matter tissue structure. Each anatomical plane shows

randomly oriented axons in the dorsal and ventral horns. Axons are illustrated in green while cell

nuclei are in blue [11]. Reprinted with permission ......................................................................... 9

Figure 1-9: White matter tracts in a human spinal cord. The image is by Polarlys and Mikael

Häggström – CC by SA 3.0 .......................................................................................................... 10

Figure 1-10: Histological staining of white matter tissue structure. Long axons are seen in the

coronal and sagittal planes while cross sections of axons are seen the transverse plane. Axons are

illustrated in green while cell nuclei are in blue [11]. Reprinted with permission ....................... 10

Figure 1-11: Etiology of adult SCI [14] ........................................................................................ 11

Figure 1-12: Level of injury of adult SCI [14] ............................................................................. 12

Figure 1-13: Anatomical and physiological differences between the rat and human spinal cord.

The primary differences are the physical dimensions of the spinal cord as well as the location of

the white matter tracts [28]. Reprinted with permission ............................................................... 13

Figure 1-14: Magnetic resonance imaging of a Sprague-Dawley rat (A), Yucatan miniature pig

(B), and a human (C) at the T10 level. The prominent CSF layer (white layer of liquid)

surrounding the spinal cord is observed in both human and porcine images. The figure was

adapted from Lee et al. [29]. Reprinted with permission. ............................................................ 15

Figure 1-15: SCI fracture patterns and injury mechanisms. Sagittal view of a burst fracture

causing a contusion injury mechanism (A), sagittal view of a dislocation injury causing a

dislocation injury mechanism (B), transverse view of a burst fracture causing a contusion injury

mechanism (C), and a transverse view of a dislocation injury causing a dislocation injury

mechanism (D) [37]. Reprinted with permission ......................................................................... 16

xii

Figure 1-16: Maximum principal strain distribution of various material property combinations

for the grey and white matter tissue using Model A (a), Model B (b), Model C (c). The resultant

tissue damage from the NHP contusion injury was stained using histological analysis (d). This

figure was adapted from Jannesar et al. [8]. Reprinted with permission ...................................... 26

Figure 1-17: Confined compression schematic. The tissue is represented by the dark grey block

applying the reaction force on the nonporous metal indenter. The variable d(t) represents a

displacement controlled actuator that applies a displacement onto the nonporous indenter

deforming the tissue. Reprinted with permission [69] .................................................................. 28

Figure 1-18: Sample Stress-strain data from several studies of spinal cord mechanical properties

in tension [72]. Reprinted with permission. .................................................................................. 30

Figure 2-1: Custom biopsy punch. The punch tube was welded within an adapter and was

threaded onto a handle. ................................................................................................................. 43

Figure 2-2: Cross-section of the spinal cord showing grey matter axial (GA) (a), grey matter

transverse (GT) (b), white matter axial (WA) (c), and white matter transverse (WT) (d)

specimens. The circle and rectangle illustrate specimens that are ollected axially (through the

page) and transversely (across the page) respectively. The sample dimensions denoted by the

circles and rectangles are roughly to scale. The amount of grey and white matter in the spinal

cord is specific to the spinal cord region (cervical, thoracic, and lumbar). As such the image may

not accurately reflect the amount of grey and white matter observed in the spinal cord tissue used

in this study. The image is adapted from Polarlys – CC by SA 3.0.............................................. 44

Figure 2-3: Confined compression schematic of tissue sample. A sectional view of the adapter is

shown illustrating key components involved in confined compression. The specimen shown is

approximately to scale. ................................................................................................................. 45

Figure 2-4: Confined compression apparatus with key components labeled. The electromagnetic

actuator was mounted above the confined compression fixture. The magnetic end effector was

threaded into the actuator. The nonporous indenter is not shown in this figure due to its small

size. It is shown in Figure 2-6 instead........................................................................................... 47

Figure 2-5: Confined compression fixture with parts labeled. This fixture was machined by the

British Columbia Cancer Agency machine shop. ......................................................................... 48

Figure 2-6: Nonporous indenter with parts labeled. The welding was performed by the British

Columbia Cancer Agency machine shop. ..................................................................................... 49

Figure 2-7: The nonporous indenter was inserted into the adapter and initially supported with a

spacer to avoid contact with the specimen. ................................................................................... 50

Figure 2-8: Magnetic end effector with parts labeled. .................................................................. 51

Figure 2-9: Magnetized connection between the magnetic end effector and the nonporous

indenter. The magnetized steel ball and the nonporous indenter were initially disconnected from

each other. To use, the steel ball was lowered until it attracted the nonporous indenter below at

which point the spacer was removed. Since the nonporous indenter was already constrained

within the bore of the adapter, the alignment issue was mitigated. .............................................. 53

Figure 2-10: The schematic from Figure 2-3 was updated to show the placement of the square

profile O-ring. This prevented tissue leakage from occurring between the porous filter and the

biopsy punch tube interface. ......................................................................................................... 54

xiii

Figure 2-11: The square profile O-ring was first slipped onto the punch tube prior to lowering the

biopsy punch tube (a). Once the punch tube was lowered, the adapter holder was further lowered

until it contacted the O-ring and compressed it against the porous screen (b). ............................ 55

Figure 2-12: Pilot test for testing the permeability of various screens ......................................... 58

Figure 2-13: Pilot test apparatus for measuring the time independent and dependent properties of

spinal cord tissue. The electromagnetic actuator (a) and the proof of concept confined

compression fixture (b) are shown. ............................................................................................... 59

Figure 2-14: Displacement vs. time graph (top) and Stress vs, time graph (bottom) of pig spinal

cord white matter tissue ................................................................................................................ 60

Figure 2-15: The intact spinal cord with dura mater excised. A ruler is placed in proximity for

scaling purposes to show length (a) and diameter (b). The thoracic spinal cord is the smaller one

compared to the neighbouring cervical spinal cord ...................................................................... 61

Figure 2-16: An aluminum plate with demarcated lines was used to reduce the length of the

spinal cord. The “cross-section” cutting cradle (shown in black) was used to assist with cutting

cross-sections. The finished product is shown on the left hand side. ........................................... 62

Figure 2-17: The "separator" cutting cradle is used to separate the lateral white matter from the

central grey matter ........................................................................................................................ 63

Figure 2-18: A toothpick was inserted through the custom biopsy punch and marked to denote

the specimen height (2.8 ± 0.5 mm) ............................................................................................. 64

Figure 2-19: Immunofluorescence images of white matter specimens. Axons are stained in green

(SMI), myelin is stained in red (MBP), and neuronal cell bodies are stained in blue (Tub). (a)

Cross-section of WA specimen. (b) Cross-section of WT specimen. (c) Close-up of WA

specimen. (d) Close-up of WT specimen. ..................................................................................... 74

Figure 2-20: Sample eriochrome cyanine stained images of grey matter specimens. Myelin

(white matter) is in orange and grey matter is in blue (a) Cross-section of GA specimen. (b)

Cross-section of GT specimen. ..................................................................................................... 75

Figure 3-1: Mean (blue) plus/minus one standard deviation (red) for GA (a), GT (b), WA (c), and

WT (d) specimens of all 11 pigs ................................................................................................... 76

Figure 3-2: Mean stress-strain response for porcine spinal cord specimen types (indicated in the

legend)........................................................................................................................................... 77

Figure 3-3: Mean stress-time response for porcine spinal cord specimen types (indicated in the

legend)........................................................................................................................................... 77

Figure 3-4: Experimental stress-time data and constitutive model fit of GA (a), GT (b), WA (c),

and WT (d) specimen data. The mean (blue) was plotted along with the loading (orange) and

relaxation (yellow) curve fits for pig #11. .................................................................................... 78

Figure 3-5: Column plot of mean peak stress (mean ± SD) for GA, GT, WA, and WT specimens

....................................................................................................................................................... 81

Figure 3-6: Column plot of mean aggregate modulus (mean ± SD) for GA, GT, WA, and WT

specimens ...................................................................................................................................... 82

Figure 3-7: Column plot of mean time constant (mean ± SD) for GA, GT, WA, and WT

specimens ...................................................................................................................................... 84

Figure 3-8: The effect of time post-mortem on peak stress of GA, GT, WA, and WT specimens.

A linear trendline was plotted for each of the four specimen types.............................................. 85

xiv

Figure 3-9: H&E stained spinal cord sections showing gross morphology of GA (a), GT (b), WA

(c), WT (d) specimens. The scale bar represents 500 μm. ............................................................ 86

Figure 3-10: H&E stained spinal cord sections showing close-up of gross morphology of GA (a),

GT (b), WA (c), and WT (d) specimens. Cell nuclei are stained in blue. The scale bar represents

250 μm. ......................................................................................................................................... 87

Figure 4-1: Geometry of GA (left) and GT (right) specimens during sample collection. The circle

and rectangle represents an approximated scaled sample. The image is adapted from Polarlys –

CC by SA 3.0 ................................................................................................................................ 95

Figure B-1: Pilot test data in air. The same strain rate and strain were implemented to measure

the background noise that is generated when there is no specimen within the adapter. The

increase in noise at the end is when the indenter is being removed from the adapter causing a

spike in load. This is not a part of the testing protocol ............................................................... 121

Figure D-1: Repeatability study using silicone specimen #1. Four confined compression tests

were performed and their load-time curves are shown. COV was calculated resulting in 6%

variability. ................................................................................................................................... 123

Figure D-2: Repeatability study using silicone specimen #2. Three additional confined

compression tests were performed and their load-time curves are shown. COV was calculated

resulting in 4% variability. .......................................................................................................... 124

Figure G-1: Hand calculations for the analytical solution to the constitutive model used to model

stress relaxation. The final solution for the ramp phase (Eq. 1) and the hold phase (Eq. 2) are

shown. ......................................................................................................................................... 129

Figure J-1: All stress-time plots for GA (a), GT (b), WA (c), and WT (d) specimens for all 11

pigs .............................................................................................................................................. 140

Figure J-2: Peak Stress between specimen types for all pig specimens tested ........................... 142

Figure J-3: Aggregate Modulus between specimen types for all pig specimens tested ............. 142

Figure J-4: Time constant between specimen types for all pig specimens tested ....................... 143

xv

List of Abbreviations

ANOVA – Analysis of variance

CAD – Computer-aided design

CCM – Centre for Comparative Medicine

CNS – Central nervous system

COV – Coefficient of variation

CSF – Cerebrospinal fluid

EC – Eriochrome cyanine R

GA – Grey matter axial

GT – Grey matter transverse

H&E – Hematoxylin & eosin

ICORD – International Collaboration on Repair Discoveries

LVDT – Linear variable differential transformer

MBP – Myelin basic protein

MRE – Magnetic resonance elastography

MRI – Magnetic resonance imaging

NHP – Non-human primate

OCT – Optimal cutting temperature

OIBG – Orthopaedic & Injury Biomechanics Group

PBS – Phosphate buffered saline

PDGFRα – Platelet-derived growth factor receptor α

PNS – Peripheral nervous system

xvi

QLV – Quasi-linear viscoelastic

SCI – Spinal cord injury

SMI – SMI312

SD – Standard deviation

SEM – Standard error of the mean

Tub – β-tubulin III

UBC – University of British Columbia

WA – White matter axial

WT – White matter transverse

xvii

Acknowledgements

I would like to acknowledge the support and guidance of Dr. Tom Oxland throughout this

project. You have made yourself readily available whenever I needed assistance whether it be the

conversations in your office, over the phone, or over email. You have taught me what academic

research is about. You have also showed me the perseverance of conducting, and finshing a self-

guided independent study.

Thank you to my colleagues Neda Manouchehri, Kitty So, and Megan Webster from Dr. Brian

Kwon’s lab. Your help with coordinating and harvesting spinal cord tissue out at the Centre for

Comparative Medicine, especially those that took place at midnight was appreciated. This project

could have not been possible without your collaboration.

Thank you to my colleagues Oscar Seira Oriach, and Kathleen Kolehmainen from Dr. Wolfram

Tetzlaff’s lab for teaching and helping me with the various histological methods.

Lastly, thank you to all of my colleagues in the OIBG group. You have provided me with a

thriving and collaborative environment for conducting research.

1

Chapter 1: Introduction

1.1 Background & Motivation

Spinal cord injury (SCI) is a devastating event often resulting in a debilitating condition. SCIs

occur from a mechanical insult to the spinal cord resulting in tissue damage. A damaged spinal

cord results in neurological impairment, which depending on level of injury and completeness of

injury, affects motor, sensory, and/or autonomic function [1]. This has attracted clinicians and

scientists as there is a clinical need and currently no effective therapies. Numerous treatment

trials have been conducted in humans, however no therapy has produced a major improvement in

neurological recovery or a meaningful increase in function [2]. It is hypothesized that a

discrepancy between human trials and pre-clinical experimental SCI animal models exist due to

their inability to represent the human condition [2].

This lack of translation between pre-clinical research and human trials may be due to the

heterogeneity of human SCI. This means the population sustaining injury, mechanisms of injury,

level of injury, and severity are among many factors that have an impact on SCI cases [2]. Pre-

clinical SCI animal models used to study human SCI often represent only a single injury model

therefore disregarding the heterogeneity of human SCI [2].

Mechanisms of injury contributing to SCI heterogeneity can be studied using computational

models. These models help relate spinal cord impact with spinal cord tissue damage. The

reliability of these models are dependent on the underlying spinal cord material behaviour. The

intrinsic differences in the biomechanical properties of grey and white matter can influence the

onset, magnitude and distribution of tissue damage when studying human SCI [3]. Knowledge of

the tissue tolerances of grey and white matter will relate injury mechanisms with tissue damage

patterns and ultimately their neurological deficits. This may help reduce the gap between pre-

clinical research and human trials [4].

My thesis continues a line of research at the Orthopaedic & Injury Biomechanics Group (OIBG)

at the University of British Columbia (UBC) to better understand the link between spinal cord

impact and the resulting tissue damage. One long-term goal of this research is to establish a fully

developed spinal cord computational model so that it can be added to full human body computer

2

models. This will prove useful for automobile and helmet safety testing as well as inspire new

treatment and prevention based SCI therapies. Specifically, my thesis focuses on determining the

ex-vivo mechanical properties of the spinal cord grey and white matter and their anisotropy (ie.

directional differences).

1.2 Project Definition

When studying SCI biomechanics with the purpose of improving human injury modeling,

computational models such as finite element methods are used. Their validity however depends

on the underlying assumptions that are made during model development. When it comes to the

material constitutive model of the spinal cord, it is usually assumed to exhibit homogeneous, and

isotropic properties [4]–[7]. However recent research suggests that accounting for anisotropy is

important for predicting spinal cord damage and its inclusion will improve the biofidelity of

finite element models [8]. This has brought forth the need to determine the mechanical properties

of spinal cord grey and white matter and their anisotropy.

1.3 Anatomy of the Human Spine and Spinal Cord

The mechanical properties of biological and non-biological tissues are a function of their

underlying morphologies. Spinal cord grey and white matter tissue possess distinct structural

characteristics. To understand these differences and how they are modeled, it is first necessary to

understand the relevant anatomy and physiology associated with the spinal cord.

1.3.1 The Spinal Column

The spinal column serves to protect the spinal cord, provide structural support for the human

body, and enable movement (Figure 1-1). It consists of 24 articulating vertebrae separated by

intervertebral discs that are divided into three distinct regions. These are the cervical, thoracic,

and lumbar regions. There are 7 cervical vertebrae (C1-C7), 12 thoracic vertebrae (T1-T12), and

5 lumbar vertebrae (L1-L5). The cervical spine corresponds with the neck of the body and its

purpose is to support and provide motion to the head. The thoracic spine corresponds to the mid-

back and together with the rib cage protects crucial organs such as the heart and lungs. The

lumbar spine corresponds to the low back and supports the weight of the body along with any

external loads carried by the body. Below the lumbar spine are the sacral and coccygeal (ie.

tailbone) regions. The vertebrae here are fused and thus unable to articulate independently. There

3

are 5 sacral vertebrae (S1-S5) and 4 coccygeal vertebrae. Only the cervical and thoracic regions

of the spine are relevant to the work discussed in this thesis because the spinal cord terminates

before the first lumbar vertebrae. As a result, additional details covering the other spinal regions

will not be further discussed.

Figure 1-1: The vertebral column. The spine consists of 24 articulating vertebrae and 5

distinct regions: cervical, thoracic, lumbar, sacral, coccygeal. The image is adapted from:

https://opentextbc.ca/anatomyandphysiology/chapter/7-3-the-vertebral-column/ - CC by

4.0

There are differences between the cervical and thoracic vertebrae but they possess the same basic

characteristics. A typical vertebrae consists of a vertebral body and a vertebral arch (Figure 1-2).

The vertebral arch is posterior to the vertebral body. It is made of pedicles which extend

posterolaterally from the vertebral body and laminae which extend posteromedially from the

pedicles thus forming the vertebral foramen. Adjacent vertebrae are aligned such that the

vertebral foramen forms the spinal canal encompassing and protecting the spinal cord. Seven

bony projections known as processes extend from the arch: two transverse processes are found

laterally, one spinous process is found posteriorly, two superior and two inferior articular

processes are found posterolaterally. The processes serve as attachment points for ligaments, and

muscles. The superior articular processes pair with the inferior articular processes between

adjacent vertebrae forming the facet joints guiding motion in the spine.

4

Figure 1-2: Anatomy of typical vertebra. The image is from:

https://opentextbc.ca/anatomyandphysiology/chapter/7-3-the-vertebral-column/ - CC by

4.0

The intervertebral disc is located between the adjacent vertebral bodies below C2. They help

with absorbing impact during weight bearing movements. Each intervertebral disc consists of the

annulus fibrosis and nucleus pulposus (Figure 1-3). The annulus consists of concentric rings

surrounding the nucleus and are made of lamellae of fibrocartilage while the nucleus is a gel-

filled substance found in the centre comprised mainly of water. The nucleus acts similar to a ball

bearing allowing motion between adjacent vertebral bodies.

Figure 1-3: A mid-sagittal section (left) and a 3D isometric view (right) of the intervertebral

disc. The nucleus pulposus (NP) and annulus fibrosis (AF) along with the typical features

are shown – CC by 4.0 [9].

5

The vertebral bodies are joined together by several ligaments along the length of the spinal

column. These act to limit the mobility of the spinal column by preventing excessive backward

or forward bending movements. Since the emphasis of this thesis is on the spinal cord, ligaments

will not be further discussed.

1.3.2 The Spinal Cord

The spinal cord is a thin cylindrical structure extending caudally from the medulla oblongata in

the brainstem that passes through the vertebral foramen. It is part of the central nervous system

(CNS) and is made of nervous tissue. The distal end of the spinal cord structure is no longer

cylindrical as it becomes a bundle of nerves and rootlets known as the cauda equina [10].

The spinal cord serves as a conduction pathway for nerve signals connecting the brain to the

peripheral nervous system (PNS). It branches into 31 pairs of spinal nerves with one pair (left &

right) exiting the spinal cord at each vertebral level. There are 8 pairs of cervical nerves, 12 pairs

of thoracic nerves, 5 pairs of lumbar nerves, 5 pairs of sacral nerves, and one pair of coccygeal

nerves [10]. Each spinal nerve includes sensory and motor fibres. Dorsal nerve fibres relay

sensory (afferent) information to the brain while ventral nerve fibres relay motor (efferent)

information away from the brain. These fibres extend out forming the PNS and innervate

dermatomes (skin receptors), myotomes (muscle fibres), and the autonomic nervous system

leading to bodily sensation, movement, and organ function respectively (Figure 1-4).

6

Figure 1-4: Dermatome pattern indicating which spinal nerves innervate specific areas of

the body. The image is by Mikael Häggström, used with permission.

The spinal cord is protected and enveloped by three layers of membranes known as meninges

(Figure 1-5). The dura mater is the outermost layer made of dense connective tissue forming the

toughest and thickest protective membrane. Beneath the dura mater is the middle protective layer

known as the arachnoid mater for its spider web like appearance. The third and innermost

protective layer is the pia mater and is directly attached to the spinal cord. The spinal cord is

anchored by the denticulate ligaments over its entire length. The ligaments attach at 21 points on

each side of the spinal cord connecting it to the arachnoid mater and dura mater. The space

7

existing between the arachnoid mater and the pia mater is the subarachnoid space which contains

cerebrospinal fluid (CSF) bathing the entire spinal cord.

Figure 1-5: The pia mater, arachnoid mater, and dura mater surround the spinal cord and

are known as the meninges. The image is by Mysid Inkscape – public domain.

1.3.3 Grey Matter and White Matter

A transverse section of the spinal cord reveals the butterfly shaped grey matter in the centre, and

the surrounding white matter (Figure 1-6). The grey matter consists of neuronal cell bodies, glial

cells, dendrites, and unmyelinated axons. In contrast the white matter does not contain any

neuronal cell bodies and is largely comprised of myelinated axons with fewer glial cells.

Figure 1-6: Grey matter and white matter in the spinal cord. The image is from:

https://opentextbc.ca/anatomyandphysiology/chapter/13-2-the-central-nervous-system/ -

CC by 4.0

8

Neurons are nerve cells located within the spinal cord. The neuron is constructed of a cell body,

dendrites, and an axon (Figure 1-7). The cell body contains the nucleus and organelles to

produce the necessary proteins to maintain the cell’s functions. Dendrites are nerve fibre

projections that receive electrical signals from other neurons. The axon is a nerve fibre and is the

pathway through which the neuron sends its electrical signal. These signals travel as action

potentials which manifests as a change in cell voltage due to ion movement. Axons are typically

surrounded by a fatty substance known as myelin. The myelinated sheath insulates the axons

enabling faster signal conduction. At the terminal end are axon terminals which connect

neighbouring neurons via a synapse. Here an electrochemical process takes place and

information flows from one neuron to the next.

Figure 1-7: Anatomy of a neuron. Electrical impulses travel from the left hand side to the

right hand side. The image is from:

https://opentextbc.ca/anatomyandphysiology/chapter/12-2-nervous-tissue/ - CC by 4.0

Glial cells are supporting nerve cells located in the spinal cord and do not conduct electrical

signals. These include oligodendrocytes, astrocytes, microglia, and ependymal cells, all of which

have differing functions to support neurons. Oligodendrocytes are responsible for producing the

myelin sheath around axons. Astrocytes are star-shaped, provide structural support to other nerve

cells, and provide nutrients to nervous tissue among many other roles. Microglia are the first line

of immune defense for the spinal cord. Ependymal cells line the central canal with cilia and are

involved with the circulation of CSF throughout the spinal cord while delivering nutrients to

neurons and filtering out harmful molecules.

9

Grey matter is primarily subdivided into two distinct regions, the dorsal horn and the ventral

horn (Figure 1-6). The dorsal horn contains sensory neurons that receive information from

dermatomes while the ventral horn contains motor neurons that communicate with myotomes.

Interneurons also exist within the grey matter and are responsible for the reflex arc. Interneurons

relay signals between sensory and motor neurons without communicating with the brain. As a

result of the grey matter’s functions, the tissue structure consists of randomly oriented axons

with numerous cell bodies dispersed throughout (Figure 1-8).

Figure 1-8: Histological staining of grey matter tissue structure. Each anatomical plane

shows randomly oriented axons in the dorsal and ventral horns. Axons are illustrated in

green while cell nuclei are in blue [11]. Reprinted with permission

White matter consists of distinct tracts with separate afferent and efferent pathways (Figure 1-9).

The nomenclature is such that ascending tracts use the term “spino” as a prefix and descending

tracts use the term “spinal” as a suffix. For example the spinothalamic tract is an ascending

pathway that connects the spinal cord to the thalamus whereas the corticospinal tract is a

descending pathway that connects the cortex to the spinal cord. As a result of the white matter’s

functions, the tissue structure has a directional bias consisting of axons running rostralcaudally

throughout the length of the spinal cord (Figure 1-10).

10

Figure 1-9: White matter tracts in a human spinal cord. The image is by Polarlys and

Mikael Häggström – CC by SA 3.0

Figure 1-10: Histological staining of white matter tissue structure. Long axons are seen in

the coronal and sagittal planes while cross sections of axons are seen the transverse plane.

Axons are illustrated in green while cell nuclei are in blue [11]. Reprinted with permission

11

1.4 Overview of Spinal Cord Injury

1.4.1 Epidemiology and Etiology

In Canada, the estimated prevalence of traumatic and non-traumatic SCIs is greater than 85,000

people [1]. The United States estimated up to 347,000 people are affected by SCI with 17,000

new SCI cases per year [12]. SCI results in impaired mobility and function depending on the

level of injury as well as the completeness of injury. In general a higher level of injury is more

detrimental as it results in more bodily dysfunction. Moreover, all spinal levels below the level

of injury will also be affected potentially leading to paraplegia or tetraplegia. This leads to

socioeconomic burden of the patient which includes increased divorce rate, and reduced

employment [12]. Depending on the level of neurological impairment, the average annual

expenses can range between $350,000 to $1,000,000 in the first year and between $43,000 to

$185,000 each subsequent year. In total it can be worth millions of dollars over a lifetime [12].

The etiology indicates that vehicular crashes (~45%) continue to be the leading cause of SCI.

Fall injuries specifically have seen an increasing trend through the years and are the second

leading cause of SCI (~20%) [13]. A breakdown of the causes of SCI are shown in Figure 1-11.

Figure 1-11: Etiology of adult SCI [14]

Motor Vehicle Related

Work

Sports & Recreation

Falls

Violence

12

The injury profile reveals cervical SCIs to be the most prevalent. High cervical SCIs have

increased over the past five decades whereas low cervical SCIs have decreased. Injuries

involving spinal cord levels from T1 to S3 have remained relatively constant [13]. The incidence

of SCI with respect to the level of injury is shown in Figure 1-12.

-

Figure 1-12: Level of injury of adult SCI [14]

1.4.2 Pathophysiology of Spinal Cord Injury

SCI involves a primary and secondary injury [14]. Primary injury is the damage produced by the

initial mechanical deformation. The insult produces mechanical stresses and strains on the tissue

leading to acute tissue damage such as severed axons, demyelination, vascular disruption, and

cellular necrosis [15].

Secondary injuryinvolves a cascade of biochemical and cellular processes that arise as a result of

the primary injury and causes further damage to the spinal cord [14]. Within hours of injury, the

spinal cord swells, and vascular disruption results in hemorrhage of both the grey and white

matter. Consequently this causes ischemia leading to the death of neurons and oligodendrocytes

[15].

1.5 Experimental Modeling of Spinal Cord Injury

The severity of primary and secondary injury of SCI has been shown to be contingent on several

biomechanical parameters in experimental models of SCI. This includes mechanism of injury,

C1-C7

T1-T11

T12-L1

L2-S5

13

velocity of injury, depth of injury, as well as duration of spinal cord compression [16]–[24]. The

effects of each of these parameters are studied in animal model surrogates to understand the

varying degrees of spinal cord tissue damage and subsequent biological responses following SCI.

1.5.1 Animal Models of SCI

The rodent model is the most common animal model used to study experimental SCI. It offers

both advantages and disadvantages. The advantages include their relatively low cost, and similar

pathophysiology to humans. This has allowed researchers to study the pathological cascade of

events that occur from the secondary injury making them the main model for evaluating

experimental treatment strategies [25], [26]. The disadvantages of using a rodent model include

its anatomical and physiological differences with humans. The diameter of the rat spinal cord is

3.5 mm and 90 mm in length which is significantly smaller than a human spinal cord [27]. The

white matter tracts are also organized slightly different than that of humans (Figure 1-13) [28].

Figure 1-13: Anatomical and physiological differences between the rat and human spinal

cord. The primary differences are the physical dimensions of the spinal cord as well as the

location of the white matter tracts [28]. Reprinted with permission

It is perhaps due to these differences between rats and humans that have led to few successes

when translating experimental treatments from rodent models to clinical trials of human SCI [2].

The rat spinal cord is more than three times smaller than the human spinal cord in terms of

14

diameter. This makes it over one order of magnitude smaller in terms of overall volume. Lee et

al. hypothesized that drug efficacy may not be achievable in humans given that the

biodistribution of the drugs therapeutic effects within the rat and human spinal cord are over one

order of magnitude apart [29], [30]. Moreover, the difference in axonal growth that is millimetres

in a rodent model may not translate to centimetres of growth within a human [29].

This disparity in anatomical size between rodent models and humans has prompted the use of

higher order animals as surrogates for SCI research. One of the findings in a survey concluded

that 65%-77% of researchers within the SCI research community agreed that larger animal

models of SCI would be beneficial for pre-clinical research [31]. Being able to demonstrate drug

efficacy in a larger animal after small animal testing was believed to improve the translation of

experimental therapies from animal models to humans.

A larger animal model such as a pig offers several advantages over rodent models. The pig spinal

cord is closer in diameter to that of a human compared to a rat. At the T10 level the pig spinal

cord measures 7 mm in diameter while a human and a rat measure 8.5 mm and 2.5 mm

respectively [29]. The pig spinal cord is also surrounded by a prominent layer of CSF like the

human spinal cord (Figure 1-14). This is clinically advantageous for evaluating the

biodistribution of drugs and their administration either extradurally or intrathecally. The enlarged

CSF space allows for physiological and biochemical monitoring with probes which is otherwise

not possible in rodent models [29], [30]. CSF has also been suggested to protect the spinal cord

by lessening mechanical deformation to the spinal cord [32]. This is an important factor for

studying SCI biomechanics.

The disadvantage of a porcine model is mainly its cost. It is substantially more expensive than

rodent models in terms of initial purchase and ongoing care. Animal care facilities and veterinary

support are required to be able to conduct experimental SCI work on pigs further adding to the

cost of the study [29].

15

Figure 1-14: Magnetic resonance imaging of a Sprague-Dawley rat (A), Yucatan miniature

pig (B), and a human (C) at the T10 level. The prominent CSF layer (white layer of liquid)

surrounding the spinal cord is observed in both human and porcine images. The figure was

adapted from Lee et al. [29]. Reprinted with permission.

1.5.2 Spinal Cord Injury Mechanisms

There are five types of injury mechanisms used in animal modeling of SCI to replicate clinically

relevant primary injuries. These are dislocation, contusion, compression, distraction, and

transection models [16], [17], [23], [33], [34].

The contusion model is historically the most widely used model for producing experimental SCI

and involves an impact on a surgically exposed spinal cord in the dorsoventral direction [16],

[19], [20], [22], [27], [29], [33]–[36]. A weight drop impactor or an electromagnetic impactor are

typically used to contuse the spinal cord causing an acute injury. Weight drop impactors use a

prescribed height, and mass to study SCI while the electromagnetic actuator uses a controlled

displacement (depth) or force to impact the cord with a metal impactor [33].

Contusion impact is thought to be biomechanically similar to vertebral burst fractures which

represent 30% of SCIs [14]. Burst fractures are caused from high energy axial compression

events such as head first impacts or fall from heights leading to spinal cord compression from a

bony fragment (Figure 1-15).

16

Figure 1-15: SCI fracture patterns and injury mechanisms. Sagittal view of a burst

fracture causing a contusion injury mechanism (A), sagittal view of a dislocation injury

causing a dislocation injury mechanism (B), transverse view of a burst fracture causing a

contusion injury mechanism (C), and a transverse view of a dislocation injury causing a

dislocation injury mechanism (D) [37]. Reprinted with permission

The compression model is different from the contusion model such that slow impingement

and/or extended compression of the spinal cord are involved. The latter introduces a temporal

aspect to the injury model. Clip compression and balloon compression are among several

methods used to mimic compression injury models. Clip compression uses a modified aneurysm

clip to generate a SCI controlling for force and compression time following the initial impact.

Balloon compression uses a catheter fed inflatable balloon to compress the spinal cord. This

method relies on inflation volume and rate of inflation to produce a SCI but is typically not

representative of an acute SCI. While force and duration of compression are measured in the

former method, only duration of compression is measured in the latter. In both cases, impact

velocity is not typically measured. Compression models are often combined with contusion

17

models to produce a contusion-compression model whereby an acute impact followed by

prolonged compression are used. This model replicates characteristics of burst fractures where

sustained compression is observed following SCI [33].

Distraction models involve tensile stretching of the spinal cord to produce SCIs. An

electromagnetic actuator controlling for displacement and force is one method that can be used

for this model. A set of vertebrae are held stationary and a set of vertebrae are distracted caudally

[16], [34]. This model replicates flexion-distraction injuries seen in motor vehicle accidents.

Dislocation models displace one vertebrae over an adjacent vertebrae either dorsoventrally or

mediolaterally to generate a SCI. The result is that the adjacent vertebrae are no longer aligned

correctly. The act of dislocating adjacent vertebrae produces a shear force on the spinal cord.

Fiford et al. was first to develop the dislocation model of experimental SCI by using a linear

actuator to laterally dislocate two adjacent vertebrae [17]. In contrast Choo et al. used an

electromagnetic actuator to dorsally dislocate two adjacent vertebrae [16]. In both cases, a set of

vertebrae are held stationary and an adjacent set are displaced laterally or dorsally [16], [17].

Both setups control for displacement and force to create varying degrees of SCI in an animal

model. This model is used to represent a fracture-dislocation injury, the most clinically prevalent

injury occurring in 40% of all SCI cases (Figure 1-15) [14].

Transection models can be either complete or partial. The former fully severs the rostral and

caudal segments of the spinal cord whereas the latter involves selectively severing the spinal

cord. Full transections are useful for investigating axonal regeneration, and are easily

reproducible. While they are highly reproducible, they are not particularly clinically relevant as

complete transections are not commonly seen. Partial transections are useful for comparing

deficits between healthy and injured fibers as in the case of a hemisection [33].

Each of these injury paradigms has been shown to produce different patterns of tissue damage.

Contusion, transection, and compression models directly injure a surgically exposed spinal cord.

However, they are not representative of human SCIs where closed column injuries are more

relevant. Choo et al. performed a study that compared contusion, dislocation, and distraction

injury models. Both distraction and dislocation were closed column injuries. In terms of white

matter damage, there was peripheral white matter sparing with contusion models whereas

dislocations disrupted axons in the lateral white matter [34]. Rostral from the lesion site, it was

18

observed that dislocation and distraction models exhibited more white matter damage than

contusion models [16]. The amount of hemorrhage between models showed that contusion and

dislocation models exhibited similar amounts within grey matter while distraction models saw

almost none [16].

There were differences in observed damage between anterior-posterior and lateral fracture-

dislocation models, introducing an effect of loading direction. A significantly larger volume of

hemorrhage was observed with anterior-posterior dislocation than lateral dislocation. Anterior-

posterior dislocation saw dorsal and ventral white matter damage rostrally and caudally

respectively. In contrast lateral dislocation saw left lateral and right lateral white matter damage

rostrally and caudally respectively. Both models saw tissue damage at the injury epicenter [23].

These differing findings highlight the importance of injury mechanisms and their consideration

when experimentally modeling SCI.

1.5.3 Effect of Velocity, Depth, and Duration

While mechanisms of injury have resulted in varying tissue damage patterns, the effects of injury

velocity, injury depth (displacement), and duration of compressive injury have illustrated varying

severities of injury when modeling SCI in animal models.

The effect of injury depth has shown to be correlated with injury severity. Noyes et al. was

among several researchers who conducted a contusion study with incremental increases in injury

depth. They showed that increased injury depths resulted in an increased lesion volume [18]. A

similar trend was also seen in the fracture-dislocation model by Fiford et al. where increasing

dislocation displacement between adjacent vertebrae led to more axonal injury [17].

The effect of velocity was also shown to correlate with injury severity in a contusion study by

Sparrey et al.. Both hemorrhage volume and axonal disruption were measured for injury

velocities of 3 mm/s and 300 mm/s. For white matter, higher velocity injuries saw a significantly

higher hemorrhage volume and 62% more axonal disruption compared to slower velocity

injuries. For grey matter, it was shown that hemorrhage volume was similar regardless of injury

velocity. It was determined for slow injuries that 83% of the hemorrhage occurred in grey matter

in contrast to 17% in white matter [19].

19

Studies involving the combined effects of injury depth, and injury velocity revealed that both of

these parameters interact together to predict injury severity. Kearney et al. used contusion depths

of 25% - 65% with varied velocities between 1.5 m/s – 6 m/s. The results showed that few

animals recovered beyond 50% injury depth regardless of injury velocity. Moreover, a velocity

and compression product (velocity x compression) greater than two demonstrated the combined

effects of both parameters as no animals recovered beyond this point [20].

Lam et al. also studied these interactive effects while varying velocities of 8 mm/s, 80 mm/s, and

800 mm/s with depths of 0.9 mm and 1.5 mm. There was little difference in grey and white

matter sparing when the 0.9 mm depth was held constant and injury velocities were varied.

However much larger differences were observed in tissue sparing between velocities when a 1.5

mm depth was used. The effect of injury depth, velocity, and their interaction significantly

affected white matter sparing where only the effect of injury depth significantly affected grey

matter sparing. This revealed the effect of different mechanical parameters on the spinal cord

constituents. Here injury depth was a more consistent predictor for injury severity while velocity

became more relevant once an injury depth threshold was surpassed [22].

The effect of duration and residual compression was also shown to play a role in predicting

injury severity. Residual compression is defined as a percentage of spinal cord occlusion and

duration of occlusion in the spinal canal. Sjovold et al. applied 0%, 40%, and 90% residual

compression in a contusion model for a duration of 60 mins. It was observed there was 60%-85%

more neuronal nuclei damage in the grey matter at 90% compared to 40% residual compression

[38]. Dimar et al. conducted two experiments in which both residual compression and duration

were varied independently. The first experiment placed spacers in the spinal canal to occlude the

spinal cord by 0%, 20%, 35%, and 50% respectively while measuring neurological recovery over

six weeks. The results showed that significantly better functional recovery occurs with lower

occlusions except for 35% and 50% residual compression where it was non-significant. The

second experiment maintained 35% residual compression for up to 72 hours prior to

decompression and subsequently measured neurological recovery. Ambulation was restored

when the spinal cord was decompressed before the six hour mark. At 24 hours, motor function

was slightly impaired and at 72 hours, the rat remained paraplegic [21].

20

Speidel et al. recently investigated behavioural outcomes in rats while looking at the combined

effects of velocity and residual compression in a dislocation model. Injury velocities of 5 mm/s

and 500 mm/s were varied along with compressive durations of 24 mins and 240 mins. A fixed

dislocation displacement and residual compression depth of 1.45 mm and 0.8 mm were used

respectively. The findings suggested that increased velocity led to increased behavioural deficits

however the effect of decompression had no effect [24]. These studies on residual compression

suggested that minimizing spinal canal occlusion was important in minimizing SCI severity

while early decompression saw mixed results.

1.6 Spinal Cord Finite Element Model

The majority of biomechanical SCI animal experiments are primarily focused on correlating

mechanical parameters such as mechanisms of injury, injury depth, injury velocity and duration

of compression with the extent of injury [16], [17], [19]–[22], [24], [38], [39]. Computational

models such as finite element models complement experimental work when studying SCI

biomechanics as they provide insight into how mechanical stresses and strains are distributed

within the spinal cord following impact. This links spinal cord impact with spinal cord damage

therefore associating tissue damage distributions with specific pathologies [4]. In order to

understand computational modeling, the basics of finite element modeling will briefly first be

explained.

1.6.1 Finite Element Modeling

Finite element modeling is a computational engineering analysis tool used to evaluate the

structural mechanics of materials in terms of mechanical stresses and strains. Stress is defined as

force per unit area while strain is defined as normalized deformation through a material

respectively. This method discretizes a continuous material into a set of elements connected at

nodes. These elements are small enough such that the mechanical behaviour of the material is

well described. The model computes stresses and strains at each node describing nodal

behaviour. This determines the stresses and strains within the material. Given that this thesis

focuses on experimental work as opposed to finite element modeling, the mathematics behind

finite element theory will not be discussed.

21

1.6.2 Constitutive Models

The approximation of internal stresses and strains from finite element modeling is dependent on

the constitutive material model of the structure. Specific to nervous tissue, linear elastic, non-

linear elastic, linear viscoelastic, quasi-linear viscoelastic (QLV), non-linear viscoelastic,

poroelastic, isotropic, and transversely isotropic models have been used [4], [5], [40], [41]. Each

of these models describe how stresses relate to strains.

A linear elastic model is the most common model used for engineering materials. It has

described materials such as metal as well as biological tissue such as bone. It uses a linear

relationship to relate stress and strain by the material’s elastic modulus (E). This is shown by the

equation below.

𝜎 = 𝐸𝜖 (1)

Bulk modulus (K) is an extension of elastic modulus describing a solid or fluid’s resistance to

compression in three dimensions. It is defined as the decrease in volume of a material

(volumetric strain) due to the increase in pressure (volumetric stress) surrounding the material. It

has been used to describe the compressibility of brain grey and white matter tissue [53]–[55].

This is shown by the following equation.

𝑃 = −𝐾(𝑉𝑛 − 𝑉𝑜)

𝑉𝑜 (2)

Where P is the applied pressure, Vo is the original volume of a material, and Vn is the reduced

volume of a material from the applied pressure.

Non-linear elasticity is used to describe a material that exhibits a non-linear relationship between

stress and strain. There are several non-linear material models that exist such as hyperelasticity

and elastoplasticity. An example of a non-linear model that has been used to describe several

biological tissues such as ligament, tendon, and spinal cord is shown below [42]–[44].

𝜎 = 𝐴(𝑒𝐵𝜖 − 1) (3)

Where A, and B are material constants and stress is represented by an exponential function of

strain.

22

Viscoelasticity describes a material that exhibits time dependent properties. These materials

exhibit both viscous (fluid) and elastic (solid) behaviour. Creep and stress relaxation are common

loading protocols that can be used to characterize viscoelasticity. Creep refers to a protocol

where a constant stress is applied resulting in strain increasing over time. In contrast, stress

relaxation refers to a protocol where strain is applied (loading phase) and then held constant

(relaxation phase). The applied strain leads to increased stress while the holding phase leads to

decreased stress over time.

There are many existing models that describe viscoelastic materials. Linear viscoelastic models

correspond to materials undergoing small strain where stress varies linearly with strain. It uses

Boltzmann’s superposition principle which states that all incremental stresses and strains are

additive. The complete stress at any time (σ(t)) is obtained by integrating all strain increments

from time zero to time t, over all dꞇ increments. This results in the following integral.

𝜎(𝑡) = ∫ 𝐺(𝑡 − 𝜏)𝑑𝜖(𝜏)

𝑑𝜏𝑑𝜏

𝑡

0

(4)

Where G(t) is the relaxation function.

Linear viscoelastic models are inadequate at characterizing soft tissues. This is due to the non-

linear relationship between stress and strain and the larger strains found in mechanical testing of

soft tissues. In these cases, non-linear viscoelasticity is used.

Non-linear viscoelasticity can be described using both a QLV model and a fully nonlinear

viscoelastic model. QLV models have been widely used to describe the viscoelastic behaviour of

several soft tissues in the literature [8], [41]–[48]. This formulation assumes the time dependent

and elastic portion of the mechanical behaviour as separable. This results in a time dependent

relaxation phase, and a strain-dependent loading phase as shown in the following equation.

𝜎(𝜖, 𝑡) = ∫ 𝐺(𝑡 − 𝜏)𝑡

0

𝜕𝜎𝑒(𝜖)

𝜕𝜖

𝜕𝜖(𝜏)

𝜕𝜏𝑑𝜏 (5)

Where, 𝜎𝑒(𝜖) is the stress corresponding to an instantaneous strain during a uniaxial loading

phase and 𝐺(𝑡) is the reduced relaxation function (where G(0) = 1) during the relaxation phase.

Often a first order exponential such as Equation (3) can be used to illustrate the shape of the

loading response while a 3-term Prony series (Equation (6)) consisting of decaying exponential

23

functions can be used to illustrate the shape of the relaxation response of biological soft tissue

[8], [41]–[48].

𝐺(𝑡) = 1 − ∑ 𝑔𝑖(1 − 𝑒−

𝑡

𝜏𝑖)

3

𝑖=1

(6)

Where 𝑔𝑖 are the relaxation moduli corresponding to 𝜏𝑖 time constants in the relaxation phase.

The strain history 𝜖(𝑡) for stress relaxation commonly applies a ramp strain followed by holding

of the maximum strain. This is modeled by the following piecewise function.

𝜖(𝑡) = {𝜖̇𝑡, 𝑓𝑜𝑟 0 < 𝑡 < 𝑡0

𝜖̇𝑡0, 𝑓𝑜𝑟 𝑡 ≥ 𝑡0 (7)

Where 𝜖̇ is the strain rate, 0 < 𝑡 < 𝑡0 represents the loading portion, and 𝑡 ≥ 𝑡0 represents the

hold portion of the strain profile.

Equations (3), (6), (7) can be substituted into Equation (5) and integrated over both loading and

hold portions of the strain profile to describe the non-linear viscoelastic behaviour of spinal cord

tissue.

The difference between the QLV and a fully nonlinear viscoelastic model is the relaxation

modulus is both strain and time dependent [49]. This is shown by the two equations below.

𝜎(𝜖(𝑡), 𝑡) = ∫ 𝐺(𝜖(𝜏), 𝑡 − 𝜏)𝑡

0

𝜕𝜖(𝜏)

𝜕𝜏𝑑𝜏 (8)

𝐺(𝜖, 𝑡) = 𝐺∞(𝜖) + ∑ 𝐺𝑖(𝜖)𝑒−

𝑡

𝜏𝑖

3

𝑖=1

(9)

Where 𝐺∞(𝜖) represents the strain-dependent long term modulus and 𝐺𝑖(𝜖) represents the strain-

dependent moduli corresponding to 𝜏𝑖 time constants.

Poroelastic models describe the viscoelastic behaviour of biphasic materials containing both

solid and fluid phases (ie. porous materials) where specific knowledge of fluid flow is desired. It

is traditionally used to characterize cartilage tissue but has been extended for use in brain tissue

due to its porous nature [40], [50], [51]. The model assumes the solid phase to be elastic and

incompressible. The interstitial fluid phase is assumed to be incompressible. Viscoelasticity is

24

then described by the solid-fluid interaction of both phases [52]. During a stress relaxation

protocol involving compression, the fluid phase is exuded from the tissue as strain is applied.

This allows the solid phase to compact due to its porous nature. While the strain is held, the fluid

remaining in the tissue redistributes within the interstitial spaces leading to an equilibrium state.

As a result, this model is a function of permeability and the aggregate modulus of the tissue.

Permeability describes the relative fluid motion with respect to the porous solid matrix. It

indicates how slowly or quickly stress relaxation occurs. A lower permeability means a lower

exudation rate yielding higher stresses and a slower relaxation and vice-versa [50]. Aggregate

modulus describes the equilibrium stiffness of the tissue.

Isotropy and transverse isotropy refers to whether or not a material exhibits directional

properties. Isotropic materials have uniform properties in all directions whereas anisotropic

materials do not. Transverse isotropy is a subset of anisotropy. These materials exhibit uniform

properties in the local sagittal, and coronal planes and different properties in the transverse plane.

Grey and white matter tissue are hypothesized to exhibit isotropic and transversely isotropic

material properties respectively [11], [41], [56], [57].

1.6.3 Spinal Cord Computational Models

Various constitutive models have been combined and tested using computational finite element

models to investigate internal stress and strain distributions within the spinal cord [4]–[8], [58].

Stress and strain distributions reveal highly concentrated areas which may correlate with

localized tissue damage allowing one to establish a stress and/or strain based injury criterion.

Computational models and their outputs are completely dependent on their underlying material

properties. This was shown in two studies that compared their finite element outputs with tissue

damage in animal SCI models. Maikos et al. and Russell et al. both used a non-linear viscoelastic

constitutive model to characterize the spinal cord however there were many assumptions to their

models. Viscoelastic properties were taken from brain tissue material properties, differences

between grey and white matter properties were omitted, and isotropy of the spinal cord was

assumed [4], [5]. Maikos et al. modeled a weight drop contusion experiment in rats and observed

a stronger correlation with grey matter tissue damage (R2=0.84) than white matter tissue damage

(R2=0.56) when correlated with maximum principal strain [4]. Russell et al. modeled the

25

contusion and dislocation experiments performed by Choo et al.’s study and showed satisfactory

correlations with tissue damage and maximum principal strain. A stronger correlation was found

for contusion (R2=0.86) than dislocation (R2=0.52) injury mechanisms. Grey matter tissue

damage showed a stronger correlation (R2=0.93) while white matter tissue damage correlations

varied depending on the white matter region (0.38 < R2 < 0.96) with maximum principal strain

[5]. It is likely that the lack of conclusive spinal cord material properties led to decreased

biofidelity in these computational models.

In order to increase the reliability of these computational models, recent research has identified

the importance of using separate grey and white matter properties and the inclusion of their

anisotropy [8]. In this study, Jannesar et al. compared a spinal cord finite element model with

histological analysis of tissue damage sustained from a contusion experiment in a non-human

primate (NHP) [8]. This finite element model used distinct material property combinations for

both grey and white matter and are shown in Table 1-1.

Table 1-1: Material property combinations for modeling the spinal cord in finite element

simulations adapted from Jannesar et al. [8]

Model A Model B Model C*

Different grey and white

matter properties

Different grey and white

matter properties

Same grey and white matter

properties

Anisotropic white matter Isotropic white matter Isotropic white matter

Isotropic grey matter Isotropic grey matter Isotropic grey matter

* Identical to the one used in Maikos et al. [4]

The three proposed models above led to substantial differences in strain distributions when

modeled with a finite element simulation. These distributions as well as the resultant tissue

damage observed from the histological analysis are shown in Figure 1-16.

26

Figure 1-16: Maximum principal strain distribution of various material property

combinations for the grey and white matter tissue using Model A (a), Model B (b), Model C

(c). The resultant tissue damage from the NHP contusion injury was stained using

histological analysis (d). This figure was adapted from Jannesar et al. [8]. Reprinted with

permission

The key characteristics of tissue damage from the histology were: the sparing of contralateral

white matter from the impactor site, and the sparing of peripheral white matter underneath the

impactor. Of the three models, model A most closely resembles this case however it is still not

ideal. The magnitude of maximum principal strain observed in model A varies as it propagates

throughout the spinal cord and it is not yet clear whether this translates into an injury criterion

for grey and white matter tissue damage seen in the histology. Model B showed elevated strains

on the contralateral side where there was no tissue damage from histology. Model C

underestimated the tissue damage at the impactor site [8]. This study reinforces the need for

accurately quantifying the material properties of both grey and white matter tissues within the

spinal cord.

1.7 Spinal Cord Mechanical Properties

The mechanical properties of spinal cord grey and white matter tissues have been measured in

several ways in past studies. These different methods have shown that spinal cord tissue

properties are sensitive to several experimental variables. This includes strain rate, time post-

mortem, sample orientation, loading type (ie. compression, tension, shear), material composition

(intact spinal cord, grey matter, white matter), pre-conditioning, species, pre-load, and spinal

level [8], [11], [41]–[43], [47], [56], [57], [59]–[63]. The intact spinal cord is defined as having

27

its dura mater excised but its pia mater intact. Prior to understanding the mechanical properties of

the spinal cord, the relevant types of loading will first be explained.

1.7.1 Loading Types

The mechanical behaviour of the spinal cord was first studied in tension. Tensile deformation is

produced by stretching the spinal cord tissue axially. Both in-vivo and ex-vivo tensile testing of

the intact spinal cord has been performed. The in-vivo studies used multiple sets of rings placed

around the spinal cord with the help of cyanoacrylate adhesive [64]–[66]. The ex-vivo studies

clamped the extremities of the spinal cord between two rigid clamps (ie. plates or pipes) with the

help of cyanoacrylate adhesive [42]–[44], [59], [63], [67]. To perform the test, one end of the

spinal cord is fixed while the other end is displaced axially. Longer tissue lengths are required

for tensile testing as squeezing spinal cord tissue at the extremities introduces undesirable stress

concentrations. If the tissue length was short, this boundary condition will influence the

structural behaviour of the tissue.

The mechanical behaviour of spinal cord white matter tissue has been previously characterized

using unconfined compression. Unconfined compression compresses spinal cord tissue axially

between two rigid parallel platens and allows for lateral expansion of the sample [41], [47]. The

tissue sample needs to possess an aspect ratio opposite to that of tensile testing as the tissue

should not buckle during the test.

Compression of spinal cord tissue can also be performed using confined compression however

this has not been done. Both brain and cartilage tissue have been studied using confined

compression [40], [51], [52], [68], [69]. This loading type places the tissue in a 1D deformation

(uniaxial) state (Figure 1-17). The tissue is placed within a confining chamber possessing rigid

walls on three surfaces. This prevents radial expansion along the side walls unlike in unconfined

compression. A non-porous indenter is used to compress the specimen. The outer diameter of the

indenter is matched as close as possible with the internal diameter of the confining chamber to

create a sliding fit between both mating parts. This tight tolerance prevents expansion of the

tissue at this interface as well. A porous filter is placed below the specimen. Given the biphasic

nature of the tissue, as the tissue is compressed, the fluid exudes through the porous filter

allowing for deformation of the solid phase. The porosity of the filter is selected such that only

the fluid phase is allowed to flow through and not the solid phase.

28

Figure 1-17: Confined compression schematic. The tissue is represented by the dark grey

block applying the reaction force on the nonporous metal indenter. The variable d(t)

represents a displacement controlled actuator that applies a displacement onto the

nonporous indenter deforming the tissue. Reprinted with permission [69]

Indentation measures the local compressive mechanical properties of tissue. It uses a spherical

indenter to compress the tissue sample to prescribed depths. The difference between indentation

and unconfined/confined compression is that the indenter does not cover the full cross-sectional

area of the tissue. It has been used to study grey and white matter tissue [11], [56].

Pipette aspiration measures localized mechanical properties of tissue by applying negative

pressure to aspirate the tissue [60]. The tissue deformation produced using this method was

shown to be comparable to that of tensile deformation [70]. The pipette is connected to a vacuum

pump. The vacuum pump applies negative pressure to the system allowing the pipette to aspirate

the tissue during the experiment. The pipette was used to selectively aspirate both grey and white

matter tissues measuring their mechanical properties [60].

Shear measures the mechanical properties of tissue using mediolateral deformation. There are

currently no studies that have performed shear on the spinal cord. It uses two parallel plates

similar to unconfined compression. Instead of axial deformation, the plates apply mediolateral

deformation. To ensure that no slip occurs between the plate and specimen, cyanoacrylate

adhesive, and/or sand paper are used. Pre-compression of the tissue during the experimental

setup is also required to ensure that the plates are in contact with the specimen. Although it has

29

been previously used to study brain tissue, it has not been used to study spinal cord tissue [57],

[71].

Each loading type deforms the material in a different manner allowing one to investigate the

tissue structure’s sensitivity to different loading types. In the literature, these types of loading

were applied to deform the intact spinal cord, grey matter, and white matter tissue to measure

their respective mechanical properties.

1.7.2 Intact Spinal Cord Mechanical properties

The intact spinal cord’s mechanical properties in tension have been measured both in-vivo and

in-vitro [42]–[44], [65]–[67]. Sample data is shown in Figure 1-18 and the key experimental

parameters are shown in Table 1-2. The in-vivo studies were conducted in puppies and cats. The

stress-strain curves revealed slight strain-stiffening behaviour when small strains were applied.

During the unloading of the spinal cord, hysteresis was observed indicating that the spinal cord

exhibits viscoelastic properties [65], [66].

The in-vitro studies collected spinal cords post-mortem from humans, rats, and pigs. Spinal cords

were tested within 1 hour, 8 hours, and 24 hours for the pig, rat, and human studies respectively

[42]–[44], [67]. Hysteresis was not measured in these studies as a stress relaxation protocol was

used instead. Similar to the studies performed by Hung et al., the spinal cord exhibited a non-

linear stress-strain response with stiffness increasing with increasing strain. Additionally all of

these studies observed the effect of strain rate whereby increasing strain rate increases stiffness

[42]–[44]. For rat and pig studies, peak stress was used as a surrogate for elastic modulus.

30

Figure 1-18: Sample Stress-strain data from several studies of spinal cord mechanical

properties in tension [72]. Reprinted with permission.

31

Table 1-2: Key parameters used in the literature investigating intact spinal cord

mechanical properties [42]–[44], [65]–[67], [73]. The shaded cells indicate that the author(s)

did not measure that quantity.

Author Hung et

al., 1981

Bilston et

al., 1996

Fiford et

al., 2005

Clarke et

al., 2009

Sheteye et

al., 2014

Ramo et al.,

2018

Species Cat, Dog Human Rat Rat Pig Pig

Loading

Type

Tension Tension Tension Tension Tension Tension

Strain rate 0.021

mm/s

0.068 –

0.21 s-1

0.002 –

0.02 s-1

0.002 – 2

s-1

0.1s-1 0.1s-1

Strain 2% 10% 2 – 5% 2 – 5% 1 – 5% 1 – 5%

Time Post-

Mortem

In-vivo 24 hrs 8 hrs 8 hrs 1 hr In-vivo

Intact Spinal Cord

Peak Stress

(kPa)

60 – 190 15 – 75 5 – 15 70 30

Elastic

Modulus

(kPa)

258, 265 1020 –

1370

Equilibrium

Stress (kPa)

50 – 150 15 – 50 2.5 – 8 18 - 35 12 - 22

Time

constant (s)

234 376 83 100 100

Viscoelasticity of the intact spinal cord was described as non-linear viscoelastic [42]–[44], [67],

[73]. The time dependent properties revealed the tissue relaxing to an equilibrium stress in all

studies. The applied strain had a direct correlation on the equilibrium stress with increased strain

leading to increased equilibrium stress. The relaxation behaviour was described using time

constants (ꞇ) within the Prony series. For simplicity’s sake, only the final time constant (ꞇ) is

reported in Table 1-2 as it describes the time it takes for the tissue to relax to an equilibrium. The

relaxation time constants in the majority of these studies were determined from fitting the Prony

series but the majority were reported as non-unique solutions [42]–[44]. Shetye et al., and Ramo

32

et al. reported unique solutions demonstrating that an apparent equilibrium stress was reached

after 100 secs [67], [73]. A limitation to these two studies was that 100 secs of relaxation was not

indicative of the equilibrium behaviour of the spinal cord.

Time post-mortem between euthanasia and mechanical testing has been proposed to affect the

mechanical properties of the intact spinal cord [62], [73], [74]. This may explain the wide range

of peak stress and equilibrium stress results seen in Table 1-2 between ex-vivo and in-vivo

studies. Ramo et al. showed that the time independent and dependent mechanical properties of

the spinal cord change as early as 60 mins after death. The ex-vivo time independent properties

showed greater stiffness than the in-vivo properties. The ex-vivo time dependent properties

showed greater relaxation than the in-vivo properties [73]. Oakland et al., performed tensile

testing on spinal cord tissue using post-mortem times of 3, 24, 48, and 72 hours. They

demonstrated that the tangent modulus of the tissue increased by 15%, 50%, 60%, and 95%

respectively as signs of tissue breakdown and degeneration [62]. Garo et al. performed a similar

study using brain tissue where it was found that the elastic modulus was constant up to a

threshold time of 6 hours, after which the stiffness increased at a rate of 0.45 Pa per minute [74].

These studies provide one possible explanation as to why the human spinal cord peak stress and

aggregate modulus were significantly higher than other studies.

The strain stiffening behaviour observed was an exponential curve and is analogous to that of

collagen fibres under tension. Collagen fibres are known to be initially wavy until fully

straightened out at which point they bear load, thus explaining the exponential phenomenon [75].

This may indicate that axons within the spinal cord may not be fully load bearing until a certain

load is reached. For instance, the axons in the white matter are organized in tracts running

rostralcaudally but the axons within the grey matter are randomly oriented and wavy.

Heterogeneities like this may introduce slack in the spinal cord initially before becoming fully

load bearing. Moreover these studies left the pia mater intact. This is a sheath that is made of

connective tissue and possesses collagen fibres, therefore contributing to the phenomenon

described herein [76].

The effect of pia mater was observed to have a significant effect on the overall stiffness of the

spinal cord structure [77]. One study compared the elastic moduli of spinal cord tissue with pia

mater attached and unattached. To remove the effect of the pia mater, circular incisions were

33

made on the pia mater so that it was discontinuous along its length. The results showed that the

effect of pia mater led to an elastic modulus that was over 10 times stiffer than without it [77].

This shows that the pia mater plays an important structural role in the spinal cord. This study also

provides the need to further investigate the mechanical properties of the spinal cord in terms its

constituents (ie. grey and white matter tissue).

1.7.3 Spinal Cord Grey Matter and White Matter Mechanical properties

The mechanical properties of grey and white matter within the spinal cord are controversial.

Some researchers have found the grey matter to be stiffer than the white matter [11], [59], [63],

one has found the white matter to be stiffer than the grey matter [58] and one saw no difference

between the two [60].

Table 1-3 highlights key parameters used for comparing grey matter and white matter

mechanical properties. Similar to the intact spinal cord, several mechanical variables influenced

the mechanical properties of the grey and white matter tissue during ex-vivo testing. It was noted

that four of six studies shown in Table 1-3 reported completing their mechanical tests within 6

hours of euthanasia.

34

Table 1-3: Key parameters used in the literature to compare grey and white matter

properties from the literature [11], [41], [47], [59], [60], [63]. The shaded cells indicate that

the author(s) did not measure that quantity.

Author Ichihara et

al., 2001

Ichihara et

al., 2003

Ozawa et

al., 2001

Koser et al.,

2015

Sparrey et

al., 2011

Jannesar et

al., 2018

Species Cow Cow Rabbit Mouse Pig NHP

Loading Type Tension Tension Pipette

Aspiration

(Tensile)

Indentation Unconfined

compress-

ion

Unconfined

compression

Strain rate 0.05 s-1 0.0003 –

0.03 s-1

1 cm

H20/s

0.02 s-1 0.005 – 5 s-1 0.3 – 77 s-1

Strain 5 - 40% 10 - 30% 5 cm H20 0.4 – 0.7% 40% 45%

Time Post-

mortem

Not

specified

Not

specified

1 hr 6 hrs 4 hrs 1 hr

Grey Matter

Peak Stress

(kPa)

42 3 – 34

Elastic

Modulus (kPa)

166* 64 – 112* 3.3 0.127

Equilibrium

Stress (kPa)

1 – 13

Time constant

(s)

White Matter

Peak Stress

(kPa)

26 3 – 19 0.8 – 3.9 7 – 21

Elastic

Modulus (kPa)

94* 30 – 64* 3.2 0.067

Equilibrium

Stress (kPa)

1 – 5 2 0.5

Time constant

(s)

54 2

*Tangent modulus was measured in the linear region of the loading curve

35

The time independent properties for grey and white matter exhibited similar trends to the intact

spinal cord described earlier. The stress strain relationship of both grey and white matter tissue

exhibited a strain stiffening curve regardless if the tissue was in tension or compression. Strain

rate was also directly correlated with increased peak stress [41], [47], [59].

The time dependent properties for grey and white matter also exhibited similar trends to the

intact spinal cord. Grey and white matter tissue showed immediate relaxation when the

maximum strain was held. The behaviour was described as non-linear viscoelastic [41], [47],

[59]. The behaviour showed that increased overall strain led to increased equilibrium stress [59],

[63]. It also characterized the relaxation behaviour using several time constants. The final time

constants are reported in Table 1-3. It was not specified whether these solutions were unique and

so interpretations of these time constants will not be made.

Grey and white matter tissue equilibrium stress was observed to be minimally affected by strain

rate. This was not observed in the intact spinal cord. In tensile studies, equilibrium stress

remained unchanged despite applied strain rates that were two orders of magnitude apart [59]. In

compressive studies which were only performed for white matter, it remained unchanged despite

using strain rates that were two to three orders of magnitude apart [41], [47]. A limitation to this

analysis was that the relaxation times in these studies were held for only 60 – 100 secs which

may not be fully indicative of the equilibrium behaviour of the tissue.

The compressive strain stiffening behaviour of spinal cord tissue cannot be explained using the

collagen theory proposed earlier. It has been hypothesized that axons in nervous tissue act

similarly to collagen fibres in tendons or ligaments such that fibres carry negligible load in

compression [8], [78]. Instead biphasic theory can be used to explain this phenomenon. This

theory is well established in the cartilage community for explaining strain stiffening behaviour

[79]–[81]. The spinal cord is in fact a porous biphasic structure. It is composed of both solid

(neurons, axons, glial cells) and fluid phases (CSF, blood plasma). One study measured the

spinal cord to have a wet weight of 66% [82] while another study measured brain tissue to have a

wet weight of 82% [51], indicating that the solid-fluid interaction within nervous tissue is an

important consideration. As the spinal cord tissue is initially compressed, the flow of interstitial

fluid escapes through the permeable solid matrix. As further compressive strain continues, there

is a decrease in permeability within the tissue as the solid matrix compacts on itself and the pores

36

shrink in size. This increases the flow resistance of the interstitial fluid leading to higher stresses

required to compress the tissue [40], [80]. During the relaxation phase, the solid matrix

compaction is held and the fluid redistributes within the tissue resulting in stress relaxation until

an equilibrium is reached [79].

The results of in-vivo and ex-vivo tissue properties comparing grey and white matter concluded

different results. Most studies involving ex-vivo tissue testing indicated that grey matter is stiffer

than white matter based on their elastic modulus and peak stress according to Table 1-3 [11],

[59], [63]. A recent study by Sharkey et al., revealed that white matter was twice as stiff as grey

matter [58]. The difference in this study was that the results collected were modeled after an in-

vivo animal model contusion study conducted previously [83]. The method used an inverse finite

element approach whereby the mechanical properties of the spinal cord tissues were estimated

based on the deformation seen within the grey and white matter. The deformation was recorded

using MRI images taken during the actual contusion injury of the animal [58]. Although peak

stress nor elastic modulus were directly measured, the relative properties between the grey and

white matter were estimated. It is likely that these results differ than that of ex-vivo studies due to

the effect of time post-mortem, and the higher strain rates used. A limitation to this study was the

resolution of the MR images made it difficult to precisely characterize the deformation of both

grey and white matter tissue.

Sharkey et al.’s study was the first to report white matter to be stiffer than grey matter in the

spinal cord. Comparing this study with brain tissue mechanical properties, it is consistent with

Feng et al.’s ex-vivo study where white matter was found to be stiffer than grey matter in shear

and indentation [56]. However Prange & Margulies also performed shear on brain tissue and

observed that grey matter was stiffer than white matter [57]. These inconsistencies in both spinal

cord and brain tissue literature highlight the need to further investigate grey and white matter

mechanical properties.

1.7.4 Spinal Cord Grey Matter and White Matter Anisotropy

Spinal cord tissue anisotropy has not been studied often and is often neglected. This is surprising

as other biological tissues possessing a distinct fibre orientation were found to have anisotropic

mechanical properties. The directional nature of spinal cord white matter (Figure 1-10) suggests

37

that anisotropy may play an important role in the mechanical properties of the spinal cord. The

few key studies summarizing this topic are discussed below.

Galle et al. first modeled the spinal cord white matter as transversely isotropic. Quasi-static axial

tensile tests were performed on white matter and were characterized using different theoretical

mathematical models (ie. strain energy density functions). Two distinct strain energy functions

were used to characterize the experimental data. The first was an isotropic material model

whereas the second augmented the first model with a function that represented the contribution

of the axons [84]. The latter proved to be a better fit than the former indicating that white matter

likely behaves like a transversely isotropic material in tension.

Jannesar et al. conducted a similar study to Galle et al. that expanded on the former study’s

findings. The strain energy function here was conditional depending on whether the white matter

tissue was loaded in compression or tension. In compression the model described an isotropic

material whereas in tension it switches to a transversely isotropic model. This was to incorporate

the mechanical contribution of axons in tension while ignoring them in compression. This model

was shown to accurately characterize various white matter compression and tension studies

within the literature indicating that white matter likely behaves like a transversely isotropic

material [8], [47], [59].

In the same study, Jannesar et al. tested various spinal cord grey and white matter material

combination models in a finite element simulation. Theycompared their results to a contusion

injury on a NHP to further assess the validity of transverse isotropy in white matter tissue. This

was illustrated in Table 1-1 and Figure 1-16. To reiterate, Model A which accounted for the

white matter’s transverse isotropy most closely resembled the features observed in the in-vivo

injury revealing that accounting for white matter anisotropy resulted in better correlations with

tissue strain distributions [8].

The studies conducted by Galle et al. and Jannesar et al. proposed theoretical models to describe

white matter anisotropy but did not involve experimental testing of specimens in different

directions. A literature search revealed only two studies that experimentally evaluated the

directional properties of spinal cord grey and white tissue [11], [60]. In these studies grey matter

was tested in two orthogonal orientations while white matter was tested with axon fiber direction

parallel and perpendicular to the applied load. An anisotropy ratio between transverse and axial

38

directions was included to quantify the degree of anisotropy that exists between orthogonal

directions. These results are shown in Table 1-4.

Table 1-4: Key parameters used in the literature to compare grey and white matter

anisotropy properties from the literature [11], [60].

Author Ozawa et al., 2001 Koser et al., 2015

Species Rabbit Mouse

Loading Type Pipette Aspiration (Tensile) Indentation

Strain rate 1 cm H20/s 0.02 s-1

Strain 5 cm H20 0.4 – 0.7%

Grey Matter

Axial Transverse Sagittal Axial Transverse Sagittal

Elastic Modulus (kPa) 3.4 3 3.5 0.125 0.128 0.127

Anisotropy Ratio 0.9 1.0

White Matter

Axial Transverse Sagittal Axial Transverse Sagittal

Elastic Modulus (kPa) 3.4 3.5 2.8 0.048 0.075 0.077

Anisotropy Ratio 1.0 1.6

The results suggested that grey matter behaved like an isotropic material as its anisotropy ratio

was approximately equal to one. White matter displayed mixed results with one study suggesting

that it behaved like an isotropic material (anisotropy ratio equal to one) and the other suggesting

that it behaved like an anisotropic material (anisotropy ratio not equal to one).

There are limitations to the study by Ozawa et al. as their test protocol involved aspiration of

tissue while the spinal cord was still intact. It was not clear whether the meninges were removed

prior to testing. This confounds the results as it was seen earlier that the pia mater had an impact

on the stiffness of the spinal cord.

The study by Koser et al. is consistent with the transversely isotropic theoretical model proposed

by Galle et al. and Jannesar et al. above. For white matter, both transverse and sagittal planes

39

displayed identical elastic moduli while the axial plane showed a significantly lower elastic

modulus. This reaffirms that axons bear negligible load in compression. For grey matter, it is

hypothesized as isotropic as it consists of randomly oriented axons, dendrites and neurons. These

distinct features are consistent with the tissue structures seen in Figure 1-8 and Figure 1-10 [11].

There is a limitation to the study by Koser et al.. Although these studies used isolated grey and

white matter tissue samples unlike Ozawa et al., it was performed at the cellular level. This may

not be indicative of SCI where bulk tissue deformation is often encountered [11]. This is

important as the mechanical properties of the tissue may more likely be governed by the

extracellular matrix than the cells themselves during SCI.

A literature review of mechanical anisotropy in brain grey and white matter was included to

supplement the scarcity of spinal cord tissue data presented in Table 1-4. Here the test protocols

were similar to that used for spinal cord tissue. Brain grey matter was tested in two orthogonal

orientations and brain white matter was tested with axon fiber direction parallel and

perpendicular to the applied load. Table 1-5 summarizes the anisotropy ratio for both grey and

white matter tissue within the brain. Although loading type and outcome variable (ie. peak stress,

shear modulus, elastic modulus) differ from study to study, anisotropy ratio is a dimensionless

quantity allowing for comparisons to be made between studies.

Table 1-5: Brain anisotropy ratio in the literature, categorized by loading type [56], [57],

[71], [85]. The shaded cells indicate that the author(s) did not measure that quantity.

Study Loading Type Grey Matter White matter

Prange & Margulies, 2002 Shear 1.0 0.7

Feng et al., 2013 Shear 1.0 0.6

Indentation 1.0 2.4

Budday et al., 2017 Tension 0.7

Compression 1.7

Schmidt et al., 2017 Shear 0.8

Magnetic Resonance Elastography

(MRE)

0.8

40

It is evident from the data in Table 1-5 that grey matter exhibits isotropic properties and that

white matter exhibits anisotropic properties in the brain. Interestingly, white matter was observed

to exhibit different mechanical properties depending on the loading type that was applied. White

matter was stiffer when shear was applied parallel to the axons as opposed to perpendicular to

the axons. This was also true for when axons were loaded in tension. On the contrary, the

opposite was true when a compressive load was applied parallel to the axons. This is consistent

with the models proposed previously explaining that axons carry negligible load in compression

[8], [11]. The findings shown in brain tissue studies further reinforce the need to investigate the

directional properties of spinal cord grey and white matter.

1.7.5 Gap in literature

There is a need to better understand the mechanical properties of spinal cord grey and white

matter in terms of tissue type and direction. There is little consensus on whether grey matter is

stiffer than white matter or vice-versa. Furthermore, few researchers have examined the

directional properties of both tissue types. Lastly, the spinal cord’s mechanical response to

confined compression has not been studied.

1.8 Thesis

1.8.1 Research Question

This study aims to provide an understanding to answer the following research question:

“What is the effect of tissue type (grey matter vs. white matter) and the effect of direction (axial

direction vs transverse direction) on the mechanical properties of the spinal cord under confined

compression.”

1.8.2 Thesis Objectives

The objectives for this thesis were:

1) To design and build a confined compression apparatus capable of individually testing

spinal cord grey and white matter tissue;

2) To characterize the non-linear viscoelastic nature of spinal cord grey and white matter

tissue in confined compression using a constitutive model;

41

3) To examine the effect of tissue type, direction, and their interaction on the mechanical

properties of spinal cord grey and white matter in confined compression.

1.8.3 Hypotheses

The hypotheses for this thesis are:

1) Grey matter will exhibit a larger stiffness than white matter regardless of direction in

confined compression;

2) Grey matter will exhibit isotropic properties (ie. Anisotropy ratio = 1) in confined

compression;

3) White matter will exhibit anisotropic properties (ie. Anisotropy ratio ≠ 1) with stiffness

greater in the transverse direction relative to its axial direction in confined compression.

1.8.4 Scope

The current study will investigate the mechanical properties of the spinal cord grey and white

matter by conducting ex-vivo tissue testing in a porcine model immediately following euthanasia.

The confined compression apparatus will be designed and integrated with an electromagnetic

actuator. This apparatus will test four individual sample types: grey matter axial direction, grey

matter transverse direction, white matter axial direction, white matter transverse direction. A

stress relaxation protocol and a constitutive model will be used to quantify the time independent

and dependent mechanical properties. This study will involve a 2x2 factorial design investigating

the effects of tissue type and direction on the mechanical properties of the spinal cord. Lastly

following mechanical testing, histology will be conducted to qualitatively verify the grey and

white matter tissues that were tested.

42

Chapter 2: Methods

2.1 Mechanical Design of the Biopsy Punch & Confined Compression

Apparatus

The overall goal of the design was to collect spinal cord tissue and measure its mechanical

properties in confined compression. Due to the lack of an apparatus capable of performing

confined compression within the OIBG lab, the following design criteria were developed to

guide the mechanical design process of a new confined compression apparatus.

1) To collect four spinal cord tissue samples of grey and white matter in different

orientations from the pig spinal cord;

2) To maintain the orientation of the tissue sample after collection from the spinal cord and

for mechanical testing;

3) To minimize tissue degradation from post-mortem effects;

4) To test the spinal cord tissue with a stress relaxation protocol to measure its time

independent and time dependent properties. This protocol consists of:

a. A quasi-static strain rate followed by holding of the peak strain and

b. Measuring the loading and relaxation behaviour of the tissue;

5) To measure the mechanical properties of the tissue with high repeatability.

The final mechanical design consisted of two components: a custom biopsy punch and a

confined compression apparatus. The custom biopsy punch addressed design criteria numbers

one to three. Its integration with a confined compression apparatus addressed design criteria

numbers four and five. All computer-aided design (CAD) models were drafted using Solidworks

(2017, Dassault Systems, Concord, MA). The engineering drawings are included in Appendix A.

2.1.1 Biopsy Punch Design

The custom biopsy punch was a novel biopsy punch design modeled after an off the shelf skin

biopsy punch. The literature demonstrated that off the shelf skin biopsy punches were effective

for collecting isolated spinal cord tissue samples [41], [47]. Their effectiveness is a product of

their sharpened circular blade whereby twisting and punching motions are able to cut spinal cord

tissue.

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The design for the custom biopsy punch consisted of three individual elements that were the

handle, adapter, and punch tube (Figure 2-1). The punch tube (New England Small Tube,

Litchfield, NH) was 2 mm nominal diameter and was sharpened at one end for cutting. This

punch tube was welded within the adapter, and the handle was threaded into the adapter.

Figure 2-1: Custom biopsy punch. The punch tube was welded within an adapter and was

threaded onto a handle.

The 2 mm diameter punch tube was selected based on the available amount of grey and white

matter tissue in their different orientations. Four samples were collected: grey matter axial (GA),

grey matter transverse (GT), white matter axial (WA), and white matter transverse (WT).

Although the pig spinal cord measured approximately 6 mm in diameter, the maximum diameter

of tissue samples available was 2 mm. This served as a design constraint to maintain as much

homogeneity as possible within the collected tissue samples. Maintaining homogeneity meant

preventing contamination of grey matter tissue samples with white matter tissue and vice-versa.

Figure 2-2 highlights the approximate spinal cord tissue location of where samples were

collected.

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Figure 2-2: Cross-section of the spinal cord showing grey matter axial (GA) (a), grey

matter transverse (GT) (b), white matter axial (WA) (c), and white matter transverse (WT)

(d) specimens. The circle and rectangle illustrate specimens that are ollected axially

(through the page) and transversely (across the page) respectively. The sample dimensions

denoted by the circles and rectangles are roughly to scale. The amount of grey and white

matter in the spinal cord is specific to the spinal cord region (cervical, thoracic, and

lumbar). As such the image may not accurately reflect the amount of grey and white matter

observed in the spinal cord tissue used in this study. The image is adapted from Polarlys –

CC by SA 3.0

Figure 2-2 shows that the biopsy punch is able to collect the four specified specimen types thus

meeting the first design criteria. The rationale for collecting these four specimens types were to

compare the mechanical properties between tissue type and direction. The axial direction

denoted tissue samples parallel with the axial (rostralcaudal) direction, whereas transverse

direction denoted tissue samples collected perpendicular to the direction of the axons.

The second and third design criteria were met by the custom biopsy punch’s removable feature.

The adapter can be removed from the handle and integrated within the confined compression

apparatus. This feature allowed the adapter to be re-used as the vessel for performing confined

compression. During preliminary work with spinal cord tissue, a standard skin biopsy punch was

45

used. The tissue sample had to be transferred out of the punch and into another vessel for

mechanical testing. The transferring led to a lack of containment around the tissue resulting in

tissue degradation. Spinal cord tissue samples without their pia mater were observed to collapse

under their own weight. During the transfer the specimen was also able to rotate in space leading

to a loss of specimen orientation. These reasons provided justification for the biopsy punch

design. By keeping the tissue within the punch tube, the punch tube walls preserved its structure

and orientation prior to mechanical testing.

2.1.2 Confined Compression Apparatus Design

The confined compression apparatus was designed to model the confined compression schematic

shown in Figure 1-17. It incorporated identical components that were the nonporous indenter, a

confining chamber, and a porous filter. The goal of the apparatus was to integrate the biopsy

punch adapter within it since the spinal cord tissue was left within the biopsy punch tube. This

led to the following design concept meeting the fourth design criteria (Figure 2-3).

Figure 2-3: Confined compression schematic of tissue sample. A sectional view of the

adapter is shown illustrating key components involved in confined compression. The

specimen shown is approximately to scale.

46

The concept used the biopsy punch tube walls as the confining chamber for the spinal cord

tissue. The biopsy punch tube was positioned vertically so that it sat flush with a porous filter

below it. This meant that the spinal cord tissue within it would also be positioned on top of the

porous filter. A nonporous indenter was inserted into the biopsy punch tube from above. This

nonporous indenter was connected to an actuator that applied uniaxial deformation to the spinal

cord tissue. A load cell was mounted beneath the porous filter to measure the mechanical

behaviour of the spinal cord tissue.

2.1.1.1 Confined Compression Apparatus Overview

The confined compression apparatus (Figure 2-4) consisted of four components: an

electromagnetic actuator (TestBench ELF LM-1, TA Instruments, New Castle, DE), a magnetic

end effector, a nonporous indenter, and a confined compression fixture. The overview for this

apparatus will be described from the bottom up.

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Figure 2-4: Confined compression apparatus with key components labeled. The

electromagnetic actuator was mounted above the confined compression fixture. The

magnetic end effector was threaded into the actuator. The nonporous indenter is not shown

in this figure due to its small size. It is shown in Figure 2-6 instead.

2.1.1.2 Confined Compression Fixture

The confined compression fixture (Figure 2-5) was designed to position the specimen so that

uniaxial deformation of the specimen occurred. It incorporated the confining chamber, porous

filter, and load cell elements from Figure 2-3. The entire fixture was placed underneath the

actuator. The biopsy punch adapter was placed within the adapter holder. This positioned the

biopsy punch tube containing the spinal cord tissue vertically. The adapter holder could be

lowered and raised vertically using the Z-axis translation table. This lowered the biopsy punch

tube against the porous filter (PN#: 9446T32, McMaster Carr, Aurora, OH) below it. The porous

filter was placed in a filter holder which sat atop a 10 N load cell (Sensotec 31E, Honeywell

Corp., Columbus, OH).

48

Figure 2-5: Confined compression fixture with parts labeled. This fixture was machined by

the British Columbia Cancer Agency machine shop.

2.1.1.3 Load Cell Sizing

The load cell used in this design was selected based on peak stresses measured in Haslach et al.’s

confined compression study of brain tissue. The measured force was calculated using their stress

criterion and the 2 mm diameter specimen geometry in this study. Haslach et al. measured peak

stresses ranging from 16 kPa – 171 kPa [51]. This resulted in measured peak forces of 0.05 N –

0.6 N for this work. This amounted to 0.5% - 6% of a 10 N load cell’s full scale capacity. In

theory, it would be better to use a 1 N load cell however static weight which included the

adapter, porous filter, and filter holder were placed on top of the load cell. This static weight

weighed 71 g (0.7 N). With the added weight, the operating range was between 7.5% – 13% of

the load cell’s full scale. As a result, the 10 N load cell (Sensotec 31E, Honeywell Corp.,

Columbus, OH) was selected.

49

2.1.1.4 Nonporous Indenter

The nonporous indenter consisted of a carbon steel disc, a head piece and a shaft (Figure 2-6).

The carbon steel disc possessed the same diameter as the head piece. It was attached to the head

piece with tape along the circumference of both parts. The shaft was welded within the head

piece. The diameter of the shaft (New England Small Tube, Litchfield, NH) was sized to be a

sliding fit (<0.05mm) with the biopsy punch tube. The nonporous indenter was inserted into the

biopsy punch adapter from above.

Figure 2-6: Nonporous indenter with parts labeled. The welding was performed by the

British Columbia Cancer Agency machine shop.

While it was being inserted, a spacer was added to initially support the nonporous indenter. The

nonporous indenter was supported to avoid premature compression of the spinal cord tissue

within the biopsy punch tube during setup and prior to mechanical testing (Figure 2-7). A folded

piece of cardboard was sufficient to support the weight of the spacer.

50

Figure 2-7: The nonporous indenter was inserted into the adapter and initially supported

with a spacer to avoid contact with the specimen.

The tolerance between the nonporous indenter and punch tube of the adapter was minimized by

the manufacturer to prevent any fluid and/or tissue extrusion through this interface. Gervaso et

al. performed a computational study on a non-specific biphasic soft tissue (elastic modulus = 0.5

MPa) to study the effect of a gap existing between the nonporous indenter and the confining

chamber. They showed that a 2% gap was directly correlated with 2% error in aggregate

modulus and 6% error in permeability for up to 25% strain in the soft tissue [86]. The percentage

gap for the design presented in this study was calculated with the following equation.

% 𝑔𝑎𝑝 =𝑑𝑐𝑜𝑛𝑓𝑖𝑛𝑖𝑛𝑔 𝑐ℎ𝑎𝑚𝑏𝑒𝑟 − 𝑑𝑛𝑜𝑛𝑝𝑜𝑟𝑜𝑢𝑠 𝑖𝑛𝑑𝑒𝑛𝑡𝑒𝑟

𝑑𝑐𝑜𝑛𝑓𝑖𝑛𝑖𝑛𝑔 𝑐ℎ𝑎𝑚𝑏𝑒𝑟∗ 100 (10)

Where d represents the diameter of both the confining chamber and the nonporous indenter. The

gap for this design was calculated to be a maximum of 2.3%. Relative to other confined

compression studies of brain tissue, and cartilage, this was within the range of 0.12% - 3.5%

which has been reported previously [51], [68], [87]. It was important to note that this gap cannot

51

be removed. Otherwise, the nonporous indenter will not move smoothly in relation to the biopsy

punch tube.

2.1.1.5 Magnetic End Effector

The magnetic end effector was mechanically threaded into the actuator above. It consisted of an

extended shaft with a magnetized tip (Figure 2-8) at the distal end. The magnetic tip was

constructed with a carbon steel plate, magnet, a steel washer, and 3/8” carbon steel ball. The

carbon steel plate was glued onto the distal end of the shaft. The magnet was placed on the

carbon steel plate. The steel washer was placed on the magnet, and the carbon steel ball was

seated on the washer. The purpose of the washer was to prevent the ball from rolling around.

Figure 2-8: Magnetic end effector with parts labeled.

2.1.1.6 Actuator

The electromagnetic actuator (TestBench ELF LM-1, TA Instruments, New Castle, DE) was

controlled by WinTest7 Software (EnduraTEC, Penetanguishene, ON, Canada) with a

proportional-integrative-derivative controller, and an internal linear variable differential

52

transformer (LVDT, EnduraTEC, Model 310111, Penetanguishene, ON, Canada). The actuator

was mounted on an elevator shaft. This elevator was driven by a servomotor and adjusted the

physical height of the actuator. The actuator was responsible for applying uniaxial deformation

to the spinal cord tissue within the biopsy punch tube using the magnetic end effector and the

nonporous indenter.

2.1.1.7 Design Feature #1: Connection between the Nonporous Indenter and the Magnetic End

Effector

In order for deformation to be applied, the nonporous indenter sitting in the biopsy punch tube

below needed to be connected to the actuator above. However the nonporous indenter and the

magnetic end effector were initially disconnected. This design was necessary in order to mitigate

alignment issues that were identified during proof of concept testing. Initially the nonporous

indenter was mounted directly onto the actuator above and was carefully guided into the

confining chamber below. This introduced two alignment issues resulting in long precarious

setup times. First there was the need to perfectly align the nonporous indenter above with the

confining chamber below. This was difficult due to the tight tolerance between the indenter and

the confining chamber. Second, it was necessary to ensure that the actuator above was perfectly

leveled. Any tilt introduced unwanted transverse and frictional forces between the indenter and

the confining chamber.

In order to mitigate the alignment issues discussed, the nonporous indenter was connected to the

actuator above by the magnetic attraction between the magnetic end effector and nonporous

indenter (Figure 2-9). To enable this connection to the actuator, the actuator was physically

lowered until the nonporous indenter was in close proximity with the magnetic end effector.

Once the nonporous indenter was attached to the actuator, the spacer was removed.

This design feature had two advantages. It solved the issue of perfect concentric alignment as the

nonporous indenter was already guided within the confining chamber. Second, the ball point

contact guaranteed only uniaxial forces were transmitted onto the nonporous indenter. This

solved the leveling issue of the actuator as transverse forces will not be introduced.

53

Figure 2-9: Magnetized connection between the magnetic end effector and the nonporous

indenter. The magnetized steel ball and the nonporous indenter were initially disconnected

from each other. To use, the steel ball was lowered until it attracted the nonporous indenter

below at which point the spacer was removed. Since the nonporous indenter was already

constrained within the bore of the adapter, the alignment issue was mitigated.

2.1.1.8 Design Feature #2: Tissue Leakage Prevention

Preliminary trials showed tissue leakage between the punch tube and porous filter when the

nonporous indenter compressed the tissue. The design intended for the punch tube to sit flush

with the porous filter providing an impermeable seal at this interface. However asperities were

formed at the porous filter and punch tube interface resulting in tissue leakage.

To address this issue, a square profile O-ring (PN#: 1170N15, McMaster Carr, Aurora, OH) was

inserted around the outer diameter of the punch tube to provide a seal at this interface (Figure

2-10). It was placed prior to lowering the adapter against the porous filter (Figure 2-11a). The

tolerance between the internal diameter of the O-ring and the external diameter of the punch tube

was +0.035mm making it easy to slide on by hand. To ensure the O-ring provided a tight seal,

54

the adapter holder was lowered further after the biopsy punch tube contacted the porous filter to

compress the O-ring (Figure 2-11b). This added compression filled the crevices forming an

impermeable seal at this interface.

Figure 2-10: The schematic from Figure 2-3 was updated to show the placement of the

square profile O-ring. This prevented tissue leakage from occurring between the porous

filter and the biopsy punch tube interface.

55

Figure 2-11: The square profile O-ring was first slipped onto the punch tube prior to

lowering the biopsy punch tube (a). Once the punch tube was lowered, the adapter holder

was further lowered until it contacted the O-ring and compressed it against the porous

screen (b).

Although the added compression of the O-ring was successful with sealing the interface, its

viscoelastic load-relaxation behaviour was measured by the load cell. The O-ring exhibits

viscoelastic properties given that it is made of rubber. This brought the need to introduce a

stabilization protocol. Before beginning each test, the entire system was left to stabilize from

compression of the O-ring. This meant that the rubber was allowed to relax to an equilibrium

before initiating compression on the spinal cord tissue. This was done to avoid confounding the

mechanical properties of the rubber with the tissue.

The stabilization protocol was proven successful through several air tests. The procedure for

these air tests involved no compression of tissue. The O-ring was first compressed with a pre-

compression of 0.6 N and then allowed to relax to an equilibrium state. An equilibrium state was

reached when the load cell measurement did not fluctuate beyond +/-0.015 N over a couple of

minutes. The nonporous indenter was then prescribed a displacement to verify whether any

forces would result throughout the stroke of the actuator. It was observed that the load cell did

56

not measure any load behaviour from the O-ring. The results for this test are shown in Appendix

B.

2.1.2 Verification of the Load Cell Accuracy

To ensure the accuracy of load cell, it was necessary to calibrate the load cell with standard

weights prior to data collection. Standard weights were chosen based on the measuring range for

this study. It was estimated earlier that 7.5% - 13% of the load cell’s full scale will be used in the

experiments. As such, three standard weights of 50 g, 100 g, and 150 g equating to 5%, 10%, and

15% of the load cell’s full scale were used. Each mass was measured using the load cell and the

error was computed with the following equation.

𝐸𝑟𝑟𝑜𝑟 % =|𝑚𝑡𝑟𝑢𝑒 − 𝑚𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑|

𝑚𝑡𝑟𝑢𝑒∗ 100% (11)

Where 𝑚𝑡𝑟𝑢𝑒 and 𝑚𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 were the true and measured weights as described above. All

measurements were tabulated and shown in Appendix C. The error measured was approximately

+3%, meaning the load cell overestimated the true weight. As a result the voltage gain factor

originally applied to relate force and voltage was decreased by this amount.

2.1.3 Verification of the Confined Compression Apparatus Repeatability

The repeatability of the mechanical design was measured and validated to meet the fifth design

criteria. For this, an inert surrogate material (QM Skin 30) was used in place of spinal cord

tissue. This was a silicone elastomer that was previously developed in the OIBG lab as a

surrogate spinal cord. This material was chosen as it exhibited a similar compressive stiffness

(elastic modulus = 0.20 MPa) to that of in vivo animal spinal cords [88].

The repeatability analysis involved repeated confined compression of the silicone specimen. To

prepare the specimen, a 2 mm cross-section of the silicone spinal cord was cut using a scalpel.

The custom biopsy punch was then used to core out a specimen. The adapter was integrated into

the confined compression apparatus and the silicone was compressed repeatedly using the same

parameters.

The variability between repeated confined compression tests of the same silicone specimen was

measured in this repeatability analysis. The rationale for re-using the same silicone specimen was

to maintain the same geometric imperfections within the specimen throughout each test. To

57

ensure that previous stress-strain history within the material did not affect each successive test,

the specimen was allowed to relax for at least 30 mins between tests. Coefficient of variation

(COV) was used as a metric to measure the variability between tests. It was calculated with the

equation below. The maximum peak stress COV was found to be between 4 – 6%, which was

deemed acceptable. The results are shown in Appendix D.

𝐶𝑂𝑉 =𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛

𝑀𝑒𝑎𝑛 (12)

It was recognized that silicone was not a porous biphasic material like spinal cord tissue.

However repeatable peak stresses were achieved using an inert material. This demonstrated that

the confined compression apparatus was capable of measuring results with precision.

2.1.4 Pilot Test Validation for Mechanical Design

There were several pilot tests performed prior to finalizing the design of the custom biopsy

punch and confined compression apparatus discussed in Section 2.1.1 and 2.1.2. These were

necessary to confirm the validity of individual components to the design. These pilot tests

ensured:

1) That tissue did not clog the porous filter in confined compression;

2) That the load cell and LVDT used were capable of measuring the tissue’s time

independent and dependent properties.

2.1.4.1 Porous Filter

The porosity of the porous filter needed to be sized to allow fluid but not tissue flow. The

literature demonstrated that confined compression of brain tissue could lead to tissue clogging

the porous filter due to its soft nature [40]. A 20 micron and a 40 micron porous filter were

trialed as these were previously used by Haslach et al. [51]. The sizing refers to the pore size of

the filter indicating the largest particle size that can pass through. A pilot test (Figure 2-12)

involving the following setup was used to verify the appropriate filter size.

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Figure 2-12: Pilot test for testing the permeability of various screens

The pilot test involved several components to replicate the confined compression setup in Figure

1-17. An acrylic disc was drilled through its centre using a 2 mm diameter drill bit to be used as

the confining chamber. A small container was used to hold the porous screen so that the acrylic

disc can be placed on top. The tissue was collected using a skin biopsy punch and then

transferred into the acrylic disk. The 2 mm drill bit used to bore the hole was turned upside down

so that the flat end could be used as the nonporous indenter to compress the tissue. This allowed

for a tight tolerance fit between the nonporous indenter and the confining chamber.

The filter was verified under a microscope following tissue compression. It was observed that no

tissue clogged the 20 micron filter while the 40 micron filter showed residue within the pores of

the filter. As a result the 20 micron screen was selected for the final design of the confined

compression apparatus.

2.1.4.2 Measuring Time Independent and Dependent Properties of Spinal Cord Tissue

The second pilot study verified the LVDT and load cell’s sensitivity to measuring the time

independent and dependent properties of spinal cord tissue. In other words, the instrumentation

needed to measure a strain-stiffening behaviour during its loading phase followed by immediate

relaxation when subjected to a displacement profile involving a linear ramp strain followed by

the peak strain being held.

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A proof of concept confined compression apparatus (Figure 2-13) was used. It was adapted from

the components used in Figure 2-12. There were three differences to the setup. The first was that

a 10 N load cell was attached to the base of the apparatus. The second was that the porous filter

was squeezed between two pieces of acrylic using a set of two screws and nuts. This was to

prevent any fluid or tissue from escaping between the confining chamber and the porous screen

interface. Lastly, instead of the drill bit, a nonporous indenter was threaded onto the

electromagnetic actuator above and guided into the confining chamber so that deformation could

be applied.

Figure 2-13: Pilot test apparatus for measuring the time independent and dependent

properties of spinal cord tissue. The electromagnetic actuator (a) and the proof of concept

confined compression fixture (b) are shown.

Spinal cord tissue was obtained using a skin biopsy punch and was transferred into the specimen

holder. The results of the pilot test were positive. Both strain stiffening behaviour and stress

relaxation behaviour were observed. The parameters used were a quasi-static strain rate

(0.001/sec) up to 25% peak strain followed by holding of the peak strain for 300 secs. The

displacement-time and stress-time curves were plotted in Figure 2-14. The peak stress observed

was in the same range of values reported by Haslach et al. thus validating the accuracy of the

instrumentation used.

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Figure 2-14: Displacement vs. time graph (top) and Stress vs, time graph (bottom) of pig

spinal cord white matter tissue

2.2 Spinal Cord Sample Preparation

For the experiments to address the thesis objectives, spinal cords were harvested from the

thoracic and cervical regions (C5-C7, T5-T7, and T10-T14) of freshly euthanized Yorkshire and

Yucatan pigs (21.5 – 48 kg) with the help of Dr. Brian Kwon’s lab group at the UBC Centre for

Comparative Medicine (CCM). It was noted that the majority of pigs underwent acute SCI at

either the T2 or T10 level as part of the research conducted by their lab. Euthanasia of pigs after

SCI varied between 2 hours – 3 months after SCI. The spinal cord used for this study was

harvested at least two spinal levels away from the injury epicentre.

The dura mater was removed with surgical scissors by the animal surgeon immediately after

euthanasia (Figure 2-15). The intact spinal cord was placed in a vial filled with phosphate-

buffered saline (PBS) solution. The vial was then placed in a Styrofoam cooler filled with ice

and transported back to ICORD for further processing. The travel time required was

approximately 30 mins.

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Figure 2-15: The intact spinal cord with dura mater excised. A ruler is placed in proximity

for scaling purposes to show length (a) and diameter (b). The thoracic spinal cord is the

smaller one compared to the neighbouring cervical spinal cord

The spinal cord was cut to produce the four types of specimens (GA, GT, WA, and WT).

Although both cervical and thoracic spinal cord regions were collected, no distinction in sample

preparation was used to differentiate between spinal cord region. This was decided because the

effect of spinal cord region was not analyzed in this study. There were two cutting techniques

used to collect specimens. The first technique was used to collect GA and WA specimens while

the second technique was used to collect GT and WT specimens.

The GA and WA specimens were prepared by following these steps. The spinal cord was

removed from the vial onto a flat plate with demarcated lines (Figure 2-16). Since the spinal cord

provided was typically quite long, the spinal cord was first cut to a length of 15 mm using a #10

scalpel blade. This was simply for ease of handling the tissue. The remaining segment was

temporarily placed back in the PBS filled vial for use later. A custom 3D printed “cross-section”

cutting cradle was used to cut 2.5 mm nominal thickness cross-sections. This cutting cradle

featured a scalpel guide line so that the spinal cord could be butted against the wall for a more

repeatable cut (Figure 2-16).

62

Figure 2-16: An aluminum plate with demarcated lines was used to reduce the length of the

spinal cord. The “cross-section” cutting cradle (shown in black) was used to assist with

cutting cross-sections. The finished product is shown on the left hand side.

A flash freezing protocol was used to freeze spinal cord cross sections prior to collecting the GA

and WA specimens. Flash freezing was shown in the literature to reduce specimen geometry

variation during cutting and sectioning procedures without compromising the mean mechanical

response of the tissue [89], [90]. To do this, the spinal cord cross section was transferred on a

sheet of aluminum foil and placed into a Styrofoam cooler of dry ice for 60 secs.

After flash freezing, it was immediately placed on a piece of foam and the custom biopsy punch

was used to core the specific GA or WA specimens. The location for the WA and GA samples

were the lateral white matter and the ventral horn of the spinal cord respectively. The foam

provided a soft surface such that the punch could be pushed through the spinal cord without

dulling its blade. Once collected, the specimen was left within its respective punch and placed

aside for 10 mins to thaw [89]. After the thawing process, it was integrated within the confined

compression fixture for mechanical testing.

The GT and WT specimens were prepared by following a similar procedure to GA and WA

specimens. The spinal cord was cut to 4 mm lengths using the same demarcated aluminum plate.

This section of spinal cord was flash frozen following the same procedure above and then placed

in the “separator” cutting cradle (Figure 2-17). This cradle featured scalpel guidelines to separate

the centrally located grey matter from the lateral white matter. The guidelines were spaced to

yield sections of 2.5 mm nominal thickness. The lateral white matter sections or the central grey

63

matter section were then placed flat on the foam to collect GT and WT specimens using the

custom biopsy punch. Similarly, the specimens were left to thaw before integrating it within the

confined compression apparatus.

Figure 2-17: The "separator" cutting cradle is used to separate the lateral white matter

from the central grey matter

It was important to note that the pia mater remained on the WT specimen. It was not possible to

remove the pia mater beforehand as it was observed to keep the spinal cord intact while cutting.

If the pia mater was removed at an earlier stage, the tissue was observed to liquefy resulting in

tissue degradation. This introduced unnecessary geometric variation when the WT specimen was

prepared. As a result, it was necessary to leave the pia mater intact throughout the specimen

preparation process.

To eliminate the effect of the pia mater, the custom biopsy punch collected the WT specimen by

cutting from the lateral side of the tissue through to the medial side. In doing so, the position of

the pia mater was placed superiorly in the punch tube. This was crucial as the nonporous indenter

and porous filter are located above and below the specimen respectively. Since the interface

between the nonporous indenter and the tissue was theoretically impermeable, it was assumed

that the pia mater would have no effect on the overall test if it was located here. However if the

pia mater interfaced with the porous filter, the porosity of the pia mater, which is likely different

from that of white matter tissue, may prevent fluid exudation. This may also result in clogging of

64

the filter. Ultimately, this would negatively affect the measured mechanical properties for the

WT specimen.

After the tissue was collected, a flattened tip toothpick was used to measure the height of the

specimen within the biopsy punch (Figure 2-18). It was inserted through the superior end of the

adapter until it contacted the specimen within. A pen was used to mark the toothpick at the same

height or parallel to the superior surface of the adapter. A digital caliper was then used to

measure the length of toothpick that was immersed within the adapter. The height of the

specimen was calculated by subtracting the measured toothpick length from the overall length of

the adapter. The accuracy of this spinal cord sample preparation method yielded an average

specimen height of 2.8 ± 0.5 mm (mean±SD).

Figure 2-18: A toothpick was inserted through the custom biopsy punch and marked to

denote the specimen height (2.8 ± 0.5 mm)

2.3 Confined Compression Testing Protocol

2.3.1 Time Post-Mortem Criterion

The mechanical testing of each pig spinal cord was completed within six hours of euthanasia.

This criterion was established to limit the effect of time post-mortem on the mechanical

properties of spinal cord tissue. The six hours included the time to harvest the spinal cord, to

transport the tissue to ICORD from CCM, to prepare the four sample types, and mechanical

testing of each sample type.

Preliminary tests revealed that 8-12 specimens could be tested within the six hour window.

Given that there were four types of specimens, this resulted in two to three specimens (ie. data

points) per specimen type. Due to the lack of multiple data points, averages of GA, GT, WA, and

WT specimen data points were calculated per specimen type per porcine specimen. This helped

65

reduce the impact from outliers within each specimen type and helped maintain a balanced

design for the statistical analysis.

2.3.2 Test Order

A block design for test order chronology was used to help further minimize the effect of time

post-mortem. Grey and white matter specimen blocks were formed for determining the test

sequence. Each pig spinal cord was divided into two blocks. Each block contained all four types

of specimens.

Block 1 grouped the four types of samples by tissue type. This meant that both grey matter

samples (GA and GT) were tested before both white matter (WA and WT) samples or vice-versa.

Block 2 grouped the four types of samples by tissue type but the sequence of the sample

direction was opposite to that of Block 1. For example, if GA then GT were tested in block 1,

then GT and GA would be tested in block 2. This applied to white matter samples as well. An

example test order is shown in Table 2-1. The permutations were rearranged for every successive

porcine specimen tested. The complete testing order for all porcine specimens is found in

Appendix E.

Table 2-1: Example specimen testing order in a six hour window

Trial Block Pig #1

1 1

GA

2 GT

3 WA

4 WT

5 2 WT

6 WA

7 GT

8 GA

66

2.3.3 Sample Size

A power analysis determined the number of porcine specimens required for testing. The

calculated number represented the minimum sample size required to detect whether an effect can

be detected between sample populations. The effects that were analyzed with this study were the

effect of tissue type (ie. grey matter vs. white matter) and direction (ie. axial vs transverse) on

spinal cord mechanical properties.

The power analysis depended on three factors: type I error (α), type II error (β) and effect size.

Type I error was the chance of mistakenly rejecting the null hypothesis (false negative) while

type II error was the chance of mistakenly accepting the null hypothesis (false positive). The

effect size (d) was “the degree to which the null hypothesis is false” [91]. In the context of this

research, the null hypotheses were:

1) There was no difference between grey and white matter tissue mechanical properties;

2) There was no difference between GA and GT specimen mechanical properties;

3) There was no difference between WA and WT specimen mechanical properties;

The analysis assumed the following α and β values:

𝛼 = 0.05

𝛽 = 0.2

The effect size (Equation (13)) was estimated based on similar studies conducted in the literature

[57]. The three null hypotheses meant that three separate effect size calculations were

individually performed (ie. one for each null hypothesis). Null hypothesis #3 was used as an

example here The data for the calculation is shown in Appendix F.

𝑑 =|𝜇𝑊𝐴 − 𝜇𝑊𝑇|

𝑆𝐷𝑡𝑜𝑡𝑎𝑙 (13)

𝑆𝐷𝑡𝑜𝑡𝑎𝑙 = √(𝑛𝑊𝐴 − 1)𝑆𝐷𝑊𝐴

2 + (𝑛𝑊𝑇 − 1)𝑆𝐷𝑊𝑇2

𝑛𝑊𝐴 + 𝑛𝑊𝑇 − 2 (14)

67

Where 𝜇 represented the mean stiffness between WA and WT specimens, 𝑆𝐷𝑡𝑜𝑡𝑎𝑙 represented

the pooled standard deviation of both WA and WT specimens, 𝑛𝑊𝐴 and 𝑛𝑊𝑇 represented the

respective WA and WT sample sizes in the study.

The sample size (N) was calculated with Equation (15) [92]. The t distribution chart was used as

the true standard deviation for GA, GT, WA, and WT populations were unknown. The number

of samples required for null hypotheses #1, #2, and #3 were 9, 17, and 11 respectively. Based on

pig availability, a sample size of 11 was chosen for this study.

𝑁 ≥

2 (𝑡1−𝛼

2− 𝑡𝛽)

2

𝑑

(15)

2.4 Experimental Protocol

For the confined compression test, the adapter containing the spinal cord specimen was first

inserted into the adapter holder. The O-ring was then inserted around the punch tube. The

adapter holder was lowered until the punch tube contacted the porous filter using the Z-axis

translation table. The adapter holder was further lowered to compress the O-ring until the load

cell measured approximately 0.6 N of compression. A spacer was placed atop the adapter, and

the nonporous indenter was inserted into the punch tube. The actuator was lowered using the

servo-driven elevator until it magnetically attracted the nonporous indenter. This prompted the

removal of the spacer. Finally the system was left to stabilize. This meant that the O-ring was

allowed to relax to an equilibrium prior to starting the test.

While the system was stabilizing, the parameters for the mechanical test were set. The data was

sampled at 10 Hz and filtered using a low pass filter at 30 Hz. After stabilization, a pre-load of

0.02 N was applied to establish contact between the specimen and the nonporous indenter. No

pre-conditioning was used for this protocol. A strain profile involving a quasi-static strain rate

(0.001/sec) up to a maximum of 10% peak strain was applied. Immediately after, the maximum

strain was held for 120 secs. This stress relaxation protocol was repeated for all spinal cord

specimens.

Several adapters were fabricated allowing spinal cord specimens to be collected in advance. This

allowed continuous testing by swapping out the previous adapter at the end of one test with the

68

following adapter for the next test. Once the new adapter was inserted into the adapter holder, the

steps described previously were repeated. This mechanical design allowed for a quick

changeover between adapters.

The time between tests was approximately 20 mins. The bottleneck of the experimental setup

had to do with the stabilization step needed to remove the mechanical behaviour of the O-ring.

This ensured that the load cell measured only the mechanical behaviour of the spinal cord tissue.

2.5 Constitutive Modeling

All data files collected from each porcine spinal cord were averaged with respect to the four

spinal cord specimen types. The GA, GT, WA, and WT averaged data were then processed using

MATLAB (R2018a, Mathworks, Natick, MA) for constitutive modeling. A QLV model was

used to describe viscoelastic nature of GA, GT, WA, and WT spinal cord specimens [8], [41]–

[48].

The QLV theory modeled stress relaxation mechanical behaviour. The experimental protocol in

Section 2.4 used a ramp deformation followed by holding of the maximum deformation as

described in Equation (7). The first order exponential function (Equation (3)) described the non-

linear strain-stiffening behaviour of the tissue. A 1-term Prony series described the relaxation

behaviour of the tissue (Equation (16))

𝐺(𝑡) = 1 − 𝑔 (1 − 𝑒−𝑡

𝜏) (16)

Equations (3), (7), (16) were substituted into Equation (5) and integrated over the duration of the

experiment. The hand calculations are shown in Appendix G, and the final solutions describing

the stress at any time are shown below.

𝜎(𝑡) = 𝐴𝐵𝜖̇ ((1 − 𝑔

𝐵𝜖̇𝑒𝐵�̇�𝑡 +

𝑔𝑒𝐵�̇�𝑡

𝐵𝜖̇ +1

𝜏

) − (1 − 𝑔

𝐵𝜖̇+

𝑔𝑒−𝑡

𝜏

𝐵𝜖̇ +1

𝜏

))

𝑓𝑜𝑟 0 ≤ 𝑡 < 𝑡0

(17)

69

𝜎(𝑡) = 𝐴𝐵𝜖̇ ((1 − 𝑔

𝐵𝜖̇𝑒𝐵�̇�𝑡0 +

𝑔𝑒(𝐵�̇�+1

𝜏)𝑡0𝑒−

𝑡

𝜏

𝐵𝜖̇ +1

𝜏

) − (1 − 𝑔

𝐵𝜖̇+

𝑔𝑒−𝑡

𝜏

𝐵𝜖̇ +1

𝜏

))

𝑓𝑜𝑟 𝑡 ≥ 𝑡0

(18)

2.5.1 Parameter Optimization

The four parameters (A, B, g, ꞇ) in the constitutive model above were determined through a non-

linear least squares error minimization algorithm (Equation (19)) [48]. This approach required an

initial estimate of the parameter values and iteratively minimized the error between the

experimental data and the value of the analytical model from Equations (17) and (18) at every

time point where a data point was collected. As the algorithm iterated, the error was constantly

optimized (ie. reduced to the smallest error possible), until the parameter values converged to a

set of final values.

𝑀𝑖𝑛(𝐸𝑟𝑟𝑜𝑟) = ∑ [𝜎𝑗𝑒𝑥𝑝(𝑡𝑗) − 𝜎𝑗

𝑚𝑜𝑑𝑒𝑙(𝑡𝑗)]2

𝑡0

𝑡𝑗=0

+ ∑ [𝜎𝑘𝑒𝑥𝑝(𝑡𝑘) − 𝜎𝑘

𝑚𝑜𝑑𝑒𝑙(𝑡𝑘)]2

𝑡𝑒𝑛𝑑

𝑡𝑘=𝑡0

(19)

Where the superscript “exp” represented the data points from the experimental data and “model”

represented the data points from the analytical model using the most recent parameter estimation.

This minimization algorithm was performed using Matlab’s fmincon function. This was a

constrained optimization function. It applied the following constraints to facilitate the

optimization process.

1) Upper and lower variable bounds

a. Amax = 2000 kPa, Bmax = 100, gmax = 1, ꞇmax = 100 secs

b. Amin = 0 kPa, Bmin = 0, gmin = 0, ꞇmin = 0 secs

2) Inequality constraints

a. A > 0 , B > 0, g < 1

70

A sensitivity analysis was conducted to verify the convergence of the algorithm based on the

constraints used. The constraints were varied several times. Despite this, the analysis converged

to the same set of final values each and every time. The complete MATLAB script used to

perform constitutive modeling and parameter optimization is shown in Appendix H.

2.5.2 Outcome Variables

The outcome variables collected from the constitutive modeling were peak stress, aggregate

modulus, and time constant. Peak stress described the time independent properties of the tissue

while aggregate modulus and time constant described the time dependent properties of the tissue.

Peak stress was defined as the maximum stress measured during testing (ie. where maximum

strain occurred). Aggregate modulus (Ha) was defined as the stiffness at equilibrium when the

test ended. It was calculated using the following equation.

𝐻𝑎 =𝜎𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚

𝜖𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 (20)

Where 𝜎𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 and 𝜖𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 were the stress and strain at equilibrium respectively. In

order to calculate the stress at equilibrium, Equation (18) was simplified with the condition that

time (t) approaches infinity resulting in the following equation.

𝜎𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚 = 𝐴𝐵𝜖̇ (1 − 𝑔

𝐵𝜖̇(𝑒𝐵�̇�𝑡0 − 1)) (21)

Time constant (ꞇ) was defined as the time taken for the specimen to relax 63% from its peak

stress. This was a characteristic of the 1-term Prony series equation. It was computed from the

constitutive model fit. Time constant was directly related to the overall relaxation time behaviour

of the tissue. A larger time constant meant a longer relaxation time was required for the tissue to

reach equilibrium.

2.6 Statistical Methods

2.6.1 Effect of Tissue Type and Direction

The three outcome variables were analyzed using SPSS (v.24, IBM Corporation, Armonk, NY)

statistical software. The Shapiro Wilks test was used to test for normality and the Levene’s test

was used for homogeneity of variances. A significance level of p<0.05 was used in all cases. A

71

two-way analysis of variance (ANOVA) was used to analyze all parametric data. The

independent variables for this study were tissue type (grey matter & white matter) and direction

(axial & transverse directions). The dependent variables for this study were peak stress,

aggregate modulus, and time constant.

The data were presented in a 2x2 factorial design. This meant that no post-hoc tests were

necessary for any statistical significances found between main effects. For statistical

significances found for the interaction effects, the simple main effects were tested using pairwise

comparisons with Bonferroni adjustment.

2.6.2 Effect of Time Post-Mortem

The relationship between peak stress and time post-mortem was analyzed with a linear

regression model for GA, GT, WA, and WT specimens. This was performed using Microsoft

Excel (2013). A significance level of p<0.05 was used for this analysis.

2.7 Histological Methods

Following mechanical testing, every specimen was removed from the biopsy punch, and fixed

with 10% neutral buffered formalin for 24 hours prior to submerging it in 30% sucrose solution

for 72 hours for cryoprotection. Specimens were then transferred into moulds and immersed in

optimal cutting temperature (OCT) compound before freezing on dry ice. The moulds were

organized such that each mould contained only one specimen type per pig. As a result, GA, GT,

WA, and WT specimens were placed in their respective moulds. In total there were four moulds

per porcine specimen tested. Specimens within each mould were aligned such that 20 μm cross-

sections were cut on the cryostat. Once the slides were prepared, they were placed in a -80oC

freezer.

All sections were stained with hematoxylin and eosin (H&E). This process began with drying

and thawing of the slides. The slides were rehydrated with xylene for 10 mins, followed by a

descending series of ethanol concentrations (EtOH, 100%, 100%, 95%, 70%) for 3 mins each.

Finally slides were placed in distilled water for 6 mins completing rehydration. For staining, the

slides were placed in hematoxylin (Sigma-Aldrich, St. Louis, MO) for 5 mins, rinsed in tap water

for 3 mins, placed in acid ethanol (0.5% HCl in 70% EtOH) for 10 secs, rinsed in tap water for 3

mins, placed in sodium bicarbonate (NaHCO3, 1.5%) for 5 secs, rinsed in tap water for 3 mins,

72

placed in 95% EtOH for 2 mins and finally placed in Eosin (Fisher Healthcare, Waltham, MA)

for 15 secs. The slides were dehydrated with an ascending series of ethanol concentrations

(EtOH, 95%, 100%, 100%) for 2 mins each and then with xylene for 4 mins. The full staining

procedure is included in Appendix I. Lastly the slides were mounted with Permount and cover

slips were placed on top of the slide. Slides were imaged under a light microscope (Axio Imager

M2, Carl Zeiss, Oberkochen, Germany).

H&E stained the spinal cord tissue such that gross morphology and anatomy were revealed. This

included the illustration of both grey matter and white matter tissue as well as underlying

structures such as cell bodies and axonal orientation. This was used to qualitatively validate the

sample types (GA, GT, WA, WT) that were mechanically tested revealing the degree of

contamination with other tissues while also confirming the orientation of the specimen.

Please note that the preliminary histology studies (Section 2.7.1 and 2.7.2) involved different

staining protocols. Due to H&E being simpler, less expensive, and quicker, it was chosen over

the other protocols as the staining protocol for this study.

2.7.1 White Matter Axon Direction Verification

The purpose of this verification study was to visually identify the orientation of the axons within

the white matter. All sections were stained with immunofluorescence. This process began with

drying of the slides for approximately one hour. The slides were then outlined with a PAP pen

creating a hydrophobic barrier. Next the slides were rehydrated with 0.01 M PBS for 10 minutes

before de-lipidation in an ascending series of ethanol concentrations (EtOH, 50%, 70%, 90%,

95%, 100%) followed by a descending series of ethanol concentrations (same as ascending but

in reverse order). Slides were incubated in blocking solution (500 μL/slide) composed of 10%

normal donkey serum (Jackson ImmunoResearch Laboratories, West Grove, PA) and 90%

Triton-PBS 0.1% for one hour. Primary antibodies used were SMI-312 (SMI) (Mouse host,

1:1000, Covance, Princeton, NJ), myelin basic protein (MBP) (Chicken host, 1:500, Aves Labs,

Tigard, OR), β-tubulin III (tub) (rabbit host, 1:1000, Covance, Princeton, NJ) and Platelet-

derived growth factor receptor alpha (PDGFRα) (Goat host, 1:100, Cedarlane Laboratories,

Burlington, ON, Canada) to stain for axons, myelin, and oligodendrocytes. This solution required

300 μL per slide composed of 5% normal donkey serum, the above antibody ratios by volume,

and Triton-PBS 0.1%. Sections were then washed with Triton-PBS 0.1% three times for 10 mins

73

each. Secondary antibodies conjugated with Alexa Fluor 488 (donkey host, mouse antigen,

Jackson ImmunoResearch Laboratories, West Grove, PA) Alexa Fluor 594 (donkey host,

chicken antigen, Jackson ImmunoResearch Laboratories, West Grove, PA), Alexa Fluor 405

(donkey host, rabbit antigen, Jackson ImmunoResearch Laboratories, West Grove, PA) and

Alexa Fluor 674 (donkey host, goat antigen, Jackson ImmunoResearch Laboratories, West

Grove, PA) were applied and the slides were allowed to incubate for two hours. This secondary

solution required 300 μL per slide composed of the above antibody ratios and PBS. All slides

were then washed with 0.01 M PBS and mounted with Fluoromount-G (Southern Biotech,

Birmingham, AL). Slides were imaged under a fluorescence microscope (Axio Imager M2, Carl

Zeiss, Oberkochen, Germany). The immunofluorescence images are shown in Figure 2-19.

74

Figure 2-19: Immunofluorescence images of white matter specimens. Axons are stained in

green (SMI), myelin is stained in red (MBP), and neuronal cell bodies are stained in blue

(Tub). (a) Cross-section of WA specimen. (b) Cross-section of WT specimen. (c) Close-up of

WA specimen. (d) Close-up of WT specimen.

The histological images in Figure 2-19 revealed key morphological structures with respect to the

orientation of the specimen. From Figure 2-19a and c, the WA specimen revealed cross-sections

of myelinated axons confirming the axial orientation. From Figure 2-19b and d, the WT

specimen revealed axons running rostralcaudally confirming the transverse orientation. This

confirmed that both WA and WT specimens were in the correct orientation. It was noted that a

small amount of grey matter (ie. contamination) was collected in Figure 2-19a as a result of the

sample collection procedure.

a

c d

b

75

2.7.2 Grey Matter Heterogeneity Verification

The purpose of this verification study was to visually quantify the percentage of grey matter to

white matter area ratios within the GA and GT specimens. The rationale behind this was that

there was some concern regarding whether a fully homogeneous grey matter sample was

obtainable. Given that the nominal diameter of the punch tube was 2 mm, it was hypothesized

that the samples collected would be heterogeneous. Eriochrome cyanine (EC) (Sigma-Aldrich,

St. Louis, MO) was used to stain for myelin. The procedure for this is included in Appendix H.

The following sample images (Figure 2-20) were generated using a digital slide scanner (Aperio

CS2, Leica, Wetzlar, Germany).

Figure 2-20: Sample eriochrome cyanine stained images of grey matter specimens. Myelin

(white matter) is in orange and grey matter is in blue (a) Cross-section of GA specimen. (b)

Cross-section of GT specimen.

Aperio ImageScope (Leica Biosystems, Wetzlar, Germany) was used for analyzing the amount

of grey matter area relative to white matter area. An algorithm configured with a set of tuning

parameters: hue value = 0.627, hue width = 0.506, colour saturation = 0.19 within the software

was employed to calculate the difference in contrast between both white and grey matter. The

grey matter samples were found to have an averaged grey matter to white matter ratio of 70:30.

This contamination of grey matter samples with white matter tissue was considered to be a

limitation to this study.

a b

76

Chapter 3: Results

3.1 Stress-Strain and Stress Relaxation Responses

In total, 12 porcine specimens were tested in confined compression. One specimen was removed

from the sample set as the data was observed to be greater than two standard deviations away

from the mean, thus it was deemed an outlier. Since the two-way ANOVA was selected for the

statistical analysis, this entire porcine specimen (GA, GT, WA, WT) was removed from the

sample set even though only GA’s data point was found to be an outlier. This was done to

maintain a balanced design for the statistical analysis.

Mean stress-time responses of GA, GT, WA, and WT specimens were tabulated for 11 porcine

specimens and graphed using MATLAB (Figure 3-1). The mean and standard deviation for each

specimen type is shown here while the all the raw data are shown in Appendix J.

Figure 3-1: Mean (blue) plus/minus one standard deviation (red) for GA (a), GT (b), WA

(c), and WT (d) specimens of all 11 pigs

77

Mean stress-strain and stress-time responses for each specimen group and for all pigs were

plotted (Figure 3-2 and Figure 3-3) to illustrate the mechanical behaviour of each specimen type

with respect to each other.

Figure 3-2: Mean stress-strain response for porcine spinal cord specimen types (indicated

in the legend)

Figure 3-3: Mean stress-time response for porcine spinal cord specimen types (indicated in

the legend)

0

20

40

60

80

100

120

140

0 0.02 0.04 0.06 0.08 0.1 0.12

Stre

ss (

kPa)

Strain

GA

GT

WA

WT

0

20

40

60

80

100

120

140

0 50 100 150 200 250

Stre

ss (

kPa)

Time (secs)

GA

GT

WA

WT

78

3.2 Constitutive Model Fit

The constitutive model described in Section 2.5 was used to fit each of the raw data curves

shown in Appendix J. This approach used the parameter optimization technique in Section 2.5.1

to determine the four material constants. As an example, one pig specimen’s set of data and its

respective model fit are shown below (Figure 3-4).

Figure 3-4: Experimental stress-time data and constitutive model fit of GA (a), GT (b), WA

(c), and WT (d) specimen data. The mean (blue) was plotted along with the loading

(orange) and relaxation (yellow) curve fits for pig #11.

The average value for each of the four material constants are reported in the Table 3-1. For the

independent curve fitted material constants, see Appendix J.

79

Table 3-1: Material constants A, B, g, and ꞇ (mean ± SD) for GA, GT, WA, and WT

specimens

Specimen A (kPa) B g ꞇ (secs)

GA (n=11) 124 ± 33 17 ± 2.7 0.97 ± 0.02 11.1 ± 3.2

GT (n=11) 168 ± 90 15 ± 3.8 0.95 ± 0.02 12.3 ± 3.2

WA (n=11) 120 ± 28 15 ± 1.3 0.98 ± 0.01 10.1 ± 2.0

WT (n=11) 136 ± 56 16 ± 2.5 0.98 ± 0.01 7.9 ± 2.1

3.2.1 Outcome Variables

The mean and standard deviation for each outcome variable and sample type are shown in Table

3-2. For all of the raw data from each of the pig specimens, see Appendix J.

Table 3-2: Peak stress, aggregate modulus, and time constant (mean ± SD) for GA, GT,

WA, and WT specimens

Specimen Peak Stress (kPa) Aggregate Modulus (kPa) Time Constant (secs)

GA (n=11) 124 ± 20 166 ± 57 11.1 ± 3.2

GT (n=11) 127 ± 26 244 ± 91 12.3 ± 3.2

WA (n=11) 75 ± 22 99 ± 40 10.1 ± 2.0

WT (n=11) 84 ± 14 107 ± 45 7.9 ± 2.1

All specimen type data sets exhibited a non-linear strain stiffening response followed by

immediate relaxation typical of spinal cord tissue according to Figure 3-2 and Figure 3-3. From

Table 3-2, grey matter was observed to have a higher peak stress and aggregate modulus than

white matter given the same strain regardless of direction. With respect to direction, although

grey matter peak stress was similar, grey matter’s aggregate modulus was larger in the transverse

direction. For white matter, its transverse direction was slightly larger in terms of both peak

stress and aggregate modulus than its axial direction. Both grey and white matter showed

relaxation to near zero stress at which point an apparent equilibrium was seen. Grey matter

experienced a slightly longer relaxation time than white matter overall. With respect to direction,

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GT was slightly longer than GA specimens while the inverse was true for white matter

specimens (ie. WA > WT).

3.3 Statistical Results

3.3.1 Verifying Two-way ANOVA Assumptions

The Shapiro-Wilk’s score was used to test for normality [93]. The results for this are shown in

the Table 3-3.

Table 3-3: Summary of Shapiro-Wilk scores for each specimen and dependent variable

Specimen Dependent Variable

Peak Stress Aggregate Modulus Time Constant

GA 0.28 0.31 0.03

GT 0.60 0.60 0.73

WA 0.52 0.31 0.71

WT 0.86 0.10 0.41

There was one violation of normality (p<0.05) according to the Shapiro-Wilk’s score (shown in

red). Given that the two-way ANOVA requires approximately normal data and that it is quite

robust to violations of normality, it was assumed that the normality test was satisfied [94].

The Levene’s test score was used to test for homogeneity of variance [95]. The results for this

are shown in the Table 3-4.

Table 3-4: Levene’s test score for homogeneity of variance for each dependent variable

Dependent Variable Levene’s Test Score (p-value)

Peak Stress 0.136

Aggregate Modulus 0.014

Time Constant 0.120

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There was one violation of the homogeneity of variance test (p<0.05) according to the Levene’s

test score (shown in red). Again, the ANOVA is generally quite robust to this violation as long as

the group sizes are equal [96]. Since the group sizes were equal in this study, it was assumed that

homogeneity of variance was satisfied.

3.3.2 Peak Stress Results

From the ANOVA the effect of tissue type was significant (F(1,40)=54.8, p<0.0001) such that

grey matter (126 ± 4.4 kPa; mean ± SEM) had higher peak stress than white matter (80 ± 4.4

kPa) while the effect of direction on peak stress was non-significant (F(1,40)=0.94, p=0.338).

The interaction between both effects was found to be non-significant (F(1,40)=0.25, p=0.619).

This is shown in Figure 3-5.

Figure 3-5: Column plot of mean peak stress (mean ± SD) for GA, GT, WA, and WT

specimens

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During the loading phase, grey matter was approximately 58% stiffer than white matter.

Although the effect of direction was insignificant, it was observed that there was almost no

difference between directions for grey matter (2%). For white matter, a marginally softer

response (11%) was seen in white matter’s axial direction relative to its transverse direction.

3.3.3 Aggregate Modulus Results

From the ANOVA the effect of tissue type was significant (F(1,40)=30.7, p<0.0001) such that

grey matter (205 ± 13 kPa) had higher aggregate modulus than white matter (103 ± 13 kPa). The

effect of direction was also significant (F(1,40)=5.3, p=0.027) such that the transverse direction

(175 ± 13 kPa) was greater than its axial direction (133 ± 13 kPa). The interaction between both

effects was found to be non-significant (F(1,40)=3.6, p=0.067). This is shown in Figure 3-6.

Figure 3-6: Column plot of mean aggregate modulus (mean ± SD) for GA, GT, WA, and

WT specimens

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During the relaxation phase, grey matter reached an equilibrium stiffness that was approximately

double (100%) that of white matter. The transverse direction was 32% stiffer than the axial

direction. Upon closer review of the individual specimen responses, there was a 50% difference

between GA and GT specimen stiffness compared to only an 8% difference between WA and

WT specimens. It is clear that the effect of direction was more influenced by grey matter’s

directional differences than that of white matter.

3.3.4 Time Constant Results

From the ANOVA the effect of tissue type was significant (F(1,40)=10.8, p=0.002) such that

grey matter (11.7 ± 0.6 secs) had a longer relaxation time than white matter (9.0 ± 0.6 secs). The

effect of direction was found to be non-significant (F(1,40)=0.42, p=0.521). The interaction

between both effects was found to be significant (F(1,40)=4.3, p=0.043). This is shown in

Figure 3-7.

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Figure 3-7: Column plot of mean time constant (mean ± SD) for GA, GT, WA, and WT

specimens

Given that the interaction effect was significant, multiple simple effect tests were conducted and

the main effects were ignored [97]. This breaks the interaction effect into parts and tests these

individual parts for significance using pairwise comparisons. In this case there were four

additional comparisons that were analyzed:

1) Differences in tissue type on relaxation times for the transverse direction;

2) Differences in tissue type on relaxation times for the axial direction;

3) Differences in direction on relaxation times for grey matter tissue;

4) Differences in direction on relaxation times for white matter tissue;

Since multiple comparisons were made, a Bonferroni adjustment was included. Of the four cases,

only case #1 was found significant. This meant for the transverse direction, grey matter tissue

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possessed a 55% longer relaxation time (F(1,40)=14.4, p<0.001) than white matter. For the axial

direction, tissue type had no effect (F(1,40)=0.72, p=0.403) as it was only 10% different. For

grey matter tissue, direction had no effect (F(1,40)=1.0, p=0.315) as was the same for white

matter tissue (F(1,40)=3.7, p=0.060). Respectively these were only 10% and 28% different.

3.3.5 Effect of Time Post-Mortem on Peak Stress Results

The linear regression analysis examining peak stress and time post-mortem was non-significant

for GA (p=0.279), GT (p=0.980), WA (p=0.399), and WT (p=0.985) specimen types. This is

shown in Figure 3-8.

Figure 3-8: The effect of time post-mortem on peak stress of GA, GT, WA, and WT

specimens. A linear trendline was plotted for each of the four specimen types.

0

50

100

150

200

250

300

00:00 01:12 02:24 03:36 04:48 06:00 07:12

Pea

k St

ress

(kP

a)

Time Post-Mortem (hours:mins)

The Effect of Time Post-motem on Peak Stress

Grey Axial Grey Transverse White Axial

White Transverse Linear (Grey Axial) Linear (Grey Transverse)

Linear (White Axial) Linear (White Transverse)

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3.4 Histology

The H&E stain revealed cell nuclei (glial cells, neurons) in blue, cytoplasm in pink, with all

other structures in shades of pink. These shades distinguished the grey matter from the white

matter (Figure 3-9 and Figure 3-10). Please note that the sections have been slightly adjusted to

illustrate a higher level of contrast between grey and white matter structures using Zen imaging

software (Carl Zeiss, Oberkochen, Germany).

Figure 3-9: H&E stained spinal cord sections showing gross morphology of GA (a), GT (b),

WA (c), WT (d) specimens. The scale bar represents 500 μm.

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Figure 3-10: H&E stained spinal cord sections showing close-up of gross morphology of GA

(a), GT (b), WA (c), and WT (d) specimens. Cell nuclei are stained in blue. The scale bar

represents 250 μm.

The histology of GA, GT, WA, and WT specimen types for one porcine specimen are shown in

the figures above. Figure 3-9 shows a general overview of the specimens while Figure 3-10

shows a closer look at the morphology.

The GA specimens were observed to be heterogeneous such that there was contamination of

white matter within the grey matter samples (Figure 3-9a and Figure 3-10a). A white line was

drawn indicating both tissue types. The grey matter horn was found within the boundary line.

This boundary was evident based on the numerous stained neuronal and glial cell nuclei in blue.

The larger cell nuclei were neuronal cell bodies whereas the smaller cell nuclei were glial cell

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bodies. The depiction of the grey matter horn confirmed that the correct specimen orientation

was tested; in its axial direction.

The GT specimens were also observed to be heterogeneous such that there was contamination of

white matter within the grey matter samples (Figure 3-9b and Figure 3-10b). A white line was

drawn indicating both tissue types. The grey matter was located centrally. The white matter was

found on both left and right sides of the grey matter. The central region revealed a large density

of cell nuclei representative of grey matter tissue. In contrast the left and right side regions

revealed fewer cell nuclei and longitudinal structures representative of axons in white matter

tissue. The depiction of the axons running longitudinally as well as the presence of grey matter

confirmed that the correct specimen orientation was tested; in its transverse direction.

The WA specimens were observed to be predominantly homogeneous. The contamination of

grey matter within the white matter specimen was practically negligible. This contamination can

only be seen in Figure 3-9c where the grey matter was shown by the different hue on the left and

upper left hand side of the section. Figure 3-10c showed few cell nuclei and numerous white

circular structures. These white circular structures represented myelin as neither hematoxylin or

eosin stained for myelin. These cross-sections of myelin confirmed that the correct specimen

orientation was tested; in its axial direction.

The WT specimens were observed to be predominantly homogeneous. The contamination of

grey matter within the white matter specimen was non-existent. Figure 3-10d showed few cell

nuclei and numerous longitudinal structures representative of axons. This confirmed that the

correct specimen orientation was tested; in its transverse direction

In general there was contamination of white matter in grey matter tissue sections while negligible

amounts of grey matter were found in white matter tissue sections. The pilot study performed in

Section 2.7.2 confirmed that on average grey matter specimens were contaminated with 30%

white matter tissue. In comparison, white matter specimens were contaminated with a maximum

of 10% grey matter tissue.

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Chapter 4: Discussion

4.1 Overview

In this thesis, a novel experimental method for testing the mechanical properties of spinal cord

grey and white matter in confined compression was developed. This research contributes to an

existing body of literature on spinal cord mechanical properties. It is the first attempt at

investigating the anisotropic time dependent mechanical properties of spinal cord grey and white

matter. The effect of tissue type and direction are relevant properties as further insight will

explain stress and strain states within the spinal cord in the hopes of developing an injury

criterion relating tissue damage patterns to their pathologies.

4.2 Mechanical Property Findings

4.2.1 Time Independent Mechanical Properties

The time independent mechanical properties demonstrated a nonlinear strain stiffening response

with increasing compressive strain. This was observed for all specimen types. This behaviour is

characteristic of grey and white matter tissue as described in the literature [41], [47], [59], [63].

The magnitude of mean peak stresses in this study ranged from 75 – 127 kPa for grey and white

matter. This is consistent with that of Haslach et al. who performed confined compression using

brain tissue and measured 16 – 171 kPa using similar peak strains and strain rates [51].

There were 12 pig specimens initially tested but one was removed since its peak stress was found

beyond two standard deviations from the mean. It was found that this specimen was undersized

within the punch. This meant that when the specimen was compressed, it was required to first

expand to fill out the confining chamber. Mow et al. stated that imperfections in specimen

geometry led to pre-expansion of the specimen before true confined compression was attained

[79]. This led to an underestimation of the tissue’s peak stress when peak strain occurred.

During the loading phase of the tissue, occasional sharp stress drops were observed. The drops in

stress indicated the tissue’s resistance to the nonporous indenter was momentarily lost. This

phenomenon was observed by Haslach et al. who attributed this as subfailure tissue damage.

These subfailures occurred from the rearrangement of substructures as the tissue was compressed

and the fluid phase within the tissue was redistributed [51].

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The time independent mechanical properties showed that the effect of tissue type was

statistically significant while the effect of direction was non-significant. Grey matter was 1.6

times stiffer than white matter regardless of direction. These results suggest the spinal cord is

heterogeneous and exhibits isotropic properties in compression.

The literature looking at the effect of tissue type on the time independent mechanical properties

of the spinal cord are controversial. The current findings agree with other ex-vivo tissue studies

by Ichihara et al., and Koser et al. where grey matter was found to be 1.74 – 2.13 times stiffer

than white matter. Ichihara et al. performed tension while Koser et al. performed indentation

[11], [59], [63]. Given that the grey matter samples in this study were contaminated with white

matter, it is plausible that the results would be even more agreeable with that of Ichihara et al.,

and Koser et al. if no contamination was present.

The current findings disagree with Ozawa et al.’s, and Sharkey’s work. The first saw no

difference while the other saw white matter to be two times stiffer than grey matter [58], [60].

Ozawa et al. potentially found a lack of significant difference between tissue type as low peak

strains were used. Ichihara et al. compared their data with that of Ozawa et al. and observed that

there was no significant difference between tissue type in their tensile study for strain levels up

to 5% [59]. Sharkey’s study quantified the in-vivo mechanical properties of the spinal cord

however the resolution of the MR images was poor [58]. This made it difficult to precisely

characterize the deformations seen in the spinal cord, possibly leading to inaccurate predictions

of its mechanical properties.

The mechanical properties of brain grey and white matter tissue are also controversial. Feng et

al. conducted indentation work using brain grey and white matter, and found white matter to be

approximately two times stiffer than grey matter [56]. Budday et al. performed shear,

compression, and tension tests on brain grey and white matter within the same study. They

concluded that grey matter was between 2.5 – 5 times stiffer than white matter. This highlights

the complexity of studying nervous tissues as differences exist between brain and spinal cord

mechanical properties.

The literature looking at the effect of direction on the mechanical properties of the spinal cord

are sparse. The current study agrees with both Ozawa et al. and Koser et al. who found no

difference in directional properties for spinal cord grey matter tissue [11], [60]. In relation to

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brain grey matter tissue, there is also a strong consensus as all studies showed no statistical

difference in mechanical properties between grey matter directions [56], [57], [71]. The results of

these numerous studies agree with the underlying morphological structure of grey matter as it

consists of randomly oriented cell bodies and axons. This further confirms that grey matter tissue

behaves like an isotropic material.

The studies focusing on the directional properties of white matter show mixed results. The

current study agrees with Ozawa et al. but disagrees with Koser et al.. The latter study found

spinal cord white matter to be 1.6 times stiffer in its transverse direction than axial direction in

indentation [11], [60]. Brain white matter tissue also showed mixed results. Budday et al. saw

non-significant differences when the tissue was measured in tension and compression [71].

However Prange & Margulies, Feng et al., and Schmidt et al. all saw statistical significances

between the directional properties of white matter in shear, indentation, and MRE respectively.

These latter studies reported anisotropy ratios ranging between 0.6 – 2.4 [56], [57], [85].

Spinal cord white matter was recently hypothesized to behave like a transversely isotropic

material. This is due to its highly aligned fibre orientation. Jannesar et al. proposed a conditional

transversely isotropic mathematical model for characterizing white matter [8]. The condition

meant that white matter was transversely isotropic in axial tension and isotropic in compression.

Axons were shown to be sensitive to loading type; bearing negligible load in compression while

bearing additional load in tension. This study agrees with the compressive behaviour

hypothesized by Jannesar et al. however it does not rule out the possibility that the spinal cord

may be transversely isotropic since other loading types were not investigated.

4.2.2 Time Dependent Mechanical Properties

The time dependent mechanical properties showed that all tissues demonstrated immediate

relaxation while the displacement of the nonporous indenter was fixed. In all cases, the sample

types relaxed approaching an equilibrium stress that was near zero stress. This near zero stress

indicates that spinal cord tissue behaves somewhat like a Maxwell fluid model. This emphasizes

the important role that the fluid phase plays in the relaxation phase of the tissue.

The relaxation phase was characterized by a 1-term Prony series instead of the conventional 3-

term Prony series used by other researchers [8], [41], [43], [44], [47], [73]. Additional Prony

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series terms provide better fits to data however additional coefficients are introduced making

comparisons between specimen types difficult. This is true for comparing relaxation times

between specimens since multiple time constants are used. A sensitivity analysis showed that the

1-term Prony series was adequate in characterizing the spinal cord tissue’s response. The

drawback of the 1-term Prony series was that it provided a slight overestimation of the aggregate

modulus. Nonetheless it is advantageous as it provides a unique solution to the constitutive

model so that all four specimen types can be compared.

4.2.2.1 Aggregate Modulus

The amount of relaxation from the peak stress seen in this study is similar with what others have

described for brain tissue in compression [40], [51]. The differences in experimental setup

between studies resulted in different ranges of aggregate moduli. Here the reported mean

aggregate modulus was 99 – 244 kPa for all specimen types. Cheng & Bilston measured 0.350

kPa using 5% strain and unconfined compression [40]. The aggregate modulus determined by

Cheng & Bilston was lower than the range found in this study due to the lower peak strain used.

Ichihara et al. showed that an increase in aggregate modulus is directly correlated with an

increase in peak strain [59]. Moreover, Cheng & Bilston performed their study in unconfined

compression. This meant that fluid was allowed to escape laterally. This led to lower measured

forces than in a fully confined setup. In another study, Haslach et al. saw a maximum aggregate

modulus of 50 kPa. This was lower than the range found in this study due to the use of both a 40

and a 20 micron porous filter above and below the specimen [51]. This setup is different from

this study where only one 20 micron filter was used below the specimen. It is likely the added

filter allowed fluid to exude superiorly and inferiorly leading to a lower aggregate modulus.

For aggregate modulus, the effects of tissue type and direction were statistically significant. The

aggregate modulus for grey matter was two times stiffer than white matter regardless of

direction. The aggregate modulus for the transverse direction was 1.3 times stiffer than the axial

direction regardless of tissue type. These results suggest that the spinal cord exhibits time

dependent mechanical properties that are heterogeneous and anisotropic. It was noted that the

difference between GA and GT had a larger impact on the statistical significance than WA and

WT. The anisotropy ratio between GT and GA was 1.5 while between WT and WA it was 1.1.

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This study is consistent with several others in the literature when comparing the aggregate

modulus of grey and white matter. Ichihara et al. compared grey and white matter tissue

equilibrium stress after 100 secs of relaxation in axial tension. At 20% and 30% fixed strain, grey

matter was 1.3 and 2.5 times stiffer than white matter [59]. Budday et al., measured the

compressive stress in the cortex (grey matter) and corpus callosum (white matter) after 5 mins of

relaxation using 10% strain. They saw that the cortex was 1.5 times stiffer than corpus callosum

[71]. Prange & Margulies analyzed the shear modulus during relaxation of both the cortex and

corpus callosum tissues as well. Although an equilibrium condition was not reached, they

showed that the cortex had a statistically significantly stiffer modulus at every time point

compared to corpus callosum [57].

This study is inconsistent with the study by Prange & Margulies with regards to the effect of

direction. Although both studies demonstrated a statistically significant effect of direction, the

anisotropy ratios were opposite to each other. Prange & Margulies showed the cortex exhibited

no difference between orthogonal directions. For corpus callosum they showed the transverse

direction of corpus callosum was half the stiffness of the axial direction. This reveals differences

in mechanical properties between shear and compression modalities of nervous tissue.

4.2.2.2 Time Constant

For time constant, the interaction effect was found to be statistically significant. Four pairwise

comparisons were performed revealing only one statistically significant difference. The

relaxation time for grey matter was found to be 60% longer than white matter specifically in the

transverse direction.

This study is consistent with the study by Budday et al. It was observed that corpus callosum

relaxed 78% from its peak stress in 5 mins compared to 62% from the cortex [71]. Although this

is not a direct measure of relaxation time, it is consistent in that the grey matter took longer to

relax than white matter.

The significantly longer relaxation behaviour of grey matter in contrast to white matter can also

be explained with the concept of permeability. While it was not directly measured in this study,

white matter has been hypothesized to have a larger permeability than grey matter [98]. The

larger stiffness of grey matter along with the randomly oriented unmyelinated axons are

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dispersed throughout the grey matter offering structural resistance to dilatation and larger fluid

flow resistance than that of white matter [98]. Lai et al. demonstrated for cartilage that increased

permeability led to a quicker relaxation to equilibrium as the decreased resistance to fluid flow

facilitates fluid redistribution within the tissue [80].

4.2.3 Effect of Time Post-Mortem on Peak Stress

The linear regression analysis saw no significant increase in stiffness in peak stress with

increasing time post-mortem. This was found for all four sample types when mechanical testing

was completed with six hours of euthanasia. This is consistent with Garo et al. who studied the

mechanical properties of brain tissue and found that the mechanical properties were constant up

to 6 hours after euthanasia [74]. These results are inconsistent with those of Ramo et al., and

Oakland et al. who saw increases in stiffness under six hours [62], [73].

The time criterion for this study was chosen due to the numerous sample types that needed to be

tested. This was necessary to address the proposed research question in this thesis. No significant

correlations between time post-mortem and peak stress were found indicates that the effect of

time post-mortem did not affect the results presented in this study. This validated the use of six

hours post-mortem for mechanical testing.

4.3 Comparison to Histological Parameters

The histology of each specimen type revealed underlying morphologies that helped further

explain some of the observed findings. The time independent properties can be explained by the

cellular components that distinguish grey matter from white matter. From the histology it was

observed that grey matter possessed neuronal cell bodies while white matter did not. It was also

shown that grey matter had a larger density of cell bodies compared to white matter. Cellular

stiffness’ of neurons and glial cells (astrocytes) have been previously measured in terms of their

rheological characteristics in the literature. Although both types of cell bodies exhibit more

elastic solid behaviour than viscous fluid behaviour, glial cells were found to be twice as soft as

neurons [99], [100]. In another study, Koser et al. stained for cell bodies and correlated the

number of cell bodies with measured stiffness’ in grey and white matter. They saw that an

increase in cell body density was directly correlated with an increase in stiffness [11]. These

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results further support the effect of tissue type with respect to the time independent properties

seen in this study where grey matter was significantly stiffer than white matter.

The viscous fluid behaviour of neurons and astrocytes support the viscoelastic properties seen

here for both grey and white matter. Ayala et al. modeled the rheological viscoelastic behaviour

of both these cell body types and reported that neurons have a higher viscosity than astrocytes

[100]. The higher stiffness and viscosity of neurons relative to astrocytes further supports the

argument that grey matter exhibits not only a larger aggregate modulus but also a longer

relaxation time than white matter.

The time independent and dependent properties between grey matter directions were unique. The

results showed that GT specimens exhibited an aggregate modulus that was 1.5 times stiffer than

GA specimens despite nearly identical peak stresses between them. Testing of GA and GT

samples in the literature has shown no significant differences in both stiffness and aggregate

modulus when comparing two orthogonal directions [11], [56], [57], [60]. It is hypothesized that

the phenomenon seen here is a result of tissue contamination and its interaction with the porous

filter. Contamination refers to the fact that the grey matter tissue samples were slightly

contaminated with white matter tissue. The GA and GT specimens that were collected are shown

in Figure 4-1.

Figure 4-1: Geometry of GA (left) and GT (right) specimens during sample collection. The

circle and rectangle represents an approximated scaled sample. The image is adapted from

Polarlys – CC by SA 3.0

Figure 4-1 illustrates that both GA and GT specimens interact with the porous filter differently.

This is shown by the different percentages of grey matter area interfacing with the porous filter.

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GT specimens possessed more grey matter at this interface. As a result GT was estimated to have

stiffer cellular bodies and more solid-like behaviour than GA. This may be the reason why GT

had a higher aggregate modulus than GA specimens. It could also be said the contamination of

white matter in the GA sample at the interface permits more fluid evacuation due to its increased

permeability. Increased permeability leads to an increased relaxation rate. This phenomenon is

consistent with the results of this study as GA’s aggregate modulus was found to lie between GT

and white matter specimen types.

The permeability of spinal cord tissue was recently measured using diffusion-weighted MRI. It

was found to be contrary to what was found in this study. The permeability from highest to

lowest reported was WA, grey matter, and WT [101]. No distinction was made between GA and

GT specimens as isotropy was assumed. It was recognized that this model was limited as it

assumed a constant axon diameter of 4 μm between both grey and white matter [101], [102].

The permeability model was adapted for use in this study to more accurately quantify the tissue

permeability with respect to the parameters of this study. Given that white matter samples were

taken from the lateral white matter, a diameter of 3.2 μm was used instead. This was found to be

the diameter of axons in the corticospinal tract [103]. Grey matter dendrites and axons on the

other hand were estimated to be approximately 1 μm [101]. The permeability for each specimen

type was recalculated using these new measurements. From highest to lowest, it was found to be

WA, WT, and grey matter. The estimated values of permeability were 1.6 x 10-13 m2, 3.2 x 10-14

m2, and 1.2 x 10-14 m2 for WA, WT, and grey matter respectively [104]. This is consistent with

the relaxation behaviour observed in this study

The permeability model used here is not without its limitations. The mathematical models used

are a function of axon diameter only. In addition it considered ideal flow through a hexagonal

array for white matter tissue [104]. From Section 1.3.3, it is observed that the structure of white

matter is more complex than a hexagonal array as axonal fibres are not perfectly straight. Axon

diameter and density also vary throughout introducing heterogeneity within white matter tissue

[103]. The vasculature that is prevalent across grey and white matter also influences the fluid

flow through the spinal cord which was not considered. Perhaps these added complexities is the

reason the interaction effect between tissue type and the transverse direction was observed.

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4.4 Clinical Relevance to SCI

The current expected stress-strain state of contusion SCI on both grey and white matter is

compressive stress-strain at the point of impact, generating tensile stress-strain in the

rostralcaudal direction [4]–[6], [8]. The typical assumptions of computational models often

include a homogeneous and isotropic spinal cord [4]–[6]. This means the stress-strain states in

both grey and white matter are equal in magnitude and are distributed equally in every direction.

4.4.1 The Effect of Time Independent Mechanical Properties on SCI

The time independent mechanical properties provide insight into the spinal cord stress-strain

state following impact to the spinal cord. The statistically significant difference in stiffness

between grey and white matter suggests that grey matter exhibits higher stresses than white

matter in the spinal cord cross-section. This is supported by the finite element analysis by

Nishida et al.. They modeled the spinal cord with stiffer grey matter than white matter in their

model. They showed that increasing transverse compression of the spinal cord resulted in a

higher stress distribution in grey matter than white matter in the cross-section of the spinal cord

[7]. Additionally, Maikos et al. conducted a sensitivity analysis whereby the stiffness of white

matter was 20% less stiff than grey matter. They showed that grey matter experienced a higher

stress relative to white matter [4].

The increased stiffness of grey matter suggests that grey matter undergoes less strain than white

matter following impact at the injury epicentre and rostralcaudal from the epicentre. At the injury

epicentre, Jannesar et al used stiffer grey matter than white matter properties and showed that

white matter exhibited increased strain compared to grey matter within the cross-section of the

spinal cord [8]. This is also supported by the sensitivity analysis performed by Maikos et al.. The

sensitivity analysis showed that decreasing the stiffness of white matter relative to grey matter

saw increased strain in the white matter compared to grey matter [4]. Jannesar et al. also

investigated the rostralcaudal propagation of strain from the epicentre. They found for the stiffer

grey matter that strain steadily decreased by up to 70% at greater rostralcaudal distances from the

injury epicentre. In contrast white matter strain was nearly constant even at further rostralcaudal

distances from the injury epicentre [8].

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Mechanical strain has been widely used to correlate with SCI in animal models [4], [5], [8]. The

different amount of strain propagation in both grey and white matter tissue discussed above show

consistency with the tissue sparing observed by Lam et al. after SCI in a rat. This study used a

combination of contusion depths and velocities to perform SCI. As an example, the tissue

sparing from a contusion depth of 1.5 mm and a velocity of 800 mm/s will be used for this

discussion.

Grey matter saw 20% tissue sparing at the injury epicentre. At +/- 1 mm from the epicentre, there

was 60% tissue sparing. Beyond this there was practically no damage seen. With the same

biomechanical injury parameters, the less stiff white matter saw 30%, 65%, and 85%, tissue

sparing at the epicentre, +/- 1 mm from the epicentre, and +/- 2 mm from the epicentre. After

which there was no more observed damage. This distribution of injury in the grey and white

matter was observed for all combinations of impact velocity and injury depth [22]. Lam et al.’s

study demonstrated that tissue damage propagated further rostralcaudally in the white matter

than grey matter when quantified by the amount of tissue sparing. These tissue sparing results by

Lam et al. correlate well with the elevated strains that were found to propagate further in white

matter compared to grey matter when modeled by Jannesar et al..

The higher stiffness of grey matter relative to white matter suggests that grey matter tissue

damage may be strain based. The stiffer grey matter exhibits significantly more stress than white

matter when both are strained equally [63]. Lam et al. showed that grey matter sparing was only

significantly affected by impact depth and not velocity despite varying both parameters [22].

This is further supported by Sparrey et al. who studied the effect of velocity at a fixed contusion

depth. The hemorrhage volume within grey matter was the same regardless of velocity [19].

These studies suggest that strain may be a good predictor for grey matter tissue damage.

The non-significant difference between axial and transverse directions suggests that both stress-

strain states propagate uniformly in both directions. This is consistent with the model

assumptions by both Maikos et al. and Jannesar et al.. The former assumed isotropic material

properties. The latter proposed white matter to exhibit transversely isotropic properties in tension

and isotropic properties in compression. This study confirms the second half of that statement

and future work investigating spinal cord anisotropic behaviour should include tensile testing.

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4.4.2 The Effect of Time Dependent Mechanical Properties on SCI

The time dependent properties suggests how spinal cord tissue stresses and strains change with

respect to time from persistent compressive strain. This has not been studied in computational

models of SCI. The findings from this study suggest three things. The statistically significant

difference in time constant indicates that transverse stresses applied to the spinal cord recover

significantly quicker in white matter than in grey matter. Second, the significant difference

between grey and white matter aggregate modulus show that grey matter maintains a higher

stress state than white matter following persistent compressive strain. Third, the significant

difference between transverse and axial direction aggregate modulus suggests that transverse

loading results in a higher spinal cord stress state than from axial loading. Higher residual stress

states in grey matter and the transverse direction of the spinal cord may point towards further

tissue damage in these areas following persistent compressive strain.

4.4.3 The Effect of Spinal Cord Tissue Bulk Moduli

Spinal cord tissue bulk moduli were not determined in this study, however the findings suggest

that grey matter has a higher bulk modulus than that of white matter. This is due to the higher

stiffness found for grey matter than white matter. The increased grey matter stiffness likely

means that a higher pressure is required to decrease the volume of grey matter in comparison to

white matter. This provides insight into the compressibility of grey and white matter tissue upon

spinal cord deformation.

This is contrary to the bulk moduli reported for brain grey and white matter tissue in the

literature. Zhou et al. modeled a higher bulk modulus for white matter than grey matter in their

computational model of brain injury. However it was noted that their model assumption was

made at a time when there was no supporting experimental data [53], [54].

A study by McElhaney et al. found the bulk modulus of brain tissue and water were not

significantly different [55]. This suggests the mechanical behaviour of nervous tissue behaves

similarly to that of a fluid. This reinforces the fluid behaviour that was observed in this study (ie.

the relaxation to a near zero stress).

To the author’s knowledge, bulk moduli of grey and white matter tissue have only been reported

for studies of brain tissue. This material property has been used to study brain injury using

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computational models. Given its application, this is an important consideration as it may be

extended for use in SCI computational models.

4.4.4 Drug Delivery

The relaxation time behaviour provided indirect insight into the permeability of spinal cord

tissue. Permeability is an important parameter because it characterizes the spinal cord as a porous

media through which drug delivery can be studied. This is an important to consider as different

permeabilities within the spinal cord may hinder targeted therapies from being delivered to the

appropriate location within the spinal cord.

The results suggest the permeability of white matter to be larger than grey matter. This means

that interstitial fluid will flow more easily through white matter than grey matter. The increased

flow resistance of grey matter may mean that a larger pressure gradient is needed to deliver drugs

through grey matter tissue [105].

Venton et al. modeled white matter permeability as anisotropic with WA greater than WT [101].

This would suggest that interstitial fluid flow would flow more easily rostralcaudally than

mediolaterally. Although this was not observed in this study, additional work investigating the

porous properties of spinal cord tissue is encouraged.

4.5 Limitations

4.5.1 Heterogeneity of Samples

From the histology that was performed, it was evident that the grey matter samples were

heterogeneous compared to the white matter samples. Although the results were quite clear

when comparing grey and white matter mechanical properties, the contamination of grey matter

samples with white matter tissue prevented the measurement of the true mechanical properties of

grey matter in this study.

This issue could be solved by the combination of the following two approaches. The first is to

collect from the cervical and/or lumbar enlargements as there is a larger amount of grey matter in

these regions. The second is to reduce the diameter of the collected specimen. The latter should

be optimized to be as large as possible. This is because measured forces are a function of the

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diameter squared. In other words decreasing the diameter by half would result in a quarter of the

force.

4.5.2 Strain Rate and Strain Sensitivity

Spinal cord tissue as well as its constituents are strain rate and peak strain sensitive as described

in the literature. They experience an increase in stiffness the faster and the more they are strained

regardless of how it is deformed as shown. This was shown for both its time independent and

dependent properties [41]–[44], [47], [59].

This study compressed tissue samples to a maximum of 10% strain. This is a limitation as it does

not cover the range of spinal cord deformations seen in SCI. Experimental models of SCI have

used spinal cord compression depths between 0% and 90% to study the effect of depth [17]–[22],

[24], [38]. Larger than 10% strains were attempted in preliminary tests. It was found that beyond

this peak strain, the data no longer experienced a strain-stiffening behaviour due to subfailure

tissue damage. This was also shown by Haslach et al.. They showed that peak stresses occurred

anywhere between 2% - 28% strain. Beyond this point the strain-stiffening behaviour was no

longer apparent [51]. Subfailure tissue damage was avoided in this study as it made it difficult to

compare data sets and draw conclusions between specimen types.

Future studies incorporating larger strains may be possible by using a porous filter above and

below the specimen. In doing so will allow greater fluid evacuation which should allow for

larger deformations. This was the experimental setup used by Haslach et al. [51]. It was not

possible for this study due to the pia mater that remained on the superior surface of the WT

specimen.

This study compressed tissue samples using a quasi-static strain rate of 0.001/sec. This is a

limitation as it does not cover the range of spinal cord impact velocities seen in SCI.

Experimental models of SCI have used velocities between 3 mm/s – 6000 mm/s to study the

effect of velocity [19], [20], [22], [24]. The constitutive model parameters developed in this

study can be used to predict the mechanical behaviour of spinal cord tissue at faster strain rates.

However these would need to be compared to future experimental studies involving multiple

strain rates to verify the parameters’ predictions.

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4.5.3 Loading Type

Spinal cord tissue is sensitive to loading type (ie. shear, compression, tension, etc.) as described

in the literature [42], [47], [59], [60]. This study only included confined compression of spinal

cord tissue in the axial and transverse directions. This is a limitation as compression does not

fully describe the stress-strain state of the spinal cord. The stress-strain state of SCI involves

transverse compression and axial tension [4], [5], [8]. Tensile anisotropy will need to be included

into future studies to fully describe the anisotropic behaviour of SCI.

4.5.4 Ex-Vivo Tissue

The mechanical properties discussed in this thesis were found from using ex-vivo and not in-vivo

tissue. The in-vivo properties may not necessarily be the same as the ex-vivo properties

concluded in this study. Future studies should explore methods to test spinal cord tissue in-vivo.

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Chapter 5: Conclusion

5.1 Conclusions

This work found that the spinal cord grey and white matter mechanical properties are

heterogeneous and slightly anisotropic. The effect of tissue type was prevalent across all

outcome variables measured. Grey matter was observed to be stiffer than white matter by

exhibiting significantly higher peak stress, and aggregate modulus. Grey matter was also

observed to have a longer relaxation time than white matter specifically in the transverse

direction. The effect of direction was only significant for the aggregate modulus outcome

variable. The transverse direction had a stiffer aggregate modulus than the axial direction. These

findings emphasize the important differences between tissue type and to a lesser extent direction

when modeling spinal cord grey and white matter tissue in finite element models for studying

SCI biomechanics.

This work met the proposed thesis objectives (Section 1.8.2) in the following ways:

1) A novel experimental approach to evaluating grey and white matter tissue anisotropy was

developed. A custom biopsy punch integrated within a custom confined compression

apparatus were designed. The punch preserved tissue structure after collecting the

specimen, and integration within the confined compression apparatus maintained tissue

orientation. This allowed for GA, GT, WA, and WT specimens to be mechanically tested

in confined compression.

2) A QLV model incorporating a first-order exponential function and a one-term Prony

series was used to characterize the non-linear viscoelastic response of spinal cord grey

and white matter tissue highlighting important parameters such as peak stress, aggregate

modulus, and relaxation time. Peak stress was easily identified while aggregate modulus

and relaxation time were approximated using a 1-term Prony series.

3) The effect of tissue type, direction, and their interaction on the mechanical properties of

spinal cord grey and white matter in confined compression were adequately analyzed in

this study. A two-way ANOVA permitted the analysis of these effects. The analysis

revealed a strong effect of tissue type and a weak effect of direction. This means that the

spinal cord exhibits heterogeneous and slightly anisotropic mechanical properties.

104

5.2 Contributions

This research is the first investigation of spinal cord grey and white matter tissue mechanical

properties in a confined compression test. This research examined both the effect of tissue type

and direction. This was done by evaluating both time independent and dependent mechanical

properties of the spinal cord.

The study adds to the controversial literature surrounding the mechanical properties of the spinal

cord grey and white matter; the effect of tissue type. It corroborates with previous work stating

that grey matter is stiffer than white matter in terms of peak stress and aggregate modulus. It is

the first to report relaxation times comparing spinal cord grey and white matter and corroborates

with brain tissue studies.

The study adds to the sparse literature surrounding the directional properties of spinal cord grey

and white matter. The time independent directional properties corroborates with previous work

stating that the spinal cord is isotropic in compression. The time dependent directional properties

are the first to be reported and states that the aggregate modulus in the transverse direction is

larger than the axial direction.

The mechanical design and protocol used to collect isolated tissue samples is a novel design. The

mechanical design can be adapted for future studies of spinal cord confined compression. The

sample collection protocol can be adapted for future studies examining the mechanical properties

of spinal cord grey and white matter in other loading types.

5.3 Recommendations for Future Work

In order to continue improving existing spinal cord material models for studying SCI

biomechanics, several recommendations for future work are described:

1) Tensile anisotropy should be studied to better characterize the stress-strain state of the

spinal cord in SCI. The sample preparation protocol described could be adapted to collect

specimens. The difficulty will be in testing transverse specimens of grey and white

matter. The spinal cord provides limited lengths for grey and white matter transverse

specimens. Clamping of short tissue lengths results in tissue behaviour that is dominated

by end effects. As such a novel attachment method will need to be developed to apply

105

transverse tension. This will not be a problem for axial specimens as longer lengths can

be collected from the spinal cord.

2) Computational models of SCI should be updated to include the mechanical property

findings from this study. These properties are different than those assumed and used by

current models. This would yield a new stress-strain distribution for the spinal cord. The

new stress-strain distribution can be correlated with injury mechanisms from

experimental models of SCI; ultimately relating stress-strain distribution with histological

tissue damage. This may provide insight into developing a stress-strain injury criterion

for spinal cord tissue.

3) The differences in mechanical properties existing between cervical, thoracic, and lumbar

regions can be studied. The emphasis should be placed on studying the cervical spinal

cord region. This is due to the prevalence of SCI occurring at this level. Cervical and/or

lumbar regions also feature enlargements in grey matter because these regions feature the

neurons responsible for upper and lower limb motor function. Testing of these regions

may result in slightly different stress-strain distributions.

4) MRE has recently been used to evaluate the in-vivo mechanical properties of spinal cord

tissue [106]. This would be useful as the in-vivo mechanical properties are more

representative of spinal cord mechanical properties rather than the ex-vivo properties

measured here. Kruse et al. have only provided initial evidence to quantify the shear

stiffness of the spinal cord in-vivo using MRE. This work is ongoing and requires

validation. Future studies should explore the use of MRE in the hopes of quantifying the

in-vivo mechanical properties of spinal cord tissue.

5.4 Concluding Statement

The current research refutes the assumption of spinal cord homogeneity and isotropy when using

computational models to study SCI biomechanics. In order to accurately model the link between

spinal cord impact and the resulting tissue damage, the material properties of the spinal cord

need to be meticulously studied. Continued understanding of spinal cord material properties will

provide further understanding of SCI stress-strain states. Knowledge of tissue tolerances will

relate injury mechanisms to tissue damage patterns and ultimately to their respective pathologies.

This will promote the discovery of targeted therapies and treatments for SCI.

106

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114

Appendix A – Engineering Drawings

Please note that the engineering drawings found in this Appendix are not final. The following

revisions were made:

- The indenter (Item No. 12) shown on GWMA-001 was discarded. Instead the magnetic

end effector shown in Section 2.1.1.5 was used.

- A carbon steel disc was taped to the top surface of GWMA-006 as shown in Section

2.1.1.4. The carbon steel disc was machined to have the same diameter as the head piece

of the shaft. This allowed the tape to be placed around the circumference of both parts.

- Drawing# GWMA-009 was discarded and instead the magnetic end effector shown in

Section 2.1.1.5 was used

115

116

117

118

119

120

121

Appendix B – Pilot Test Data in Air

Figure B-1: Pilot test data in air. The same strain rate and strain were implemented to

measure the background noise that is generated when there is no specimen within the

adapter. The increase in noise at the end is when the indenter is being removed from the

adapter causing a spike in load. This is not a part of the testing protocol

122

Appendix C – Load Cell Calibration

Table C-1: Load cell calibration using standard weights. The gain in the load cell was

adjusted based on the error

Mass (g) True Weight (N) % FS Measured Weight (N) % Error

52.68 0.52 5.17% 0.53 3.04%

102.07 1.00 10.01% 1.03 2.97%

153.08 1.50 15.02% 1.55 2.93%

123

Appendix D – Repeatability Analysis of Confined

Compression Apparatus

Figure D-1: Repeatability study using silicone specimen #1. Four confined compression

tests were performed and their load-time curves are shown. COV was calculated resulting

in 6% variability.

124

Figure D-2: Repeatability study using silicone specimen #2. Three additional confined

compression tests were performed and their load-time curves are shown. COV was

calculated resulting in 4% variability.

125

Appendix E – Specimen Testing Order

Table E-1: Specimen testing order for all pigs (n=11)

Pig # Block 1 Block 2

1 W W G G G G W W

A T A T T A T A

2 W W G G W W G G

T A T A A T A T

3 G G W W G G W W

A T A T T A T A

4 G G W W G G W W

T A T A A T A T

5 W W G G W W G G

T A A T A T T A

6 G G W W G G W W

T A A T A T T A

7 W W G G W W G G

A T T A T A A T

8 G G W W G G W W

A T T A T A A T

9 W W G G W W G G

A T A T T A T A

10 G G W W G G W W

A T A T T A T A

11 W W G G W W G G

T A T A A T A T

In the situation that more than two blocks can be tested in the six hour time window, the blocks

are repeated from block one.

126

Appendix F – Power Analysis

Table F-1: Power analysis (Part 1) calculation used to calculate minimum sample size for this thesis. The study by Prange &

Margulies, 2002 was used as reference [57]

Strain Shear Relaxation Modulus (Pa)

2.5% -

50% Gray Matter Corona Radiata Corpus Callosum

Relax

Time

(msec)

D1

(Axial)

Std

dev

D2

(Transverse)

Std

dev

D1

(axial)

Std

dev

D2

(Transverse)

Std

dev D1

Std

dev D2 Std dev

100.00 218.00 17.31 197.00 6.67 225.00 37.77 155.00 14.29 100.00 15.24 180.00 28.58

900.00 140.00 15.74 120.00 4.76 140.00 15.74 90.00 11.43 65.00 7.62 120.00 9.53

2500.00 120.00 15.74 95.00 2.86 115.00 15.74 80.00 6.67 55.00 2.86 110.00 14.29

abs(A

- T)

Std

Dev

(P)

Effect Size

(d)

abs(A

- T)

Std

Dev

(P)

Effect Size

(d)

abs(A

- T)

Std

Dev

(P)

Effect

Size

(d)

100.00 21.00 14.83 1.42 70.00 32.32 2.17 80.00 22.91 3.49

900.00 20.00 13.32 1.50 50.00 14.53 3.44 55.00 8.63 6.38

2500.00 25.00 13.15 1.90 35.00 13.57 2.58 55.00 10.31 5.34

Note: The nonmenclature used: A = Axial, T = Transverse, P = Pooled standard deviation, d = Effect Size.

127

Table F-2: Power analysis (Part 2) calculation used to calculate minimum sample size for this thesis. The study by Prange &

Margulies, 2002 was used as reference [57].

Using the T-distribution Table

Sample

Size 12.00 6.00 12.00 6.00 6.00 6.00

Dof 11.00 5.00 11.00 5.00 5.00 5.00

t (1-

alpha/2) 2.20 2.57 2.20 2.57 2.57 2.57

t (beta) -0.84 -0.84 -0.84 -0.84 -0.84 -0.84

Minimum Samples Req'd:

GA vs

GT

WA vs

WT

WA vs

WT

N

13.06 16.43 8.54 10.74 6.66 6.66

12.32 15.50 5.38 6.76 3.65 3.65

9.73 12.24 7.17 9.02 4.36 4.36

Minimum Samples Req'd:

GM vs

WM

abs(A

- T)

Std Dev

(P)

Effect

Size (d)

Sample

Size Dof

t(1-

alpha/2) t(beta) N

Grey

Matter 207.50 67.50 18.36 3.68 18.00 17.00 2.11 -0.84 4.73

Marginal

Means 130.00 37.50 11.74 3.19 5.45

107.50 25.00 12.13 2.06 8.45

White

Matter 140.00 12.00 11.00 2.20 -0.84 5.03

Marginal

Means 92.50 5.79

82.50 8.97

128

Appendix G – Constitutive Modeling Hand Calculations

Please note that the hand calculations shown here uses a 3 term Prony series.

129

Figure G-1: Hand calculations for the analytical solution to the constitutive model used to

model stress relaxation. The final solution for the ramp phase (Eq. 1) and the hold phase

(Eq. 2) are shown.

130

Appendix H – Constitutive Modeling Matlab Script

%Constants - Variable length to be changed depending on # of Excel

%Files

dia = 2; %Enter specimen diameter in mm

thk = [2.77 3]; %Enter specimen thickness in mm for all tests

t0 = [100 100 100 100 100 100 100 100]; %Enter time when loading -->

Relaxation

t1=(0:0.5:100)'; %Ensure this goes beyond t0

t2=(100:0.5:220)';

gam = abs(-0.001); %Strain Rate during loading phase

Strain = (0:0.0001:0.1)';

global index;

n = 50; %For plotting only; Plots every nth data point

c = [141.7988 17.3676 0.9903 0.1710]; %initial values for c -> doesn't matter

%initial values for c0 -> guess as close as possible

%# of rows depends on # of Excel Files

c0 =[

141.7988 17.3676 0.9903 0.1710

];

%Reading Multiple Excel Files - Change Folder Location if Necessary

Dir = 'C:\Users\Justin\Documents\University of British

Columbia\Research\Testing\Stress Relaxation Data\10 N Load Cell Trial\070419

- Euthanasia\GA\Raw Data';

Source = dir(fullfile(Dir,'*.csv'));

%variable bounds

for b = 1:length(Source)

ub(b,:) = [2000 100 1 101];

lb(b,:) = [0 0 0 0];

end

131

%linear constraints

% Inequality Constraints

% A & B material constants must be >= 0

% Time constants tau1 >= tau2 and tau2 >= tau3

% Equality Constraints

% Time constants tau1 = 1, tau2 = 10, tau3 = 100

% Gss + G1 + G2 + G3 = 1 at t = 0

A = [

-1 0 0 0;

0 -1 0 0;

0 0 1 0;

];

B = [0; 0; 1];

Aeq = [];

Beq = [];

%Main Body + Constitutive Modeling

for i = 1:length(Source)

F = fullfile(Dir,Source(i).name);

[Source(i).num,Source(i).txt,Source(i).raw] = xlsread(F);

Data{i} = Source(i).num(:,[2,4,5]);

Data{i}([1:45],:)=[];

Elem(i) = numel(Data{i}(:,1));

area = pi*(dia/1000)^2/4;

DispData{i} = Data{i}(:,2) - Data{i}(1,2) + thk;

Stress{i} = abs((Data{i}(:,3)-Data{i}(1,3))/area/1000); %in kPa

index = i;

J = [c0(i,:) i]; % Combining i with initial guesses to be brought into the

function

%Constitutive Modeling

[c(i,:),fval(i,:),exitflag(i,:)]=fmincon('qlvfitunworkinprogress1',c0(i,:),A,

B,Aeq,Beq,lb,ub); %Minimizes least squares in function – SEE BELOW FOR SCRIPT

132

%c =

constants

%fval = value

of the objective function (should be ~0)

%exitflag -

if equal to 1 then the solution converges

c

%Plotting the Data

figure(i)

subplot(3,1,1)

plot (Strain,abs(Stress{i}(1:1001,1)))

ylabel ('Stress (kPa)'); xlabel ('Strain');

subplot(3,1,2)

plot (Data{i}(:,1),abs(Stress{i}(:,1)))

ylabel ('Stress (kPa)'); xlabel ('Time (secs)');

subplot(3,1,3)

plot (Data{i}(:,1),abs(Stress{i}(:,1)))

ylabel ('Stress (kPa)'); xlabel ('Time (secs)');

hold on

for k = 1:201 %generating values for loading phase

sig{i}(k,1)=c(i,1)*c(i,2)*gam*...

(((1-c(i,3))*exp(c(i,2)*gam*t1(k,1))/(c(i,2)*gam)+...

c(i,3)*exp(c(i,2)*gam*t1(k,1))/(c(i,4)+c(i,2)*gam)...

)-...

((1-c(i,3))/(c(i,2)*gam)+...

c(i,3)*exp(-c(i,4)*t1(k,1))/(c(i,4)+c(i,2)*gam)...

));

end

hold on

plot(t1(:,1),sig{i}(:,1),'*')

hold on

133

for k = 1:241 %generating values for relaxation phase

sig2{i}(k,1)=c(i,1)*c(i,2)*gam*...

(((1-c(i,3))*exp(c(i,2)*gam*t0(i))/(c(i,2)*gam)+...

c(i,3)*exp(-

c(i,4)*t2(k,1))*exp((c(i,4)+c(i,2)*gam)*t0(i))/(c(i,4)+c(i,2)*gam)...

)-...

((1-c(i,3))/(c(i,2)*gam)+...

c(i,3)*exp(-c(i,4)*t2(k,1))/(c(i,4)+c(i,2)*gam)...

));

end

plot(t2(:,1),sig2{i}(:,1),'*')

legend('Experimental','QLV-Loading','QLV-Relaxation');

StressDiscrete{i} = [Stress{i}(750,1),750;

Stress{i}(800,1),800;

Stress{i}(900,1),900;

Stress{i}(1000,1),1000;

max(Stress{i}),find(Stress{i}==max(Stress{i}),1,'last')];

%Collects discrete points for peak stress and

%stiffness calculation

StressFinal{i} = c(i,1)*c(i,2)*gam*...

((1-c(i,3))*exp(c(i,2)*gam*t0(i))/(c(i,2)*gam)-...

((1-c(i,3))/(c(i,2)*gam)));

%Calculates the equilibrium stress as t --> infinity

Stiffness{i}=[

(StressDiscrete{i}(4,1)-StressDiscrete{i}(1,1))/...

((StressDiscrete{i}(4,2)-StressDiscrete{i}(1,2))/10000);

(StressDiscrete{i}(4,1)-StressDiscrete{i}(2,1))/...

((StressDiscrete{i}(4,2)-StressDiscrete{i}(2,2))/10000);

(StressDiscrete{i}(4,1)-StressDiscrete{i}(3,1))/...

((StressDiscrete{i}(4,2)-StressDiscrete{i}(3,2))/10000)

];

134

%Calculates the Modulus based on Stress/Strain

end

%Truncating + Average + Standard Deviation

truncate = min(Elem);

for b = 1:length(Source)

Datatimemod{b} = Data{b}(1:truncate,1);

Datatimemat(:,b) = cell2mat(Datatimemod(b));

Dataloadmod{b} = Data{b}(1:truncate,3);

Dataloadmat(:,b) = cell2mat(Dataloadmod(b));

stressmod{b} = Stress{b}(1:truncate,1);

stressmat(:,b) = cell2mat(stressmod(b));

stiffnessraw(:,b) = (stressmod{b}(1000,1)-stressmod{b}(900,1))/...

((1000-900)/10000);

end

for bb = 1:truncate

Dataloadmean(bb,1) = mean(Dataloadmat(bb,:));

Dataloadstddev(bb,1) = std(Dataloadmat(bb,:));

stressmean(bb,1) = mean(stressmat(bb,:));

stressstddev(bb,1) = std(stressmat(bb,:));

end

stresspeakstddev = stressstddev(1000,1);

stiffnessstddev = std(stiffnessraw);

135

Non Linear Least Squares Optimization Function

function H = qlvfitunworkinprogress(c)

dia = 2; %Enter specimen diameter in mm

area = pi*(dia/1000)^2/4;

%c = [1 1 1 1 1 1 1 1];

t0 = [100 100 100 100 100 100 100 100]; %t0 where Loading phase transitions

to Relaxation phase

%Length of vector depends on # of

%Excel Files in Folder

gam = abs(-0.001); %Strain Rate during loading phase

global index;

%index = 1;

f1{index}(1,:) = [0.]; %initial values for f1 and f2

f2{index}(1,:) = [0.];

Dir = 'C:\Users\Justin\Documents\University of British

Columbia\Research\Testing\Stress Relaxation Data\10 N Load Cell Trial\061019

- Euthanasia\WT';

Source = dir(fullfile(Dir,'*.csv'));

%ii = int8(J(10))

%c = J(1:9);

F = fullfile(Dir,Source(index).name);

[Source(index).num,Source(index).txt,Source(index).raw] = xlsread(F);

Data{index} = Source(index).num(:,[2,4,5]);

Data{index}([1:45],:)=[];

Data{index} = Data{index}';

Stress{index} = abs((Data{index}(3,:)-Data{index}(3,1))/area)/1000; %Units in

kPa

for j = 1:1000 %Length = # of data points in loading phase

t1{index}(1,j)=Data{index}(1,j); %Putting tramp into a column vector

136

%Calculating least squares sum for loading phase

f1{index}(1,:) = f1{index}(1,:)+(c(1)*c(2)*gam*...

(((1-c(3))*exp(c(2)*gam*t1{index}(1,j))/(c(2)*gam)+...

c(3)*exp(c(2)*gam*t1{index}(1,j))/(c(4)+c(2)*gam)...

)-...

((1-c(3))/(c(2)*gam)+...

c(3)*exp(-c(4)*t1{index}(1,j))/(c(4)+c(2)*gam)...

))-...

Stress{index}(1,j))^2;

end

for k = 1:1200 %Length = # of data points in relaxation phase

%MatLab is only allowing a total of 3865 points due to

%air file

t2{index}(1,k)=Data{index}(1,k+1000); %Putting time into t variable

%Calculating least squares sum for relaxation phase

f2{index}(1,:) = f2{index}(1,:)+(c(1)*c(2)*gam*...

(((1-c(3))*exp(c(2)*gam*t0(index))/(c(2)*gam)+...

c(3)*exp(-

c(4)*t2{index}(1,k))*exp((c(4)+c(2)*gam)*t0(index))/(c(4)+c(2)*gam)...

)-...

((1-c(3))/(c(2)*gam)+...

c(3)*exp(-c(4)*t2{index}(1,k))/(c(4)+c(2)*gam)...

))-...

Stress{index}(1,k+1000))^2;

end

f{index}(1,:) = f1{index}(1,:)+f2{index}(1,:); %Sum of least squares sum

of loading + relaxation data

% end

H = cell2mat(f)

index

end

137

Appendix I – Staining Protocols

Hemtoxylin & Eosin Staining Protocol

1. Xylene 2 – 5 minutes

2. Xylene 1 – 5 minutes

3. 100% EtOH – 3 minutes

4. 100% EtOH – 3 minutes

5. 95% EtOH - 3 minutes

6. 70% EtOH – 3 minutes

7. Distilled Water - 3 minutes

8. Distilled Water – 3minutes

9. Hematoxylin Gill 2x – 5 minutes

10. Water 3x – 1 minute/each

11. HCl (0.5% in 70% EtOH) – 10 seconds

12. Water 3x – 1 minute/each

13. NaHCO3 (1.5%) – 5 seconds

14. Water 3x – 1 minute/each

15. 95% EtOH – 2 minutes

16. Eosin Y – 15 seconds

17. 95% EtOH – 2 minutes

18. 100% EtOH – 2 minutes

19. 100% EtOH – 2 minutes

20. Xylene 1 – 2 minutes

21. Xylene 2 – 2 minutes

138

Eriochrome Cyanine (EC) Stain (for myelin)

Make 10% FeCl3

- 33g FeCl3 ∙ 6H2O (= 5g FeCl3) in 50ml dH2O

- keep the rest in the falcon tube for later use

Make EC stain

- add 0.08g EC in 40mL dH2O with 200uL H2SO4

- add 2mL 10% FeCl3, top up to 50mL

- filter into brown bottle

- can reuse stain

- Store at RT

Make 0.5% NH4OH (for differentiation)

- 1M stock solution is 3.5%

- dilute 1 in 7

- make fresh if over 1 week old

1. Thaw slides 1hr

2. Xylene II (in fumehood) 5 min

3. Xylene I (in fumehood) 5 min

4. 100% EtOH 2 min

5. 90% EtOH 2 min

6. 70% EtOH 2 min

7. 50% EtOH 2 min

8. dH2O 2 min

9. EC 10 min

10. dH2O rinse x 2

11. NH4OH ~ 2 min (until differentiation)

12. dH2O rinse x 2

13. 1% Neutral Red (only if you want a counter stain) 2 min

139

14. 50% EtOH 2 min

15. 70% EtOH 2 min

16. 90% EtOH 2 min

17. 100% EtOH 2 min

18. Xylene I (in fumehood) 2 min

19. Xylene II (in fumehood) 2 min

20. Coverslip with SHUR/mount (in fumehood)

Alcohol waste goes into alcohol waste can

Xylene waste goes into xylene recovery red can

140

Appendix J – Raw Data: Stress-time curves, Constitutive

Model Fit, Outcome Variables

Figure J-1: All stress-time plots for GA (a), GT (b), WA (c), and WT (d) specimens for all

11 pigs

141

Table J-1: Constitutive model material constants for GA, GT, WA, and WT specimens for

all pigs

Date Specimen A B g ꞇ Date Specimen A B g ꞇ

0610 GA 91.95 22.20 0.98 0.13 0911 GA 117.62 19.13 0.99 0.11

0610 GT 60.53 21.82 0.94 0.08 0911 GT 121.18 19.93 0.99 0.15

0610 WA 128.28 15.85 0.99 0.10 0911 WA 120.14 16.52 0.99 0.14

0610 WT 141.80 17.37 0.99 0.17 0911 WT 192.84 15.29 0.99 0.12

0626 GA 173.12 16.41 0.98 0.12 0913 GA 111.59 19.87 0.97 0.11

0626 GT 125.76 14.58 0.92 0.07 0913 GT 190.36 14.65 0.94 0.07

0626 WA 116.50 15.02 0.97 0.11 0913 WA 125.97 16.95 0.97 0.11

0626 WT 251.39 14.24 0.99 0.20 0913 WT 117.31 17.86 0.98 0.11

0627 GA 70.20 17.56 0.93 0.06

0627 GT 107.63 14.19 0.91 0.06

0627 WA 168.27 16.74 0.98 0.10

0627 WT 111.57 18.73 0.99 0.15

0704 GA 180.51 16.29 0.97 0.10

0704 GT 363.68 11.69 0.98 0.08

0704 WA 117.75 14.68 0.98 0.13

0704 WT 138.91 16.64 0.97 0.14

0718 GA 135.19 17.16 0.96 0.07

0718 GT 101.03 15.90 0.94 0.06

0718 WA 147.55 14.96 0.99 0.10

0718 WT 172.83 16.39 0.99 0.15

0808 GA 142.18 17.02 0.98 0.09

0808 GT 292.38 11.74 0.96 0.09

0808 WA 131.40 14.22 0.97 0.07

0808 WT 75.50 16.65 0.97 0.08

0813 GA 92.52 17.28 0.97 0.07

0813 GT 77.06 20.85 0.96 0.13

0813 WA 59.40 13.82 0.97 0.09

0813 WT 64.25 21.58 0.97 0.13

0904 GA 125.78 13.54 0.94 0.07

0904 GT 162.67 12.08 0.97 0.07

0904 WA 124.05 13.33 0.97 0.10

0904 WT 112.96 15.88 0.99 0.13

0909 GA 149.04 18.24 0.98 0.12

0909 GT 208.82 15.07 0.96 0.08

0909 WA 85.33 13.06 0.97 0.08

0909 WT 70.88 16.54 0.94 0.09

142

Figure J-2: Peak Stress between specimen types for all pig specimens tested

Figure J-3: Aggregate Modulus between specimen types for all pig specimens tested

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143

Figure J-4: Time constant between specimen types for all pig specimens tested

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