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UBC Theses and Dissertations

The human spinal cord : an improved physical model Reed, Shannon Gail 2005

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THE HUMAN SPINAL CORD: AN IMPROVED PHYSICAL MODEL by SHANNON GAIL REED B.Sc, Queen's University, 2003 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA December 2005 © Shannon Gail Reed, 2005 A b s t r a c t Spinal cord injury is a devastating condition which can occur by impact of bone fragments during spinal fracture as well as from spinal motion which exceeds the normal physiologic range. The deformation undergone by the spinal cord during these injuries is currently poorly understood. This information is important for the validation of mathematical models of spinal cord injury and in the evaluation of animal models to determine if they are representative of human spinal cord injuries. An accurate surrogate physical model of the human spinal cord would allow measurement of the cord deformations during in vitro spine injury experiments. The objectives of this study were to develop a physical model of the in vivo human spinal cord. This included identifying a material which matches the in vivo modulus of elasticity of the spinal cord, testing its behaviour in uniaxial tension and transverse compression with and without the dura mater and the CSF present. QM Skin 30 elastomer was identified as the best surrogate material for the in vivo human spinal cord. The modulus of elasticity of QM Skin 30 in tension and compression matched that reported for the in vivo spinal cord. A burst fracture injury was simulated with the dura mater and CSF surrounding the surrogate cord indicating that this form of the surrogate cord is the best match for the in vitro bovine spinal cord in similar conditions. Uniaxial tension tests performed at different strain rates indicated that it is viscoelastic. However, the viscoelasticity of the surrogate cord is less than desired. A quasilinear viscoelastic and general linear model were presented to describe the relaxation and creep response. The surrogate cord developed in this study incorporates a range of mechanical properties which have been reported for the spinal cord but which have not all been included in one surrogate cord before now. By virtue of its concordance with in vivo spinal cord properties and our advanced understanding of its behaviour it is appropriate for in vitro spine experiments. ii Table of Contents Abstract » Table of Contents • iii List of Tables vii List of Figures ' x Acknowledgement xiii Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Spinal Cord Injury and its Consequences 1 1.3 Anatomy 3 1.4 Mechanisms of Spinal Cord Injury : 7 1.5 Biomechanics of Spinal Cord Injury 12 1.5.1 Methods Used to Study Spinal Cord Injury 12 1.5.2 Methods Used to Study Canal Deformation 14 1.5.3 Methods Used to Study Cord Deformation 17 1.5.4 Limitations of the Previous Methods 18 1.5.5 In Vivo and In Vitro Mechanical Properties of the Spinal Cord 19 1.5.6 Animal and Human Spinal Cord Properties 20 1.5.7 The Necessity for an Improved Surrogate Cord 20 1.6 Objectives 21 1.7 Road Map 22 1.7.1 Chapter 2: The Development of a Surrogate Cord 22 1.7.2 Chapter 3: Viscoelastic Behaviour of the Spinal Cord 22 1.7.3 Chapter 4: Transverse Compression of the Spinal Cord 23 1.7.4 Chapter 5: Conclusion 23 1.8 References • 24 Chapter 2 The Development of a Surrogate Cord 28 2.1 Introduction 28 2.1.1 Geometrical Properties of the Human Spinal Cord 28 2.1.2 In Vivo Spinal Cord Deformation (Human) 29 2.1.3 In Vitro Human Studies 29 2.1.4 In Vivo Animal Spinal Cord Properties 30 2.1.5 Surrogate Spinal Cord 34 2.2 Objectives 37 2.3 Materials and Methods 38 2.3.1 Performance Requirements 38 2.3.2 Material Search 40 iii 2.3.3 Molding Process 40 2.3.4 Testing Protocol 45 2.3.5 Testing Equipment 49 2.4 Results 52 2.4.1 Determination of the Surrogate Cord Material 52 2.4.2 Final Surrogate Cord Material 56 2.5 Discussion • 59 2.5.1 Assigning QM Skin 30 as the Surrogate Material 59 2.5.2 Evaluation of QM Skin 30 (10:1.2) in Quasistatic Tension 61 2.5.3 Limitations and Future Work 62 2.5.4 Conclusions 62 2.6 References 64 Chapter 3 Viscoelastic Behaviour of the Spinal Cord 66 3.1 Introduction 66 3.1.1 Viscoelastic Properties of the Human Spinal Cord 66 3.1.2 Viscoelastic Properties of the Animal Spinal Cord 68 3.1.3 Creep Behaviour •••69 3.2 Objectives 71 3.3 Materials and Methods 72 3.3.1 Testing Protocol -72 3.3.2 Testing Equipment 76 3.4 Results 78 3.4.1 The Effect of Strain Rate on the Modulus of Elasticity 78 3.4.2 Relaxation Behaviour 81 3.4.3 Creep Behaviour 86 3.5 Discussion 87 3.6 References 92 Chapter 4 Transverse Compression of the Spinal Cord 94 4.1 Introduction 94 4.1.1 Traumatic Compression of the Spinal Cord 94 4.1.2 In Vivo Transverse Compression 94 4.1.3 In Vitro Transverse Compression 96 4.1.4 Effect of the Dura Mater and CSF , 97 4.1.5 Transverse Compression of the Surrogate Cord 100 4.1.6 An Improved Surrogate Cord 101 4.2 Objectives 101 4.3 Materials and Methods 102 4.3.1 . Surrogate Cord Specimens 102 4.3.2 Rectangular Specimens 102 4.3.3 Rectangular Specimen Compression Tests 102 4.3.4 Quasistatic and Intermediate Rate Testing..... 103 4.3.5 Impact Testing 105 4.4 Results 113 4.4.1 Rectangular Specimens in Compression 113 iv 4.4.2 Surrogate Cords in Transverse Compression - Quasistatic and Intermediate Strain Rates 115 4.4.3 Transverse Compression Impact Tests 117 4.5 Discussion 127 4.5.1 The Modulus of Elasticity in Compression 127 4.5.2 Effect of Strain Rate on the Force Response 128 4.5.3 Effect of the Dura Mater and CSF 131 4.5.4 Comparison of the Surrogate Cord with the Bovine Spinal Cord 131 4.6 References 137 Chapter 5 Conclusion 139 5.1 Uniaxial Tension 139 5.2 Viscoelastic Properties of the Surrogate Cord 140 5.3 Transverse Compression at Quasistatic and Intermediate Strain Rates ....142 5.4 Impact in Transverse Compression 144 5.5 Future Work 146 5.6 Limitations 148 5.7 Final Conclusions 150 5.8 References 154 Appendix A Measurement of Strain in the Surrogate Cord , 155 A.l Crosshead Strain 155 A.2 Linear Potentiometer Accuracy 157 A. 3 Velocity Calibration 159 Appendix B Quasilinear Viscoelasticity 160 B. l Fung's Quasilinear Viscoelastic Theory 160 B.2 References 162 Appendix C Stress Decay During Relaxation of the Surrogate Cord .....163 Appendix D General Linear Model for Relaxation and Creep 165 D. 1 Relaxation Constants 165 D. 2 Creep Constants 166 Appendix E Rectangular Specimens of Q M Skin 30 169 E. 1 Material Properties 169 E. 2 Statistical Results 169 Appendix F Load Cell Calibration 170 F. l LCFA-10 Load Cell 170 F.2 SBL-lOkN Load Cell... 171 Appendix G Temperature Profile in the Surrogate Cord 172 Appendix H Pressure-Velocity Calibration 174 v Appendix I Matlab Code 175 1.1 Normalize the Image 175 1.2 Process Images ; 175 Appendix J Transverse Compression of the Surrogate Cord 179 Appendix K Stiffness of the Surrogate Cord in Transverse Compression 180 vi List of Tables Table 1-1 - Spinal column injuries which are associated with spinal cord injuries in adults49 .' 8 Table 1-2 - Surrogate cords developed previously 19 Table 2-1 - Modulus of Elasticity for in vivo spinal cords measured from during quasistatic tension tests.6'7'12'13 38 • 1 1 1 2 1 7 22 Table 2-2 - Performance Requirements for the surrogate spinal cord. ' ' ' 39 Table 2-3 - Candidate Surrogate Cord Materials 40 Table 2-4 - Materials tested in quasistatic tension. 47 Table 2-5 - Modulus of Elasticity for the different surrogate cord materials tested 56 Table 2-6 - Mean values for the modulus of elasticity (MPa) measured from the first quasistatic tension test in Groups 2 and 3. Values are given for the modulus measured from 5% and 12% strain data with one standard deviation given in parentheses 57 Table 2-7 - SNK results (p values) between quasistatic tension tests performed on surrogate cords 65 through 74 (Group 2) to a) 5% strain and b) 12% strain. The mean value for the modulus of elasticity is provided in MPa 58 Table 3-1 - Viscoelastic tests performed with the surrogate cord. A total of 34 surrogate cords were constructed. Group 1 (14 cords) was used for impact transverse compression tests, Group 2 (10 cords) was used for uniaxial tension at varying strain rates, and Group 3 (10 cords) was used for relaxation, creep, and non-impact transverse compression tests 73 Table 3-2 - Quasilinear viscoelastic parameters for the relaxation test measured after an instantaneous strain (0.32s"1) to 12% strain including the means and standard deviations (SD) 82 Table 3-3 - Mean quasilinear viscoelastic model parameters for the fast and instantaneous strain rates to 12% strain 82 Table 3-4 - Mean stress and stress decay for relaxation tests performed at each strain rate .' 83 Table 3-5 - Comparison between the linear and quasilinear viscoelastic model for the reduced relaxation function of QM Skin 30 at the (a) fast and (b) instantaneous strain rates 84 Table 4-1 - The change in the transverse impact response across three repeated tests. Bovine data was taken from Jones.12 112 Table 4-2 - Mean strain and modulus of elasticity (E) values for the entire set of compression tests performed on rectangular specimens of QM Skin 30 114 Table C-l - Stress decay in the surrogate cord during relaxation. The surrogate cords were in 12% strain which was applied at a quasistatic strain rate (0.0025s"1) 163 Table C-2 - Stress decay in the surrogate cord during relaxation. The surrogate cords were in 12% strain which was applied at an intermediate strain rate (0.048s"1) 163 Table C-3 - Stress decay in the surrogate cord during relaxation. The surrogate cords were in 12% strain which was applied at a high strain rate (0.12s'1) 164 Table C-4 - Stress decay in the surrogate cord during relaxation. The surrogate cords were in 12% strain which was applied at an instantaneous strain rate (0.32s"1) 164 V l l Table D-l - Linear model constants determined for the relaxation test performed at a quasistatic strain rate (0.0025s"1) 165 Table D-2 - Linear model constants determined for the relaxation test performed at an intermediate strain rate (0.048s"1) 165 Table D-3 - Linear model constants determined for the relaxation test performed at a high strain rate (0.12s"1) 166 Table D-4 - Linear model constants determined for the relaxation test performed at an instantaneous.strain rate (0.32s"1) 166 Table D-5 - Linear model constants determined for the creep test performed at a quasistatic strain rate (0.0025s"1) 167 Table D-6 - Linear model constants determined for the creep test performed at an intermediate strain rate (0.048s"1) 167 Table D-7 - Linear model constants determined for the creep test performed at a high strain rate (0.12s"1) 167 Table D-8- Linear model constants determined for the creep test performed at an instantaneous strain rate (0.17s"1) 168 Table E-l - Dimensions of the rectangular specimens 169 Table E-2 - Modulus of Elasticity for multiple tests performed on the rectangular specimens of QM Skin 30 169 Table E-3 - Statistical results for the repeated measures ANOVA 169 viii List of Figures Figure 1-1 - The cause of spinal cord injuries from 2000 to 2005 2 Figure 1-2 - The vertebral regions in the spinal column51 3 Figure 1 -3 - The anatomy of a cervical vertebra (modified from Orthoteers.org43) 4 Figure 1-4 - The spinal cord within the spinal column57 4 Figure 1-5 - Anatomical planes. These planes are used in describing the relative positions of specific body parts.10 ;....5 Figure 1-6 - Cross-sectional view of the spinal cord (modified from InfoVisual.info31). .5 Figure 1-7 - Dermatomes in the human body50 6 Figure 1-8 - Spinal meninges (modified from Echo Medical Media18) 7 Figure 1-9 - The spinal cord viewed with the dura mater removed (modified from Nightingale et a/.38) 7 Figure 1-10 - Radiograph showing a potential for spinal cord injury due to elongation of the spinal cord 9 Figure 1-11 - a) A burst fracture injury in the lumbar spinal column which has transversely compressed the spinal cord1 and b) a view of a normal lumbar vertebra22 10 Figure 1-12 - a) A lateral projection of a vertebral dislocation in the cervical spinal column25 b) Radiograph of a normal cervical spinal column4 10 Figure 1-13- The narrowing of the spinal canal due to spinal stenosis2 11 Figure 1-15 - a) SCOT and IFOT arrangement in the cervical spine. Modified from Raynak et al. 4 6 b) Occlusion transducer in a cervical spine burst fracture16 15 Figure 1-16 - Pressures in the spinal canal as a results of a burst fracture in an in vitro human cervical spine. A surrogate cord made of 2.9% gelatin was positioned inside the canal mimic the response of the spinal cord to impact.45 16 Figure 1-17 - Surrogate model of the human spinal cord, brain, heak and neck for flexion and extension experiments.7 18 Figure 2-1 - The similarity between the pseudo Young's modulus for feline and canine spinal cords. Modified from Chang et al.6 31 Figure 2-2 - Increase in stiffness of the bovine in vitro spinal cord with time after death. The percentage values indicate the approximate increase in the modulus compared to that measured at 3 hours. Modified from Oakland.18 32 Figure 2-3 - Change in the modulus of elasticity of the in vitro canine spinal cord at four different time points .: 33 Figure 2-4 - Stress-strain curves for Sylgard gels of varying mixtures. Approximate values for the modulus of elasticity (E) are given. Modified from Bilston et al.2.....36 Figure 2-5 - Stress-strain curve of the in vitro human spinal cord for loads applied at various strain rates.4 37 13 Figure 2-6 - Stress-strain curve for the in vivo feline spinal cord in uniaxial tension. ...39 Figure 2-7 - Mold Type I: Acrylic Half-Cylinders.: 41 Figure 2-8 - A surrogate cord made from Sylgard 527 in its mold with a circular matrix of fibers.. 41 Figure 2-9 - Mold Type II: Aluminum Cylinder 42 Figure 2-11 - Mold Type III: Full Acrylic Cylinder 43 ix Figure 2-12 - Clamp to connect the surrogate cord to the tensile testing machine 44 Figure 2-13 - Example plot of a linear stress-strain curve and the modulus of elasticity determined by the slope 45 Figure 2-14 - Gage length of the surrogate cord 46 Figure 2-15 - Tests performed on three different groups of surrogate cords 48 Figure 2-16 - Materials testing machine 51 Figure 2-17 - The stress-strain curve and corresponding modulus of elasticity (E=0.22MPa) for a surrogate cord made of QM Skin 30 (ratio A:B = 10:1.2) 53 Figure 2-18 - Dependency of the modulus of elasticity on the silicone gel concentration (Sylgard 527). Quantity of B is given along the x-axis assuming A=l 54 Figure 2-19 - The range of the modulus of elasticity over three different cords produced from QM Skin 30 with a mixing ratio of 10:1 55 Figure 2-20 - The modulus of elasticity for three cords made of QM Skin 30 with a mixing ratio of 10:1.2 55 Figure 2-21 - The modulus of elasticity for multiple tests performed with Group 2 surrogate cords. The modulus of elasticity was measured to 12% strain 58 Figure 3-1 - Stress-relaxation curves for three in vitro human spinal cord specimens tested at different strain rates 3 67 Figure 3-2 - A comparison between experimental data and the nonlinear model for in vivo relaxation of the cat spinal cord. Modified from Chang et al. 8 69 Figure 3-3 - Secant lines used to determine the modulus of elasticity to 5% and 12% strain for two surrogate cords strained at different strain rates. .78 Figure 3-4 - The mean modulus of elasticity measured in each test for surrogate cords in Group 2. The tests are listed in the order which they were performed. Significant differences (p<0.05) are indicated by * 79 Figure 3-5 - Mean modulus of elasticity for each cord, measured for each strain rate. The modulus of elasticity was calculated to 12% strain for TQ1, TM1, and TF1 79 Figure 3-6 - Modulus of elasticity between cords tested at a quasistatic rate and cords tested at an instantaneous strain rate. The modulus of elasticity was calculated to 12% strain 80 Figure 3-7 - Comparison between the experimental relaxation data and the viscoelastic model of a surrogate cord loaded at all four strain rates 82 Figure 3-8 - The mean stress decay at each strain rate through 60 seconds of relaxation. Error bars represent one standard deviation 83 Figure 3-9 - Comparison between the experimental data and the models used to describe the relaxation of the surrogate cord after a load applied at a) a high strain rate (0.12s" ') and b) an instantaneous strain rate (0.32s"1). Selected data represents the twenty points chosen from the experimental data to describe the relaxation behaviour 85 Figure 3-10 - Comparison between the creep data and the creep curve determined by the general linear model at four strain rates '. 86 3 8 21 Figure 3-11 - The stress decay through 60 seconds of relaxation in the in vitro ' ' and in vivo5 cords and the surrogate cord. Data was chosen from tests which had an approximate strain of 9-12% applied at a strain rate of 0.2-0.3s"1 88 Figure 4-1 - The impact force, cord deformation, and time rate of energy (Ea) of the in vivo cat spinal cord to transverse compression with the CSF and dura mater present. Modified from Hung et al.1 95 x Figure 4-2 - The occlusion profile of the in vitro bovine spinal cord in transverse compression.14 The test was performed at 5.0m/s with a posterior longitudinal ligament posterior to the spinal cord 97 Figure 4-3 - a) Force-displacement with and without the dura mater present and b) stress-strain response of the in vivo feline spinal cord without the dura mater under quasistatic transverse compression. Modified from Hung et al.w 98 Figure 4-4 - The modulus of elasticity of the in vivo feline spinal cord with (cat 17) and without (cat 19) the dura mater intact. Modified from Hung et al. 1 0 99 Figure 4-5 - Stress strain relationship of the in vivo feline spinal cord (represented by the shaded area) and three different ratios of gelatin and water spinal cords (represented by the three curves)15 100 Figure 4-6 - Transverse compression of the surrogate spinal cord at 0.025s"1 and 8s"1". 104 Figure 4-11 - Experimental apparatus for the impact generation.14... 107 Figure 4-12 - Experimental apparatus for transverse compression of the surrogate cord during impact 108 Figure 4-13 - High speed video image of the impact on a bare surrogate cord 109 Figure 4-14 - Occlusion profile for the surrogate cord with dura mater and an impact velocity of 4.12m/s 110 Figure 4-15 - a) Bovine spinal cord with the dura mater removed from the end, b) Surrogate cord inserted into the dura mater (right end) 111 Figure 4-16 - Stress-strain curve for Specimen #1 in compression 114 Figure 4-17 - Modulus of elasticity of each specimen measured through three consecutive compression tests 115 Figure 4-18 - Average force-displacement response of the surrogate cord in quasistatic transverse compression (0.0025s"1). 116 Figure 4-19 - Average force-displacement response of the surrogate cord in transverse compression applied at an intermediate strain, rate (8s'1) 116 Figure 4-20 - Average force-displacement curves for surrogate cords tested at a quasistatic and medium strain rate. The tests are listed in the order that they were performed 117 Figure 4-21 - Dynamic occlusion images of a surrogate cord with dura mater and CSF through time. Image C represents the maximum occlusion 118 Figure 4-22 - a) Displacement, b) velocity, c) acceleration, and d) force profiles of the bone fragment during impact with the surrogate cord 118 Figure 4-23 - Variation in the force response of the surrogate cord in transverse compression 119 Figure 4-24 - a) Displacement, b) velocity, c) acceleration, and d) force of the bone fragment during impact with the bovine spinal cord 120 Figure 4-25 - Variation in the force response of the bovine spinal cord in transverse compression 120 Figure 4-26 - Mean maximum occlusion for the surrogate cord across the three specimen conditions. Significant differences are indicated with an * (p<0.05) 121 Figure 4-27 - Occlusion profiles for all three specimen conditions of a surrogate cord. 122 Figure 4-28 -Maximum occlusions for each individual surrogate cords and specimen condition •. 122 XI Figure 4-29 - Mean time to maximum occlusion for the surrogate cord across the three specimen conditions. Significant differences are indicated with an * (p<0.05) .123 Figure 4-30 - Mean time to maximum occlusions for individual surrogate cords and specimen condition ; 123 Figure 4-31 - Mean duration of maximum occlusion (5%) for the surrogate cord across the three specimen conditions. Significant differences are indicated with an * (p<0.05) 124 Figure 4-32 - Mean duration of maximum occlusions (5%) for individual surrogate cords and specimen condition 125 Figure 4-33 - Mean velocity of each specimen condition for the surrogate cords 126 Figure 4-34 - The relationship between maximum occlusion and original construct diameter for each surrogate cord condition 127 Figure 4-35 - The average response of the bovine and surrogate spinal cords to impactl30 Figure 4-36 - The mean maximum occlusion of the bovine and surrogate cords. Error bars represent one standard deviation. Bovine results obtained from Jones 133 Figure 4-37 - The mean time to maximum occlusion of the bovine and surrogate cords. Error bars represent one standard deviation. Bovine results obtained from Jones.12 133 Figure 4-38 - The mean duration of maximum occlusion (5%) of the bovine and surrogate cords. Error bars represent one standard deviation. Bovine results obtained from Jones.12 133 Figure 4-39 - The mean duration of maximum occlusion (25%) of the bovine and surrogate cords. Error bars represent one standard deviation. Bovine results obtained from Jones.12 134 Figure A-2 - Markers tracked on the surrogate cord '. 156 Figure A-3 - Strains measured in the surrogate cord at a strain rate of 0.0025s"1 156 Figure A-4 - Strain determined by video analysis (R2 = 0.8) and crosshead displacement (R2= l).The error bars represent one standard deviation for the marker strains at each time point 157 Figure A-5 - Calibration of the stepper motor with reference to a dial gage 158 Figure A-6 - Calibration of the linear potentiometer 158 Figure A-7 - Error in linear actuator speed determined the linear potentiometer and the LVDT 159 Figure F-l - Calibration curve for the LCFA-10 load cell in a) tension and b) compression 170 Figure F-2 - Load cell calibration for various weights mounted to the load cell 171 Figure G-l - Temperature gradient along the length of the surrogate cord. 0mm corresponds to the temperature of the cord at the point where it exits the clamp. ..173 Figure H-l - The relationship between the impact fragment and the pressure in the pneumatic cylinder 174 Figure K-l - Stiffness curves for the surrogate cord in transverse compression at 0.0025s" 1 and 8s"1 180 xii Acknowledgement I would like to express my gratitude to my supervisor, Dr. Peter Cripton, who has provided guidance, expertise, inspiration, patience and opportunities which I would not have had elsewhere. His help and mentorship have made my graduate experience a pleasant and fulfilling one. Many thanks are also extended to the collaborative efforts of Dr. Lynne Bilston at the University of Sydney, and Dr. Richard Hall and Miss Claire Jones at the University of Leeds. They were all wonderful hosts during my research stay at their university and made the collaborative research experience a memorable one. To all members, students, lab engineers, and faculty of the Injury Biomechanics Laboratory (IBL) and Division of Orthopaedic Engineering Research (DOER), thank you for your support, inspiring ideas, and technical assistance. A very special thank you goes to my family and friends who have helped support me throughout my research. Mom and Dad, thank you for your encouragement, confidence, and instilling in me the drive to work hard and pursue my goals. Nevada, thank you for your inspiration and for being such a wise younger sister and great friend. Matt, you are my strength and a guaranteed source for smiles. Thanks for always being there for me. Mom, Dad, Nevada, and Matt, without your support, friendship, love, and advice it would have been a much different experience. Financial support in the form of research grants from the Rick Hansen Man In Motion Foundation, British Columbia, Canada and Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. xiii Chapter 1 Introduction Chapter 1 Introduction 1.1 Motivation The objective of this work is to develop a physical surrogate model of the in vivo human spinal cord. This is important because it is necessary that the forces and deformations occurring in the spinal cord during human injury are understood. This will allow the development of appropriate animal models of spinal cord injury and spinal cord injury prevention devices. There are currently no methods to measure the in vivo properties of the human spinal cord which do not impose a serious risk of injury. Therefore, these properties can only be measured in a physical model of the spinal cord and using cadaveric models of the spine. The surrogate cord will provide an essential tool for measuring the forces and deformations occurring in vivo during human injury. 1.2 Spinal Cord Injury and its Consequences Spinal cord injury is the loss of function or feeling in the body as a result of damage to the spinal cord. This includes both physical and neurological damage. It is a highly devastating injury due to the fact that the spinal cord does not repair itself and there are currently no clinical procedures which have been developed to induce repair in humans. In Canada, the annual incidence of spinal cord injury is approximately 35 per million population,12 versus 40 per million in the United States.53 It is the most expensive type of injury on a per capita basis at an approximate cost of $750 million per year in Canada.48 It thus has a serious economic impact as well as a catastrophic quality of life impact on personal wellbeing and day to day activities for the injured. Persons with spinal cord injury can no longer function to perform simple everyday tasks such as feeding themselves, driving a vehicle, walking without aid, working, and breathing on their own as well as many other losses in their quality of life. 1 Chapter 1 Introduction Spinal cord injury can occur as a result o f motor vehicle accidents, falls, violence, and sports injuries. The majority o f injuries are due to vehicular crashes, fol lowed by falls, injuries related to violence, sports, and other mechanisms (Figure 1-1). O t h e r / V i o l e n c e . 1 3 . 8 % Figure 1-1 - The cause o f spinal cord injuries from 2000 to 2005 Spinal cord injury occurring at spinal levels in the cervical region results in tetraplegia, which is the loss o f function and feeling to al l four limbs, and i f high enough, the injury may also include partial loss o f function o f the neck and breathing. Injuries in the thoracic, lumbar, and sacral spinal cord regions cause paraplegia, neurological loss limited to the lower l imbs. In 1999, 5 3 % of the spinal cord injuries reported to the Canadian Paraplegic Associa t ion caused paraplegia and 47% caused tetraplegia. Thus, injuries to the cervical spinal cord represent approximately one ha l f o f the cases in Canada. 5 3 Very little is known about repairing the spinal cord. Current treatments for spinal cord injury include methods to prevent further spinal cord or neurologic damage at the time o f injury (neuroprotection) as w e l l as methods to regenerate spinal cord function post injury. Compression o f the cord is eliminated or controlled by surgery removing any masses impinging upon the cord, or by reducing swell ing in the cord wi th corticosteroids. 3 6 I f the vertebrae are displaced, realignment can be performed through open or closed reduction o f the dislocation, and immobi l iza t ion is recommended i f the vertebrae are fractured. The t iming o f treatment and the types o f treatment which are most appropriate to mitigate spinal cord injury have been studied but no concrete set o f standards have emerged to outline the best solution to treat the injury. Some believe that the injury should be treated immediately whi le others believe that a certain amount o f time is necessary before proceeding wi th treatment such as removing a bone fragment wh ich is impinging upon the spinal c o r d . 1 9 ' 5 5 Due to these conflicting opinions, surgery is not always performed. 2 Chapter 1 Introduction Medication and physical therapy can assist in functional recovery. Treatments which promise full recovery from neurological damage do not yet exist. 1.3 Anatomy The Vertebral Column The vertebral column holds the upper body in an upright position, allows for motion of the upper body, and protects the spinal cord. It is composed of five regions, each with a distinct vertebral anatomy. There are 7 cervical, 12 thoracic, 5 lumbar, 5 sacral (fused), and 4 coccygeal (fused) vertebra in an adult spinal column (Figure 1-2). The typical anatomy of a cervical vertebra is shown in Figure 1-3. Between each vertebra there is an intervertebral disc which serves as an articulation point and functions to cushion forces transferred through the column. H5> Sacrum — (5 - fused) Cervical - VertaOrae (7) C l -C7 Thoracic Vertabrae (12) T 1 - T 1 2 Lumbar Veriabrae «-1-«-5 Coccyx {4 - fused) Figure 1-2 -The vertebral regions in the spinal column 51 3 Chapter I Introduction Transverse Process Figure 1-3 - The anatomy of a cervical vertebra (modified from Orthoteers.org43) The Spinal Cord Each vertebra contains a vertebral foramen. When the vertebrae are stacked upon each other, their foramen form the spinal canal. This is where the spinal cord is located (Figure 1-4). The spinal cord serves as a pathway for the neurological impulses from the brain to the spinal nerves that run throughout our body. Figure 1-4 - The spinal cord within the spinal column57 The spinal cord is a cylindrical structure which is slightly flatter in the anterior and posterior aspects. It is symmetric about the sagittal plane (Figure 1-5). It is composed of gray and white matter. The gray matter appears as a "butterfly" within the white matter (Figure 1-6). The neurons (neural cells) are located in the gray matter whereas the white 4 Chapter 1 Introduction matter is composed mostly of axons, which carry nerve impulses between neurons. The impulses are sent throughout the body by way of the spinal nerves. A dorsal and ventral root exit the spinal cord on each side and meet to form the spinal nerve which passes through the intervertebral foramen. Frontal Plane Figure 1-5 - Anatomical planes. These planes are used in describing the relative positions of specific body parts.10 White matter Gray matter Dorsal root Spinal nerve Ventral root Figure 1-6 - Cross-sectional view of the spinal cord (modified from InfoVisual.info31). The 31 spinal nerve pairs each innervate a specific region of the body. These regions are arranged in dermatomes (Figure 1-7). A lesion in the spinal cord or a spinal nerve may reduce or inhibit function at the corresponding dermatome level and the levels below it. 5 Chapter 1 Introduction F i g u r e 1-7 - D e r m a t o m e s i n the h u m a n b o d y The spinal cord terminates at approximately the first lumbar vertebra ( L I ) . On ly one pair o f spinal nerves exits at each vertebral level (Figure 1-7). A bundle o f nerves called the cauda equina is formed past L I . The end o f the spinal cord from which the cauda equina originates is called the medullary cone. Protection o f the spinal cord is provided by the vertebra as we l l as the meninges and the cerebrospinal f luid ( C S F ) (Figure 1-8). The meninges consist o f the pia mater, arachnoid mater, and the dura mater. The inside surface o f the dura mater is coated by the arachnoid mater. The pia mater is a transparent covering around the spinal cord. The dura mater is a thick tissue which is separated from the spinal cord by the C S F . The space between the arachnoid mater and the pia mater is filled with C S F which has a water-like consistency and provides nutrients to the cord, removes waste products from the nervous system, and serves several other functions." The arachnoid and dura mater construct is connected to the spinal cord by denticulate ligaments which pass between the dorsal and ventral nerve roots to suspend the cord wi th in the dural sac (Figure 1-9). 6 Chapter 1 Introduction Pia mater Arachnoid mater / Spinal cord | Spinal nerve Dura mater Figure 1-8 - Spinal meninges (modified from Echo Medical Media ) Spinal cord Nerve roots Dura mater Denticulate ligament t W M M H l Figure 1-9 - The spinal cord viewed with the dura mater removed (modified from Nightingale et at.3*) 1.4 Mechanisms of Spinal Cord Injury Injuries to the spinal co lumn wh ich also induce spinal cord injury fal l wi th in six major categories. These are listed along wi th the frequency o f incidence in Table 1-1. Fi f ty- f ive percent o f the spinal cord injuries in adults occur in the cervical spinal co lumn. The most common spinal co lumn injury to cause spinal cord injury is fracture dislocation fo l lowed closely by burst fractures. 4 9 7 Chapter I Introduction Table 1-1 - Spinal column injuries which are associated with spinal cord injuries in adults49 Type of Bony Injury Incidence (%) Minor fracture (including compression) 10 Fracture dislocation 40 Dislocation only 5 Burst fracture . 30 SCIWORA 5 SCIWORET (included cervical 10 spondylosis) SCIWORA = spinal cord injury without obvious radiologic abnormality; SCI-WORET = spinal cord injury without obvious radiologic evidence of trauma. The injuries listed above result in non-physiologic mechanical loads being applied to the spinal cord. When they exceed the injury tolerance of the spinal cord they cause spinal cord injury. There are five main types of mechanical forces which can be applied to the spinal cord during every day activities and by injurious mechanisms: tension, transverse compression, shear, bending, and torsion. Any of these mechanical loads, applied individually or in combination, which exceed the injury tolerance of the spinal cord can damage the tissue, and cause irreversible spinal cord injury. To demonstrate a series of injuries due to excessive mechanical loads, such as those listed in Table 1-1, an example of a dislocation, burst fracture, distraction, and compression injury are presented below. The spinal cord is naturally in tension as it is suspended in the spinal canal. The strain in the cord changes as the neck is flexed and extended.37 An abrupt change in the natural length of the neck as a result of column injury can result in cervical distraction injury and an increase in the tensile forces applied to the cord causing spinal cord injury (Figure 1-10). 8 Chapter 1 Introduction Figure 1-10 - Radiograph showing a potential for spinal cord injury due to elongation of the spinal cord6 Injuries such as the burst fracture can also cause mechanical damage due to bone impingement upon the spinal cord (Figure 1-11). A burst fracture is a result of axial compression applied to the vertebral bodies. This type of force can occur when diving into a pool and hitting the bottom head first. If the compressive force exceeds the fracture tolerance, the vertebral body is fractured into several bone fragments, some of which accelerate towards the spinal cord and compress it. These are highly dynamic injuries which vary in severity depending on the force applied to the spinal cord. 9 a) b) Figure 1-11 - a) A burst fracture injury in the lumbar spinal column which has transversely compressed the spinal cord1 and b) a view of a normal lumbar vertebra22 Impact to the head or spine can also cause anterior-posterior dislocat ion (sl iding o f one vertebra relative to another), thus apply ing a shear force to the spinal cord (Figure 1-12). a) b) Figure 1-12 - a) A lateral projection of a vertebral dislocation in the cervical spinal column b) Radiograph of a normal cervical spinal column4 10 Chapter 1 Introduction Injurious spinal cord compression is not necessarily caused by dynamic forces. A spinal deformity such as spinal stenosis is a gradual change of the space in the spinal canal through time (Figure 1-13). This occurs with ageing as the ligaments calcify, bone spurs called osteophytes begin to form, or intervertebral disks begin to bulge causing a herniated disc. In all instances, the spinal canal narrows, increasing the transverse compressive force on the spinal cord. This often results in progressive pain and numbness in the limbs. Figure 1-13 - The narrowing of the spinal canal due to spinal stenosis2 The severity of loss of function in any of the instances discussed above wil l depend on the location and magnitude of the injurious forces in the spinal cord. Injuries which occur more cranially (closer to the head) wil l result in a higher loss of function. Neural transmission from the brain to the spinal cord below the injury is interrupted which prevents the neural signal from reaching its destination in the body. In any of the injuries discussed above, i f the force or elongation in the spinal cord is maintained, additional trauma may occur. The spinal cord is a viscoelastic t issue, 8 ' 1 5 , 2 0 ' 2 1 , 4 1 and therefore, i f the strain in the spinal cord is maintained, the stress in the cord wil l relax. Similarly, i f the force applied to the spinal cord is held constant, the tissue wil l elongate, otherwise known as creep. The creep behaviour of the spinal cord is of secondary importance from a clinical perspective since it occurs rarely or not at all. However, relaxation of the spinal cord occurs more frequently in distraction and dislocation injuries and is thus more widely studied. Normal Stenosis KAJDAM 11 Chapter 1 Introduction The examples given above depict a variety of injurious mechanical loads that can occur. Only by studying these injuries and the injury thresholds of the spinal cord can we gain a complete understanding of the mechanical loads which induce injury. 1.5 Biomechanics of Spinal Cord Injury 1.5.1 Methods Used to Study Spinal Cord Injury Several different methods have been developed to study spinal cord injury. These provide alternatives to studying the in vivo human spinal cord which presents a serious risk to the spinal cord and wellbeing of the individual. These methods include designing finite element models of the human spinal cord and spinal column, studying injury mechanisms using cadaveric tissue, and developing in vivo animal models to study injury and infer the behaviour of the human spinal cord. Finite element models of the spine are built by incorporating known mechanical properties of the spinal cord and spinal column, including the ligaments and intervertebral discs.5'23'56 External forces can then be imparted onto the spinal column to evaluate the behaviour of the spinal cord. These models are limited by what is known about the mechanical properties and the mathematical description of their behaviour. Appropriate models of the tissue behaviour must be programmed into the finite element model in order to ensure a biofidelic response. The models must then be validated with forces and strains which cause a known mechanical behaviour in the spinal cord. Exact values for strains, strain rates, and forces of interest can subsequently be obtained. Greaves developed a finite element model of the spinal cord and spinal column to evaluate the strain distribution in the spinal cord in compression, distraction, and Figure 1-14 - Finite „ element model of the dislocation injury mechanisms (Figure 1-14). This allowed for a human spinal cord23 comparison between the regions of most severe strains through the 12 Chapter 1 Introduction cross-section o f the spinal cord among the three injuries. Fini te element models are often compared to studies in wh ich simi lar forces and strains are replicated in in vivo animal and in vitro human models for val idat ion. A n i m a l models are also used to measure the in vivo response o f the spinal cord to injury, the mechanical properties o f the spinal cord, and the prevention and treatment o f spinal cord injury. A n i m a l and human spinal cords are composed o f the same tissues (white and gray matter) and have the same basic structure. C o m m o n animals used to study the spinal cord in vivo are the rat, mouse, primate, cat, sheep, and dog. These models have looked at regeneration o f the spinal cord after in jury , 3 2 ' 4 7 neurologic recovery after spinal cord in ju ry , 1 3 ' 1 7 ' 3 3 the tissue damage result ing f rom a given insult to the spinal c o r d , 2 7 , 3 0 ' 3 4 and the stress and strain properties o f the spinal c o r d , 1 4 ' 1 5 ' 2 6 " 3 0 among others. Because testing of the in vivo human spinal cord is unethical, the results f rom animal models are used to infer the properties and behaviour o f the human spinal co rd . 3 5 Cadaveric human tissue is tested in the lab to evaluate spinal cord injury wi th specimens which have the exact anatomy, center o f mass, moment o f inertia, geometry, and approximate in vivo mechanical properties o f the human body. Who le body cadavers have been used to measure the injury tolerance o f the cervical spine due to impact on the head 3 wh ich may in turn injure the spinal cord. Cadaver ic head and neck specimens have also been used to measure injury in the cervical spine through the use o f a drop track system. Head impact forces, impact veloci ty, and head and torso accelerations were measured to define the mechanisms of injury as the head was dropped onto an impact surface. W i l c o x et al.56 combined cadaveric and finite element models to study spinal column injury. Cadaver ic bovine thoracic spine segments were exposed to an axial impact at different speeds to simulate a burst fracture injury. A synthetic spinal cord material was poured into the spinal canal and a pressure transducer inserted to measure the pressure in the canal due to a burst fracture. A finite element model o f the experiment was also developed and the displacement o f the bone fragment f rom the burst fracture determined wi th and without the spinal cord and dura mater present. 13 • ; Chapter 1 Introduction These experimental methods all attempt to simulate the in vivo human response of the spinal column and spinal cord in order to increase our knowledge about injury to the spinal cord. This is important for various purposes including the design of preventative spinal cord injury devices, the choice of treatment methods to mitigate injury, and the development of a cure for spinal cord injury. 1.5.2 Methods Used to Study Canal Deformation Among the methods discussed above to study injury to the spinal cord, methods have also been developed to measure canal deformation. Any change in the cross-sectional area of the spinal canal implies that the shape of the spinal cord has also been altered. If the spinal cord is impacted or deformed above its injury tolerance then it can be permanently injured, causing severe neurologic damage. A Spinal Cord Occlusion Transducer (SCOT) was developed by Raynak et al.46 to measure the occlusion in the spinal canal and intervertebral foramen. A sylastic tube with an outer diameter of 15.9mm was sealed at one end and filled with saline solution to act as a resistive element. The transducer was inserted into the spinal canal and a current passed through the saline. A voltage sensing electrode was placed at each of the cervical vertebra levels along the length of the tubing. A similar design was used for the Intervertebral Foramen Occlusion Transducer (IFOT) but was smaller in diameter and had fewer sensing electrodes (Figure 1-15). Any changes in the cross-sectional area through the saline-filled tubing produced a change in the resistance and this was measured by the sensing electrodes. Thus, if inserted in the spinal canal, the occlusion could be traced to the spinal level at which it occurred and the degree of occlusion could be quantified.40'46 Similar transducers have been developed by the same group of investigators, however pressure sensors were used instead of voltage electrodes to detect occlusion.16 14 Chapter 1 Introduction SCOT Occlusion Transducer a) b ) Figure 1-15 - a) SCOT and IFOT arrangement in the cervical spine. Modified from Raynak et al. 4 6 b) Occlusion transducer in a cervical spine burst fracture16 Panjabi et al.AA measured canal occlusion by placing 1.6mm diameter steel balls in the spinal canal of cadaveric human spines. These defined the boundaries of the spinal canal which were visualized on radiographs taken during a simulated burst fracture. These provided information on the maximum occlusion of the bone fragments into the spinal canal and on the relationship between the impact energy and maximum canal encroachment. Clinically, the neurologic damage cannot always be related to the static canal occlusion. This study was the first to measure the dynamic occlusion and determine that this was 85% greater than the post-traumatic static occlusion. However, this relationship was determined without a structure simulating the effects of having the spinal cord present during such an injury. Canal Pressure Measurement Canal pressure has been measured with the use of a surrogate cord developed to mimic the transverse compression behaviour of the in vivo feline spinal cord.45 The compression of the feline spinal cord was measured with a drop-mass technique. Varying concentrations of water and gelatin were poured into a collagen casing which was then inserted into a Plexiglas tube with an elliptical cross-section. This artificial cord was also tested under a dropped mass and compared to the behaviour of the feline spinal cord. A 15 Chapter 1 Introduction gelatin concentration of 2.9% by mass was chosen as that which fell within the range of stress-strain curves under transverse compression for the in vivo feline spinal cord. Seven piezo-electric pressure sensors were positioned along the length of the artificial cord to measure the pressure at each spinal level. The cord was then placed in the spinal canal of a human cadaveric head-neck complex. A dynamic load of 600cm/s was used to impact the head and induce a burst fracture. The pressure transducers recorded pressures greatest near the location of the burst fracture (Figure 1-16), thus also indicating a greater amount of canal occlusion at these levels. Because a biofidelic spinal cord was used to measure the occlusion, the bone fragments traveled a distance into the spinal canal which is thought to be equivalent to that which would be observed in vivo for the feline spinal cord. Thus, accurate values were obtained. However this requires the assumption that the in vivo feline spinal cord behaves identically to the in vivo human spinal cord. Also, it is not recorded whether or not the CSF and dura mater were present during the in vivo feline spinal cord tests. Therefore we do not know if these experiments replicate the behaviour of the bare spinal cord in vivo or if they incorporate the dura mater and CSF which would simulate the true in vivo conditions. Figure 1-16 - Pressures in the spinal canal as a results of a burst fracture in an in vitro human cervical spine. A surrogate cord made of 2 . 9 % gelatin was positioned inside the canal mimic the response of the spinal cord to impact.45 CO Canal pressure was also measured in vivo by Svensson et al. Two pigs were instrumented with pressure transducers in the subdural space of the cranium, the cervical 1 6 Chapter 1 Introduction spinal column, and the upper thoracic column. Several whiplash injuries were simulated and the pressure pulses measured. It was observed that the pressures were correlated with the velocity and direction of the angular motion of the vertebrae during the whiplash simulation. Extension motions caused a pressure rise and flexion caused a pressure drop. It was speculated that spinal ganglia injuries were related to these pressure changes because no tissue injuries were identified. 1.5.3 Methods Used to Study Cord Deformation A surrogate cord developed by Bilston et al. was also used to evaluate the spinal cord's deformation during injury in a plastic human model.6 This surrogate cord was validated against the in vitro human spinal cord response in uniaxial tension. Human spinal cord samples were tested in tension to a maximum of 20% strain for loading rates between 0.02 and 0.3s"1. Specimens obtained more than 24 hours since death were rejected. A Sylgard silicone gel was mixed in varying concentrations to obtain the most appropriate material to imitate the human spinal cord in tension. The surrogate cord was combined with a model of the human brain and placed into a surrogate head and cervical spine. Flexion and extension motions of the spine were used to validate the vertebral motions and measure the strains in the surrogate cord. The strains observed in the cord were similar to those measured in vivo by Margulies et al?1 17 Chapter 1 Introduction of grid In spinal cord Figure 1-17 - Surrogate model of the human spinal cord, brain, heak and neck for flexion and extension experiments.7 The development of surrogate cords to infer in vivo behaviour and the measurement of canal occlusion with the design of occlusion transducers has led to the successful development of models which measure the properties of the spinal cord in compression and tension. A further understanding of the forces and strains in the cord has thus been possible without the risk of injury to in vivo human spinal cord tissue. 1.5.4 Limitations of the Previous Methods Present surrogate cords (Table 1-2) have been designed to measure canal occlusion and to evaluate spinal cord biomechanics under a single direction of loading. Raynak et a/.46 designed a surrogate cord to measure the occlusion in the spinal canal as well as the compression of the spinal nerves as they transit through the intervertebral foramen. This surrogate cord was not validated to match the mechanical properties of the human spinal cord. The surrogate cord produced by Pintar et al. was validated in transverse compression against the response of the in vivo feline spinal cord 4 5 The fact that the spinal cord is a viscoelastic material was not discussed and no indication of the velocity of the drop-mass was given. Bilston et al. 's6 surrogate cord neglected the transverse compression properties and instead validated their cord in uniaxial tension by comparing it to the response of the in vitro human spinal cord. Thus, the change in properties of the 18 Chapter 1 Introduction cord once it is removed from a living host was not accounted for in their surrogate cord. In addition, none of the previous surrogate cords accounted for the dura mater and CSF, which may affect the response of the surrogate cord under mechanical loads.26'30 In order to address these issues, the present surrogate cord will attempt to combine the mechanical properties of the spinal cord in tension and compression into one surrogate cord which is a close approximation for the in vivo human spinal cord. Table 1-2 - Surrogate cords developed previously Surrogate Cord Material Validation Author Sylgard 527 In vitro human spinal cord tested in uniaxial tension. E g o a i = 0 . 9 2 - 2 . 8 M P a Bilston et al., 1993 Gelat in and Wate r In vivo fel ine spinal cord tested in t ransverse compress ion . The stress-strain curves of the spinal cord and the surrogate cord were matched. P in ta re f al., 1996 1.5.5 In Vivo and In Vitro Mechanical Properties of the Spinal Cord The difference in mechanical response to loads applied to the in vivo and in vitro spinal cords has been reported for the feline,15'29 canine,14'27 and bovine41'42 spinal cords. These differences were evaluated by measuring the modulus of elasticity of the spinal cord in uniaxial tension. The bovine spinal cord was only tested in vitro, however the increase in the modulus of elasticity as time after death increased was measured. A significant difference (of approximately 0.5MPa) in the modulus was measured between 3 and 24 hours (p<0.001). In contrast, the feline and canine spinal cords were first evaluated in vivo and then again after death over a range of time periods. Both spinal cords saw an approximate increase of 150% in the modulus of elasticity after death. It thus must be recognized that the in vitro mechanical properties of the spinal cord are not a true representation of the in vivo response to loads. Thus, although, Bilston et al.6 validated their surrogate cord against the modulus of elasticity of the in vitro human spinal cord, their surrogate cord is not an appropriate model of the human spinal cord in vivo. 19 Chapter I Introduction 1.5.6 Animal and Human Spinal Cord Properties The spinal cord serves the same basic functions in animals and humans; to send and receive neurological impulses controlling the function and feeling of the body. The tissue is made of the same basic components, white and gray matter. The same cellular components exist in these tissues. However, the specific functions among species may differ. Thomas et al.54 provide the example of the corticospinal tract to demonstrate this difference. In the human, the corticospinal tract controls the fine motions whereas in the rat this is less evident. Another example is given by the walking function of dogs which is controlled in the spine, but in the brain for humans.9 The differences between species are also in the geometry of the spinal cord. The spinal cord in the rabbit ends in the sacrum,24 whereas the human spinal cord typically terminates at LI. The cross sectional area of the spinal canal which the spinal cord occupies can vary, as well as the diameter of the cord. Despite these differences, in vivo animal spinal cords are our closest approximation to the human in vivo spinal cord and provide important insights into the injury and healing mechanisms of the spinal cord. 1.5.7 The Necessity for an Improved Surrogate Cord Current experimental models used to replicate and study spinal cord injury use in vitro human spinal cords or in vitro and in vivo animal models. These studies are being performed in order to improve our understanding of the injury mechanisms causing spinal cord injury and of treatment methods which will improve the chance of recovery for a patient with spinal cord injury. Therefore, the ideal model for answering these unknowns is the in vivo human spinal cord. Testing the mechanical properties of the in vivo human spinal cord is not possible for ethical reasons. Thus, animal models are used to infer the behaviour of the in vivo human spinal cord. Yet, the relationship between the in vivo animal spinal cord and the in vivo human spinal cord is not known. Therefore, the assessment of the biofidelity of animal models and in vitro human spinal cords, which are used in laboratory experiments to infer 20 Chapter 1 Introduction spinal cord injury mechanisms for the human spinal cord, is made possible with the use of a surrogate model of the in vivo human spinal cord is necessary. The development of a surrogate human spinal cord with in vivo material properties will allow for an accurate tool to study the in vivo response of the spinal cord to injurious loads without using human subjects. A n accurate surrogate cord can be used in the laboratory to study the forces applied to the cord during injurious conditions. It wil l behave with an appropriate response to measure the strains in the cord during injury and can infer how the strain rate affects the mechanical response of the cord. This information is required to appropriately design and evaluate treatments for the spinal cord. It wi l l also provide a more precise model against which the animal models for spinal cord injury can be compared. 1.6 Objectives The primary objective of this study is to design a surrogate model of the in vivo human spinal cord suitable for use in burst fracture experiments. The most important mechanical properties to incorporate into the surrogate cord were chosen as the uniaxial tension and transverse compression behavior because these properties are known for the in vivo spinal cord. In addition, any effects induced in the mechanical response by the presence of the dura mater and CSF should be also incorporated. These requirements outline the following goals for the development of the surrogate cord as follows, 1. Identify a material for the surrogate cord which models the behaviour of the in vivo human spinal cord in uniaxial tension. 2. Evaluate the viscoelastic properties of the surrogate cord and compare these to the viscoelastic properties of the human and animal spinal cord as reported in the literature. 3. Determine the modulus of elasticity of the surrogate material in compression. 4. Measure the force-deformation response of the surrogate cord in transverse compression. 21 Chapter I Introduction 5. Evaluate the biofidelity of the surrogate cord in transverse compression with and without the dura mater and CSF by comparing it to the behaviour of the in vitro bovine spinal cord under the same conditions. 1.7 Road Map This Master's thesis work has been subdivided into three separate projects, each assigned to an individual chapter. Together, these chapters follow the development of the surrogate cord and its mechanical evaluation. The current chapter outlined the causes and severity of spinal cord injury, the anatomy of the spinal cord and column, and provided information about the methods used to study spinal cord injury including previous surrogate cords. 1.7.1 Chapter 2: The Development of a Surrogate Cord Chapter 2 introduces the search for a surrogate material, the criteria outlined for the material, the production process for the surrogate cord, and the characterization of the uniaxial tension of the surrogate cord. The modulus of elasticity of the surrogate cord is compared to that reported for the canine and feline in vivo spinal cords.14'15'27"29 1.7.2 Chapter 3: Viscoelast ic Behaviour of the Spinal Cord The second project was undertaken to further evaluate the mechanical behaviour of the surrogate cord in uniaxial tension. This consisted of measuring its response to strains applied at different strain rates, as well its relaxation and creep behaviour. These are the viscoelastic properties of the surrogate cord. The in vivo and in vitro spinal cords also have a viscoelastic response to loads and strains.8'15'41 The similarities and differences of the viscoelastic behaviour between the surrogate cord and in vivo and in vitro spinal cords are discussed with reference to the literature. 22 ' Chapter I Introduction 1.7.3 Chapter 4: Transverse Compress ion of the Spinal Cord An immediate end goal for the surrogate cord is to be able to use it in a burst fracture injury experiment to measure the compression of the spinal cord as it would occur in vivo. Thus, the last project evaluates the transverse compression behaviour of the surrogate cord. This is studied at several strain rates. An evaluation of any changes in behaviour in transverse compression due to the presence of the dura mater and CSF is performed and compared to the behaviour of the in vitro bovine spinal cord under similar conditions. 1.7.4 Chapter 5: Conc lus ion The final chapter provides a general overview of the three projects and their impact on the overall research questions. The mechanical properties of the surrogate cord are discussed and its proximity to behaving as an in vivo human spinal cord evaluated. The limitations of the present study and recommendations for future work are also presented. 2 3 Chapter 1 Introduction 1.8 References 1. Access Excellence at the National Health Museum Resource Center. Burst Fracture: Lumbar Vertebra, 2001. Available at: www.accessexcellence.org. Accessed October, 2005. 2. ADAM Inc. Nonspecific back pain, 2005. Available at: http://health.allrefer.com. Accessed October, 2005. 3. Alem NM, Nusholtz GS, Melvin JW. 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Journal of Biomechanical Engineering 1998;120:787-91. 47. Richter MW, Fletcher PA, Liu J, et al. Lamina propria and olfactory bulb ensheathing cells exhibit differential integration and migration and promote differential axon sprouting in the lesioned spinal cord. J Neurosci 2005;25:10700-11. 48. Rick Hansen Man In Motion Foundation. Spinal Cord Injury in Canada -Removing Disincentives to Employment, 2004. Available at: www.rickhansen.com. Accessed November, 2005. 49. Sekhon LH, Fehlings MG. Epidemiology, demographics, and pathophysiology of acute spinal cord injury. Spine 2001;26:S2-12. 50. Shobab L. Regaining control: treatment options for spinal cord injury bladder dysfunction. Journal of Young Investigators 2003 ;6. 51. Spinal Cord Injury Recovery Center. Spinal Cord Injuries [Online], 2005. Available at: http://www.sci-recovery.org. Accessed October, 2005. 52. Svensson M, Aldman B, Hansson H, et al. Pressure Effects in the Spinal Canal during Whiplash Extension Motion: A Possible Cause of Injury to the Cervical Spinal Ganglia. IRCOBI Conference. Eindhoven, Netherlands, 1993. 53. The National SCI Statistical Center. Spinal Cord Injury, Facts and Figures at a Glance: The University of Alabama at Birmingham, 2005. 54. Thomas CK, Noga BR. Physiological methods to measure motor function in humans and animals with spinal cord injury. J Rehabil Res Dev 2003;40:25-33. 55. Vaccaro AR, Daugherty RJ, Sheehan TP, et al. Neurologic outcome of early versus late surgery for cervical spinal cord injury. Spine 1997;22:2609-13. 56. Wilcox RK, Boerger TO, Allen DJ, et al. A dynamic study of thoracolumbar burst fractures. J Bone Joint Surg Am 2003;85-A:2184-9. 26 Chapter 1 Introduction 57. Yale New Haven Health. Spinal cord anatomy, 2005. Available at: http://yalenewhavenhealth.org. Accessed October, 2005. 27 Chapter 2 Chapter 2 The Development of a Surrogate Cord The Development of a Surrogate Cord 2.1 Introduction The spinal cord serves as a pathway for neurological transmission between the brain and the peripheral nervous system. It has a highly complex structure, composed of several different types of tissues, each with their own material and functional properties. In the design of the surrogate human spinal cord the mechanical properties are of primary importance. Determining the in vivo mechanical properties of the human spinal cord is presently impossible since applying non-physiological loads may cause injury. Researchers have studied the properties of the spinal cord through in vitro human spinal cord testing as well as in vitro and in vivo animal spinal cord analysis. 2.1 .1 Geometrical Properties of the Human Spinal Cord A biofidelic surrogate cord must match the dimensions of the human spinal cord. The morphologic features of cadaveric spinal cords have been measured by Kameyama et al.15 In their study, they acknowledge that the size of the spinal cord varies among individuals; however, the relative ratios of the cross sectional area of one segment to another are similar among persons. Twelve cadaveric cords were obtained (five male, seven female) from specimens aged 42-77 years old. The cross sectional area, ratios of grey and white matter, transverse and sagittal diameters, and compression (sagittal diameter divided by the transverse diameter multiplied by 100) and area ratios were measured from slices of the spinal cord at each segment from C2 to S3. The largest mean value for the transverse diameter of the spinal cord in the cervical region was measured as 12.6 ± 0.7mm which occurred at C6. The largest sagittal diameter was measured at C2 with a dimension of 6.4 ± 0.4mm. the cross sectional area of the spinal cord was found to be highest in the cervical region. 28 Chapter 2 The Development of a Surrogate Cord 2.1.2 In Vivo Spinal Cord Deformation (Human) In order to determine the strain for which the behaviour of the surrogate cord should be studied, the natural strain of the human spinal cord was replicated. The natural extension and flexion of the spinal cord has been measured in vivo through the use of magnetic resonance imaging by Margulies et al.]6 Two volunteers performed a range of flexion and extension motions of the neck while an MRJ recorded images of the spine. Images were digitized and the angle of flexion and extension of the head relative to Tl was measured. These images were also used to measure the stretch ratio (the final length divided by the reference length) of the spinal cord. The largest average stretch ratio measured was 1.12 at C7, indicating an elongation of 12% of the reference length. This occurred in flexion. In extension, the largest deviation from the original length was an average stretch ratio of 0.75. This translates into a shortening of 25% of the spinal cord. It is important to note that these tests were performed at very low strain rates. The natural extension and flexion strains will differ when the head and neck move at the increasing speeds that occur during trauma. 2.1.3 In Vitro Human Studies The behaviour of the spinal cord when exposed to different types of loads is also an important factor for our understanding of its response to injurious situations. Due to its complex structure and the difficulties in measuring certain properties, the mechanical properties of the in vitro spinal cord are not well known. The properties of interest include its response to tensile, compressive, shear, torsion, and bending loads. These mechanisms are all applied naturally and in varying degrees to the in vivo human spinal cord. To date, in the human cord, only properties for the in vitro cord have been studied and these have only been studied in tension. Bilston and Thibault5 measured the stress response of 13 human spinal cords from the cervical level, without dura mater, at several strain rates. The spinal cords were tested within 24 hours of death. The effects of changing the strain rate will be discussed in the 29 Chapter 2 The Development of a Surrogate Cord following chapter. In Bilston and Thibault's study,5 a quasistatic tensile load was applied to the cord, after which the strain was held constant and the relaxation of the material measured for a duration of one minute. Each test was then repeated without removing the cord from the test setup. These tests revealed that repeated loading, up to four times, did not produce significantly different stress-strain responses in the spinal cord. The data also revealed a nonlinear response with increased strain. For a strain rate of 0.068s"1, the modulus of elasticity calculated from the stress-strain curve to 9% strain had an average of 1.02MPa (with a standard deviation of 0.75). Additional testing on in vitro human spinal cords applied loads at varying strain rates of 0.02 to 0.3s"1 to strains of 10 to 20%. The modulus of elasticity for these cords was measured to be in the range of 0.92 and 2.8MPa.2 The moduli were dependant on the strain rate, where an increased strain rate increased the modulus of elasticity. 2.1.4 In Vivo Animal Spinal Cord Properties Very little information is known about the behaviour of the human spinal cord in response to mechanical loading and testing possibilities are limited for ethical reasons. Thus, extensive research has been performed with the in vivo animal spinal cord in order to gain a thorough understanding of its mechanical properties. The most prominent studies in this area were performed by Hung et al. and Chang et a/.6'12"14 on canine and feline spinal cords. In these studies, all tensile tests of the in vivo spinal cord were performed at a constant quasistatic strain rate to a predetermined strain. The stress-strain response of the feline spinal cord shows that until 5% strain, there is a linear response, after which point the stress-strain relationship becomes non-linear and the slope of the curve decreases. The range of the modulus of elasticity determined by fi 17 tests performed on the canine spinal cord was between 0.215-0.295MPa. ' The tests performed on feline spinal cords show very similar results. In the first experiment, before performing the initial test,14 several pairs of spinal roots were dissected from the feline spinal cord. As a result, the modulus of elasticity was measured as 0.4MPa for strains less than 5%. Subsequently, another 17 tests were performed during which the spinal roots 30 Chapter 2 The Development of a Surrogate Cord were not dissected. The modulus of elasticity was then measured to be in the range of 0.23 to 0.29MPa. An additional set of tests which also measured the elastic response of the feline spinal cord,13 calculated a modulus of elasticity of 0.22 to 0.295MPa (with a mean of 0.26MPa). In their report on the stress-strain measurement of the canine spinal cord, the modulus of elasticity was plotted together with the previously measured modulus of elasticity for the feline spinal cord.6 This plot shows the similarity in elastic modulus between the two species (Figure 2-1). . | , r— • * » ° \ t o I -• o # 0 0 ° • • -o Feline -• Canine i i 1 i 0 0.01 0.02 0.03 0.04 0.05 Strain e0 Figure 2-1 - The similarity between the pseudo Young's modulus for feline and canine spinal cords. Modified from Chang et at.6 In Vitro Animal Cords 12 Analysis of the in vitro animal spinal cord has been performed using canine and bovine spinal cords.6'12'18'19 Oakland performed very similar tests to those performed on the in vitro human spinal cord by Bilston et a/.5'18 Fifteen conditioning cycles were applied to the in vitro bovine spinal cord at a quasistatic strain rate. A tensile relaxation test was then performed to a predetermined strain and maintained for ten minutes. The steepest portion of the stress-strain curve was evaluated to determine the modulus of elasticity of the tissue. The average value was measured as 1.30 ± 0.38MPa. Additional in vitro 18 measurements of the bovine spinal cord were performed by Oakland. For strain rates in the range of 0.173 to 0.229s"1, the cords exhibited a mean modulus of elasticity of 1.25 ± 31 Chapter 2 The Development of a Surrogate Cord 0.07MPa and a stiffness of 8.01 ± 0.84N/mm. These results are comparable to those measured by Bilston et al.5 (1.02MPa ± 0.75) for the in vitro human spinal cord. In Vivo Versus In Vitro Effects Like the in vitro human spinal cord, the in vivo animal spinal cord exhibits a characteristic nonlinear stress-strain curve, but has a much lower modulus of elasticity. It has been suggested by some that this difference is due to the change in tissue properties after death. Oakland measured the stiffness of 36 bovine spinal cord specimens under uniaxial tension at different times from death. He used a strain rate of approximately 0.23 - 0.25 s"1 to apply a tensile load to a preset strain. The steepest tangent of the stress-strain curve was used to calculate the stiffness of the cord 3, 24, 48, and 72 hours after slaughter. A statistical difference was reported between the modulus measured at 3 and 24 hours after slaughter, indicating a significant change in the tissue properties had occurred. Thus it is concluded that with time after slaughter, the stiffness of the cord increases (Figure 2-2). Oakland was also an author of a similar study which published these results in terms of the stiffness of the bovine spinal cord.19 In this report, the authors suggest that cellular crosslinking occurs after the cord is removed from its natural environment, thus creating a stiffer tissue. 2.5 £ H 2.0 1.5 1 10 0.5 0.0 25% 3 3 % 62% 3 hours 24 hours 48 hours 72 hours Time intervals after slaughter (hrs) Figure 2-2 - Increase in stiffness of the bovine in vitro spinal cord with time after death. The percentage values indicate the approximate increase in the modulus compared to that measured at 3 hours. Modified from Oakland.18 32 Chapter 2 The Development of a Surrogate Cord Similar results were measured by Hung et al)2 in a study which tensioned the in vivo canine spinal cord at a quasistatic rate, and repeated the test one hour after death. In this case, the modulus of elasticity after death was calculated and found to increase to 0.36MPa from an in vivo range of 0.215 to 0.295MPa. To further explore the effect of the change in modulus over time and due to lack of moisture, another three tests were performed on the same spinal cord specimen over 20 minute increments once removed from the animal. The results are shown in Figure 2-3. These results depict a similar trend to the increase in stiffness measured in Oakland et a/.'s19 work. One hour after death, the modulus of elasticity of the canine spinal cord increased by approximately 38%. Another hour later without having been kept moist, the modulus of elasticity of the cord increased by approximately 20 times the in vivo modulus and was 15 times greater than the initial modulus measured after death. 6 | • T 1 1 1 1 E (MPa) 2 " 0 20 40 60 TIME (MIN.) Figure 2-3 - Change in the modulus of elasticity of the in vitro canine spinal cord at four different time points.12 Since these tests performed on the canine spinal cord are for one single specimen, it can be questioned whether or not the increase in modulus of elasticity is due to repeated loading. The testing performed by Bilston et al.5 on the in vitro human spinal cord involved repeated loading and they reported that no significant change in the stress-strain response was observed. Thus it is reasonable to assume that the increase in stiffness of the canine spinal cords over time, at least for the in vitro tests, is due solely to the change in tissue properties after death. 33 Chapter 2 The Development of a Surrogate Cord The change in the modulus of elasticity due to death was also reported for the feline spinal cord.7 Prior to death, the modulus of elasticity for one cat was 0.23MPa up to 0.7% strain. After death, the spinal cord was kept in situ in a bath of Normosol (a cerebrospinal fluid substitute) at 37°C for 90 minutes. A second test was performed and the modulus of elasticity was measured to have increased by 150%. These experiments, which compare the modulus of elasticity of in vivo and in vitro spinal cords, demonstrate the importance of measuring the mechanical properties of the cord in vivo to ensure that the measured properties are in fact those of the living tissue. 2.1.5 Surrogate Spinal Cord There are currently no methods to measure the in vivo properties of the human spinal cord. This has inspired the development of a surrogate spinal cord in several studies. The surrogate cord can be outfitted with specially designed measuring devices tailored to the purpose of the study and designed to behave in a particular manner as required. The goal of the current surrogate cord development was to encompass the tension and transverse compression properties of the in vivo cervical human spinal cord into a cord which could be developed in the lab and used repeatedly. This surrogate cord should lend itself well to experiments which are designed to quantitatively evaluate its interaction with soft tissues or bone which surround the cord in the human body. Using the surrogate cord in cadaveric spines will allow the researcher to come as close as possible to analyzing the behaviour of the in vivo spinal cord in the lab. The current surrogate cord was inspired by other spinal cord surrogates which were developed to measure spinal cord deformations, to assess clinical techniques to repair the spinal cord, to measure the pressures throughout the cord during a compression fracture in the spine, and to measure neural-space occlusions. To assess the spine's ability to maintain the space where the spinal roots pass through the intervertebral foramen, Raynak et al.21 developed a transducer to place in the canal to 34 Chapter 2 the Development of a Surrogate Cord measure the occlusion of this neural-space. Two different designs were developed, namely the spinal canal occlusion transducer (SCOT) and the intervertebral foramen occlusion transducer (IFOT). Each transducer consists of a sylastic tube filled with 0.9% saline solution. The saline solution acts as a resistive element through which a current travels until it reaches the ground electrode at the distal end of the cord. The voltage along the length of the tube is measured by eight sensing electrodes. When the transducers are arranged inside the spinal canal (Figure 1-17), occlusion throughout the canal and the intervertebral foramen at different levels can be measured. A study by Pinter et al. chose to evaluate a surrogate cord with the purpose of studying injury mechanics associated with the cervical spine and their treatment protocols.20 The surrogate cord was designed to measure the pressure along the length of the canal during injurious loading of the spinal column. The surrogate cord was produced in a collagen casing and incorporated seven pressure sensors. The surrogate material was a gelatin and water mixture for which the ratio of gelatin to water was chosen so that the response of the surrogate cord to a dropped mass was similar to that for the in vivo feline cord. The feline cord properties were measured in their study, however not enough data was provided in order to use the feline cord properties to validate the current surrogate cord. The piezoelectric sensors were placed anterior to the surrogate cord and inserted into a human cadaver head and neck. A dynamic compressive load was applied to the vertex of the head at 600cm/s to create a burst fracture with retropulsion bone fragments causing transverse compression to the cord (Figure 1-11). While the surrogate cord developed by Pintar et al. mimicked the response of the spinal cord to transverse compression, the surrogate cord developed by Bilston et al? imitates the response of the spinal cord in tension (E = 1.02MPa).4 A Sylgard silicone gel was used as the surrogate material due to the variability in mechanical properties that could be obtained by simply changing the ratio of catalyst to polymer. Rectangular surrogate material samples (20 x 3 x 80mm) were tested in tension to measure the modulus of elasticity for the given mixtures (Figure 2-4). 35 Chapter 2 The Development of a Surrogate Cord Stiff Gel •a — Medium Gel Soft Gel A "*~~E *0.2MPa 08 0.12 0-16 Strain 0.2 Figure 2-4 - Stress-strain curves for Sylgard gels of varying mixtures. Approximate values for the modulus of elasticity (E) are given. Modified from Bilston et al? The range in their moduli of elasticity spanned 0.003 to 3.0MPa. The final surrogate cord was made with 29% Sylgard 527 polymer, 68% Sylgard catalyst, and 3% Sylgard 184 catalyst (measured by volume) in a mold to produce a 150mm long surrogate cord with a 10mm diameter. The modulus of the surrogate cord fell in the range of moduli measured for the in vitro human spinal cord, however it did not exhibit the typical "J-shaped" curve of the in vitro spinal cord as shown in Figure 2-5 due to its linear elastic behaviour. 36 Chapter 2 The Development of a Surrogate Cord 0.10 0.08 ^ 0.06 8 0.04 0) -CO 0.02 0.00 Strain Rate — - • — 0.048s" 1 - - • - - 0 . 1 2 0 S " 1 0.225s •1 i w i ^ — — i 1— 0.00 0.02 0.04 0.06 0.08 0.10 Strain Figure 2-5 - Stress-strain curve of the in vitro human spinal cord for loads applied at various strain rates.4 This surrogate cord was placed in a model head and neck, along with a surrogate brain. Flexion and extension motions were applied to the head-neck complex and the motion of the surrogate cord and brain tracked during these movements. This information was used to validate the motion of the surrogate cord to the motions produced naturally in the human spinal canal. Another iteration of this cord was made by Bilston and Thibault to measure spinal cord deformations during hyperflexion and hyperextension of a model head-neck with the surrogate cord in place. This surrogate cord differed from the original in that 40 Dacron fibers were positioned around the outer rim.of the cylinder. The fibers were added to model the longitudinally oriented axons of the white matter in the spinal cord. No information is presented on the mechanical properties of this surrogate cord in tension and how the different materials mimic white and gray matter.1 2.2 Objectives A surrogate spinal cord has been developed previously1'2 to encompass the tensile properties of the human spinal cord. However, it was based on in vitro properties and it is known that these are not a true representation of the in vivo properties. Thus a material which has tensile properties which match the in vivo cord would be a more useful tool for 37 Chapter 2 The Development of a Surrogate Cord evaluating the response of the spinal cord to injurious loads. The surrogate cord developed in the current study has been designed to replicate the in vivo tensile properties. This chapter addresses the search for the surrogate material, the construction of the surrogate cords, and its evaluation in uniaxial tension. 2.3 Materials and Methods 2.3.1 Performance Requirements The performance requirements were derived from in vivo animal spinal cord data.7'19 There is no evidence that the mechanical properties of animal spinal cords are identical to those for the human spinal cord, however the literature review above indicates that after death, the properties of the cord change drastically within 24 hours. Generally, human spinal cords which are tested for in vitro mechanical properties, are obtained up to 24 hours after death, thus too long after death to measure even approximations of in vivo mechanical properties. The in vivo modulus of elasticity in quasistatic tension for the feline (Figure 2-6) and canine spinal cords has similar magnitudes as seen in Table 2-1. Table 2-1 - Modulus of Elasticity for in vivo spinal cords measured from during quasistatic tension tests.6'7'12'13 Species Modulus of Elasticity (MPa) Reference Feline 0.220-0.295 (average = 0.260) Hung etal., 1980 0.213-0.255 (average = 0.230) Chang etal., 1988 Canine 0.215-0.295 (average = 0.265) Hung and Chang, 1981 0.265 Chang etal., 1981 3 8 Chapter 2 The Development of a Surrogate Cord 96X10? dyne?:: 32X103 0 0 sV-:... Figure 2-6 - Stress-strain curve for the in vivo feline spinal cord in uniaxial tension.13 Based on the similarities between feline and canine spinal cords, as seen in Table 2-1, one can postulate that the human spinal cord would also have a similar magnitude for the modulus of elasticity. Although it is not known if the in vivo animal spinal cord behaves identically to the in vivo human spinal cord, in this study, we consider the in vivo animal spinal cord properties as the most appropriate approximation for the in vivo human spinal cord versus in vitro human spinal cord properties. This is also supported by the proximity of the modulus of elasticity of the in vitro bovine spinal cord to the in vitro human spinal cord and the fact that the modulus of elasticity of the in vitro spinal cord increases with time after death.7'12'19 Thus it is assumed that the measured values for the in vitro human spinal cord are an over estimate of its true in vivo properties. Thus, the desired properties for the surrogate cord of the in vivo human spinal cord were chosen as the following (Table 2-2). Table 2-2 - Performance Requirements for the surrogate spinal cord.11'12' Proper ty V a l u e Reference No tes P o i s s o n ' s Rat io 0.49 Bilston, 1998 Human in vitro Elas t i c m o d u l u s ( tension) 0.260 Mpa Hung and Chang, 1981 Feline and Canine in vivo Elas t i c M o d u l u s ( t ransverse c o m p r e s s i o n ) 0.28 MPa Hung ef a/., 1982 Approximate value taken from the published stress-strain graph (ie. geometry is not considered) Relaxa t ion decay 14% Chang ef a/., 1988 Approximate value from 5% strain and 30s of relaxation. Tested on an in vivo feline spinal cord. Hypere last ic i ty u=0.1, a=25 Bilston, 1998 Human in vitro STRESS V-0. S T R A I N £ o 39 Chapter 2 The Development of a Surrogate Cord 2.3.2 Material Search The spinal cord is a nonlinear, viscoealstic material.5'7 One suitable candidate material for the surrogate cord is an elastomer, since elastomers exhibit non-linear viscoelastic properties and have a poisson's ratio equal to that assumed for the human spinal cord. 4'' ''1 7 A search for elastomers was performed in order to find several different candidate materials which could be tested and compared to the known properties of the spinal cord (Table 2-3). The list of performance requirements (Table 2-2) was used to communicate the desired material specifications to companies who specialize in producing materials which were considered to be potential surrogate materials. The list was also sent to BIOMCH-L, a newsgroup which acts as a discussion tool for topics related to biomechanics and movement science. BIOMCH-L has approximately 4000 subscribers (http://isb.ri.ccf.org/biomch-l/). Responses from this list included suggestions such as ballistics gel and dental impression materials as well as resources for more information. Below is the final list of materials tested for the surrogate cord. Table 2-3 - Candidate Surrogate Cord Materials Material Company Sylgard 527 Dow Corning QM Skin 30 Quantum Silicones RTV 2039 A C C Silicones 3-4222 Dielectric Gel Dow Corning 3-4207 Dielectric Gel Dow Corning MED-4901 Nusil 2.3.3 Molding Process Three different methods for molding the surrogate cords were developed. The initial molding process consisted of an acrylic cylinder cut in half along,its length with feet glued to either end in order to plug the ends of the mold as well as to keep the mold level (Figure 2-7). Gel was poured into each half of the cylinder and allowed to set. Once the gel was cured, additional gel was mixed and used as a glue to attach both halves of the 40 Chapter 2 The Development of a Surrogate Cord mold into a full cylinder. Surrogate cords made of Sylgard gels were easily manufactured with this mold type. Figure 2-7 - Mold Type I: Acrylic Half-Cylinders Mold Type I was also used to manufacture composite material like cords with fibers running along their length (Figure 2-8). Because this type of mold allowed the cord to be poured in several steps, a portion of the cord was produced, nylon fishing line (Westrim, Style 896S) fibers were then laid on the cured material and more gel was poured into each half. The fibers ran longitudinally through the cord approximately three millimeters from the circumference of the cylinder. It was expected that the cords made using this technique would exhibit a higher modulus of elasticity as long as the elastic modulus of the fiber was higher than that of the cord. Figure 2-8 - A surrogate cord made from Sylgard 527 in its mold with a circular matrix of fibers Other gels adhered to the acrylic and could not be removed from the molds. Thus, a second molding type was developed. For this mold, an aluminum block was machined to 41 Chapter 2 The Development of a Surrogate Cord imitate mold type I as shown in Figure 2-9. This second type o f mold was also developed in order to produce the surrogate cord in one step. The two halves o f the cylinder were fastened together and the gel poured in from an opening at the top. To remove the cured gel, the top a luminum ha l f was s imply disconnected from the mold . F i g u r e 2-9 - M o l d T y p e II: Aluminum Cylinder Similar to mold type I, a selection o f gels adhered to the a luminum mold . Despite this disadvantage, the mold performed very w e l l when trying to make cords o f two materials. Several cords were made using a mold o f a smaller diameter. Once cured, this smaller surrogate cord was suspended in the mold o f the original diameter. A different type o f gel was then poured around it and left to cure to complete the cord. This type o f cord was termed a Core Cord (Figure 2-10). Core cords were developed to experiment wi th the effect o f using two different materials in order to adjust the properties to the desired modulus o f elasticity. 42 Chapter 2 The Development of a Surrogate Cord Figure 2-10 - Two versions of a Core Cord. The left cord (A) is made with a core of Sylgard 527 (Dow Corning) and an outer layer of RTV 2039 (ACC Silicones). Cord B is made of the same materials, but in the opposite position. The final mold was much less intricate than the original molds; however, each mold could only be used once. Mold type III was developed to allow bubbles to escape from the gel, thus eliminating any imperfections in the cured surrogate cord. Thicker gels entrapped air during the mixing process and without an escape route for the air bubbles incorporated into the mold, this would produce large bubbles and imperfections in the cords. To accommodate this requirement, a thin walled acrylic tube was used with a longitudinal slit (Figure 2-10). The slit served as an escape route for any bubbles entrapped in the gel. Each end of the tubing was plugged with aluminum dowels before pouring the gel. After the gel had hardened, the acrylic tube was cracked open to remove the surrogate cord. Figure 2-11 - Mold Type III: Full Acrylic Cylinder Each elastomeric gel tested in these experiments was a two part gel. The ratio for mixing Part A with Part B was provided by the manufacturer. These specifications were used to mix the original cords made from each material. Iterations of the same material were produced by varying the ratio of Part A to Part B (polymer to catalyst) which was 43 Chapter 2 The Development of a Surrogate Cord expected to alter the modulus of elasticity of the cured elastomer. The two-part gel was mixed by hand in an aluminum dish for approximately five minutes. If the mixture was fluid, a syringe was immediately used after mixing to pour the gel into the molds. Otherwise, highly viscous gels were exposed to a vacuum for 15-20 minutes or until any air bubbles had escaped. Following the vacuum, these gels were also poured into a syringe and injected into the molds. Care was taken to avoid introducing further air bubbles during this process. If air bubbles were present, they were very few and escaped through the slit in the mold before the gel cured. The length of time necessary for each gel to cure varied amongst materials. Some required only a few hours whereas others were left for a week before being removed from the mold. After being removed from the mold, clamps were attached to either end of the surrogate cord. These consisted of a one-inch long piece of acrylic tubing which was press fit a half-inch down onto a one-inch length of aluminum dowel. Each aluminum dowel was drilled and tapped to fit the attachments on the material testing machine and load cell. The surrogate cord was glued into the remaining half-inch of acrylic tube with a cyanoacrylate adhesive (Loctite 401; Henkel Loctite Corporation). Figure 2-12 shows an example of these clamps. Figure 2-12 - Clamp to connect the surrogate cord to the tensile testing machine 44 Chapter 2 The Development of a Surrogate Cord 2.3.4 Testing Protocol A commonly measured material property of soft tissues, including the spinal cord, is t modulus of elasticity, E. The value of E is calculated by dividing the stress (cr) by the strain (e) (Figure 2-13): E = - (Eq2.1) Figure 2-13 - Example plot of a linear stress-strain curve and the modulus of elasticity determined by the slope Values for stress and strain are calculated using the following equations: F cr = — A (Eq. 2.2) e = AX L (Eq. 2.3) In the above equations, F is the force, A the original cross-sectional area of the specimen, AL the change in length, and L the gauge length of the specimen (Figure 2-14). AL was measured using either the calculated crosshead displacement from the command to the testing machine or linear potentiometer data. Before mounting the surrogate cord into the materials testing machine, the gauge length was measured as the length between the clamps as shown in Figure 2-14: 45 Chapter 2 The Development of a Surrogate Cord Gage Length 10 11 Figure 2-14 - Gage length of the surrogate cord The cord was then mounted to the load cell. The load associated with the free hanging surrogate cord (ie. weight) was measured before clamping the distal end of the cord to the base of the materials testing machine. The load was measured again and the crosshead repositioned until the free hanging load was matched. This procedure was used to ensure that the surrogate cord was in a nominal tension before testing began. After performing these adjustments, the length was recorded and compared to the gage length to measure the strain in the cord immediately prior to testing. The most recent surrogate cord validated in tension is that developed by Bilston et al. They used a silicone gel, Sylgard 527 (Dow Corning), and a matrix of fibers to design a cord which has a modulus of elasticity matching that for the human spinal cord in vitro. The first step to improve upon this surrogate cord involved finding a material which would instead match the modulus of elasticity of the in vivo spinal cord. This target modulus was chosen to be in the range of 0.21-0.26MPa which is the range measured by Chang et al., 1988. Dr. Hung and Dr. Chang were from the same research group and they measured the material properties of feline and canine spinal cords by applying a constant 1 7 19 strain rate of approximately 0.0025s" to the in vivo cord. ' Thus all testing performed during the search for a surrogate cord material applied this same strain rate which • • 12 allowed for direct comparison against the results reported by Hung et al. and Chang et al.1 The natural strain of the human spinal cord through a natural range of motion has been measured by to be approximately 12%.16,22 Thus surrogate cords were strained to 12%. 46 Chapter 2 The Development of a Surrogate Cord Because Sylgard 527 (Dow Corning) is the material used to produce the surrogate cords designed by Bilston et al., testing began with this material in order to gain a complete understanding of the mechanical properties of the existing surrogate cord. Techniques for surrogate cord production and material property alteration were obtained onsite at the Prince of Wales Medical Research Institute, Sydney, Australia by the author. Subsequent surrogate cords involved several more materials. Table 2-4 identifies all materials tested in order to find the most appropriate material for the surrogate cord. Table 2-4 - Materials tested in quasistatic tension Material Mixing Ratio (A:B) Number of Cords Tested Number of tests 1:2 2 3 1:3 1 1 1:3 with fibers 1 1 1:4 with fibers 1 1 Sylgard 527 1:6 1 1 1:7 5 1:7 with fibers 1 2 1:8 1 3 1:9 1 1 1:10 1 2 10:1 48 QM Skin 30 10:1 with fibers 1 1 10:1.2 6 RTV 2039 10:1 1 2 3-4222 Dielectric Gel 1:1 1 3 3-4207 Dielectric Gel 1:1 1 1 MED-4901 1:1 10 RTV in 527 10:1 in 1.7 1 1 527 in RTV 1.7 in 10:1 1 1 While testing the various surrogate cords made with and without fibers, with different mixing ratios, and with different combinations of gels, the specimens were strained until failure or until the maximum stroke length (7.6cm) of the materials testing machine was reached. Extensive tests were carried out to study the tensile modulus of the elastomer that was eventually selected (QM Skin 30). A set of 34 surrogate cords were produced with this 47 Chapter 2 The Development of a Surrogate Cord material using a mixing ratio of 10:1.2. Mold type III was used to create these cords. The molds were 150mm long with a diameter of 12.7mm, a diameter similar to that for the human cervical spinal cord.15 With clamps attached, the length of the final cords ranged from 105 to 126mm. Their diameters were roughly 12.7 to 13.1mm. Of the 34 cords, fourteen were used for the high rate transverse compression tests (a complete discussion of these experiments is provided in Chapter 4). All 34 cords were tested in quasistatic tension, however only the fourteen cords used for high rate transverse compression did not undergo further tensile testing (Figure 2-15). The remaining 20 surrogate cords were tested three times in quasistatic tension. The first tension test provides the previously unstressed modulus of elasticity for the cord, while the subsequent tests provide the repeatable modulus of elasticity for the material after the initial test. A minimum of 24 hours was allotted between consecutive tests on each cord. This ensured complete relaxation of the material before it was tested again. Surrogate Cord Testing Group 1 N=14 Quasistatic Test (1) Transverse Compression Impact Group 2 N=10 1 Quasistatic Tests (3) Tension Quasistatic, Intermediate, High Strain Rate Tests Relaxation Quasistatic Strain Rate Test Quasistatic tests were performed intermittently among all tests to ensure that the modulus of elasticity had not changed significantly. Group 3 N=10 1 Quasistatic Tests (3) Relaxation & Creep Intermediate, High, Instantaneous Strain Rate Tests Transverse Compression Quasistatic & Intermediate Strain Rate Tests Figure 2-15 - Tests performed on three different groups of surrogate cords 48 Chapter 2 The Development of a Surrogate Cord 2.3.5 Testing Equipment Initial material testing during the surrogate material search was performed using a 222N (501b) load cell (LCCA-50, Omega Engineering Inc.)- Specimens were strained until failure or until the maximum stroke length (7.6cm) of the materials testing machine was reached. Thus a 222N load cell ensured that it would not be overloaded, given that a full understanding of the load at failure of each material was not always known (ie. fibers had been introduced, mixing ratios had been altered, and cords were made of two materials). Once QM Skin 30 (Quantum Silicones) was chosen as the surrogate cord material, a 44.5N load cell (LCFA-10, Omega Engineering Inc.) replaced the 222N load cell for increased accuracy. The programming language Galil 2.3 (Galil Motion Control) was used to control the loading pattern applied to the surrogate cords. Displacement control was processed through an interconnect module (ICM-1100, Galil Motion Control) to Galil 2.3. Load cell data was recorded by a personal computer running LabView 7.1 (National Instruments). Before data collection, the signal was passed through a custom made strain gage amplifier with an analog 1000Hz low-pass filter. Load and displacement data was imported into Excel 2002 (Microsoft Corporation) where data analysis was performed. The accuracy of using the calculated crosshead strain was validated using image analysis to measure the strain in one cord by tracking the displacement of a grid of dots placed mid-length on the surface of the cord (Appendix A). The use of crosshead displacement to measure strain has also been validated by Fiford and Bilston.10 Markers on an in vivo rat spinal cord were tracked with video analysis and compared to the crosshead strains. Their results determined that the crosshead strain lies within one standard deviation of the strains measured from video analysis. The crosshead strains measured in this study were also within one standard deviation of the video analysis strains (±0.04mm). The linear actuator motion was verified by a linear potentiometer (3541H-1-102, Bourns) connected to a wire sensor (WPS-750-MK30-P, Micro-Epsilon) (Figure 2-16), a dial 49 Chapter 2 The Development of a Surrogate Cord gage, and a linear variable differential transformer (LVDT) (LD300-25, Omega). The dial gage was taken as the gold standard (0.0005" accuracy). Accuracies of the additional devices were plotted against the displacement recorded by the dial gage. The calibration factor for the potentiometer was 0.0148V/mm with an R2 value of 0.98. Steps were also taken to confirm that the linear actuator moved at the command speed. This was verified using the potentiometer with and without a load suspended from the linear actuator. The maximum error in the speed of the linear actuator was 2.4% with a lib weight suspended from the actuator. The results demonstrated that the linear actuator displaced by the input displacement (R =1), and this displacement was accurately measured by the potentiometer (R2=0.99). See Appendix A for the validation analysis. The linear potentiometer was not available for these initial tests, however it was used to validate the calculation of the strain once it was obtained. Thus, all of the strains reported for the tests presented in this chapter were measured using the calculated motion of the linear actuator. 50 Chapter 2 The Development of a Surrogate Cord F i g u r e 2-16 - M a t e r i a l s t e s t i n g m a c h i n e . Statistical Analysis To measure the statistical differences for the modulus o f elasticity between Group 2 and 3 surrogate cords, a Student's t-test was used. A paired t-test was employed to evaluate differences between the first and second tests for cords in Group 3 because only two quasistatic tests were performed wi th these cords. After each test using Group 2 surrogate cords, a repeated measures A N O V A statistical analysis (Statistica, p<0.05) was used to track the change in the modulus o f elasticity due to repeated testing. Elastomeric materials are subject to a change in material properties and break down due to repeated testing, inherent imperfections, and degradation caused by environmental factors. 1 7 Thus, 51 Chapter 2 The Development of a Surrogate Cord in order to ensure that the original material properties of the surrogate cord were being tested and no significant change in the modulus of elasticity was apparent, a statistical analysis was performed after each test to confirm this. In addition, a desired property for the surrogate cord is that it be used multiple times in biomechanical experiments without altering the experimental results. Thus, this will also provide crucial information about the approximate number of uses of the surrogate cord before a change in the material properties occurs. It is important to note here that the quasistatic tension tests presented for Group 2 were not necessarily consecutive tests. In some cases, other tests such as tensile tests at higher strain rates were performed between quasistatic tension tests. However quasistatic tests were performed intermittently as a standard measure to determine if the mechanical properties of the surrogate cord had been altered by further testing. 2.4 Results 2.4.1 Determination of the Surrogate Cord Material To evaluate whether each candidate surrogate cord approximated the behaviour of the in vivo spinal cord, the modulus of elasticity was measured to compare with the values determined by Hung et al. and Chang et al6,7'12'14 for the in vivo feline and canine spinal cords. To obtain this value for the surrogate cord, the engineering stress and strain (Eq. 2.2 and 2.3) were calculated using the load and displacement data collected during an uniaxial tension test. The initial toe region was avoided by ensuring that the surrogate cord was in slight tension before testing began as described in section 2.3.4. The stress and strain was plotted and the slope of the curve measured using a linear trendline. The slope of this curve for stress versus strain represents the modulus of elasticity for the material (Eq. 2.1) (Figure 2-17). 52 Chapter 2 The Development of a Surrogate Cord 4000 -I 1 1 1 1 1 1 0 0.01 0.02 0.03 0.04 0.05 0.06 Strain Figure 2-17 - The stress-strain curve and corresponding modulus of elasticity (E=0.22MPa) for a surrogate cord made of QM Skin 30 (ratio A:B = 10:1.2) Different plots of 5% and 12% strain for each surrogate cord were made. The 5% strain represents the modulus of elasticity comparable to that measured by Hung et al. 1 2 . Strain to 12% of the initial length was also used to measure the modulus since this is the natural strain experienced by the human spinal cord 1 6' 2 2 . In some cases (not QM Skin 30), the surrogate cord had a crack initiate during the testing which eventually lead to the cord splitting before 5 or 12% strain. In these cases, the linear portion of the curve was used to measure the modulus of elasticity to the failure strain. Altering the mixing ratio and repeated testing Sylgard 527 was the first material tested since it had been used for this application previously.2,3 The concept of mixing the ratio of elastomer base to catalyst (A:B) and adding fibers to the cord was explored to the greatest extent with this material. For plain surrogate cords, which only had an altered mixing ratio, the modulus of elasticity was tested over a range of mixing ratios between 1:2 and 1:10. The highest modulus of elasticity was measured with a ratio of 1:7 (Figure 2-18). An increase or decrease from this ratio, resulted in a decreased modulus. For all of these ratios, the surrogate cords had a tendency to crack or split before the first test was completed. A fourth order polynomial was fit to the data with an R2 value of 0.7763. A linear, 2nd, and 3rd order polynomial 53 Chapter 2 The Development of a Surrogate Cord were also attempted to fit to the data with lower R2 values of 0.3802, 0.757 and 0.7731 respectively. 0.12 * • • Modulus of Elasticity Poly. (Modulus of Elasticity) 0.02 y = -7E-05X 4 + 0.0022X 3 - 0.0255X 2 + 0.1311x - 0.1478 R 2 = 0.7763 0 0 2 4 6 8 10 12 Amount of catalyst to one part polymer (A:B = 1:B) Figure 2-18 - Dependency of the modulus of elasticity on the silicone gel concentration (Sylgard 527). Quantity of B is given along the x-axis assuming A=l. Alterations in the mixing ratio were also performed with QM Skin 30 (Quantum Silicones). The 10:1.2 mixing ratio produced a higher modulus of elasticity. Figure 2-19 and Figure 2-20 give the modulus of elasticity for the first tests performed on each cord at both of these mixing ratios. A significant difference between the two sets of cords was measured (Student's t-test, p=0.007). 54 Chapter 2 The Development of a Surrogate Cord 0.25 Q. S 0.2 £ 0.15 UJ o 0.1 0.05 27 29 31 32 Surrogate Cord # 34 • Q M Skin 30 10:1 42 Figure 2-19 - The range of the modulus of elasticity over three different cords produced from QM Skin 30 with a mixing ratio of 10:1 0.3 -I 0.25 -2 £ 0.2 -u » o » 0.1 "5 o 0.05 0 43 a Q M Skin 30 10:1.2 45 Surrogate Cord # Figure 2-20 - The modulus of elasticity for three cords made of QM Skin 30 with a mixing ratio of 10:1.2 Addition of Fibers When fibers were added to different silicone gel ratios of Sylgard 527, often the modulus of elasticity increased beyond the modulus measured for the material without fibers (Table 2-5). 55 Chapter 2 The Development of a Surrogate Cord Modulus of Elasticity of the Candidate Surrogate Cords The results for each surrogate cord type, grouped by material and its variations, are given in Table 2-5 below. Table 2-5 - Modulus of Elasticity for the different surrogate cord materials tested Material Mixing Ratio (A:B) Number of Cords Tested Number of tests Average E (MPa) Standard Deviation (MPa) 1:2 2 3 0.029 0.006 1:3 1 1 0.070 NA 1:3 with fibers 1 1 2.000 NA 1:4 with fibers 1 1 0.200 NA Sylgard 527 1:6 1 1 0.092 NA 1:7 5 0.100 0.019 1:7 with fibers 1 2 1.500 0.707 1:8 1 3 0.084 0.020 1:9 1 1 0.092 NA 1:10 -) 2 0J)6a_ 0.014 10:1 48 0.185 0.030 QM Skin 30 10:1 with fibers 1 1 0.173 NA 10:1.2 6 0.245 0.024 ~ ~ 2 ~ ~TJBT4" ™~rjr j33~ 3-4222 Dielectric Gel 1:1 1 3 0.085 0.020 3-4207 Dielectric Gel 1:1 1 1 0.356 NA MED-4901 1:1 10 0.100 0.010 RTV in 527 10:1 in 1.7 1 1 0.381 NA 527 in RTV 1.7 in 10:1 1 1 0.518 NA The average moduli of elasticity for the different surrogate cords tested range from 0.029MPa (Sylgard 527, 1:2) to 2.0MPa (Sylgard 527, 1:3 with fibers). 2.4.2 Final Surrogate Cord Material QM Skin 30 was chosen as the material which most closely represents the modulus of elasticity of the in vivo spinal cord (Figure 2-17). The mixing ratio was altered to 10:1.2 in order to obtain a mean modulus of elasticity of 0.245 ± 0.024MPa (measured from the initial candidate surrogate cords). A set of 34 additional surrogate cords of QM Skin 30 (mixing ratio of 10:1.2) were produced to fully quantify its modulus of elasticity in quasistatic tension. This group of 34 cords was split into three sub groups. The first group 56 Chapter 2 The Development of a Surrogate Cord (Group 1) consists of 14 cords which were later used in experiments for dynamic transverse compression (Figure 2-15). The second (Group 2) and third (Group 3) groups of 10 surrogate cords each were used to quantify the properties of this material in uniaxial tension under quasistatic and dynamic loads, as well as in transverse compression applied at a constant strain rate. Only tests which were performed to measure the modulus of elasticity in quasistatic tension will be discussed here. Results from dynamic and compressive loading are presented in the succeeding chapters. A quasistatic uniaxial tension test was only performed once for the surrogate cords in Group 1 (average E = 0.261 + 0.018MPa). Surrogate cords in Groups 2 and 3 were measured several times. The mean values for the modulus of elasticity for the two groups measured to different strains are provided in Table 2-6 below. Table 2-6 - Mean values for the modulus of elasticity (MPa) measured from the first quasistatic tension test in Groups 2 and 3. Values are given for the modulus measured from 5% and 12% strain data with one standard deviation given in parentheses. Strain 5% 12% Group 2 0.247 (0.009) 0.228 (0.008) Group 3 0.205 (0.011) 0.189 (0.009) The trend in the modulus of elasticity (measured to 12% strain) due to multiple tests is shown in Figure 2-21. 57 Chapter 2 The Development of a Surrogate Cord 0.25 Cord 65 Cord 66 Cord 67 Cord 68 Cord 69 Cord 70 Cord 71 Cord 72 Cord 73 Cord 74 Test 1 Test 2 Test 3 T e s t # Test 4 Figure 2-21 - The modulus of elasticity for multiple tests performed with Group 2 surrogate cords. The modulus of elasticity was measured to 12% strain. The following table gives the p-values measured between the multiple tests of surrogate cords in Group 2. Values less than 0.05 were considered significant. Table 2-7 - SNK results (p values) between quasistatic tension tests performed on surrogate cords 65 through 74 (Group 2) to a) 5% strain and b) 12% strain. The mean value for the modulus of elasticity is provided in MPa. a) Test 1 Test 2 Test 3 Test 4 Mean E: .2469610 .2425656 .2466504 .2347545 Test 1 — 0.243091 0.908194 0.000651 Test 2 — 0.137129 0.006953 Test 3 0.000476 Test 4 b) Test 1 Test 2 Test 3 Test 4 Mean E: .2279902 .2198509 .2259088 .2164402 Test 1 — 0.010636 0.426711 0.000803 Test 2 0.026485 0.197104 Test 3 ~~~~— 0.002998 Test 4 For values measured to 5% strain among the surrogate cords in Group 3, the two tailed p-value was approximately 0.17 and that for 12% strain was approximately 0.23. Both of these results indicate that there was no statistical difference between the first and second test for these cords. An analysis between the initial quasistatic modulus of elasticity for cords in Group 2 versus Group 3, at both the 5% and 12% strain levels, provided p-values less than 0.001, thus indicating that the two sets of cords were significantly different. 58 Chapter 2 The Development of a Surrogate Cord 2.5 Discussion A surrogate spinal cord which matches the properties of the in vivo human spinal cord could assist in measuring the stress, strain, and strain rates which occur in vivo as well as those that occur during injurious loading. This would lead to further understanding of the mechanical loads applied to the spinal cord which occur in vivo and as a result, direct treatment procedures towards more appropriate methods to mitigate and prevent spinal cord injury. A material search was performed to identify a material with a modulus of elasticity matching that of the in vivo human spinal cord. 2.5.1 Ass ign ing Q M Skin 30 as the Surrogate Material Sylgard 527 Sylgard 527 was extensively evaluated as the first candidate material for the surrogate cord. Changes in the modulus due to different mixing ratios and the addition of fibers in the gel were explored. The highest modulus of elasticity for a Sylgard 527 cord without fibers was 0.112MPa which is too low for the desired modulus of the surrogate cord (0.26MPa). Fiber Reinforced Sylgard 527 When fibers were added to the gel, the modulus increased. Interestingly, the cord for which the mixing ratio was 1:4 and contained a matrix of fibers along its length, the modulus of elasticity only slightly increased compared to the modulus predicted by the curve fit in Figure 2.5.3 (approximately 0.08MPa), whereas, for cords with mixing ratios of 1:3 and 1:7, the modulus increased more than ten times with the addition of fibers. Surrogate cords made with fibers were excluded as possible candidates for the final surrogate cord. These cords were difficult to reproduce with the exact same fiber 59 Chapter 2 The Development of a Surrogate Cord orientation and pretension. Additionally, after being tensioned the first time, their properties changed considerably. Reasons for their change in behaviour include possible material property changes in the fibers as well as a separation between the fiber and the ground substance of the matrix, Sylgard 527. If separation occurs, then it is expected that the strength contribution of the fibers to the surrogate cord would be eliminated on subsequent load applications. This separation is also likely because the clamps cannot grip the fibers. Therefore as the cord is tensioned, the clamp can only pull the surrogate cord material and not the fibers. Thus the fibers are only strained if the bond between the fiber and the gel is strong enough. Due to the high variability and unrepeatable material properties, these cords were not carried through for further testing. Although the fiber reinforced surrogate cords were excluded in this study, Bilston et al. successfully produced and validated surrogate cords with fibers oriented longitudinally throughout a matrix of Sylgard 527. * Due to the much too low modulus of elasticity for Sylgard 527, and the inconsistency of surrogate cords with fibers observed in this study, Sylgard 527 was eliminated from the material choices for the surrogate cord and other materials were tested. Two Material Composite The surrogate cords made of two different materials were also unrepeatable. In the two cords of this type, significant cracks occurred in the Sylgard 527 (Figure 2-22). Thus repeated testing would result in a different modulus of elasticity as the number of cracks increased. Consequently, these cords were also excluded from the possible choices for the surrogate material. Figure 2-22 - Cracks in the core cord made of an inner core of Sylgard 527 and an outer shell of RTV 2039. Two views are given for Cord #25 to demonstrate the cracks due to tensile loads. 60 : Chapter 2 The Development of a Surrogate Cord QM Skin 30 From the remaining cords, there were no visible reasons to doubt that the cord could not be tested multiple times. A large number of tests were performed on QM Skin 30 (10:1). Results for these cords were fairly consistent and within a maximum of 0.1 MPa from the desired modulus of elasticity. Therefore, no changes due to repeated stretching or environmental degradation were observed. Another iteration of the mixing ratio of QM Skin 30 was tested as an attempt to obtain a modulus of elasticity closer to that for the in vivo spinal cord. This attempt was successful. A mixing ratio of 10:1.2 produced an average modulus of elasticity of 0.245MPa among three different cords. This falls within the range of the in vivo moduli (0.215-0.295MPa) identified by Hung et al.12 Thus QM Skin 30, with a mixing ratio of 10:1.2 was chosen as the material for the surrogate cord. 2.5.2 Evaluation of Q M Skin 30 (10:1.2) in Quasistatic Tension The initial group of surrogate cords (47 through 60) had a mean modulus of elasticity of 0.261 ± 0.018MPa (measured to 12% strain). This is slightly below the mean value, 0.265MPa, measured for the in vivo canine spinal cord. However, the modulus for the canine spinal cord is within the range of moduli measured in this group of surrogate cords. Groups 2 and 3 had mean moduli up to 12% strain of 0.228 and 0.189MPa respectively, both somewhat lower than the mean for Group 1 (0.261 ± 0.018MPa). All cords were made from different batches of QM Skin 30 which may account for the differences in moduli. The dissimilarities may also be attributed to changes in ambient temperature during molding or testing of the surrogate material. The effects of changing the temperature of the cord on the modulus of elasticity were not evaluated. Using data up to 5% or 12% strain to calculate the modulus of elasticity resulted in different values for the modulus of elasticity. In all cases, the value measured from 5% strain data was higher than that measured from 12% strain data. This is due to the slightly non-linear stress-strain curve at the quasistatic strain rate. Repeated testing changed the mechanical properties of the surrogate cord (Table 2-7). However, similar to the in vivo 61 Chapter 2 The Development of a Surrogate Cord spinal cord, the surrogate cord behaves linearly up to strains of 5%. ' Beyond 5% 13 strain, the modulus of elasticity of the in vivo spinal cord progressively decreases. This behaviour was also observed in the surrogate cord as demonstrated by the lower values for the modulus measured to 12% strain. 2.5.3 Limitations and Future Work As seen by the significant difference between the initial modulus of elasticity for the cords in all groups, it is recommended that further measures be taken to determine which parameters affect the modulus of elasticity of the surrogate cord. Specific parameters of interest are the humidity and temperature in the room where the surrogate cords are being produced. The length of time spent in the vacuum may also be a factor in their final properties. Additionally, the cord temperature at the time of testing may also contribute to the difference in moduli. These factors would not only be relevant during production, but may also affect the analysis of moduli across repeated testing. Significant differences determined through statistical analysis of the moduli may have resulted from conditions on the day of testing, not simply from the fact that they had been subjected to multiple tensile tests. It is likely that factors such as temperature would contribute to a different measured modulus of elasticity since the graph for surrogate cords in Group 2, which depicts the change in modulus across four tests, does not show a constant increase or decrease in the moduli across all cords (refer to Figure 2-21). 2.5.4 Conc lus ions This surrogate cord, made of QM Skin 30, is similar to that developed by Bilston et al. with Sylgard 5271'2 since it is an elastomeric material. However, the QM Skin 30 surrogate cord is a closer approximation of the in vivo spinal cord.6'7,12"14 This is based on multiple tests of QM Skin 30 and the assumption that the in vivo animal spinal cord is a more appropriate estimate for the in vivo human spinal cord mechanical properties than the in vitro human spinal cord. In addition, unlike cords made of Sylgard 527, the QM 62 Chapter 2 The Development of a Surrogate Cord Skin 30 surrogate cords did not split and crack during testing. It can thus be used for multiple testing. The modulus of elasticity in quasistatic tension does not completely describe the material properties of the spinal cord or of the surrogate material. The viscoelastic properties of the spinal cord have been measured previously.5'7'9'10 Thus further testing was required to determine the viscoelastic properties of the surrogate cord. One of the many uses of the surrogate cord will be to determine the injury mechanisms to the spinal cord during a burst fracture. Therefore the behaviour in transverse compression and under high loading rates was also required. These analyses are discussed in the following chapters. 63 Chapter 2 The Development of a Surrogate Cord 2.6 References 1. Bilston LE. The Biomechanics of the Spinal Cord During Traumatic Spinal Cord Injury. Bioengineering. Pennsylvania: University of Pennsylvania, 1994:204. 2. Bilston LE, Meaney DF, Thibault L. The Development of a Physical Model to Measure Strain in a Surrogate Spinal Cord During Hyperflexion and Hyperextension. IRCOBI Conference. Eindhoven, Netherlands, 1993. 3. Bilston LE, Thibault LE. Biomechanics of cervical spinal cord injury in flexion and extension: a physical model to estimate spinal cord deformations. International Journal of Crashworthiness 1997;2:207-18. 4. Bilston LE, Thibault LE. The mechanical properties of the human cervical spinal cord in vitro. Ann Biomed Eng 1996;24:67-74. 5. Bilston LE, Thibault LE. The mechanical properties of the human cervical spinal cord in vitro. Ann Biomed Eng 1995;24:67-74. 6. Chang GL, Hung TK, Bleyaert A, et al. Stress-strain measurement of the spinal cord of puppies and their neurological evaluation. J Trauma 1981 ;21:807-10. 7. Chang GL, Hung TK, Feng WW. An in-vivo measurement and analysis of viscoelastic properties of the spinal cord of cats. J Biomech Eng 1988; 110:115-22. 8. Ching RP, Watson NA, Carter JW, et al. The effect of post-injury spinal position on canal occlusion in a cervical spine burst fracture model. Spine 1997;22:1710-5. 9. Fiford R, Bilston LE. Strain distribution and relaxation behaviour of rat spinal cord. Advances in Bioengineering, proceedings of the ASME International Mechanical Engineering Congress,. Anaheim, USA, 1998:247-8. 10. Fiford RJ, Bilston LE. The mechanical properties of rat spinal cord in vitro. J Biomech 2005;38:1509-15. 11. Flint E, Rogers L, Fowler B. Viscoelastic Material Properties in a High Pressure Environment. 3rd National Turbine Engine High Cycle Fatigue Conference. San Antonio, Texas, 1998. 12. Hung TK, Chang GL. Biomechanical and neurological response of the spinal cord of a puppy to uniaxial tension. J Biomech Eng 1981;103:43-7. 13. Hung TK, Chang GL, Chang JL, et al. Stress-strain relationship and neurological sequelae of uniaxial elongation of the spinal cord of cats. Surg Neurol 1981;15:471-6. 14. Hung TK, Chang GL, Lin HS, et al. Stress-strain relationship of the spinal cord of anesthetized cats. J Biomech 1981;14:269-76. 15. Kameyama T, Hashizume Y, Sobue G. Morphologic features of the normal human cadaveric spinal cord. Spine 1996;21:1285-90. 16. Margulies SS, Meaney DF, Bilston LB, et al. In Vivo Motion of the Human Cervical Spinal Cord in Extension and Flexion. IRCOBI Conference. Verona, Italy, 1992:213-24. 17. MSC Software. Nonlinear Finite Element Analysis of Elastomers: MSC Software Corporation, 2002. 64 Chapter 2 The Development of a Surrogate Cord 18. Oakland RJ. A Biomechanical Study of the Spinal Cord in the Burst Fracture Process. School of Mechanical Engineering. Leeds: The University of Leeds, 2003. 19. Oakland RJ, Wilcox RK, Hall RM, et al. The mechanical response of spinal cord to uniaxial loading. 48th Annual Meeting of the Orthopaedic Research Society. Dallas, Texas, 2002. 20. Pintar FA, Schlick MB, Yoganandan N, et al. Instrumented artificial spinal cord for human cervical pressure measurement. Bio-Medical Materials and Engineering 1996;6:219-29. 21. Raynak GC, Nuckley DJ, Tencer AF, et al. Transducers for dynamic measurement of spine neural-space occlusions. Journal of Biomechanical Engineering 1998;120:787-91. 22. Yuan Q, Dougherty L, Margulies SS. In vivo human cervical spinal cord deformation and displacement in flexion. Spine 1998;23:1677^ 83. 65 Chapter 3 Viscoelastic Behaviour of the Spinal Cord Chapter 3 Viscoelastic Behaviour of the Spinal Cord 3.1 Introduction The injury mechanisms which lead to serious spinal cord injury are not completely understood. In order to gain insight into the cause of injury and methods for treatment and prevention, animal models are often used to simulate human spinal cord injury. Thus animal and human spinal cords have been tested to obtain information regarding the response of the spinal cord to mechanical loads applied at various strains and strain rates. From these experiments, it is known that injurious mechanical loads applied to the spinal cord occur at varying strain rates and the degree of injury is related to the rate at which a force is applied.17'23 A material whose response is determined by the rate at which a force is applied to it and which exhibits creep and relaxation behaviour is called a viscoelastic material. The spinal cord has been measured to be such a material.3'5'8'9 Thus, to be considered as an appropriate model for the human spinal cord, a suitable surrogate cord should exhibit similar viscoelastic behaviour to that of the in vivo spinal cord. It can then be used in laboratory experiments to measure the stresses and strains in the spinal cord during experiments to study spinal cord injury. 3.1.1 Viscoelast ic Properties of the Human Spinal Cord In Vitro Studies Bilston and Thibault used a range in strain rates of 0.04-0.24S"1 to test the viscoelastic properties of the in vitro human spinal cord.3 Often, viscoelasticity is measured by a relaxation test. A constant tensile strain is applied to the spinal cord and is held for a length of time to measure how rapidly the stress in the cord decays with time. They held human spinal cord specimens at a constant strain for one minute.3 The relaxation in the cord was measured during this time, however it was suggested that a longer relaxation 66 Chapter 3 Viscoelastic Behaviour of the Spinal Cord time would be necessary in order to allow complete relaxation. The decay of stress with time is given in Figure 3-1 for three different strain rates. Approximately 20 to 30% of the stress decayed within the first 30 seconds of relaxation. The initial magnitude of stress decay in the tissue was related to the strain rate, as was the modulus of elasticity. Strain Rate 0.048s"1 0.120s"1 0.225s 1 Time (s) Figure 3-1 - Stress-relaxation curves for three in vitro human spinal cord specimens tested at different strain rates 3 Several models were used to mathematically describe the relaxation of the spinal cord. Among these was the quasilinear viscoelastic model developed by Fung10 which has been used to describe the behaviour of soft tissues such as ligaments, ' ' ' collagen fibers, mesentery,6 dura mater,24 and the spinal cord.3'21 The relaxation time for the spinal cord, could be described by models with time constants of 0.1-1 sec and 1-10 sec.3 However, there were several combinations of constants which would provide similar solutions, thus these time constants cannot be considered as definite relaxation times due to the lack of a unique solution for this problem. (0 Q_ 0.20 0.15 0.10 67 Chapter 3 Viscoelastic Behaviour of the Spinal Cord 3.1.2 Viscoelast ic Properties of the Animal Spinal Cord Viscoelastic models have also been used to describe the relaxation behaviour of various 5 8 9 21 animal spinal cords both in vivo and in vitro. ' ' ' In Vitro Rat Spinal Cord Fiford and Bilston8'9 tested the in vitro rat spinal cord to maximum strains of 5% and allowed the spinal cord to relax for 30 minutes. Similar to the behaviour of the in vitro human spinal cord during a relaxation test, the rat spinal cord exhibited an initial non-linear stress response whose stiffness was dependent on the strain rate. The stress decay during the initial 30 seconds of relaxation increased with increased strain rates. The peak mean stress was also observed to increase. A viscoelastic constitutive model was fit to the stress-strain data.9 This model fit the data, lying within the standard deviations of the experimental results. However, it was found that the model best fit the data from higher strain rate testing. In Vitro Bovine Spinal Cord Relaxation tests performed on the in vitro bovine spinal cord21 were fit with Fung's quasilinear viscoelastic model11 and a four-element spring-dashpot model. The quasilinear viscoelastic model fit the data well during loading and during relaxation. The spring-dashpot model provided an accurate fit for the relaxation behaviour only. In Vivo Feline Spinal Cord The in vivo spinal cord also exhibits non-linear viscoelastic behaviour, however the initial loading curve is linear to approximately 5% strain5 whereas that for the in vitro rat and human cords has been measured to be non-linear.3'8'9 The relationship between stress and strain is defined as the modulus of elasticity. Hung et al. found the modulus of elasticity to be constant to strains of 5% at a strain rate of 0.002s"1.16 Thus there is a linear response in the in vivo feline spinal cord up to 5% strain. 68 Chapter 3 Viscoelastic Behaviour of the Spinal Cord Chang et al. fit a linear and non-linear viscoelastic model to the stress-strain data for the in vivo feline spinal cord (Figure 3-2).5 The linear model was calculated using Boltzmann's convolution integral and non-linear results were determined with an equation developed by Schapery. Non-linear behaviour was determined to occur with strains greater than 0.7%. The theoretical results matched well with the experimental data for strains less than 20% and a strain rate of 0.003s"1. T Strain 0.06 0.11 | Figure 3-2 - A comparison between experimental data and the nonlinear model for in vivo relaxation of the cat spinal cord. Modified from Chang et al.8 Both in vivo and in vitro spinal cords have been shown to behave viscoelastically. Non-linear viscoelastic models have been successfully developed to model the spinal cord's relaxation behaviour. These account for the elastic and viscous properties as well as the strain history, all important mechanical properties of the spinal cord tissue. 3.1.3 Creep Behaviour The creep test for a material is similar to a relaxation test, however instead of measuring the stress decay with time as the strain is held constant, a creep test measures the increase in strain necessary to maintain a constant load. No published creep tests were identified 69 Chapter 3 Viscoelastic Behaviour of the Spinal Cord which described the behaviour of the spinal cord under tension. This is most likely because there are no obvious physiological situations for which creep in the spinal cord would occur in vivo. However, creep tests are a standard part of the viscoelastic characterization of materials. Therefore, despite a lack of in vivo or in vitro spinal cord creep data, creep tests were performed as a part of this study in order to fully quantify the mechanical properties of the surrogate cord. Although the creep behaviour of the spinal cord is not known, there are several studies which have investigated the creep behaviour of ligaments14'19'22 and other connective tissues.7'14'18 In particular, the medial collateral ligament of the rabbit was tested in both relaxation and creep in order to establish a relationship between the two responses as suggested by Fung.11'22 Fung describes a quasilinear viscoelastic model which states that the reduced relaxation function, G(/), is related to the reduced creep function, J(t), by the following relationship J(s)G(s) = ^ (Eq.3.1) s where J(s) and G(s) are the Laplace transforms of J(t) and G(t) respectively and s is a 1 1 99 real number. Thornton et al. applied this relationship to a general linear model for J(t) to predict G(i). The predicted form of G(t) was then compared to the experimental data for G(f). A similar analysis was performed to predict J(f) from G(t). The equations used in this analysis are given as follows: G(0 - Axe~Al' + A3e~Atl + AY (Eq. 3.2) J(t) = Bxe-B>' + B3e~Bt' + B5 (Eq. 3.3) where Ai and B\ are constants and G(f) and J(f) are calculated from experimental data given the following relationship: <7(0 = G(0o-0 (Eq.3.4) e(t) = J(t)e0 (Eq. 3.5) The results indicated that the predicted models for both the reduced creep and relaxation functions did not match the experimental results, however the original functions (Eq 3.2 70 Chapter 3 Viscoelastic Behaviour of the Spinal Cord and 3.3) fit the data well. Thus, for the rabbit medial collateral ligament, Fung's relationship (Eq. 3.1) does not hold true. The discrepancy between Thornton et al.'s results22 and Fung's description for the relationship between the relaxation and creep behaviour in a quasilinear viscoelastic model" was explained by Lakes and Vanderby.19 They assumed a separable form of the creep function between a time and stress dependent portion (Eq 3.6). This assumption leads to a non separable form of the relaxation response (Eq 3.7) with the application of Fung's relationship (Eq. 3.1). In the above equations, J(t, cr) follows the quasilinear theory because it is separable into a stress and time dependent portion, however G(t, s) is not separable and thus does not fall within the quasilinear viscoelastic description of a material. The inverse relationship can also be implied. Thus if Fung's model is used to describe the reduced relaxation function then according to Lakes and Vanderby, the creep function cannot be separable between time and stress. However, for a viscoelastic material, it is necessary that the creep response is dependent on the loading history. Therefore, the creep and relaxation functions cannot both be described using a single Fung-type quasilinear viscoelastic model and inverting it mathematically. Instead, separate creep and relaxation equations must be used to describe a material's behaviour. A model for the viscoelastic properties of both the human and animal spinal cords allows for a more complete understanding of the mechanical behaviour of the cord. This is expected to be especially important for the highly dynamic spinal cord deformations occurring during injury. A surrogate cord that matches this behaviour will provide a tool against which to validate animal models that are used to evaluate injury mechanisms and treatment protocols for human spinal cord.injury. Our objectives were to measure the (Eq3.6) (Eq 3.7) 3.2 Objectives 71 Chapter 3 Viscoelastic Behaviour of the Spinal Cord viscoelastic properties of the surrogate cord under creep and relaxation loading protocols to compare with the in vivo animal spinal cords as a model of in vivo human spinal cord behaviour. If its viscoelastic behaviour can be shown to match that of the in vivo spinal cord then this would be further evidence to support its use as a surrogate for the in vivo human spinal cord. 3.3 Materials and Methods 3.3.1 Testing Protocol Following quasistatic tension tests, described in Chapter 2, the effect of varying the strain rate was evaluated by testing one set of ten surrogate cords to measure the modulus of elasticity for dynamic strain rates in simple tension (Group 2). The creep and relaxation functions of the cord at three different strain rates were evaluated using the additional surrogate cords (Group 3). A summary of the viscoelastic and quasistatic tension tests performed is provided in Table 3-1. Ten surrogate cords were tested in each group to make certain that there was redundancy in case of material failure or significant damage to one surrogate cord. Ten cords also provided for an adequate statistical comparison between tests with a power of 0.90 and a standard deviation of 0.1 MPa. The maximum strain rates for each test type were limited by equipment capabilities. The viscoelastic tests required feedback control, either by displacement or load. The strain rate limits between these control methods were different. The strain rates for tests meant to apply instantaneous strain were chosen to take full advantage of the equipment capabilities. Therefore, the maximum strain rates varied among the different types of tests (Table 3-1). 72 Chapter 3 Viscoelastic Behaviour of the Spinal Cord Table 3-1 - Viscoelastic tests performed with the surrogate cord. A total of 34 surrogate cords were constructed. Group 1 (14 cords) was used for impact transverse compression tests, Group 2 (10 cords) was used for uniaxial tension at varying strain rates, and Group 3 (10 cords) was used for relaxation, creep, and non-impact transverse compression tests. Test Type Number Tested Strain Rate (s1) Test Repetition Group # 10* 0.0025 3 2 Uniaxial 10 0.048 2 2 Tension 10 0.12 2 2 5 0.8 1 3 10 0.0025 1 2 Relaxation 10** 0.048 1 3 10 0.12 1 3 5 0.32 1 3 10 0.0025 1 3 Creep 10 0.048 1 3 10 0.12 1 . 3 5 0.17 1 3 * These were quasistatic tests and they are described in Chapter 2 ** The second set of surrogate cords was used at this point to continue testing due to a significant difference seen in the modulus of elasticity within Group 2 surrogate cords Surrogate cords were immediately removed from the materials testing machine following test completion. Subsequent tests were performed a minimum of 24 hours later. Quasistatic tension tests were performed between tests performed at other strain rates to monitor the change in Young's modulus due to repeated testing and changes in the strain rate. A repeated measures ANOVA and SNK test (post-hoc) was performed in Statistica 5.1 (StatSoft Inc.) to determine these changes (p<0.05). Group 2 surrogate cords were also tested once in quasistatic relaxation. The initial modulus of elasticity was measured from this test and a statistical analysis performed. Statistical results indicated that the quasistatic Young's modulus had changed significantly (from an average of 0.228 to 0.204MPa) and thus a second set of surrogate cords (Group 3) was made to continue testing (p<0.05) (see Table 3-1). Group 3 cords were tested in quasistatic tension twice to determine the modulus of elasticity for each cord. Uniaxial Tension (see Table 3-1) The viscoelastic behaviour of the spinal cord has also been reported for in vivo animal tests3'5 and an in vitro human test.3 In order to measure the effect of loading rate on the 73 . Chapter 3 Viscoelastic Behaviour of the Spinal Cord material properties o f the surrogate cord, two strain rates were replicated f rom Bi ls ton "X 1 \ and Thibaul t 's experimental protocol . The strain rates chosen were 0.048s" and 0.12s" 1. A third higher strain rate o f 0.8s" 1 was applied to represent the h igh strain rate and a quasistatic strain rate o f 0.0025s' 1 was also applied to these specimens as described in Chapter 2. Relaxation Tests (see Table 3-1) For relaxation testing, a constant tensile strain rate was appl ied to each cord unti l it was strained to 1 2 % . 2 0 Strain rates were identical to those used for the tension tests (0.0025s" 1, 0.048 s" 1, and 0.12 s" 1). Relaxat ion tests at each strain rate were only performed once per surrogate cord. The relaxation was measured for sixty seconds at wh ich point the surrogate cord was returned to its or iginal length. B i l s ton and Thibaul t 3 indicated that a relaxation time o f 60 seconds was too short to measure the relaxation behaviour. However , the stress decay in the surrogate cord was smaller than that in the in vitro human spinal cord. Prel iminary tests indicated that a relaxation t ime o f 60 seconds was adequate to reach an equi l ibr ium stress in the surrogate cord. A n addit ional higher rate relaxation test was performed on f ive cords f rom Group 3. The ramp speed for these f ive cords was chosen such that a strain rate o f 0.32s" 1 resulted, thus approximating instantaneous displacement (in approximately 0.8s) f rom zero to 12% strain. The constant strain in this case was held for 300 seconds. The relaxation time was increased for this test because it was expected that the stress decay wou ld be greater due to instantaneous displacement. The data was analyzed using Fung 's quasil inear viscoelast ic m o d e l 1 1 (Appendix B ) . The solve function in E x c e l 2002 (Microsof t Corporat ion) was used to determine the parameters o f the viscoelastic model so that the fit the experimental data was opt imized. The experimental data consisted o f twenty points wh ich described the behaviour o f the surrogate cord. The data was l imited to 20 points to ease the solve process in E x c e l 2002. A general linear model (Eq 3.2) 2 2 was also fit to the relaxation portion o f the experimental data and compared wi th the results f rom Fung 's quasil inear viscoelastic model . 74 Chapter 3 Viscoelastic Behaviour of the Spinal Cord Creep Tests (see Table 3-1) Three creep tests per cord, one for each strain rate (0.0025s" , 0.048 s" , and 0.12 s" ), were run at a load of 4.ON. A load of 4.ON was chosen by approximating the maximum load measured during the quasistatic tensile tests (thus approximating 12% strain for the initial displacement). Creep was measured for sixty seconds while maintaining a constant load in the cord of 4.ON and then unloading to a level of ON. The ramp to 4.ON and subsequently to ON was displacement controlled using identical strain rates to those used for the relaxation tests. Similar to the final relaxation test, an additional creep test was performed on five surrogate cords by applying an instantaneous ramp from zero to approximately 4.ON at a strain rate of 0.17s"1 (in approximately 1.9s) and held for 300 seconds to ensure that the entire relaxation period was measured. These were the five surrogate cords from the Group 3 set of ten cords which had not been exposed to an instantaneous relaxation test. Fung's Quasilinear Viscoelastic Model Fung's quasilinear viscoelastic theory" was implemented to determine an equation for the stress in the material which takes into account the strain history (Eq. 3.8) (full details are given in Appendix B). -Similar to Bilston and Thibault's analysis,3 three exponential terms were used in the reduced relaxation function. Constants for Eq. 3.9 below were calculated using the experimental data from each surrogate cord test. (Eq. 3.8) a(t) = ABe*YtGieX' -t e -e for 0<f<fi — + Beo\ J 75 Chapter 3 Viscoelastic Behaviour of the Spinal Cord o-{t) = ABsoYaGier' f f i « + Bsc -1 for t>h (Eq. 3.9) The average of each parameter measured for ten surrogate cords was then calculated to determine an overall stress function for the surrogate cord at each strain rate Linear Relaxation Model A general linear model (Eq. 3.2) was also used to evaluate the relaxation of the surrogate cord at 12% strain in order to compare it to the fit from Fung's quasilinear viscoelastic model. The values of the constants for this model were determined for relaxation tests performed at each of the four strain rates. Linear Creep Model The analysis of experimental data provided by Thornton et al?2 and the mathematical explanation given by Lakes and Vanderby19 both explain that if Fung's quasilinear viscoelastic model is assumed for the relaxation behaviour of a material, then the creep behaviour cannot also be described by an inverse of the same quasilinear viscoelastic model. 1 1 ' 1 9 ' 2 2 Thus, the current creep analysis was performed by assuming a general linear 22 model similar to that employed by Thornton et al. for ligaments (Eq 3.3). The model was fit to experimental creep data obtained at four strain rates (Table 3-1). 3.3.2 Testing Equipment Equipment used for the viscoelastic tests was identical to that used in the tension tests described in 2.3.5 with a few exceptions. High speed creep tests, instantaneous relaxation Chapter 3 Viscoelastic Behaviour of the Spinal Cord and creep experiments, and the final tension tests were performed at the Division of Orthopaedics Engineering Research laboratory at Vancouver General Hospital (Vancouver, Canada). The 44.5N load cell (LCFA-10, Omega Engineering Inc.) used in the previous tests was connected in series with a l.lkN load cell (Sensotec Model 75, Honeywell) which was mounted in a DynaMight 8841 (Instron) materials testing machine. Load data was collected from both load cells. Only data from the 44.5N load cell was used for analysis. The 44.5N load cell was filtered through the identical strain gage amplifier as used in previous tests. An LVDT incorporated into the DynaMight (calibrated for 2.45mm/V) measured displacement. WaveMaker 6.4.0 (Instron) was used to control the motion of the DynaMight (Instron) and record load from the 1.1 kN load cell as well as displacement. LabView 6.1 (National Instruments) collected data for the load measured by the 44.5N load cell and displacement measured by the LVDT in the DynaMight (Instron). Statistical Analysis Before performing a statistical analysis to evaluate the differences between the modulus of elasticity calculated for each test, the data was checked to ensure that it was homogeneous and had a normal distribution. If the data met these criteria, a repeated measures ANOVA followed by an SNK post-hoc comparison was performed. P-values less than 0.05 indicated a significant difference between groups. If the data did not meet these criteria, a Friedman rank sums test was used to calculate a corrected SNK value. The corrected SNK value was used to identify significant differences among the different tests. For a statistical analysis involving only two groups, a Student's t-test was used to determine statistically significant differences between the different groups of surrogate cords (p<0.05). 77 Chapter 3 Viscoelastic Behaviour of the Spinal Cord 3.4 Results 3.4.1 The Effect of Strain Rate on the Modulus of Elasticity Tension tests performed at four different strain rates (0.0025s"1, 0.048 s"1, 0.12 s"1, and 0.8s"1) were performed on surrogate cords in Group 2 to assess the change in the modulus of elasticity with an increase in the strain rate. The secant modulus of elasticity for each cord was measured from the initial strain to 5% and to 12% strain (Figure 3-3). The modulus measured to 5% strain corresponds with stress measurements made in vz'vo 4 ' 1 5 ' 1 6 20 whereas 12% strain is the natural elongation of the human spinal cord in vivo. For all tests, except the last fast strain rate test, there was a significant difference between the moduli measured to 5% and 12% strain (Figure 3-4). 30000 25000 "ST 20000 in 15000 o 10000 5000 E 1 2 %=0.25MPa E5 %=0.27MPa ' E 1 2 %=0.22MPa E5./a=0.24MPa 0 0.02 0.04 0.06 0.08 0.1 0.12 Strain • Quasistatic Strain Rate, (0.0025S-1), 5% strain Instantaneous Strain Rate (0.8s-1), 5% strain • Quasistatic Strain Rate (0.0025s-1), 12% strain Instantaneous Strain Rate (0.8s-1), 12% strain Figure 3-3 - Secant lines used to determine the modulus of elasticity to 5% and 12% strain for two surrogate cords strained at different strain rates. 78 Chapter 3 Viscoelastic Behaviour of the Spinal Cord H E (5%) • E (12%) TQ 1 TQ2 TQ3 TM1 TM2 TQ4 TF1 Test Parameter TF2 Figure 3-4 - The mean modulus of elasticity measured in each test for surrogate cords in Group 2. The tests are listed in the order which they were performed. Significant differences (p<0.05) are indicated by *. T = tension, Q = quasistatic strain rate, M = medium strain rate, F = fast strain rate, # = indicates the test number for that particular strain rate. Statistical results indicated that the strain rates chosen had no effect on the modulus of elasticity of the surrogate material. Visual inspection of the mean values also confirms that there was very little effect on the modulus of elasticity based on strain rate (Figure 3-5). Similar results were seen for moduli measured to both 5% and 12% strain. TO Q. 5 'o '•^ </> m LU 3 T3 O 2 0.3 0.25 0.2 0.15 0.1 0.05 4 0 65 66 67 68 69 70 71 72 73 74 C o r d # m Quasistatic test (0.0025S-1) • Intermediate rate test (0.048S-1) • High rate test (0.12s-1) Figure 3-5 - Mean modulus of elasticity for each cord, measured for each strain rate. The modulus of elasticity was calculated to 12% strain for TQ1, TM1, and TF1. 79 Chapter 3 Viscoelastic Behaviour of the Spinal Cord After the last fast strain rate test (TF2) was performed, the cords were used in a relaxation test with a quasistatic strain rate (0.0025s"1). The modulus of elasticity for each cord was measured from the initial loading curve in these relaxation tests. After this relaxation test a statistical analysis revealed significant differences in the modulus of elasticity of the surrogate cords. Thus, these cords were no longer tested and the remaining tests were performed with surrogate cords from Group 3. Some of the surrogate cords from Group 3 were tested at an instantaneous strain rate (0.8s"1). Five of the cords from Group 3 were tested at a quasistatic strain rate, 0.0025s"1, and the remaining five were tested at 0.8s"1. Thus, all cords were tested under the same ambient conditions and had the same loading history. The modulus of elasticity for each cord was measured and the results between quasistatic and instantaneous strain rates compared (Figure 3-6). There was a significant difference between the moduli of both groups calculated to both 5% and 12% strain (p<0.002). «? 0.3 D_ 75 76 77 78 79 80 81 82 83 84 Cord # Figure 3-6 - Modulus of elasticity between cords tested at a quasistatic rate and cords tested at an instantaneous strain rate. T h e modulus of elasticity was calculated to 1 2 % strain. Thus, the surrogate cord exhibits an increase in the modulus of elasticity when tested at an instantaneous strain rate. This indicates that the intermediate and high strain rates (0.048 and 0.12s"1) chosen for the ten cords in Group 2 were not high enough to expose 80 Chapter 3 Viscoelastic Behaviour of the Spinal Cord this behaviour and thus all strain rates used previously can be considered as a quasistatic strain rate for this material. Prior to these tests, a quasistatic tensile test had been completed. An additional statistical test was performed on the results from this quasistatic test to confirm that the original modulus of elasticity for the two groups of five cords was not statistically different (Student's t-test, p>0.1). Thus the differences measured from Figure 3-6 are in fact due to different strain rates. 3.4.2 Relaxation Behaviour Fung's Quasilinear Viscoelastic Model An example of the curve fit generated from the quasilinear viscoelastic model at each strain rate is provided in Figure 3-7. Within the ten cords, there was little relaxation seen at the quasistatic and medium strain rates. In addition, the quasilinear viscoelastic model was unable to consistently include the peak stress in the cord measured at the intermediate strain rate. Quasilinear viscoelastic parameters are thus only reported for the fast and instantaneous strain rates. 81 Chapter 3 Viscoelastic Behaviour of the Spinal Cord 50 100 Time (s) • Experimental Data -Quasilnear Viscoelastic Model a) Quasistatic strain rate (0.0025s" 1) b) M e d i u m strain rate (0.048s' ) 35000 30000 25000 I 20000 \ 15000 10000 5000 • Experimental Data -Quasilnear Viscoelastic Model 35000 30000 25000 & 20000 % 15000 10000 5000 1 Experimental Data -Quasilnear Viscoelastic Model 10 20 30 40 50 c) Fast strain rate (0.12s") d) Instantaneous strain rate (0.32s") Figure 3-7 - Comparison between the experimental relaxation data and the viscoelastic model of a surrogate cord loaded at all four strain rates Table 3-2 - Quasilinear viscoelastic parameters for the relaxation test measured after an instantaneous strain (0.32s"1) to 12% strain including the means and standard deviations (SD). Cord# ti tj T 3 G, G 2 G 3 A B 76 2.130 14434.420 11341.473 393.393 11770.740 -7337.251 30863.777 0.00 78 1.713 5547.004 3962.205 27.809 807.838 -510.245 729.775 0.19 80 1.740 4443.777 3093.690 545.870 18315.962 -11376.745 18326.286 0.00 82 3.567 15952.706 7876.413 0.206 147.652 -48.232 0.000 7.99 84 10.308 11812.145 6882.529 6.213 155.012 -52.466 220.662 1.06 Mean 3.892 10438.010 6631.262 194.698 6239.441 -3864.988 10028.100 1.85 SD 3.666 5199.139 3295.372 256.908 8367.648 5216.329 14019.565 3.46 Table 3-3 - Mean quasilinear viscoelastic model parameters for the fast and instantaneous strain rates to 12% strain strain Rate (s"1) ti . V t 3 G , G 2 G 3 A B 0.12 370.454 370.530 31100774.006 -90022.035 90471.604 2947.623 123253.566 1.60E-04 0.32 1.561 12205.705 7329.219 7.306. . 92.863 . -29.474 0.442 10.05 The maximum stress in the cord and the stress decay wi th time were also determined for the surrogate cords at a l l four strain rates (Table 3-4). 82 Chapter 3 Viscoelastic Behaviour of the Spinal Cord Table 3-4 - Mean stress and stress decay for relaxation tests performed at each strain rate. Strain Rate (s") Ramp time (s) Relaxation time (s) Maximum Stress (kPa) Stress Decay Maximum error in stress predicted by the quasilinear model (kPa) 1 sec 5 sec 30 sec 60 sec 0.0025 4 7 . 9 6 6 6 0 3 1 . 4 0 1 .78% 2 . 0 7 % 2 . 8 7 % 3 . 6 0 % 3.01 0.048 2 . 6 2 3 6 0 3 2 . 9 7 8 . 0 2 % 9 . 4 8 % 1 0 . 7 7 % 1 1 . 6 6 % 2 . 7 2 0.12 1.595 6 0 3 3 . 0 4 6 . 7 7 % 8 . 6 9 % 1 0 . 6 8 % 1 0 . 5 9 % 2 . 8 4 0.32 0 . 8 2 3 0 0 3 0 . 2 0 8 . 2 0 % 9 . 9 2 % 1 1 . 1 8 % 1 7 . 2 8 % 6.91 There was a large amount of variation in the viscoelastic parameters measured at each strain rate and between strain rates, whereas the variation in the maximum stress with time and the stress decay was much lower at each strain rate. The maximum stress was also consistent between strain rates. Stress decay measured during tests performed at a quasistatic rate was significantly smaller than stress decays measured at the remaining three strain rates (p<0.0004) (Figure 3-8). There were no significant differences in the stress decay between the intermediate, high, and instantaneous strain rate relaxation tests (p>0.1). Full data tables for these results can be reviewed in Appendix C. —•—Quasistatic Rate —•— Medium Rate —A— Fast Rate Instantaneous Figure 3-8 - The mean stress decay at each strain rate through 60 seconds of relaxation. Error bars represent one standard deviation. Linear Relaxation Model As discussed above, only the fast (0.12s"1) and instantaneous (0.32s"1) strain rates provided adequate relaxation curves in order to study the relaxation behavior. The mean values of the five constants in the model (Eq.3.2) were evaluated to provide a general 83 Chapter 3 Viscoelastic Behaviour of the Spinal Cord linear model for the surrogate cords at two different strain rates, the first at 0.12s"1 and the second at 0.32s"1. Their respective models are given below. Constants determined for each surrogate cord are provided in Appendix D. Fast strain rate (0.12s1): G(t) = (1.59 ±4.53)e ( 0 6 8 ± 1 ' 2 0 ) ' + (-3.3713.69)e(-0046±0,2)' +(4.27 ±3.71) (Eq3.10) Instantaneous strain rate (0.32s"1): G(t) = (0.13 ± 0.059)e(0 2 8 ± 0 4 6 ) ' + (4.55 ± 7.06)e(000070±00015)' + (-3.64 ± 7.06) (Eq 3.11) The quality of the fit of the linear relaxation model and the quasilinear viscoelastic model was evaluated by comparing the experimental data to the results calculated through each model for G(t) and determining the coefficient of determination (R ). These results are provided in Table 3-5. Table 3-5 - Comparison between the linear and quasilinear viscoelastic model for the reduced relaxation function of QM Skin 30 at the (a) fast and (b) instantaneous strain rates. (a) R 2 - Fast Strain Rate (0.12s1) (b) R 2 - Instantaneous Strain Rate (0.32s1) Surrogate Cord # General Linear Model Quasilinear Viscoelastic Model Surrogate Cord# General Linear Model Quasilinear Viscoelastic Model 75 0.88 0.38 76 0.98 0.96 76 0.97 0.99 78 0.93 0.94 77 0.99 0.99 80 0.97 0.99 78 0.91 0.94 82 0.97 0.96 79 0.89 0.88 84 0.97 0.93. 80 0.95 0.96 81 0.95 0.97 82 0.92 0.94 83 0.93 0.47 84 0.67 0.94 The results at both strain rates indicate that there is no significant difference between the R2 values for the general linear model and the quasilinear viscoelastic model (Students t-test, p>0.4). A visual inspection would lead one to conclude that the general linear model provides a better fit with the experimental data. At the fast strain rate, the quasilinear viscoelastic model did not always capture the initial peak in the stress before relaxation 84 Chapter 3 Viscoelastic Behaviour of the Spinal Cord began. These differences can be assessed graphically by the two sample plots provided in Figure 3-9. 0.98 • 0.96 • _ 0.94 i ' 0.92 • 0.88 • 0.86 0.84 • a) Experimental Data • Selected Data * Linear Model & Quasilinear VIaeoelastic Model 0 10 20 30 40 50 6D 70 Tlme(s) "fr1"*^  •fy i:;:^ :yxi+y-y,: • Experimental Data • Selected Data a Linear Model & Quasilinear Viscoelastic Model 100 200 300 400 500 600 700 Tlmefs) b ) Figure 3-9 - Comparison between the experimental data and the models used to describe the relaxation of the surrogate cord after a load applied at a) a high strain rate (0.12s1) and b) an instantaneous strain rate (0.32s"1). Selected data represents the twenty points chosen from the experimental data to describe the relaxation behaviour. 85 Chapter 3 Viscoelastic Behaviour of the Spinal Cord 3.4.3 Creep Behaviour An example fit between the data and the creep model is provided in Figure 3-10 for each strain rate. • Experimental • Calculated 1.016 1.014 1.012 1.01 . 1.008 1.006 • Experimental i Calculated 20 40 60 80 Tlme(s) a) Quasistatic strain rate (0.0025s"1) b) Medium strain rate (0.048s"1) 1.035 1.03 1.025 1.02 S 1.015 1.01 1.005 1 j | i | H • Experimental • Calculated 1.06 1.05 1.04 1.03 1.02 1.01 • Experimental i Calculated 50 100 Time (s) 200 400 600 800 Time (s) c) Fast strain rate (0.12s"1) d) Instantaneous strain rate (0.17s" ) Figure 3-10 - Comparison between the creep data and the creep curve determined by the general linear model at four strain rates. The fit of the creep model for the quasistatic (0.0025s"1) and medium (0.048s"1) strain rates was poor. Thus, constants determined for the fast (0.12s"1) and instantaneous (0.17s"1) strain rates only will be discussed. Their respective equations for the reduced creep function are given below. The reduced creep functions (Eq. 3.10 and 3.11) for each strain rate had R 2 values greater than 0.94 and small standard deviations relative to the mean values for the constants, indicating an excellent fit with the data. Fast strain rate (0.12s1): J{t) = (-0.043 ± 0.003)e(0 0 4 ± 0 1 0 ) ' + (1.03 ± 0.002) (Eq. 3.10) 86 Chapter 3 Viscoelastic Behaviour of the Spinal Cord Instantaneous strain rate (0.17s1): J(t) = (-0.029 ± o.001)e(0004±00006)' + (-0.030 ± 0.004)e(0047±0003" + (1.05 ± 0.003) ( E q . 3.11) 3.5 Discussion A surrogate cord which behaves similarly to the in vivo spinal cord will allow for its use in place of the current experimental models which test animal spinal cords or in vitro human spinal cords. Thus it is necessary to understand its behaviour in order to be confident in results obtained through its use as a surrogate for the in vivo human spinal cord. The effect of varying the strain rate on the mechanical response of the surrogate cord and its relaxation and creep behaviour was analyzed through various tests in order to assess its biofidelity with the spinal cord. Unlike, the in vitro human spinal cord, the modulus of elasticity of the surrogate cord did not increase between strain rates of 0.0025 and 0.12s"1. However, it did increase at a strain rate of 0.8s"1. The in vitro human spinal cord was reported to have a 0.35MPa increase in the mean modulus of elasticity between strain rates of 0.068 and 0.21s"1.3 The increase in the modulus of elasticity for the surrogate cord between that measured at a quasistatic rate and 0.8s"1 is 0.028MPa if measured to 12% strain and 0.038MPa if measured to 5% strain. The magnitude of the increase in modulus of elasticity of the surrogate cord is considerably less than that for the in vitro human spinal cord. Unfortunately similar data is not available for the in vivo animal spinal cord. Perhaps the surrogate cord more closely matches the change in modulus of the in vivo cord. Considering that the modulus of elasticity of the in vitro spinal cord increases with time after death,5'16'21 its response to different strain rates may also be magnified. Further in vivo spinal cord testing could provide this answer and allow a direct comparison between the in vivo cord and the surrogate cord. The stress in the surrogate cord decays during the relaxation. This indicates that the cord experiences relaxation and is thus a viscoelastic material. The in vitro and in vivo spinal 3 5 8 9 21 cords are also viscoelastic tissues. ' ' ' ' The stress decay of the surrogate cord, when 87 Chapter 3 Viscoelastic Behaviour of the Spinal Cord held at 12% strain, is not as great as the stress decay exhibited by the in vitro rat or 2 8 human spinal cord. ' Within 30 seconds, the stress in the in vitro human cord3 decayed by 20-30% from strain rates in the range of 0.04-0.24s"'. Specific values for each strain rate were not provided in this study. The surrogate cord was strained at rates from 0.0025 to 0.32s"1 and only approached 11% stress decay after 30 seconds and 20% after 60 seconds at the highest strain rate (0.32s"1). The stress decay for the surrogate cord and the in vitro and in vivo spinal cords interpreted from the literature is compared in Figure 3-11. The stress decay of the in vitro and in vivo spinal cords is much greater than that measured in the surrogate cord. • Surrogate Cord (this study) • Rat - In Vitro (Fiford, 2005) • Human - In Vitro (Bilston, 1996) m Bovine - In Vitro (Oakland, 2003) • Feline - In Vivo (Chang, 1988) 1 5 30 60 Relaxation Time (sec) Figure 3-11 - The stress decay through 60 seconds of relaxation in the in vitro3'*'21 and in vivo5 cords and the surrogate cord. Data was chosen from tests which had an approximate strain of 9-12% applied at a strain rate of 0.2-0.3s"'. The quasilinear viscoelastic theory developed by Fung11 was used to describe the behaviour of the surrogate cord mathematically. There was considerable variation in the viscoelastic parameters measured for the surrogate cord. The quasilinear viscoelastic model is meant to fit data collected at any strain rate however, the parameters determined for the surrogate cord at varying strain rates are also not similar. This is in part due to the fact that there is no unique solution for the quasilinear viscoelastic model and that a reasonable fit with the data was not always achieved. A model for the fast and instantaneous strain rates has been provided in the format of the quasilinear viscoelastic 88 Chapter 3 Viscoelastic Behaviour of the Spinal Cord model and these can be used to compare with future experiments which test the mechanical properties of the spinal cord. Relaxation is relevant to the physiologic situation of the spinal cord when, for example, the vertebrae in the spinal column are displaced through distraction or dislocation and the spinal cord is held in constant strain. The relaxation tests which strain the surrogate cord instantaneously represent a typical test used to measure the relaxation of a material. When a viscoelastic material is stretched instantaneously, there is no displacement allowed by the viscous component until the strain is held constant. At this point, the material begins to relax and the decrease in stress can be measured. In the instantaneous strain rate tests performed in this study, both the general linear model and the quasilinear model for viscoelasticity provide adequate estimates for the material behaviour. However, the quasilinear viscoelastic model has an additional advantage because it also provides information about the initial load curve before the surrogate cord is held at constant strain and permitted to relax. The creep behaviour of the surrogate cord was measured following four different strain rates (0.0025s"1, 0.048 s"1, 0.12s"1 and 0.17s"1) to 12% strain. A general linear model was fit to the experimental data to describe only the creep portion of the experiment. Creep was most prominent after a fast (0.12s"1) or instantaneous (0.17s"1) strain rate. The presence of creep once the load in the cord was maintained is further evidence that the surrogate cord is a viscoelastic material. The analysis of the creep behaviour was 22 modeled after ligament data analysis because there is no experimental data to compare the surrogate behaviour in creep to either the in vitro or in vivo spinal cord. If creep data for the spinal cord is measured in the future, a comparison between the surrogate cord and the spinal cord will be possible with the results determined in this study. The lack in experimental data for the creep behaviour of the spinal cord is because there is no common injury mechanism which loads the spinal cord in a way that induces creep. Thus, the focus of this study has been directed further towards the relaxation behaviour of the surrogate cord and not the creep behaviour. 89 Chapter 3 Viscoelastic Behaviour of the Spinal Cord The creep tests performed at the instantaneous strain rates (0.17s"1) were difficult to control due to the immediate response necessary by the controller. In the instantaneous strain rate creep tests, the materials testing machine overshot the load by approximately 0.15N. Once the overshoot was recognized by the controller, the strain in the cord was reduced in order to correct it. The controller settings were adjusted to the most appropriate setting for each type of test before performing any experiments, however a certain amount of inaccuracy was unavoidable. In any test results where an overshoot was apparent, the creep model was determined from the data following the adjustment made by the materials testing machine. As a result, the model may underestimate the true creep behaviour since the initial strain at 4N was lost by the overshoot. The general linear model employed to describe the creep behaviour does not include the initial loading curve, nor does it take into account the strain rate or the initial strain. Thus, in order to compare similar specimens to the model determined in this study, identical testing conditions must be used. The majority of experimental data for the viscoelastic properties of the spinal cord are obtained from in vitro experimentation. One study was identified which studies the in vivo viscoelastic behaviour of the spinal cord in relaxation.5 In this study, the feline spinal cord was tested to a maximum strain rate of 0.012s"1. Stress decay at this strain rate was greater than that of the surrogate cord for strain rates of 0.0025s"1 and 0.048s"1.The surrogate cord would ideally represent the material properties of the in vivo spinal cord. The in vivo data does not span the range of strain rates measured in vitro or for the surrogate cord. Thus further in vivo data would allow for a more complete assessment of the biofidelity of the surrogate cord. Although the exact mechanical properties of the surrogate cord are not identical to those reported for the in vivo and in vitro spinal cords, the behaviour of the surrogate cord in uniaxial tension is appropriate to simulate the behaviour of the spinal cord. Both the surrogate cord and the spinal cord exhibit an increase in the modulus of elasticity as a result of an increase in the rate at which they are strained. Both cords are also viscoelastic 90 Chapter 3 Viscoelastic Behaviour of the Spinal Cord materials, displaying a decrease in stress when the strain rate is held constant, and an increase in strain in order to maintain a constant load. Additionally, for the two cords, the degree of stress decay during relaxation is a function of the strain rate, with higher strain rates inducing a greater amount of stress decay over the same relaxation period. The results provided here give viscoelastic data for an artificial spinal cord which has not been reported for previous surrogate cords. 91 Chapter 3 Viscoelastic Behaviour of the Spinal Cord 3.6 References 1. Abramowitch SD, Woo SL, Clineff TD, et al. An evaluation of the quasi-linear viscoelastic properties of the healing medial collateral ligament in a goat model. Ann Biomed Eng 2004;32:329-35. 2. Bilston LE. The Biomechanics of the Spinal Cord During Traumatic Spinal Cord Injury. Bioengineering. Pennsylvania: University of Pennsylvania, 1994:204. 3. Bilston LE, Thibault LE. The mechanical properties of the human cervical spinal cord in vitro. Ann Biomed Eng 1996;24:67-74. 4. Chang GL, Hung TK, Bleyaert A, et al. Stress-strain measurement of the spinal cord of puppies and their neurological evaluation. J Trauma 1981;21:807-10. 5. Chang GL, Hung TK, Feng WW. An in-vivo measurement and analysis of viscoelastic properties of the spinal cord of cats. J Biomech Eng 1988; 110:115-22. 6. Chen H, Fung Y. Stress-Strain-History Relations of Rabbit Mesentery in Simple Elongation. In 1973 Biomechanics Symposium, ASME Pub. No. AMD-2, American Society of Mechanical Engineers. New York, 1973:9-10. 7. Del Prete Z, Antoniucci S, Hoffman AH, et al. Viscoelastic properties of skin in Mov-13 and Tsk mice. J Biomech 2004;37:1491-7. 8. Fiford R, Bilston LE. Strain distribution and relaxation behaviour of rat spinal cord. Advances in Bioengineering, proceedings of the ASME International Mechanical Engineering Congress,. Anaheim, USA, 1998:247-8. 9. Fiford RJ, Bilston LE. The mechanical properties of rat spinal cord in vitro. J Biomech 2005;38:1509-15. 10. Fung Y. Biomechanics: Mechanical Properties of Living Tissueed: Springer-Verlag, 1981. 11. Fung Y. Biomechanics: Mechanical Properties of Living Tissues. 2nd ed: Springer-Verlag, 1993. 12. Funk JR, Hall GW, Crandall JR, et al. Linear and quasi-linear viscoelastic characterization of ankle ligaments. J Biomech Eng 2000;122:15-22. 13. Haut RC, Little RW. A constitutive equation for collagen fibers. J Biomech 1972;5:423-30. 14. Hingbrani RV, Provenzano PP, Lakes RS, et al. Nonlinear viscoelasticity in rabbit medial collateral ligament. Ann Biomed Eng 2004;32:306-12. 15. Hung TK, Chang GL. Biomechanical and neurological response of the spinal cord of a puppy to uniaxial tension. J Biomech Eng 1981;103:43-7. 16. Hung TK, Chang GL, Chang JL, et al. Stress-strain relationship and neurological sequelae of uniaxial elongation of the spinal cord of cats. Surg Neurol 1981;15:471-6. 17. Kearney PA, Ridella SA, Viano DC, et al. Interaction of contact velocity and cord compression in determining the severity of spinal cord injury. J Neurotrauma 1988;5:187-208. 18. Khatyr F, Imberdis C, Vescovo P, et al. Model of the viscoelastic behaviour of skin in vivo and study of anisotropy. Skin Res Technol 2004;10:96-103. 92 Chapter 3 Viscoelastic Behaviour of the Spinal Cord 19. Lakes RS, Vanderby R. Interrelation of creep and relaxation: a modeling approach for ligaments. J Biomech Eng 1999;121:612-5. 20. Margulies SS, Meaney DF, Bilston LB, et al. In Vivo Motion of the Human Cervical Spinal Cord in Extension and Flexion. IRCOBI Conference. Verona, Italy, 1992:213-24. 21. Oakland RJ. A Biomechanical Study of the Spinal Cord in the Burst Fracture Process. School of Mechanical Engineering. Leeds: The University of Leeds, 2003. 22. Thornton G, Oliynyk A, Frank C, et al. Ligament Creep Cannot be Predicted from Stress Relaxation at Low Stress: A Biomechanical Study of the Rabbit Medial Collateral Ligament. Journal of Orthopaedic Research 1997;15:652-6. 23. Torg JS, Corcoran TA, Thibault LE, et al. Cervical cord neurapraxia: classification, pathomechanics, morbidity, and management guidelines. J Neurosurg 1997;87:843-50. 24. Wilcox RK, Bilston LE, Barton DC, et al. Mathematical model for the viscoelastic properties of dura mater. J Orthop Sci 2003;8:432-4. 25. Woo SL, Gomez MA, Akeson WH. The time and history-dependent viscoelastic properties of the canine medical collateral ligament. J Biomech Eng 1981;103:293-8. 26. Woo SL, Johnson GA, Smith BA. Mathematical modeling of ligaments and tendons. J Biomech Eng 1993;! 15:468-73. 93 Chapter 4 Transverse Compression of the Spinal Cord Chapter 4 Transverse Compression of the Spinal Cord 4.1 Introduction 4.1.1 Traumatic Compress ion of the Spinal Cord The spinal cord is severely injured when the spine deforms beyond its normal range causing injurious motion or loads to the spinal cord or when it is subjected to highly dynamic impact loads. One common impact mode is transverse compression.16 This can occur due to burst fractures, vertebral dislocations, and injuries such as spinal stenosis. Burst fracture injuries occur when an impact applies an axial force through the spinal column. This can cause the vertebral body to fracture, inducing bone fragments from the vertebral body to propel towards the cord.21 This often injures the spinal cord due to the impact force or laceration. If one vertebra dislocates, shear and compressive forces are also imparted to the spinal cord. During and after dislocation, these forces will often exceed the injury tolerance of the spinal cord thus causing injury. Compression injuries to the cord also occur due to 18 compression which occurs slowly over time such as in spinal stenosis. Spinal stenosis is the narrowing of the spinal canal due to osteophytes, bulging of the intervertebral disc, and calcification of the ligaments. These are changes in the anatomy which do not occur from one single event such as dislocation or burst fractures, but instead there is a gradual change usually due to ageing. 4.1.2 In Vivo Transverse Compress ion In order to treat injuries correctly, use appropriate animal models to study injury, and design preventative devices, it is important that we understand the mechanical properties 9 4 Chapter 4 Transverse Compression of the Spinal Cord of the spinal cord. For loads applied to the human spinal cord in transverse compression, these properties are not known. However, in vivo animal models have been designed to measure the mechanical properties and study injury mechanisms. Although no values for its modulus of elasticity in compression have been reported, the 7 10 behaviour of the in vivo feline spinal cord has been described by Hung et al. ' In their first study, a weight was dropped onto the exposed spinal cord.7 The impact was filmed using a high speed video camera and later analyzed to measure the force of the weight using conservation of energy theory. The peak force in the spinal cord, approximately 1.271b (5.65N), occurred 3ms prior to the maximum amount of cord deformation with the dura mater and CSF present (Figure 4-1). Force-displacement curves of the impact were not provided in this study. T h. = 15cin ~l |_ I I l _ J 0 10 20 30 Time (msec) Figure 4-1 - The impact force, cord deformation, and time rate of energy (Ea) of the in vivo cat spinal cord to transverse compression with the CSF and dura mater present. Modified from Hung et al.1 The second study performed by Hung et al.10 on the in vivo feline spinal cord applied transverse compression at a quasistatic rate (0.002mm/s) using a materials testing machine. As the deformation of the cord increased, the force increased non-linearly with an increasing slope. 95 Chapter 4 Transverse Compression of the Spinal Cord In a separate study performed by Pintar et al.,15 the mechanical properties of the in vivo feline spinal cord were also measured. In this study, the mechanical properties measured for the feline spinal cord were replicated in an artificial spinal cord for the purpose of measuring the pressures in the spinal canal during a burst fracture injury. The material properties of the feline spinal cord with dura mater intact were measured using a drop-mass apparatus. A graphical representation of the stress-strain curve during impact was provided, but no quantitative values to describe the behaviour were given. Their method of measuring stress in this situation was also not reported. 4.1.3 In Vitro Transverse Compress ion In addition to transverse compression properties reported for the in vivo spinal cord, these properties have also been tested in vitro. The specimens obtained to validate the surrogate cord behaviour in a companion study to the present work were in vitro bovine spinal cords.12 It was thus important to review what is known about the occlusion behaviour of the in vitro spinal cord. The occlusion profile of the in vitro bovine spinal cord in transverse compression was measured by Oakland.14 A burst fracture injury was simulated by propelling a mock bone fragment towards the vertical spinal cord at 2.5, 5, and 7.5 m/s. High speed video recorded the impact and these images were used to measure the occlusion of the spinal cord tissue (Figure 4-2). As the bone fragment impacted the spinal cord, its speed decreased and at maximum occlusion it changed direction and the force in the cord decreased. 9 6 Chapter 4 Transverse Compression of the Spinal Cord 6 S 3 o . . * — - - - , • . • • • • • Experimental data from Group 6 • Finite element model (Wilcox, 2002) -0 1 4 6 8 10 Time (ms) Figure 4-2 - The occlusion profile of the in vitro bovine spinal cord in transverse compression.14 The test was performed at 5.0m/s with a posterior longitudinal ligament posterior to the spinal cord. 4.1.4 Effect of the Dura Mater and C S F In vivo animal models have also been designed to measure the mechanical properties and study injury mechanisms with and without the dura mater and cerebrospinal fluid (CSF) under quasistatic and dynamic compressive loads.7,10 An understanding of these properties is important in order to assess the biofidelity of the surrogate spinal cord in transverse compression and determine whether it is necessary to incorporate the CSF and dura mater into the surrogate cord. In their first transverse compression study, Hung et al.1 performed an impact to the spinal cord after the CSF had been drained from inside the dura mater. It was observed that the force-deformation curves of the cord with CSF and that without were similar. However, the relative deformation (maximum compression divided by the original diameter) increased once the CSF was removed. In another study which tested the response of the spinal cord to transverse compression at a constant strain rate, the response of the spinal cord with dura mater was compared to its response without.10 Spinal cords with the dura mater present exhibited a linearly elastic behaviour, whereas those without the dura mater behaved nonlinearly (Figure 4-3a). 97 Chapter 4 Transverse Compression of the Spinal Cord X(mm) a) b) Figure 4-3 - a) Force-displacement with and without the dura mater present and b) stress-strain response of the in vivo feline spinal cord without the dura mater under quasistatic transverse compression. Modified from Wmigetal.™ The modulus of elasticity for feline spinal cords with the dura mater intact as well as with the dura mater removed only from the area of contact between the loading rod and the spinal cord (as opposed to being removed from the entire surrounding area) was given graphically (Figure 4-4). The initial modulus of elasticity in compression to approximately 15% strain for the in vivo feline spinal cord with dura mater intact was approximately 0.0045 MPa (4.5xl04 dyne/cm2) and for the cord with the dura removed locally, it was approximately 0.002 MPa (2x104 dyne/cm2). Similar results were reported 17 by Sparrey for the in vivo rat spinal cord with the dura mater intact. In her tests, an indenter was also used to compress the cord. One millimeter compressions were performed at 3 and 300mm/s. The modulus of elasticity was calculated using a method developed by Zhang et al?2 which accounts for the diameter of the indenter as well as the friction between the indenter and the tissue. A finite element model5 was also used to determine the modulus of elasticity. The finite element results are limited by the fact that it used a linear elastic model and the spinal cord is in fact a non-linear material in compression.7,10 However both methods provided equivalent results. The modulus of elasticity calculated at 3mm/s was 76kPa and 299kPa at 300mm/s. A second figure of the stress and strain measured in the feline spinal cord was also provided by Hung et al.,10 depicting the response of the cord to higher strains (approximately 80%) (Figure 4-3b). Interpretation of this data provides a modulus of 98 Chapter 4 Transverse Compression of the Spinal Cord elasticity of approximately 0.28MPa in the linear region of the curve. It is suspected that the plot reporting the modulus of elasticity with strain is underestimating the elastic modulus of the in vivo cat spinal cord. This may be because the stress is dependent on the initial position of the indenter with respect to the spinal cord. If the indenter is not in full contact with the spinal cord then the tissue directly beneath the indenter is not being completely compressed. For this reason, the interpreted modulus of elasticity from the linear slope of the stress-strain curve is considered as the modulus of elasticity of the in vivo cat spinal cord for purposes of comparison in this work. It is also important to note that the methods used to derive the stress and strain are based on straightforward uniaxial stress and strain equations which simplify the stresses and strains in compression of a cylinder. These equations also do not take into account the friction effects between the indenter and the spinal cord. Thus, 0.28MPa is a rough approximation for the modulus of elasticity in compression of the in vivo feline spinal cord. This compressive modulus is close to the modulus of elasticity in quasistatic tension (0.260MPa) for the in vivo feline spinal cord without dura mater.9 20 15 10 E(kPa) g 4 3 2 1 1 : — 1 r --CAT 17 1 9 , ; • i 0.1 0.2 X/D 0.3 0.4 Figure 4-4 - The modulus of elasticity of the in vivo feline spinal cord with (cat 17) and without (cat 19) the dura mater intact. Modified from Hung et al. Oakland tested the response of the in vitro bovine spinal cord in transverse compression at impact speeds with and without the dura mater present. Results indicated that the presence of the dura mater had no significant affect on the occlusion of the spinal cord. Identical burst fracture simulations were not performed with the CSF present to determine differences due to its presence in the spinal cord construct. Thus it appears as 99 Chapter 4 Transverse Compression of the Spinal Cord though the in vitro cord behaviour in transverse compression does not change with the presence of the dura mater, similar to the in vivo results observed by Hung et al.7 for a feline cord with CSF and dura and one without. 4.1.5 Transverse Compress ion of the Surrogate Cord Pintar et a/.'s15 study which was discussed in section 4.1.2 measured the transverse compression of the in vivo feline spinal cord by a dropped mass. Identical testing methods were used to measure the response of a range of collagen-encased gelatin spinal cords (Figure 4-5). The final gelatin cord, which exhibited a response that fell within the range of responses measured for the feline spinal cord, was equipped with piezoelectric pressure sensors along its anterior surface and inserted into a cadaveric head-neck. 125-• , .i.fjf li,; /[•i^y.i , i . . f f e . : ; . : .•.:;-;?[•?;•:• 100-] .. Strain (% Compression) Figure 4-5 - Stress strain relationship of the in vivo feline spinal cord (represented by the shaded area) and three different ratios of gelatin and water spinal cords (represented by the three curves)15 A burst fracture injury was produced to confirm the pressure sensor capabilities and the ability of the model to discern levels of impact applied to the instrumented spinal cord. Although the sensor was able to measure different pressures along the cord, no information is provided to validate that the artificial cord behaves similar to the feline spinal cord after being instrumented with the electronic pressure sensors. 100 Chapter 4 Transverse Compression of the Spinal Cord 4.1.6 A n Improved Surrogate Cord The surrogate cords developed by Pintar et al. and Bilston et al. were both subjected to transverse compression. Pintar et al. validated their surrogate cord against in vivo spinal cord responses to transverse compression but did not evaluate the behaviour of the surrogate cord in tension. The effects of the dura and CSF were incorporated into the cord by validating it against a spinal cord tested with the dura and CSF present. Bilston et al.'s surrogate cord was only validated in tension and thus cannot be used in transverse compression to represent the in vivo spinal cord. None of the studies testing the spinal cord in transverse compression reported results for a compression test applied to the bare cord, a cord with only the dura mater present, and a cord with both the dura mater and CSF present, all in one study. Thus a complete understanding of the effects of the dura and CSF on the compression properties of the spinal cord cannot be drawn from these results. This may be very important since it is logical to assume a highly viscous layer such as CSF would significantly affect the mechanical response of the spinal cord during high-energy impacts. These differences are important because the in vivo spinal cord is compressed with the dura mater and CSF between the bare cord and the imposing structure. It is therefore necessary that we understand these differences in behaviour and if any differences exist, that the true in vivo behaviour be incorporated into the surrogate cord. 4.2 Objectives In order to assess the biofidelity of the surrogate cord in transverse compression, several experiments were performed to measure the modulus of elasticity, the force-displacement behaviour, and the effects of CSF and dura mater on the impact behaviour. The modulus of elasticity of four rectangular specimens of QM Skin 30 in compression at a quasistatic strain rate was measured to compare to that reported for the in vivo feline spinal cord.10 A characterization of the force-displacement behaviour of the surrogate cord in transverse compression was measured. This was performed by compressing the surrogate cords between two plates at a quasistatic and intermediate strain rate. The behaviour of the 101 Chapter 4 Transverse Compression of the Spinal Cord surrogate cord in impact was compared to that of the in vitro bovine spinal cord by simulating the burst fracture injury. The force-time profiles of these two cords were compared. The impacts were repeated with the CSF and dura mater surrounding the surrogate cord and these results compared to similar tests performed on the bovine spinal cord with CSF and dura mater. 4.3 Materials and Methods 4.3.1 Surrogate Cord Specimens Twenty-four surrogate cords were manufactured from QM Skin 30 as described in section 2.4.2. These cords were grouped into two different experimental protocols. Ten surrogate cords were tested under transverse compression at two constant strain rates (Group 3) and another fourteen were tested under transverse impact using a projectile (Group 1). The diameter of the cords produced for the burst fracture impacts, was chosen to match the diameter of the bovine spinal cord and fit inside its dura mater.14 4.3.2 Rectangular Spec imens QM Skin 30 was mixed in a ratio of 10:1.2 to produce four rectangular samples of the material with average dimensions of 40.8mm long, 26.2mm wide, and 11mm high (see Appendix E for full details). The mixing and vacuum process was identical to that used to produce the surrogate cords. 4.3.3 Rectangular Specimen Compress ion Tests Each rectangular specimen of QM Skin 30 was compressed three times with a minimum of 24 hours between each test. Quasistatic compression (0.0025s"1) was applied between two horizontal plates lubricated with Vaseline. Both plates were larger than the specimen. Vaseline was used to remove any surface friction due to the high contact surface area of the rectangular specimen. A load limit of 30N was used to halt the compression of the 102 Chapter 4 Transverse Compression of the Spinal Cord specimens. This resulted in approximately 15 ± 6% strain. The plate was then lifted off of the sample. Force and displacement data was used to measure the compressive modulus of elasticity of QM Skin 30. 4.3.4 Quasistatic and Intermediate Rate Testing Anticipating that this surrogate cord will be used to study a variety of compression injuries, three strain rates were chosen to quantify its behaviour. The first strain rate, quasistatic (0.0025s"1), is associated with non-instantaneous injuries such as spinal stenosis. Impact fragment velocities have been measured to be in the range of 3 to 5m/s 20 based on experimental burst fracture injuries performed by Wilcox. Therefore, the fastest impact velocities (approximately 3.9 to 5.0m/s) were chosen to match these results. The intermediate strain rate, 8s"1, approximates an injury which compresses the cord at a rate between the abovementioned injuries. A total of ten surrogate cords (from Group 3) were used to measure the elastic behaviour in transverse compression at strain rates of 0.0025s"1 and 8s"1. Each cord was tested three times at a quasistatic rate (0.0025s"1) and twice at the intermediate strain rate (8s"1). The initial quasistatic tests were used to measure the previously unstressed behaviour, while the following two quasistatic tests and the second tests at 8s"1 determined if the material behaviour was stable. 103 Chapter 4 Transverse Compression of the Spinal Cord Figure 4-6 - Transverse compression of the surrogate spinal cord at 0.025s"1 and 8s"1". The surrogate cord was clamped to a horizontal flat plate beneath the linear actuator on the materials testing machine (Figure 4-6). Transverse compression was applied by a second horizontal plate. Both plates were larger than the specimens, and the top compressed 32mm of the length of the cord. Before each test began, the top plate was positioned in contact with the top surface of the surrogate cord. Compression was applied to 50% strain or until the load exceeded 30N (approximately 71bs). Once either of these limits was reached, the plate was lifted off of the surrogate cord. The loads were measured by a 44.5N load cell (LCFA-10, Omega Engineering Inc.) with a non linearity of ±0.01% of full scale measured by the manufacturer (September, 2005) (Figure 4-7). The non-linearity and repeatability of measured loads was also confirmed by the author (Appendix F). Before each testing Figure 4-7-LCFA-10 Load Cell 104 Chapter 4 Transverse Compression of the Spinal Cord sequence, the load cell's accuracy was verified using a 0.454kg weight. A linear potentiometer (3541H-1-102, Bourns) was connected to a wire sensor (WPS-750-MK30-P, Micro-Epsilon) and used to measure the displacement of the linear actuator (Figure 4-8). The displacement and accuracy were measured with reference to the displacement measured by a dial gauge (Appendix A). It was determined that it operates at 0.0148V/mm and 0.12% accuracy. Programs in Galil 2.3 (Galil Motion Control) were written to control the custom materials testing machine. The voltages output by the load cell and linear potentiometer were recorded by LabView 7.1 (National Instruments) and analyzed in Excel 2002 (Microsoft Corporation). Additional testing equipment information is discussed in Chapter 2. Figure 4-8-3541H-1-102 Linear 4.3.5 Impact Testing Clamping Apparatus For impact testing, unique cryogenic clamps (Figure 4-9) designed by Oakland14 were used to suspend the surrogate cord in a tensile testing machine (AGS-lOkNJ Autograph, Shimadzu). Surrogate cords were inserted 15mm and secured in place. The clamp was filled with dry ice to capacity. The lid was then placed on the clamp. Lock nuts were used to hold the lid on. The dry ice froze the surrogate cord, thus preventing it from pulling out of the clamp. The temperature gradient along the length of the surrogate cord was measured to ensure that the location of impact was not cooled by the dry ice. A separate surrogate cord, one not tested in transverse compression, was used for this purpose. A thermocouple was used to measure the internal and surface temperatures in Figure 4-9 - Cryogenic clamp designed by Oakland14 with 15mm of the surrogate cord inside the clamp. 105 Chapter 4 Transverse Compression of the Spinal Cord 10mm increments before and after it was mounted into the cryogenic clamps. The temperature gradient measured before being placed inside the clamps was constant with a mean temperature of 21.4 ± 0.23°C (surface temperature). The maximum surface temperature once it was inserted into the clamps was 17.9°C. Approximately 20mm away from the clamps at either end, the external temperature was 17.5 ± 0.57°C. The standard deviations increase to 2°C if the measurements are taken within 10mm away from the clamps. Thus, the temperature gradient was considered stable at a distance of 20mm away from the clamps. Thus all testing occurred mid-length of the surrogate cord where the temperature was not highly affected by the cryogenic clamps. Full details are included in Appendix G. Burst Fracture Simulation Figure 4-10 - Mock bone fragment In order to simulate a burst fracture a mock bone fragment was propelled towards the surrogate cord. The bone fragment was made of Tufnol (Grade 2F/3/PTFE, Tufnol Ltd.) and designed by Oakland14 to simulate the properties of bone fragments determined by Wilcox19 (Figure 4-10). It had am impact face with a radius of 10mm. Thin dark lines were drawn around the perimeter of the impact fragment. This was done to ensure that a consistent marker on the bone fragment would be chosen between images during image analysis. Propulsion of the bone fragment was generated by an impact from a linear actuator (16mm-M134, ASCO/Joucomatic Ltd., W. Midlands, UK) which was controlled by a pressure regulator (ASCO/Joucomatic Ltd., W. Midlands, UK). The pressure was calibrated to generate bone fragment velocities in the range of 3-5m/s (Appendix H). Figure 4-11 depicts the arrangement of the pressure cylinder, the Perspex cylinder, and the bone fragment.14 106 Chapter 4 Transverse Compression of the Spinal Cord The surrogate cords were fastened in the cryogenic clamps which were then mounted into the tensile testing machine (Figure 4-12). This held the surrogate cord vertically in front of the Perspex cylinder. With the specimen relaxed, the load was zeroed and the strain measured. The strain was then increased at 5mm/min to 5% strain (based on initial length) to ensure that the cord was not in compression or slack. This also served as a method to make certain that each specimen was loaded equally, thus minimizing differences in the results between specimens. A flat rigid posterior surface was placed behind the surrogate cord to mimic the rigid posterior surface of the spinal canal. The direction of propulsion of the bone fragment was positioned perpendicular to the posterior surface. The high speed video camera was then aligned with the sagittal plane of the surrogate cord to record the impact. A ruler was attached below the Perspex cylinder to allow for measurement of the cord deformation during image analysis. 107 Chapter 4 Transverse Compression of the Spinal Cord Image Analysis The compression tests were recorded using a Kodak EktaPro high speed video camera at a frame rate of 4500frames/sec (0.22ms/frame) (Figure 4-13). The images were stored on a personal computer. A Matlab 6.5.0 (MathWorks) program11 was used to digitize key parameters such as the diameter of the cord, as well as the trajectory of the bone fragment (Appendix I). This data was imported into Excel 2002 (Microsoft Corporation) for data analysis. 108 Chapter 4 Transverse Compression of the Spinal Cord Bone Fragment Figure 4-13 - High speed video image of the impact on a bare surrogate cord. The digitization program returned the horizontal coordinates for the parameters measured. Each set of data was calibrated against the ruler in the image to determine the number of millimeters per pixel (approximately 0.4mm/pixel). Digitization points were picked by the user with a visual set of crosshairs. The accuracy of choosing the points was limited by the clarity of the images and the user. High intensity lights were used to increase the contrast of the black and white images, however this did not produce a perfectly clear image for each test. Therefore, in some cases the user had to use their best judgment to pick the location of the bone fragment, the edge of the cord, etc. Repeatability of measuring the velocity by tracking the motion of the bone fragment through three images was performed between Ms. Claire Jones and the author on the same images. Both users were within 0.02m/s of the other's measurements and each user had a standard deviation of 0.07m/s. The occlusion profile of the surrogate cord was measured by the motion of the bone fragment through time. Constants for a fifth order polynomial were determined for each 109 Chapter 4 Transverse Compression of the Spinal Cord impact test (Figure 4-14). This was then used to calculate the parameters used to quantify the injury; the maximum occlusion of the cord, the time to maximum occlusion, and the length of time that the bone fragment compressed the cord more than of 75% and more than 95% of maximum occlusion. -0.001 ! 0.001 I 0 .003 0 .005 0 .007 I t Time (sec) : *""»• tTime to Maximum Oz Figure 4-14 - Occlusion profile for the surrogate cord with dura mater and an impact velocity of 4.12m/s. The velocity, acceleration, and impact force of the bone fragment were also calculated to describe the occlusion of the surrogate cord and bovine cords. Impulse and momentum theory was used to make these measurements (Eq. 4.1). These were determined from a 41' order polynomial describing the occlusion response of the cord. Orginally, a 5l order polynomial was used due to a higher R2 value, however through double differentiation to obtain the acceleration profile, this polynomial results in inaccurate accelerations. The 4 order polynomial provided a clearer acceleration profile and maintained an R2 value above 0.98. Thus, velocity (v) and acceleration were measured by differentiating the 4th order polynomial calculated to describe the displacement of the impact fragment. Eq. 4.1 was evaluated to solve for the force (F). mv{ - JFdt + mv2 (Eq. 4.1) The force-time curve was plotted and an appropriate polynomial calculated to describe the behaviour. 110 Chapter 4 Transverse Compression of the Spinal Cord Testing with CSF and Dura Mater To incorporate the CSF and dura mater into testing with the surrogate cord, additional bovine spinal cord specimens were obtained. The dura mater was carefully removed and the surrogate cord was inserted in place of the bovine spinal cord (Figure 4-15). Each end of the dura mater was glued to the end of the surrogate cord using a cyanoacrylate glue. The cords were then inserted into the cryogenic clamps which also ensured that the dura mater was plugged at either end of the surrogate cord. a) b) Figure 4-15 - a) Bovine spinal cord with the dura mater removed from the end, b) Surrogate cord inserted into the dura mater (right end). Saline solution (0.85%) is a substitute for cerebrospinal fluid (CSF) in laboratory experiments and has been used in experiments such as the burst fracture injury conducted by Oakland on in vitro bovine spinal cords.14 Benefits of using saline solution include that it has an equivalent viscosity and density to that for in vivo CSF1 and it thus mimics the in vivo conditions of the fluid surrounding the spinal cord. Cerebrospinal fluid (CSF) was not available for these tests, thus an isotonic saline solution (0.85%) was used which will be referred to as the CSF from here on. The methods described earlier to mount and impact the bare surrogate cord were also used for these specimens. Each specimen was originally mounted with the dura mater surrounding the bare spinal cord. The first test required the presence of CSF in the dura mater. Absolute sealing of the dura was unattainable, however major holes in the dura mater were repaired with a cyanoacrylate glue before the cord was mounted in the clamps. Allowing for the CSF to partially leak ensured atmospheric pressure in the CSF 111 Chapter 4 Transverse Compression of the Spinal Cord which has been confirmed as atmospheric in the in vivo feline spinal fluid.7 Before and during the injury, a syringe was used to insert saline solution between the dura mater and the bare spinal cord. This was injected into the subarachnoid space continuously throughout the test to ensure that the subarachnoid space was always filled with CSF despite the small leaks in the dura mater. Video images confirmed the presence of the CSF by observing the change in diameter of the spinal cord construct. Subsequent to the CSF/dura test, the CSF was drained and the dura mater left intact. No adjustment to the pretension in the cord was made between these tests. Another burst fracture injury was simulated and filmed. Next, the dura mater was cut away from the spinal cord to expose the bare cord. A final burst fracture injury was performed, concluding the testing for each cord. Thus three consecutive injuries were imposed upon each cord. Because testing was performed with and without the dura mater on a single specimen, one additional bare surrogate and one additional bare bovine cord were exposed to multiple consecutive impacts. From these results, the maximum number of tests applied to the spinal cords before their response became significantly different could be determined. These tests confirmed that three tests on the bovine and surrogate cords did not produce any large change in the impact response (Table 4-1). Thus any significant differences present in the data would indicate a change in response due to the presence (or lack of presence) of the dura mater and CSF instead of occurring as a result of multiple testing on the same specimen. Table 4-1 - The change in the transverse impact response across three repeated tests. Bovine was taken from Jones.12 Surrogate Bovine Mean Standard Deviation Mean Standard Deviation Maximum Occlusion (mm) 4.17 0.29 3.79 0.44 Time to Maximum Occlusion (s) 0.001481 0.000257 Not provided Not provided Duration of Maximum Occlusion (s) 0.000593 0.000128 Not provided Not provided 112 Chapter 4 Transverse Compression of the Spinal Cord Statistical Analysis Where there was only a single test between two groups to assess, a Student's t-test was performed to evaluate statistically significant differences. Statistical analyses to observe significant differences between specimen conditions were performed in StatistiCa 5.1 (StatSoft Inc.). Data was checked for normal distribution and homogeneity of variance (ie. sphericity) using Mauchly's sphericity test. If the data was normally distributed and homogeneous, a repeated measures ANOVA and Student-Newman-Keuls (SNK) post-hoc comparison was performed to determine significant differences. A p-value less than 0.05 was considered significant. Non-normally distributed or non-homogenous data was evaluated first by the Friedman test to obtain the sum of ranks. These values were then used to calculate a corrected SNK value (q). The SNK value for an infinite number of degrees of freedom and a=0.05 was then compared to q in order to determine significant differences.4 4.4 Results AAA Rectangular Spec imens in Compress ion Four specimens of QM Skin 30 were tested three times to measure the stress-strain response of this material in compression. A typical stress-strain curve is plotted in Figure 4-16. The steepest portion of the curve was used to calculate the modulus of elasticity, thus ensuring that the specimen was in full contact in compression. The mean value for the modulus of elasticity across all tests was 0.196 ± 0.025MPa measured to approximately 15% strain (Table 4-2). 113 Chapter 4 Transverse Compression of the Spinal Cord 25000 | 20000— -15000— j|f" E = 0.211 MPa —toooo— —5000— .0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Strain Figure 4-16 - Stress-strain curve for Specimen #1 in compression. Table 4-2 - Mean strain and modulus of elasticity (E) values for the entire set of compression tests performed on rectangular specimens of QM Skin 30. Strain E (MPa) Mean 15.84% 0.196 Minimum 11.83% 0.166 Maximum 20.07% 0.242 Standard Deviation 2.57% 0.025 There were no significant differences measured among the three sets of tests performed on all four specimens (repeated measures ANOVA, p=0.22). Also, no trends were observed in the moduli due to consecutive testing (Figure 4-17). In all but one specimen, the modulus of elasticity measured from the initial test was the greatest. 114 Chapter 4 Transverse Compression of the Spinal Cord 250000 -, Specimen 1 - o - Specimen 2 Specimen 3 •X Specimen 4 160000 150000 2 3 Compress ion T e s t * Figure 4-17 - Modulus of elasticity of each specimen measured through three consecutive compression tests. 4.4.2 Surrogate C o r d s in Transverse Compress ion - Quasistatic and Intermediate Strain Rates For all surrogate cords tested in transverse compression applied at a quasistatic and intermediate strain rate (0.0025s"1 and 8s"1), the compressive force increased with compression (Figure 4-18 and Figure 4-19). With an increase in strain rate from quasistatic (0.0025s"1) to intermediate (8s"1), the compressive force at a given displacement increased. Figure 4-20 depicts this trend for the average force curves calculated among the surrogate cords at both strain rates. This trend was also evident among each individual cord (Appendix J). Quasistatic responses were described with a 3 r d order polynomial, while medium rate responses had a higher degree of linearity and were described with a 2nd order polynomial. 115 Chapter 4 Transverse Compression of the Spinal Cord Compression (mm) -Average Response 1 SD Figure 4-18 - Average force-displacement response of the surrogate cord in quasistatic transverse compression (0.0025s1). — Average Response . 1 SD Compression (mm) Figure 4-19 - Average force-displacement response of the surrogate cord in transverse compression applied at an intermediate strain rate (8s1). 116 Chapter 4 Transverse Compression of the Spinal Cord Compression (mm) •Quasistatic Test 1 -Quasistatic Test 2 - - • Quasistatic Test 3 * Intermediate Rate Test 1 x Intermediate Rate Test 2 Figure 4-20 - Average force-displacement curves for surrogate cords tested at a quasistatic and medium strain rate. The tests are listed in the order that they were performed. The stiffness curves for each transverse compression test were also calculated. In al l tests, the stiffness o f the surrogate cord (secant slope o f the force-displacement curve) increased with further compression. The stiffness was non-linear for the quasistatic compression, whereas linear for medium rate compression tests (Appendix K ) . 4.4.3 Transverse Compress ion Impact Tests Surrogate Cord The motion o f the bone fragment was traced through the high speed video images to measure the occlusion o f the surrogate cord during the impact. A set o f images describing the impact from the moment o f contact to the end o f the rebound are provided in Figure 4-21. 117 Chapter 4 Transverse Compression of the Spinal Cord A-Oms B-0.667ms C - 2.444ms D - 3.556ms E - 5.778ms Figure 4-21 - Dynamic occlusion images of a surrogate cord with dura mater and CSF through time. Image C represents the maximum occlusion. Typical displacement, velocity, acceleration, and force profiles of the impact between the bone fragment and the bare surrogate cord are provided in Figure 4-22. The impact velocity at / = Oms ranged between 3.9 and 5.0m/s. f 35 f 3 l 2 a is 1 a) IjS I 1.5 2 2.5 3 3.5 4 4.5 -3 Time (ms) 0.5 1 1.5 2 \ _ 2.5 3 3.5 4 4 5 b) 20 00 1500 1C00 — 500 I o I -500 15 -1000 < -1500 -2000 •2500 -3000 0.5 1 1.5 2 2.5 3 / 3 . 5 4 4.5 ~ 0.5 1 1.5 2 2.5 3 / 3 . 5 C ) d ) Figure 4-22 - a) Displacement, b) velocity, c) acceleration, and d) force profiles of the bone fragment during impact with the surrogate cord. Compressive forces were assigned negative values. The average response is an initial increase in force followed by a decrease with time (Figure 4-23). This was true for 8 of 118 Chapter 4 Transverse Compression of the Spinal Cord the 14 cords, however the remaining six demonstrated an immediate deceleration of the bone fragment upon contact with the surrogate cord. This is an artifact of the frame rate of the high speed video camera. If the impact occurred within the 0.22ms time between frames, the initial contact would not be captured. The initial acceleration would thus not correspond with the instant of contact between the cord and the bone fragment. If the initial acceleration had been captured, it would be expected that it would be increasing from Om/s2 (the acceleration before contact). The force with which the bone fragment impacted these surrogate cords is much greater for a given displacement than the force experienced at the quasistatic and medium strain rates. Time (ms) Figure 4-23 - Variation in the force response of the surrogate cord in transverse compression. Bovine Spinal Cord The compression response of the bovine spinal cord to an impact force was also measured. Similar methods to calculate the velocity, acceleration, and force response were used to plot its behaviour through time (Figure 4-24). The bovine spinal cord also demonstrated a high degree of variability among cords in their response to the impact of the bone fragment (Figure 4-25). 119 Chapter 4 Transverse Compression of the Spinal Cord c) d) Figure 4-24 - a) Displacement, b) velocity, c) acceleration, and d) force of the bone fragment during impact with the bovine spinal cord. Time (ms) Figure 4-25 - Variation in the force response of the bovine spinal cord in transverse compression. 1 2 0 Chapter 4 Transverse Compression of the Spinal Cord Effect of CSF and Dura Mater on Cord Occlusion Maximum Occlusion With the addition of the CSF and dura to the bare surrogate cord, the maximum occlusion increased (Figure 4-26). A closer look at the trends between individual specimens (Figure 4-27 and Figure 4-28) reveals that not all specimens have a trend in occlusion similar to that for the means. Significant differences were observed between the cord with CSF/Dura and Dura as well as between CSF/Dura and Bare (p<0.05). E E, c o '(/) _3 O o O E E x C S F _ D U R A B A R E - |- Min-Max CD 25%-75% n Median Value Figure 4-26 - Mean maximum occlusion for the surrogate cord across the three specimen conditions. Significant differences are indicated with an * (p<0.05). 121 Chapter 4 Transverse Compression of the Spinal Cord Cord 4 7 CSF/Dura Dura Bare JD TLQQ2 0.004 DJ)06 Time (s) Figure 4-27 - Occlusion profiles for all three specimen conditions of a surrogate cord. 7.00 In n_ • CSF • Dura • Bare 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Specimen Figure 4-28 -Maximum occlusions for each individual surrogate cords and specimen condition. Time to Maximum Occlusion The time to maximum occlusion increased with the addition of CSF and dura mater to the bare surrogate cord (Figure 4-29). Among most specimens, this was also the case, however Figure 4-30 shows that this was not always true. Significant differences in the time to maximum occlusion were seen across all specimen conditions except between the surrogate cord with CSF/Dura and Dura (p<0.05). 122 Chapter 4 Transverse Compression of the Spinal Cord 0.0026 0.0024 O o O 0.0020 E 0.0018 ro 0.0016 O 0.0014 +-» 0) E 0.0012 Y— 0.0010 C S F D U R A D U R A - T - Min-Max • 25%-75% n Median Value Figure 4-29 - Mean time to maximum occlusion for the surrogate cord across the three specimen conditions. Significant differences are indicated with an * (p<0.05). 0.003 § 0.0025 '35 3 o o O 0.002 0.0015 | 0.001 3 ® 0.0005 E • CSF • Dura • Bare 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Specimen Figure 4-30 - Mean time to maximum occlusions for individual surrogate cords and specimen condition. 123 Chapter 4 Transverse Compression of the Spinal Cord Duration of Maximum Occlusion Similar to the other parameters measured, the duration of maximum occlusion increased with dura and CSF present for both the top 5% and 25% of maximum occlusion measures (Figure 4-31). Individual within specimen differences for the duration of maximum occlusion at 5% is provided in Figure 4-32. Statistical differences were observed between all specimen conditions for both the top 5% and 25% of maximum occlusion (p<0.05). 0.0017 != ^ 0.0015 I " (0 t> 0.0013 "5 lO o o c w o .2 CO <J 3 O Q !=! 0.0011 0.0005 CSF_DURA DURA ~ i - Min-Max .CD 25%-75% ° Median Value Figure 4-31 - Mean duration of maximum occlusion (5%) for the surrogate cord across the three specimen conditions. Significant differences are indicated with an * (p<0.05). 124 Chapter 4 Transverse Compression of the Spinal Cord 0.0016 £ 0.0014 3 .1 0.0012 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Specimen Figure 4-32 - Mean duration of maximum occlusions (5%) for individual surrogate cords and specimen condition. Effect of Velocity and Diameter on Cord Occlusion Impact tests were performed with bovine dura mater and CSF surrounding the surrogate cord. Incorporating the dura mater and CSF with the surrogate cord changes its diameter. In order to investigate possible sources for compounding differences among the cord conditions due to factors other than the presence of the dura mater and CSF, a statistical analysis was performed with respect to fragment velocity and cord diameter. First, the fragment velocity was considered. The velocity of the mock bone fragment was determined through position and time analysis of its motion measured from the video images. The mean velocity for the bone fragment during the surrogate cord tests was 4.47m/s, with minimum and maximum values of 3.93m/s and 5.03m/s respectively. The velocity of the bone fragment affects the amount of energy with which it impacts the cord. The relationship between the velocity and the specimen condition was plotted (Figure 4-33). No significant differences were observed between specimen conditions (p=0.53). Thus no correction was made based on the velocity of the fragment. 125 Chapter 4 Transverse Compression of the Spinal Cord 5 T 4.8 -m/s] 4.6 -& 4.4 -u o 4.2 -> 4 -3.8 -CSF/Dura Dura Specimen Condition Bare Figure 4-33 - Mean velocity of each specimen condition for the surrogate cords. The second source considered as the cause for differences in occlusion was the difference in cord diameters. Correlations between the maximum occlusion and the cord diameter for each specimen condition were evaluated. Scatter plots were used to visualize this relationship (an example is given in Figure 4-34). Pearson correlation coefficients for all measured parameters were calculated and fell in the range of 0.251 to 0.581 indicating a non-existent or weak correlation between these parameters and cord diameter. Thus no corrections were made to the data. 126 Chapter 4 Transverse Compression of the Spinal Cord | 5.5 .2 5 in I 4.5 O to 3.5 S 2.5 2 10 12 14 16 Cord Diameter (mm) • CSF/Dura « Dura Bare Linear (CSF/Dura) Linear (Dura) Linear (Bare) CSF/Dura R2 = 0.0631 Dura R2 = 0.3381 Bare R2 = 0.1009 Figure 4-34 - The relationship between maximum occlusion and original construct diameter for each surrogate cord condition The analysis of the bovine spinal cord specimens was performed through collaborative work with Claire Jones at the University of Leeds. Claire performed the in vitro bovine spinal cord testing. In her analysis, she also noted that there were no effects on the occlusion parameters due to the velocity and the diameter of the spinal cords.12 4.5 Discussion 4.5.1 The Modulus of Elasticity in Compress ion Four rectangular specimens were compressed to measure the compressive modulus of elasticity of QM Skin 30. The mixture used to make the rectangular specimens was also used to make surrogate cord numbers 79 to 84 whose mean modulus of elasticity in tension was 0.185 ± 0.006MPa at 12% strain and 0.202 ± 0.009MPa at 5% strain (refer to Chapter 2). Recall that the mean value for all rectangular specimens and tests was 0.196 ± 0.024MPa to approximately 15% strain. Thus the modulus of elasticity for QM Skin 30 was similar in tension and compression. There was a variation in the modulus of elasticity of each specimen through multiple testing (Figure 4-17). However, there was no 127 Chapter 4 Transverse Compression of the Spinal Cord consistent pattern in this change among the specimens. This could in part be due to different ambient conditions or errors such as inconsistency in placing the plate fully in contact with the specimen before testing. The modulus of elasticity measured by Sparrey17 for the in vivo rat spinal cord in compression applied at 300mm/s was 0.299MPa whereas that for 3mm/s was 0.076MPa. The modulus of elasticity up to 80% strain for the in vivo feline spinal cord reported by Hung et al.{0 was interpreted from graphical results to be approximately 0.28MPa. This could be an overestimation of the modulus of elasticity due to an. indentation technique which induces friction and high stresses at the location of the indenter, as well as due to simplistic calculations for the stress and strain. However, the values reported previously for the in vivo spinal cord10'17 compare well with the modulus of elasticity of QM Skin 30 measured in compression with a difference of approximately 0.1 MPa. Thus, QM Skin 30 approximates the modulus of elasticity of the in vivo spinal cord in transverse compression. 4.5.2 Effect of Strain Rate on the Force Response The viscoelastic properties of the surrogate cord were measured in transverse compression by studying its behaviour at two different strain rates (0.0025s"1 and 8s"1). The difference in response between transverse compression of the surrogate cord applied at a quasistatic (0.0025s"1) and intermediate strain rate (8s"1) verifies that QM Skin 30 is a viscoelastic material. At the intermediate strain rate (8s"1), a higher force was necessary to compress the surrogate cord to a given displacement than at the quasistatic strain rate (0.0025s"1). In addition, its non-linear force-displacement response indicates that it is also non-linearly elastic. This agrees with its behaviour in tension, thus confirming that it also behaves as a non-linearly viscoelastic material in transverse compression. Hung era/.10 compressed the in vivo feline spinal cord in a transverse direction. A non-linear elastic response was also observed; however, there was no measurable difference in its force-deformation curve when the rate of compression was increased from 0.002 lmm/s to 0.042mm/s. If the strain rates tested on the surrogate cord are converted into a velocity 128 Chapter 4 Transverse Compression of the Spinal Cord measure, these are approximately 0.03 and lOOmm/s (quasistatic and intermediate strain rates respectively). Thus, the quasistatic rate (0.0025s"1) of the surrogate cord falls within the range at which the in vivo feline spinal cord was tested. Interpretation of the graphical results presented by Hung et al. indicate that at 4mm of compression of the in vivo feline spinal cord, approximately 2.5-3N of force were measured.10 In contrast, the surrogate cord responded with a force of 26-37N when compressed at quasistatic strain rate to 4mm. A comparison between these values is difficult for several reasons. First, the amount of compression reported is dependent upon the starting position of the indenter or the plate. Second, different forces may be measured for an indenter or a plate used to compress the cord. And last, the strain due to 4mm of compression in the feline spinal cord is higher than the strain in the surrogate cord due to a smaller diameter of the feline spinal cord. These differences in forces at 4mm of compression are thus interesting to note but do not provide evidence against the use of the surrogate cord for compression experiments. A similarity in the modulus of elasticity for both cords is a strong indication that identical testing techniques would result in similar force-deformation responses between the in vivo feline and surrogate cords. At intermediate strain rates (8s"1), the surrogate cord responded as a stiffer material. This difference was magnified during the impact tests. Because the strain rate of the impact test was not constant, a direct comparison between the intermediate strain rate tests and the impact tests is not appropriate. However, it does provide further evidence to establish that the surrogate cord behaves as a viscoelastic material in transverse compression. The force-time response of the bare in vitro bovine spinal cord was calculated to compare to the response of the bare surrogate cord (Figure 4-35). Force-displacement curves were not plotted because the strain rate was not constant in these tests. The bovine spinal cord behaved as a softer tissue, exhibiting smaller forces throughout its deformation than the surrogate cord. This is because the bone fragment is decelerated at a much faster rate by the surrogate cord. However the peak forces experienced by the surrogate and bovine spinal cords during impact were not significantly different (p=0.23). 129 Chapter 4 Transverse Compression of the Spinal Cord -25 J Time (ms) Figure 4-35 - The average response of the bovine and surrogate spinal cords to impact In most instances, the forces experienced between the cords and the bone fragment became positive, implying that the bone fragment was accelerating and in tension with the cord. However the cord could not apply a tensile force to the bone fragment. Therefore this force could be due to several factors. If the bone fragment was projected back into the cylinder, there would be a friction force as it pushes its way back inside. These forces are expected to be increased by the air pressure in the cylinder and are directed opposite to the forces applied to the bone fragment by the cord. This would thus result in positive forces. If the bone fragment did not project back into the cylinder then it would have hit the outer face of the cylinder. This could cause it to accelerate towards the cord, also resulting in a positive force. Without these effects, a positive force during the occlusion would not be expected. The force-time response was chosen as an appropriate measure to describe the behaviour of the transverse compression of the surrogate cord due to a variable strain rate throughout the compression. In order to measure the modulus of elasticity, a more complex understanding of the stresses and strains in the cross-section of a cylinder is necessary. A common theory used in this type of analysis is the Hertzian theory.6'13 This theory assumes an isotropic material, small strains, a linear response, and a very stiff material. Unfortunately, the material and testing conditions in this study do not agree 130 Chapter 4 Transverse Compression of the Spinal Cord with these assumptions. Finite element modeling is another tool used to determine the modulus of elasticity for a complex stress-strain field through a known behaviour and iteration of the material properties. This method would work well in this study, however it was outside of the scope of this project. 4.5.3 Effect of the Dura Mater and C S F During impact of the in vivo spinal cord, the impact fragment must first deform the dura and CSF surrounding the surrogate cord before any contact between the impact fragment and the spinal cord is obtained. Thus, the influence of the dura mater and CSF on the impact behaviour of the surrogate cord was investigated to compare to the in vitro bovine 12 spinal cord reported by Jones. The differences in the surrogate cord conditions were evaluated by measuring four different parameters. These are the maximum occlusion, the duration of the maximum occlusion and the time to reach the top 5% and 25% of maximum occlusion from the moment of impact. Significant differences were observed for the majority of the measured parameters due to the presence of the dura mater and CSF (p<0.05). The average for all of the parameters measured with the CSF and dura mater present were greatest followed by the surrogate cords with only the dura mater. In contrast, Oakland measured no differences due to the presence of the dura mater for the in vitro bovine spinal cord in transverse compression.14 4.5.4 Compar ison of the Surrogate Cord with the Bovine Spinal Cord The surrogate cord material was chosen to replicate the mechanical properties of the in vivo spinal cord when loaded in uniaxial tension. A characterization of its material properties in transverse compression is also important in order to assess its biofidelity. Thus, its behaviour in transverse compression was compared to a companion study of the 12 bovine spinal cord. Experiments with the in vivo cord were not possible and were thus performed using in vitro bovine spinal cords. These experiments highlight if the surrogate 131 Chapter 4 Transverse Compression of the Spinal Cord cord of one specimen condition matches the in vitro bovine cord with CSF and dura mater present, as would be the case in vivo. The tests performed with the CSF and dura mater present were performed in collaboration with Miss Claire Jones at the University of Leeds, UK. In her report, 12 Jones determined that the presence of the dura mater and CSF produced significantly different results between it and the cord with dura as well as the bare cord when the maximum occlusions were compared. The remaining measures between spinal cord conditions indicated no significant differences except between the cord with CSF and dura mater compared to the cord with only dura mater for the duration of the top 25% of maximum occlusion. These results conflict with the surrogate cord results where significant differences were seen in the majority of comparisons. However, the lack in significant differences across specimen conditions for the parameters measured indicates that the presence of the dura mater and CSF have a very small effect on the occlusion response of the in vitro bovine spinal cord. Because the in vivo conditions represent the desired mechanical properties of the surrogate cord, the surrogate cord has been compared to the in vitro bovine spinal cord with dura mater and CSF present which is the closest match to the in vivo condition studied in this experimental protocol (Figure 4-36 to Figure 4-39). The following figures were inspected to determine which surrogate cord construct matches the behaviour of the in vitro bovine spinal cord with CSF and dura mater. The surrogate cord with the CSF and dura mater present appears to be the closest match for the in vitro bovine spinal cord with CSF and dura mater. 132 Chapter 4 Transverse Compression of the Spinal Cord Specimen m Bovine CSF/Dura • Surrogate CSF/Dura • Surrogate Dura • Surrogate Bare Figure 4-36 - The mean maximum occlusion of the bovine and surrogate cords. Error bars represent one standard deviation. Bovine results obtained from Jones.12 c o '</> Jj O o O E 3 E _ ra — s o a E c re o 5 • Bovine CSF/Dura • Surrogate CSF/Dura • Surrogate Dura • Surrogate Bare Specimen Figure 4-37 - The mean time to maximum occlusion of the bovine and surrogate cords. Error bars represent one standard deviation. Bovine results obtained from Jones.12 0 .0025 E 3 E 0.002 x — I ? z. m 0.0015 ° = c o g"i re 2 i i o 5 9 Q o B a 0.001 0.0005 j.r Q Bovine CSF/Dura • Surrogate CSF/Dura • Surrogate Dura • Surrogate Bare Specimen Figure 4-38 - The mean duration of maximum occlusion (5%) of the bovine and surrogate cords. Error bars represent one standard deviation. Bovine results obtained from Jones.12 133 Chapter 4 Transverse Compression of the Spinal Cord 0.006 0.005 I § 0.004 CM O '—' 5 . 2 '•c en 2 | ° o n 0.003 3 0.002 0.001 H U M T 1 Specimen • Boune CSF/Dura • Surrogate CSF/Dura • Surrogate Dura • Surrogate Bare Figure 4-39 - The mean duration of maximum occlusion (25%) of the bovine and surrogate cords. Error bars represent one standard deviation. Bovine results obtained from Jones.12 It is also important to note that the statistical analysis between the three conditions of the surrogate cord and the bovine cord revealed that under most conditions the surrogate cord does not mimic the mechanical response of the in vitro bovine spinal cord. If the response of the in vitro cord is not similar to that of the in vivo cord then these results should be considered lightly when evaluating the biofidelity of the surrogate cord since it is meant to replicate the in vivo mechanical properties. There is evidence to suggest that the mechanical properties of the spinal cord measured in uniaxial tension change after death and with time passed after death 3' 8' 1 4. Unfortunately the link between the behaviour of the in vivo and in vitro cord in transverse compression is not known and thus cannot be applied to the results determined in this study. It is therefore recommended that further studies be performed in order to establish the relationship between the in vivo and in vitro spinal cord in transverse compression. The behaviour of the surrogate spinal cord can then be compared to in vivo data which is likely a more appropriate model for the in vivo human spinal cord. This would be accomplished by measuring the force-displacement response of the in vivo cord and repeating this test on a different specimen in vitro and repeating with multiple specimens. A comparison in the forces measured to a given displacement would then indicate whether there are differences between the in vivo and in vitro behaviour. Identical tests could then be performed on a surrogate cord with the 134 Chapter 4 Transverse Compression of the Spinal Cord same diameter and with the same testing apparatus to compare its behaviour to the in vivo compression of the spinal cord. Pintar et al.X5 reported success in matching the mechanics of the surrogate cord to the response of the in vivo feline spinal cord. The response of the feline and surrogate cords was plotted as overlapping stress-strain curves. The methods used to calculate the stress and strain in the cords were not discussed. Therefore an objective analysis of their results is not possible. Their model for the spinal cord has also not been evaluated at different strain rates. Thus, to use their surrogate cord, and be confident that its response is that of the in vivo spinal cord, an identical loading condition must be replicated. Due to the fact that the properties of the in vivo human spinal cord cannot be directly measured, an in vitro bovine model was used for comparison instead. This introduces several limitations to the study. Bovine specimens were obtained from a slaughterhouse in Leeds, UK. No information was available about the age of the specimen or its vertebral level. It is not known whether or not either of these factors would affect the transverse compression properties measured. During transverse compression, there were no spinal roots holding the cord in place which may affect the impact response of the cord for both the bovine and surrogate spinal cords. Furthermore, the surrogate spinal cord uses bovine dura mater and thus does not include the denticulate ligaments between the spinal cord and the dura mater. This could also affect the impact response of the spinal cord and could introduce differences in the behaviour between the two types of cords. The occlusion profile was measured for spinal cords with CSF present. Since the CSF lifts the dura mater away from the surface of the spinal cord, it is no longer known where the actual spinal cord is during the compression. Occlusion parameters were measured as though the deformation of the dura mater was equivalent to that of the spinal cord. Thus, the occlusion of the spinal cord alone may have been over-estimated in this study. Additional experiments are necessary to determine if the CSF acts as a solid at the moment of impact and the compression of the bone fragment is immediately transferred 135 Chapter 4 Transverse Compression of the Spinal Cord to the spinal cord through the CSF or if the CSF is pushed out of the way with increased compression, thus delaying the impact to the spinal cord. Prior to testing, the number of cords necessary to detect a difference in the amount of occlusion among the different cords was determined to be seven. This assumed that a standard deviation of 0.05mm could be obtained. The variability among cords was greater than that. A subsequent power analysis was performed to determine the number of cords necessary for a confidence level of 90%. This level of confidence requires 14 surrogate cords and 49 bovine cords. There were in fact 14 surrogate cords tested in this study, however only 9 bovine spinal cords were tested. This quantity of spinal cords returns an approximate confidence level of only 25%. Thus, the testing performed may not have been sufficient to detect differences among the bovine spinal cords. Through the compression tests performed with rectangular specimens of QM Skin 30 and with surrogate and bovine spinal cords, the biofidelity of the surrogate cord has been assessed. The modulus of elasticity of QM Skin 30 is comparable to that measured for the in vivo feline spinal cord.10 The compression of the surrogate spinal cord exhibits a non-linear behaviour with increased forces as the compression increases, similar to the response of the in vivo spinal cord.10 The force-time curves for both the surrogate and in vitro bovine spinal cords contained a large degree of variability, thus limiting the accuracy of the results. Jones reports that the presence of the dura mater and CSF have a 1 2 significant effect on the occlusion properties of the in vitro bovine spinal cord. Differences were also detected in identical experiments performed with the surrogate spinal cord. However, the surrogate cord does not exactly mimic the behaviour of the in vitro bovine spinal cord under these loading conditions. Further investigation is necessary in order to confirm that the in vitro bovine spinal cord represents the in vivo behaviour. 136 Chapter 4 Transverse Compression of the Spinal Cord 4.6 References 1. Becker J TD, Lanz E, Erdmann K. Density of cerebrospinal fluid and local anesthetics (author's transl). Anaesthesist 1979;28:81-3. 2. Bilston LE, Meaney DF, Thibault L. The Development of a Physical Model to Measure Strain in a Surrogate Spinal Cord During Hyperflexion and Hyperextension. IRCOBI Conference. Eindhoven, Netherlands, 1993. 3. Chang GL, Hung TK, Feng WW. An in-vivo measurement and analysis of viscoelastic properties of the spinal cord of cats. J Biomech Eng 1988; 110:115-22. 4. Glantz S. Primer of Bio-Statistics. 3 ed: McGraw-Hill, 1992. 5. Greaves C. Spinal Cord Injury Mechanisms: A Finite Element Study. Mechanical Engineering. Vancouver: University of British Columbia, 2004. 6. Hadley D, Ward I, Ward J. The transverse compression of anisotropic fibre monofilaments. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 1965;285:275-86. 7. Hung TK, Albin MS, Brown TD, et al. Biomechanical responses to open experimental spinal cord injury. Surg Neurol 1975;4:271-6. 8. Hung TK, Chang GL. Biomechanical and neurological response of the spinal cord of a puppy to uniaxial tension. J Biomech Eng 1981;103:43-7. 9. Hung TK, Chang GL, Chang JL, et al. Stress-strain relationship and neurological sequelae of uniaxial elongation of the spinal cord of cats. Surg Neurol 1981;15:471-6. 10. Hung TK, Lin HS, Bunegin L, et al. Mechanical and neurological response of cat spinal cord under static loading. Surg Neurol 1982;17:213-7. 11. Johnston J. Bone Fragment Trajectory: A Matlab 6.5.0 image digitization program, 2005. 12. Jones C. The effect of cerebrospinal fluid on the biomechanics of spinal cord. Medical Engineering and Biomechanics. Leeds, UK: University of Leeds, 2005. 13. Norden N. On the Compression of a Cylinder in Contact wtih a Plane Surface: US Department of Commerce. National Bureau of Standards, 1973. 14. Oakland RJ. A Biomechanical Study of the Spinal Cord in the Burst Fracture Process. School of Mechanical Engineering. Leeds: The University of Leeds, 2003. 15. Pintar FA, Schlick MB, Yoganandan N, et al. Instrumented artificial spinal cord for human cervical pressure measurement. Bio-Medical Materials and Engineering 1996;6:219-29. 16. Sekhon LH, Fehlings MG. Epidemiology, demographics, and pathophysiology of acute spinal cord injury. Spine 2001;26:S2-12. 17. Sparrey C. The Effect of Impact Velocity on Acute Spinal Cord Injury. Department of Mechanical Engineering. Vancouver: University of British Columbia, 2004:196. 18. Tierney RT, Maldjian C, Mattacola CG, et al. Cervical Spine Stenosis Measures in Normal Subjects. J Athl Train 2002;37:190-3. 137 Chapter 4 Transverse Compression of the Spinal Cord 19. Wilcox R. A Biomechanical Study of Thoracolumbar Burst Fractures. Leeds, UK: University of Leeds, 2002. 20. Wilcox R. A Biomechanical Study of Thoracolumbar Burst Fractures. School of Mechanical Engineering: The University of Leeds, 2002. 21. Wilcox RK, Boergef TO, Allen DJ, et al. A dynamic study of thoracolumbar burst fractures. J Bone Joint Surg Am 2003;85-A:2184-9. 22. Zhang M, Zheng YP, Mak AF. Estimating the effective Young's modulus of soft tissues from indentation tests—nonlinear finite element analysis of effects of friction and large deformation. Med Eng Phys 1997;19:512-7. 138 Chapter 5 Conclusion Chapter 5 Conclusion A novel artificial spinal cord was developed to replicate the mechanical properties of the in vivo human spinal cord. The mechanical behaviour of in vivo and in vitro spinal cords as documented in published studies was reviewed and incorporated into a surrogate model of the human spinal cord. The mechanical properties of the in vivo spinal cord have been extensively tested in uniaxial tension. Therefore, the surrogate cord material was chosen to first match the properties in tension and subsequently compared with what has been reported for the in vivo cord as a viscoelastic material and its behaviour in transverse compression. The modulus of elasticity of the in vivo spinal cord measured in quasistatic uniaxial tension and transverse compression was matched by the surrogate cord. Further quantification of the surrogate cord was performed to determine, and compare to in vivo results, its viscoelastic properties in tension, as well as its behaviour under transverse compression during impact. 5.1 Uniaxial Tension I The surrogate cord was developed to replicate the mechanical properties of the in vivo human spinal cord. For ethical reasons, measurement of the human spinal cord in vivo is not yet possible. Thus, a second source for experimental data of the spinal cord was necessary. The properties of the in vitro human spinal cord as well as the in vivo and in vitro animal spinal cords were considered. Published reports for the differences between in vivo and in vitro spinal cord properties indicate that the mechanical behaviour of the spinal cord changes significantly after death.3,7'13 Thus, the most appropriate representation of the human in vivo spinal cord's mechanical properties was chosen as the in vivo animal spinal cord. Several materials were tested in the search for a surrogate cord material. One elastomer, QM Skin 30 (A:B = 10:1.2), was tested in uniaxial tension and its mean modulus of 139 Chapter 5 Conclusion elasticity measured to be 0.245 ± 0.024MPa. This is within the range of moduli measured for the in vivo canine and feline spinal cords. ' '" For this reason, the surrogate cord material was chosen as QM Skin 30. The proximity of the mechanical properties of the in vivo canine spinal cord to the in vivo properties of the human spinal cord is not known, however they are believed to be made of the same tissues and from the same cells and molecules and are thus likely close approximations of each other. The surrogate cord was validated against quasistatic uniaxial tension data measured for the in vivo animal spinal cord however these tests did not measure the modulus with the dura mater or CSF present which occur naturally in vivo. The surrogate cord is thus a best approximation based on what is currently known about the bare in vivo animal spinal cord in quasistatic tension. If the technology becomes available to measure the in vivo mechanical properties of the human spinal cord without causing injury to the human subject, an assessment of the biofidelity of the surrogate cord in uniaxial tension can be revisited. 5.2 Viscoelastic Properties of the Surrogate Cord The spinal cord is a viscoelastic material, exhibiting considerable stress relaxation and although it has not been measured experimentally, creep. It also exhibits an increase in the modulus of elasticity with increasing strain rates. This has been observed in the in ] 3 5 vivo and in vitro spinal cords. '" It was thus important to characterize the viscoelastic properties of the surrogate cord to determine the extent of its biofidelity under high strain rates. To test the effect of strain rate on the modulus of elasticity, the surrogate cord was tested at four different strain rates. Although the terms "intermediate" and "high" were applied to the strain rates used in these experiments, the terms are only related to eachother and are not meant to be terms related to the loading rates causing injury in the spinal cord. These terms are instead used to distinguish between the different strain rates used in this 140 Chapter 5 Conclusion study. There were no statistically signif icant differences among the modul i measured at the first three strain rates. However , a difference was observed between the quasistatic and instantaneous strain rates (p<0.002). Therefore, the surrogate cord also exhibits a higher modulus o f elasticity at higher strain rates, but a larger change in the strain rate is necessary in order to induce a difference in its modulus o f elasticity that wou ld be simi lar to the spinal cord. Stress decay was observed for the surrogate cord in tests at al l strain rates, wi th the greatest degree o f decay measured at the high and instantaneous strain rates. However , the stress decay was signif icant ly less than that calculated for the in vivo and in vitro spinal cords at simi lar strain rates, indicating that the surrogate cord is a less viscoelastic material than the spinal c o r d . 1 ' 3 ' 4 ' 1 3 This means that as the strain rate increases, the difference between the behaviour o f the in vivo spinal cord and the surrogate cord also increases. The surrogate cord is less viscoelastic and its stiffness w i l l not increase by the same amount as the in vivo spinal cord. Thus, the closest match between the in vivo and surrogate cord w i l l occur at quasistatic strain rates. The viscoelastic properties o f the surrogate could be altered to behave simi lar to the spinal cord by incorporating a second material wi th different viscoelast ic properties. It may only be that wi th the abi l i ty to independently control two different materials that a surrogate cord could be developed to match the quasistatic and viscoelast ic behaviour o f the spinal cord in tension. Fung 's quasil inear viscoelast ic model described both the loading curve and the relaxation profi le o f the surrogate cord. Smal l amounts o f relaxation were observed at the quasistatic and intermediate strain rates. Therefore, the model was only used to describe the behaviour tested at high and instantaneous strain rates. The quasil inear viscoelast ic model was compared to a linear model wh ich was used to describe only the relaxation prof i le. The linear model provided an equivalently accurate fit; however it can only be used to describe the relaxation whereas the quasil inear viscoelast ic model can describe both the loading curve and the relaxation. The quasil inear viscoelastic model has been used 141 Chapter 5 Conclusion previously to successfully describe the relaxation of the in vitro human and bovine spinal cords.1,13 The constants for the model determined with in vitro human or bovine spinal cord data are not identical to those measured for the surrogate cord behaviour. Also, the relaxation constants determined for each surrogate cord at each strain rate were not consistent among each other. Both of these discrepancies are due to the non-unique solution provided by the quasilinear viscoelastic model and the fact that the surrogate cord does not relax at the same rate or to the same amount as the in vitro human spinal cord. Creep behaviour of the surrogate cord was evaluated but has not been reported previously for other artificial spinal cords or for in vivo and in vitro spinal cords. Creep is a viscoelastic behaviour that may not occur naturally in the spinal cord as it does in other biological tissues such as the ligament and for this reason it has not been studied previously in the spinal cord. Thus, there are no data to compare with the creep properties of the surrogate cord. A general linear model was successful in matching the experimental data for the fast and instantaneous strain rate tests where the greatest degree of creep was observed (R2>0.94). If the creep behaviour of the animal or human spinal cords is measured in the future then an analysis can be performed to assess the similarity between the spinal cord and the present surrogate cord. 5.3 Transverse Compression at Quasistatic and intermediate Strain Rates The spinal cord can sustain severe injury when compressed in the transverse direction. Transverse compression occurs in a range of situations such as spinal stenosis (gradual compression) and burst fractures (impact). These two injuries are quite different in terms of the rate at which the compression is applied. Spinal stenosis is the narrowing of the spinal canal which progresses over long periods of time whereas the burst fracture injury can occur in a matter of milliseconds. If the surrogate cord behaves similarly to the spinal cord in compression over a range of strain rates then it could be used to study these types 142 Chapter 5 Conclusion of injuries to a greater degree of accuracy compared to studies using the in vitro human spinal cord. The mean modulus of elasticity of QM Skin 30 in quasistatic compression was 0.196 ± 0.024MPa. This is slightly lower than the modulus of elasticity measured in uniaxial tension. Interpretation of the graphical results provided by Hung et al. suggest that the modulus of elasticity for the in vivo spinal cord in transverse compression is approximately 0.28MPa without the dura mater to approximately 12% strain.10 Sparrey also reports a modulus of elasticity for the in vivo rat spinal cord of 0.299MPa at a compression speed of 300mm/s.14 The in vivo feline moduli of elasticity in tension and transverse compression are equal (to within approximately 0.02MPa) as they are for the surrogate cord. The slight difference between the in vivo and surrogate moduli of elasticity in transverse compression is not alarming. The value of 0.28MPa is a transverse compression modulus interpreted from graphical results for one feline spinal cord. It is likely that the modulus would vary slightly among different spinal cords and include the modulus of elasticity of the surrogate cord in transverse compression. However, the methods used to determine the in vivo modulus of elasticity by Hung et al. and Sparrey include several assumptions, including the mathematical models used, the linear representation of material properties, and the interpretation of friction and stress concentrations between the indenter and the spinal cord.10'14 These are thus not exact values for the modulus of elasticity in transverse compression for the in vivo spinal cord. Both the in vivo and surrogate spinal cord force-deformation curves describe a non-linear behaviour under transverse compression with a concave-upward slope as the transverse compression increases. A force response of approximately 30N was measured in the surrogate cord at 4mm of compression compared to approximately 2.5N in the in vivo feline spinal cord without dura. A direct comparison between these values is difficult because a different loading mechanism was used to produce the force and the initial conditions of the spinal cord and surrogate cord were not necessarily equivalent. If the indenter was not positioned at the exact location of initial contact with the spinal cord, thi toe region of the force-displacement curve would be over or underestimated. The same 143 Chapter 5 Conclusion applies for the surrogate cord in compression between two plates. In addition, it is not clear if the transverse compression of the in vivo feline spinal cord began with compression of the dura mater against the surrogate cord or not. However, the general shape of the force-displacement curve of the surrogate cord mimics that of the in vivo feline spinal cord. 5.4 Impact in Transverse Compression The transverse compression of the surrogate cord was also compared to the in vitro 12 bovine spinal cord conducted in a collaborative study with the University of Leeds, UK. In order to choose between the in vitro modulus of elasticity of the human spinal cord and the in vivo modulus of the animal spinal cord for replication in the surrogate cord, a discussion was presented arguing that the in vitro cord is not an accurate representation of the in vivo properties. However, in vitro bovine spinal cords were tested and compared . with the material properties of the surrogate cord in transverse compression. Despite the fact that the in vitro cords were reported to be stiffer than an in vivo cord, because the change in its behaviour is known, the results from this study can be traced back to an approximate behaviour in vivo. In addition, the in vitro bovine spinal cords were specifically tested within approximately three hours after death in order to limit the changes in the mechanical properties of the spinal cord. The differences observed between the in vitro bovine and surrogate spinal cords in high rate transverse compression indicate that the surrogate cord decelerates the impact fragment at a higher rate. The average force deformation curve of the bovine spinal cord had a higher degree of non-linearity than that of the surrogate cord. The force response of the bovine spinal cord was also much less. However, the speed of the impact fragment varied throughout the test. Its velocity was dependent on the material properties of the cord and the cord's ability to decelerate the bone fragment. A comparison between the two cords is thus difficult because the spinal cord is a viscoelastic material and will thus behave differently for different impact speeds. Direct comparison of the results between cords indicates that the surrogate cord does not exactly match the behaviour of the bare 144 , Chapter 5 Conclusion bovine spinal cord in high rate transverse compression but behaves in a similar manner overall. However, this comparison ignores the fact that after the initial impact, the compression of the cord occurred at different speeds. According to the results reported by Jones, the bovine spinal cord displayed significant differences in maximum occlusion between a cord with CSF and dura versus a cord with only dura mater.12 However no significant differences were observed between a cord with CSF/dura and the bare cord or between a cord with dura and the bare cord. Oakland also observed no significant difference between an in vitro bovine spinal cord with and without dura mater.13 These results indicate that the CSF may protect the spinal cord from the impact during a burst fracture. In contrast, the surrogate cord displayed significantly different occlusion behaviour between all constructs. A comparison between the bovine and surrogate spinal cords was necessary to determine which condition of the surrogate cord most closely matched the response of the bovine spinal cord with CSF and dura, which represents the in vivo conditions. The comparison was made with respect to their impact response. No significant differences between groups were observed due to the cord diameters or the fragment velocity. However, the surrogate spinal cord was significantly different from the bovine spinal cord for the measured values of maximum occlusion, time to maximum occlusion, and the duration of the maximum occlusion under all specimen conditions (bare surrogate cord, dura mater present, and dura and CSF present). All measured parameters of occlusion for the surrogate spinal cord with CSF and dura had a closest match to the bovine spinal cord with CSF and dura (Figure 4-36 to Figure 4-39). Thus, it is recommended that the surrogate cord be used with the CSF and dura mater present. This condition does not exactly replicate the occlusion behaviour of the in vitro bovine spinal cord but it is the closest approximation for the transverse compression behaviour that was measured in this study. If the behaviour is compared to that of the in vivo spinal cord, it is expected that these differences will be further increased. This assumption is based upon the fact that the in vitro spinal cord is stiffer in uniaxial tension than the in vivo spinal cord.3'7'13 Thus, it is expected that this will also hold true for the compression response. An in vivo spinal cord 145 Chapter 5 Conclusion would likely compress a greater amount than the in vitro spinal cord. Therefore, the occlusion of the surrogate cord with the CSF and dura mater is likely much less than that of the in vivo spinal cord with CSF and dura mater. 5.5 Future Work A design for the in vivo human surrogate spinal cord was developed and evaluated. Unfortunately, in vivo human spinal cord data does not exist at the present time. As improved technologies become available for measuring mechanical properties of tissue through non-invasive techniques, the mechanical properties of the spinal cord may be measured without causing injury. When these properties are known, the surrogate cord can be re-evaluated to determine its biofidelity relative to the human spinal cord. Until then, in vitro spinal cord properties as well as in vivo animal spinal cord measurements can be used to imply biofidelic properties necessary for the surrogate cord. '" 5 ' 7 " 1 0 ' 1 3 However, there remains a significant lack of in vivo data for the animal spinal cords. Only the modulus of elasticity of the spinal cord in uniaxial tension has been adequately defined for the in vivo cord. 7 Very few experiments have been performed on the in vivo spinal cord to measure its viscoelastic and transverse compression properties. 3 ' 6 ' 1 0 In order to compare the surrogate cord to the human and animal spinal cord, we are thus relying highly on in vitro measurements. 1'4'5' 1 3 In terms of the transverse compression properties, the literature does not report exact values for the modulus of elasticity, nor appropriate calculation of the modulus for graphical results. 6' 1 0 Thus, further work is necessary to define either the mechanical properties of the in vivo spinal cord or the relationship between the in vivo and in vitro response. A large amount of research in the mechanical properties of the spinal cord has studied the in vitro cord. 1 ' 4 ' 5 ' 1 2 ' 1 3 Because these spinal cords were obtained at different times after death, it is also important to understand how the mechanical properties of the in vitro spinal cord change with time after death and relate these properties to the in vivo cord. Only then can the in vitro data be used appropriately to further understand the biomechanics and injury mechanisms of the in vivo spinal cord. 146 Chapter 5 Conclusion More immediate recommendations for future work include an in vivo experiment to test the difference in mechanical response with and without the dura mater and CSF present to a quasistatic strain in transverse compression. The response of the in vitro spinal cord with the dura mater and CSF present was tested under impact in the companion study. These results indicate that in a high rate impact, the dura and CSF change the amount of compression imparted to the spinal cord. However, in quasistatic compression, the influence of these constructs on the force-deformation characteristics of the spinal cord has not been completely defined. Thus, the influence of these constructs is important in order to match the surrogate cord behaviour to the in vivo spinal cord for a range of strain rates. It is also necessary to confirm that the in vitro behaviour in high rate compression matches the in vivo behaviour. This will ensure that the analysis performed here against the in vitro cord behaviour in transverse compression is applicable to the in vivo behaviour. It will also provide a measure for the accuracy of the surrogate cord with CSF and dura mater in transverse compression with respect to the in vivo spinal cord. Another iteration of the surrogate cord should also be designed to incorporate the spinal nerves, dentate ligaments, and other tethering ligaments. These have been reported to affect the modulus of elasticity measured in the in vivo feline spinal cord.9 It is possible that nerve roots might also affect the dynamic behaviour of the spinal cord in flexion and extension because they act as tethering ligaments between the spinal cord and the spinal column. This is an important property to investigate for any dynamic spinal column motion tests which employ the surrogate cord. The mechanical properties of the surrogate cord were not tested in bending, shear, or torsion. These forces may be imparted onto the spinal cord during every day activities and to a greater degree during injury. Thus further characterization of the surrogate cord is necessary to understand its biofidelity under these mechanical loads. In vivo experiments would also be necessary since this data is not available for the spinal cord. 147 Chapter 5 Conclusion 5.6 Limitations The surrogate cord was designed to match the in vivo material properties of the spinal cord. These were matched in quasistatic tension. However, the perfusion of the spinal cord and the difference between the white and gray matter were not incorporated into the surrogate cord. Ichihara et al. have reported that there are stiffness differences between the white and gray matter in tension and transverse compression." This could affect the relaxation, creep, and compressive behaviour of the spinal cord. The difference between the white and gray matter could be more apparent in the compressive response as the white matter is compressed before the gray matter. This could also account for the initial toe region seen in the in vivo spinal cord in transverse compression. This might result in the differences observed between the bovine and surrogate cord results. No creep data for the spinal cord was identified in the literature. Despite this lack of data with which to compare the results of the surrogate cord, its creep response was measured in order to fully describe its mechanical properties. The creep behaviour of the surrogate cord was tested at four different strain rates. Creep at the faster strain rates was difficult to control. Often, the desired load was overshot but quickly corrected by the materials testing machine. This may have resulted in an underestimation of the creep response, however creep was only characterized after the correction was performed. The compression properties of the surrogate cord were compared to the in vivo spinal cord, for which there were only two major studies.6,10 The literature reports a sudden increase in the stress strain curve after approximately 15% strain.10 It is not known if this increase is a result of full contact between the indenter and the cord which perhaps had not been achieved as expected. It could also be due to the compression of the dura and the CSF before the indenter began to compress the spinal cord tissue. Another alternative explanation could be a difference in compression properties for the white and gray matter. Perhaps the increase in the modulus of elasticity occurs because the gray matter begins to compress under the loading whereas previous to this, it was only the white matter in compression. This would indicate that a surrogate cord should be constructed to 148 Chapter 5 Conclusion represent these differences in mechanical properties, especially to study the transverse compression of the spinal cord. Future studies to investigate these factors are warranted. The transverse compression studied at an impact speed for the surrogate and in vitro bovine spinal cords was not performed with a constant speed throughout the impact. This limits the ability to perform analyses between the force-time responses of the two cords. In order to directly compare the response of the two cords, an identical impact speed should be used. However, the uncontrolled impact was also a strength of the experiment because this mimics the in vivo injury. Limitations in the experimental protocol for impact transverse compression with CSF and dura include a lack in tethering ligaments between the surrogate cord and the bovine dura mater and no spinal roots in the surrogate cord whereas both of these were present in the bovine spinal cords. If the tethering ligaments hold the dura closer to the spinal cord, then it could be that a smaller volume of CSF existed between the spinal cord and the dura for the bovine spinal cords. In this case, it is expected that the CSF would provide less protection against the impact than the CSF barrier for the surrogate cord. The leaks in the dura mater may have also influenced the results despite a strong attempt to limit these. The CSF was represented with a saline solution which may have affected the impact response if it is not an exact match with bovine CSF. The natural in vivo temperature is approximately 37°C, however the temperature of the bovine spinal cords was not monitored in this study. The cryogenic clamps limited the use of a heating bath around the bovine spinal cords, however the cords were kept hydrated with a saline solution at room temperature. Oakland measured the temperature gradient along the cord with it placed in the cryogenic clamps to confirm that it does not freeze at the location of impact.13 The results are also limited by the mechanical properties of the in vitro spinal cord which do not match the in vivo properties. It is thus possible that the surrogate cord matches the in vivo response, but not the in vitro response. However, this is not probable because death results in a stiffer cord and the surrogate cord is already stiffer than the in vitro spinal cord. Therefore, further testing is required in order to evaluate differences 1 4 9 Chapter 5 Conclusion between the surrogate and in vivo spinal cord in order to fully understand the biofidelic impact of these results for the surrogate cord. The sensors used to measure the forces and displacements during experimentation were appropriate for the loads and strains measured. In tension, the range of the load cell was not taken full advantage of (testing to approximately 10% of full scale), however in compression it was necessary that the strain be limited to ensure that the load cell not sustain damage due to loads beyond its range. The linear potentiometer was also used through its entire range. The displacements for the impact tests were measured with a high speed video camera and image analysis. Images were taken every 0.22ms and measurements were made accurate to approximately 0.4mm/pixel. However, this error is compounded by the width of the line on the bone fragment used to track its motion, which was dependent on the proximity of the camera to the impact. It was also compounded by image quality and user error which was determined to be very small through an analysis of repetitive measurements. The time between images affected the force-time results, especially at the onset of the impact between the bone fragment and the cord. The exact moment of impact, and thus the initial deceleration, was not always captured. This resulted in an inaccurate force-time curve for the compression of the cord. 5.7 Final Conclusions This surrogate human spinal cord represents a biofidelic and multiple-use spinal cord for laboratory experiments. It can be inserted into a cadaveric spinal column in order to study the spinal cord stresses and strains as well as the mechanical behaviour during injury. These experimental results can then be compared to the animal models used to study spinal cord injury in order to evaluate the concordance between the animal models and human injuries. A validation of this form is important because the animal models are currently used to infer the response of the human spinal cord to injury as well as treatment methods. 150 Chapter 5 Conclusion The surrogate cord can also be used to design preventative devices for spinal cord injury. Prevention devices are currently tested with cadaveric specimens, however spinal cord injury is inferred as a result of trauma to the bony anatomy. Vertebral fractures and spinal cord injury often occur together, but if there are no fractures, this does not indicate that there was no spinal cord injury. Thus, the presence of a biofidelic surrogate cord in these experiments will allow one to measure the stresses and strains in the cord and determine if an injury has been prevented. For example, a helmet designed to prevent spinal column injury might induce a particular motion of the neck which does not cause column injury. However, this alternative motion might instead induce spinal cord injury through hyperextension or hyperflexion of the spinal column. This can only be determined with the use of the surrogate cord to measure the stresses and strains and compare these to the injury tolerance of the spinal cord. Therefore, the surrogate cord will allow for a new method to measure spinal cord injury in the lab and will provide a tool to study the biofidelity of animal models as well as treatment and prevention measures. Prior to the development of this surrogate cord, there had been no suitable spinal cord for use in this manner which incorporated both tensile and transverse compression of in vivo spinal cord mechanical properties. One alternative has been to use the in vitro human spinal cord. However this cord is a stiffer representation of the in vivo mechanical properties.3'7,13 Another solution has been to study animal models. These provide accurate in vivo animal spinal cord properties, however a link between the animal and human spinal cord and their injury mechanisms is not fully understood. The final alternative has been to design artificial spinal cords. Previous surrogate cords which have been designed to replicate the mechanical properties of the in vivo spinal cord have only incorporated the mechanical properties measured in one loading direction. The current surrogate is thus an improvement upon previous surrogate cords as it represents the in vivo modulus of elasticity of the spinal cord in tension and has also been characterized in relaxation, creep, and transverse compression. 151 Chapter 5 Conclusion The work performed to develop and characterize the properties of the surrogate spinal cord has been presented. The following conclusions summarize the results of the surrogate cord and its biofidelity with the spinal cord. 1. A surrogate cord made of QM Skin 30 in a two part ratio of 10:1.2 matches the in 9 "\ 7 Q vivo tensile modulus of elasticity of the canine and feline spinal cords. ' '" The mean modulus of elasticity for the surrogate cord is 0.245 ± 0.024MPa. 2. The shape of the stress-strain curve in uniaxial tension of the surrogate cord is 0 7 Q concave down, similar to the in vivo spinal cord. '" 3. The viscoelastic behaviour of the surrogate cord is similar to that of the in vivo and in vitro spinal cords1'3"5. The modulus of elasticity of the surrogate cord increases with an increase in the strain rate. It also exhibits relaxation, although to a lesser extent than the spinal cord, and creep behaviour. The stress decay of the surrogate cord is significantly less than that of the in vivo and in vitro spinal cords.1'3"5 4. The modulus of elasticity of QM Skin 30 in compression is 0.196 ± 0.024MPa. This is a very close match to the interpreted modulus of elasticity of the in vivo feline spinal cord reported graphically in the literature10 and reported by a previous UBC study for the in vivo rat spinal cord at 300mm/s.14 5. The force-deformation response of the surrogate cord in transverse compression displays a non-linear behaviour with increased forces as the cord is further compressed (a "J" shaped curve). Similar behaviour has been measured for the in vivo feline spinal cord in quasistatic transverse compression.10 6. The surrogate cord behaviour in dynamic compression changes with the addition of the dura mater and CSF. However, it does not exactly match the behaviour of the in vitro bovine spinal cord with CSF and dura under identical loading 12 conditions. The surrogate cord with CSF and dura mater present is the closest match for the in vitro bovine spinal cord with CSF and dura mater present. 7. The surrogate cord is an appropriate model for the in vivo human spinal cord in tension, however its stress decay is less than that measured in vivo. The modulus of elasticity in transverse compression for the surrogate cord matches that 152 Chapter 5 Conclusion reported for the in vivo cord. Without further information about the toe region of the in vivo spinal cord compression, a more complete biofidelic analysis cannot be determined. For a burst fracture injury simulation using the surrogate cord, it is recommended that the CSF and dura mater be incorporated in order to fully represent the in vivo behaviour. 153 Chapter 5 Conclusion 5.8 References 1. Bilston LE, Thibault LE. The mechanical properties of the human cervical spinal cord in vitro. Ann Biomed Eng 1996;24:67-74. 2. Chang GL, Hung TK, Bleyaert A, et al. Stress-strain measurement of the spinal cord of puppies and their neurological evaluation. J Trauma 1981;21:807-10. 3. Chang GL, Hung TK, Feng WW. An in-vivo measurement and analysis of viscoelastic properties of the spinal cord of cats. J Biomech Eng 1988; 110:115-22. 4. Fiford R, Bilston LE. Strain distribution and relaxation behaviour of rat spinal cord. Advances in Bioengineering, proceedings of the ASME International Mechanical Engineering Congress,. Anaheim, USA, 1998:247-8. 5. Fiford RJ, Bilston LE. The mechanical properties of rat spinal cord in vitro. J Biomech 2005;38:1509-15. 6. Hung TK, Albin MS, Brown TD, et al. Biomechanical responses to open experimental spinal cord injury. Surg Neurol 1975;4:271-6. 7. Hung TK, Chang GL. Biomechanical and neurological response of the spinal cord of a puppy to uniaxial tension. J Biomech Eng 1981;103:43-7. 8. Hung TK, Chang GL, Chang JL, et al. Stress-strain relationship and neurological sequelae of uniaxial elongation of the spinal cord of cats. Surg Neurol 1981;15:471-6. 9. Hung TK, Chang GL, Lin HS, et al. Stress-strain relationship of the spinal cord of anesthetized cats. J Biomech 1981;14:269-76. 10. Hung TK, Lin HS, Bunegin L, et al. Mechanical and neurological response of cat spinal cord under static loading. Surg Neurol 1982;17:213-7. 11. Ichihara K, Taguchi T, Shimada Y, et al. Gray matter of the bovine cervical spinal cord is mechanically more rigid and fragile than the white matter. J Neurotrauma 2001;18:361-7. 12. Jones C. The effect of cerebrospinal fluid on the biomechanics of spinal cord. Medical Engineering and Biomechanics. Leeds, UK: University of Leeds, 2005. 13. Oakland RJ. A Biomechanical Study of the Spinal Cord in the Burst Fracture Process. School of Mechanical Engineering. Leeds: The University of Leeds, 2003. 14. Sparrey C. The Effect of Impact Velocity on Acute Spinal Cord Injury. Department of Mechanical Engineering. Vancouver: University of British Columbia, 2004:196. 154 Appendix Appendix A Measurement of Strain in the Surrogate Cord Two methods were used to determine the strain in the surrogate cord. The first method assumed the motion of the crosshead described the strain in the specimen and the second method used a linear potentiometer to measure the displacement directly. The validation of these measurements is provided here. A.1 Crosshead Strain To validate the strain assumed by using the input parameters for the motion of the crosshead, video analysis was used. A surrogate cord, with an array of markers on its surface (Figure A-1), was mounted in the materials testing machined and pulled in uniaxial tension to 14% strain at a strain rate of 0.0025s"1. The crosshead strains were determined given the input velocity for strain and the time between data points to calculate the change in length in the cord. This was then divided by the original cord length to measure the strain. A digital video camera (SONY Cybershot, DSC-P73) was used to record the strains of the markers at a frequency of 30Hz. The images were processed through a free trial version of MaxTRAQ (Innovation Systems, USA) available online (www.innovision- Figure A-1 - Surrogate v J ' ' v cord with markers systems.com/maxtraq.htm, February 2005). Using MaxTRAQ, the user is able to point out the markers for the software to track through a series of images. It then returns the x and y coordinates of each point through time. These can then be used to calculate the strain in the cord between two markers. • For this analysis, six markers were chosen to trace the strain in the cord (Figure A-2). Th strain between markers 1 and 2, 1 and 3, 4 and 5, and 5 and 6 were measured and plotted 155 Appendix through time. The strain measured by the crosshead displacement was also plotted with the marker strains (Figure A - 3 ) . 3 # 6 # # • • • 1#4# • Figure A-2 - Markers tracked on the surrogate cord 0.25 0.15 2 0.1 0.05 -0.05 Time (s) Figure A-3 - Strains measured in the surrogate cord at a strain rate of 0.0025s"1 A linear trendline was determined for each o f the data series. The average trendline for strains obtained through video analysis was then calculated and plotted against the trendline for the crosshead strain (Figure A-4). 156 Appendix • Markers a Crosshead displacement 60 Figure A - 4 - Strain determined by video analysis (R 2 = 0.8) and crosshead displacement (R 2 = 1). The error bars represent one standard deviation for the marker strains at each time point. There was good correspondence between the marker strains and the strain measured from crosshead displacement. The crosshead displacement strain lies within one standard deviation of the marker strain. Thus, video analysis was not required to measure the strains in each test. The crosshead displacement was determined as an appropriate method for measuring the strain in the surrogate cord. A.2 Linear Potentiometer Accuracy The displacement of the linear actuator was programmed in Galil 2.3 (Galil Motion Control). Motions were varied, moving in a positive and negative direction, and in different increments. During motion, the displacement was measured with a dial gage and a potentiometer. The dial gauge was marked in 0.001" increments however measurements were recorded at 0.0005" increments. The linear potentiometer voltage was measured by a multimeter accurate to 0.01V. The motion of the stepper motor was first compared to the displacements recorded by the dial gage. This confirmed that the stepper motor moves the amount that it is programmed to displaced with an accuracy of 0.38% with reference to the dial gage (Figure A-5). 0.15 0.1 _ c ' 2 0.05 w 0 -0.05 < # [f I I —to—« 1— 1 1 20 40 Time (s) 157 Appendix <u -3 • Dial Gage (mm) — Linear (Dial Gage (mm)) y = 1.0038X- 0.0018 R2 = 0.9998 -2.5 Dial Gage (mm) Figure A-5 - Calibration of the stepper motor with reference to a dial gage The linear potentiometer was calibrated with reference to the stepper motor. The stepper motor was chosen since the linear actuator motion was a consistent known throughout surrogate cord testing. The dial gage was not present in any tests except for calibration. The fit between the potentiometer voltage and the displacement of the stepper motor had an R2 value of 0.9807 (Figure A-6). The calibration factor of the linear potentiometer was measured as -0.0148V/mm. 9.24 -1 9.22 -• \ » 9.2 -N« 9.18 -9.14 -9.12 . . , -9r4-Potentiometer Displacement -Linear (Potentiometer Displacement) y = -0.0148x +9.1515 R2 = 0.9807 - 4 - 2 0 2 Stepper Motor Displacement (mm) Figure A-6 - Calibration of the linear potentiometer 1 5 8 Appendix A.3 Velocity Calibration The linear actuator was programmed through Galil 2.3 (Galil Motion Control) to move at a specified speed. The programmed speed was confirmed with the use of a linear potentiometer and an LVDT. Multiple tests were performed a three different speeds, both with and without a 0.45kg weight suspended from the linear actuator. The errors in the speed determined through both displacement sensors are summarized in Figure A-7. Due to the smaller errors measured by the linear potentiometer, it was used to measure the displacement and speed of the linear actuator. • LVDT Error • Potentiometer Error 5000-no 5000- 1 lb 10000-no 10000 - 1 lb 100000 - no 100000-load load load load Speed (steps/s) Figure A-7 - Error in linear actuator speed determined the linear potentiometer and the LVDT. 159 Appendix Appendix B Quasilinear Viscoelasticity B.1 Fung's Quasilinear Viscoelastic Theory The quasilinear viscoelastic theory developed by Fung2 has been used to describe the material behaviour of soft tissues.''3"5 Assuming that the viscoelastic properties of the surrogate cord are similar to those of a soft tissue, the theory developed by Fung was used in this study. Fung separated the viscoelastic response into two components, the elastic and viscous, which are dependent on the history of the material. For the relaxation behaviour, the model is dependent on the history of the strain and time, Y{t,a) = ff'{s)*G{f) G(0) = 1 (Eq. B.l) This is the relaxation function for which G(f) is the reduced relaxation function and cf(e) is the elastic response of the material. This equation is further developed with the use of the superposition principle to arrive at an expression for the stress in the material at any time, t, which is dependent on the loading history of the material. This is given below: < r ( 0 = j G ( , - r ) ^ ^ ! ^ (E q.B.2) J OS OT -CO Given that the strain history begins at t = 0 and there is no stress before this time (<r= 0) then we obtain the expression: o-(t) = o-e(0)G(t)+ \G(t-T)da ( g ( T ) ) — g T (Eq.B.3) I de dr = ' f G ( , _ r ) ^ ( £ ( £ » 3 £ a r o d£ Fung provides an equation for G(f) 160 Appendix G(t) = (Eq. B.4) where G , - £ - (Eq.B.5) In addition, Bilston and Thibault1 confirm that the following elastic response for the in vitro human spinal cord is appropriate and has thus also been used with the surrogate cord: a \ s ) = A(eBe -1) (Eq.B.6) which differentiates to the form — = ABeBe (Eq. B.7) ds At t = t\, the strain on the surrogate cord is held constant for 60 seconds. Thus, to describe the strain history until the relaxation is complete we have e(t) = £0t 0<t<t i (Eq. B.8) t>tx so tx Thus, the strain rate history is given by the following equation with h(t) denoting the Heaviside step function. s(f) = *o(l-/»(*-/,)) (Eq.B.9) Substitution of equations (B.6) and (B.9) into (B.3) give a final expression for the stress. The first is used for the ramp portion of the loading curve and second for the material relaxation. 161 Appendix a-(t) = ABeo^dGleTl -i r ( E q . B . l O ) J 0<t<t] \ -t criO^ABso^G^' e - 1 ( E q . B . l l ) — + Bso{ t>h B.2 References 1. B i ls ton L E , Thibaul t L E . The mechanical properties o f the human cerv ical spinal cord in vitro. A n n B i o m e d E n g 1996;24:67-74. 2. Fung Y . B iomechanics : Mechan ica l Properties o f L i v i n g Tissues. 2nd ed: Spr inger-Ver lag, 1993. 3. Haut R C , L i t t le R W . A constitutive equation for col lagen fibers. J B iomech 1972;5:423-30. 4. Oakland R J . A B iomechan ica l Study o f the Spinal Co rd in the Burst Fracture Process. School o f Mechan ica l Engineering. Leeds: The Univers i ty o f Leeds, 2003. 5. Thorton G , O l i y n y k A , Frank C , et a l . L igament Creep Cannot be Predicted from Stress Relaxat ion at L o w Stress: A Biomechanica l Study o f the Rabbi t M e d i a l Col lateral Ligament. Journal o f Orthopaedic Research 1997;15:652-6. 162 Appendix Appendix C Stress Decay During Relaxation of the Surrogate Cord The fo l lowing tables provide information for the relaxation tests performed wi th the surrogate cords. The ramp t ime is the amount o f t ime taken to reach 12% strain in the surrogate cord f rom its starting posit ion. The relaxation time is the length o f t ime during which the relaxation was recorded. The max imum stress is the stress recorded at the moment the cord was in 12% strain. The stress decay was calculated wi th reference to the max imum stress. The quasil inear viscoelastic ( Q L V ) model was used to predict the stress in the cord throughout the relaxation and the max imum error in its prediction is provided. Table C-l - Stress decay in the surrogate cord during relaxation. The surrogate cords were in 12% strain which was applied at a quasistatic strain rate (0.0025s" ). Cord # Ramp time Relaxation time Maximum Stress Stress Decay Maximum Error in Stress Predicted by the QLV Model (s) (s) (kPa) 1 sec S sec 30 sec 60 sec (kPa) 65 47.98 60 28.99 1.69% 1.88% 2.09% 2.20% 5.01 66 47.97 60 31.15 1.98% 1.67% 2.65% 3.11% . 5.63 67 47.97 60 29.86 3.67% 3.41% 4.19% 4.68% 3.13 68 47.97 60 29.13 1.28% 2.21% 3.12% 3.57% 3.95 69 47.96 60 34.19 2.15% 1.92% 2.61% 3.16% 0.89 70 47.96 60 32.25 2.84% 3.35% 3.88% 4.41% 6.72 71 47.96 60 31.48 0.47% 0.94% 2.10% 1.95% 0.54 72 47.97 60 31.89 0.46% 1.19% 1.90% 6.24% 1.90 73 47.96 60 32.58 2.29% 2.12% 3.52% 3.35% 5.26 74 47.96 60 32.49 0.96% 2.02% 2.61% 3.38% 7.57 Mean 47.97 60 31.40 1.78% 2.07% 2.87% 3.60% 4.06 SD 0.01 0 1.66 1.03% 0.80% 0.79% 1.25% 2.41 Table C-2 - Stress decay in the surrogate cord during relaxation. The surrogate cords were in strain which was applied at an intermediate strain rate (0.048s1). Cord# Ramp time Relaxation time Maximum Stress Stress Decay Maximum Error in Stress Predicted by the QLV Model (s) (s) (kPa) 1 sec 5 sec 30 sec 60 sec (kPa) 75 2.61 60 31.73 6.01% 7.74% 8.90% 9.73% 2.11 76 2.59 60 33.87 11.52% 12.50% 13.80% 14.03% 1.78 77 2.6 60 34.77 9.50% 10.12% 12.39% 12.25% 3.55 78 2.64 60 37.06 7.98% 8.63% 9.51% 11.93% 3.93 79 2.58 60 32.75 7.79% 11.35% 11.93% 13.76% 6.53 80 2.6 60 32.71 8.31% 8.90% 10.43% 10.68% 3.83 81 2.66 60 30.48 5.58% 8.03% 9.25% 10.05% 3.06 82 2.66 60 33.04 7.75% 9.12% 10.47% 11.35% 2.96 83 2.67 60 31.75 6.98% 8.27% 9.70% 10.13% 3.25 84 2.62 , 60 31.54 8.73% 10.13% 11.32% 12.67% 2.56 Mean 2.62 60 32.97 8.02% 9.48% 10.77% 11.66% 3.36 SD 0.03 0 1.89 1.71% 1.54% 1.57% 1.54% 1.32 163 Appendix Table C-3 - Stress decay in the surrogate cord during relaxation. The surrogate cords were in 12% strain which was applied at a high strain rate (0.12s1). Cord# Ramp time (s) Relaxation time (s) Maximum Stress (kPa) Stress Decay Maximum Error in Stress Predicted by the QLV Model (kPa) 1 sec 5 sec 30 sec 60 sec 75 1.21 60 34.24 7.32% 9.03% 11.42% 11.38% 3.71 76 1.49 60 29.94 8.69% 9.48% 12.46% 12.43% 2.03 77 1.43 60 34.01 8.14% 9.74% 10.90% 11.92% 6.93 78 1.72 60 36.23 3.44% 5.45% 7.05% 7.62% 7.09 79 1.75 60 30.58 3.58% 5.90% 10.06% 7.45% 3.77 80 1.44 60 32.24 6.58% 9.24% 11.74% 11.69% 8.32 81 1.71 60 29.47 2.24% 4.66% 6.65% 6.07% 3.35 82 1.52 60 35.36 11.16% 13.07% 14.12% 13.76% 2.07 83 1.61 60 34.35 8.95% 10.96% 12.73% 13.24% 4.00 84 1.57 60 34.02 7.63% 9.08% 9.75% 10.42% 3.07 Mean 1.55 60 33.04 6.77% 8.66% 10.69% 10.60% 4.43 SD 0.16 0 2.35 2.84% 2.60% 2.39% 2.65% 2.21 Table C-4 - Stress decay in the surrogate cord during relaxation. The surrogate cords were in 12% strain which was applied at an instantaneous strain rate (0.32s1). Cord# Ramp time (s) Relaxation time (s) . Maximum Stress (kPa) Stress Decay Maximum Error in Stress Predicted by the QLV Model (kPa) 1 sec 5 sec 30 sec 60 sec 76 0.8 60 30.32 7.68% 9.20% 10.71% 16.07% 1.02 78 0.8 60 32.26 9.06% 10.55% 12.05% 27.09% 0.84 80 0.8 60 29.60 8.87% 9.72% 11.32% 14.53% 0.90 82 0.8 60 31.03 7.74% 9.99% 10.80% 16.92% 29.45 84 . 0.9 60 27.78 7.64% 10.12% 11.01% 11.81% 15.50 Mean 0.82 60 30.20 8.20% 9.92% 11.18% 17.28% 9.54 SD 0.04 0 1.67 0.70% 0.50% 0.54% 5.82% 12.80 1 6 4 Appendix D Creep Appendix General Linear Model for Relaxation and D.1 Relaxation Constants The constants provided in the following tables were determined for the following equation (Eq. 3.2), G(0 = Ale~Al' + A3e-A<' + A5 Table D-l - Linear model constants determined for the relaxation test performed at a quasistatic strain rate (0.0025s"'). Cord# Ai A 2 A 3 A 4 A 5 65 0.752662 0.072177 0 -0.27502 0.979542 66 0.32 0.06 0 -0.260302 0.987 67 0.134902 0.040281 0 -0.271812 0.984805 68 0.699991 0.079289 0 -0.260293 0.98836 69 0.2175 0.05 0 -0.271665 0.984 70 13.9644 0.14465 -0.009908 -0.007508 1.007619 71 0.655959 0.077569 0 -0.274962 0.988436 72 0.249147 0.051741 0 -0.275389 0.983228 73 0.803912 0.083497 0 -0.270345 0.988331 74 0.701063 0.067575 0 -0.26026 0.983605 Mean 1.849954 0.072678 -0.000991 -0.242756 0.987493 SD 4.264007 0.028971 0.003133 0.082897 0.007627 Table D-2 - Linear model constants determined for the relaxation test performed at an intermediate strain rate (0.048s1). Cord # Ai A 2 A 3 A 4 A 5 75 7.392911 0.256098 -7.255401 0.256091 0.929586 76 0.488147 0.61936 -2.653141 -7.57E-05 3.555513 77 7.387996 0.223661 -7.242986 0.223663 0.918909 78 0.313126 0.464149 -17.35217 -2.09E-05 18.25541 79 7.173804 0.125855 -7.025547 0.125206 0.901366 80 0.37 0.558572 -26.34018 -1.13E-05 27.25042 81 6.826807 0.190377 -6.6721 0.190375 0.90535 82 6.789894 0.082614 -6.71311 0.082614 0.938364 83 0.169548 0.231131 -1.95078 -9.27E-05 2.858721 84 3.3E+08 8.81671 0.038183 0.078229 0.872104 Mean 33016497 1.156853 -8.316724 0.095598 5.738575 SD 1.04E+08 2.697535 7.874806 0.099489 9.263601 165 Appendix Table D-3 - Linear model constants determined for the relaxation test performed at a high strain rate (0.12s-1). Cord# Ai A 2 A 3 A 4 A 5 75 0.15012 0.221302 1.36E-13 -0.388085 0.890119 76 0.195714 0.422504 -9.088719 -4.53E-05 9.983254 77 0.222957 0.57206 -0.820367 -0.000169 1.716965 78 14.49574 4.07188 -6.956323 -4.03E-05 7.906226 79 0.070955 0.139413 -8.111274 -7.17E-05 9.056699 80 0.163463 0.312882 -0.008979 -0.021145 0.898667 81 0.095754 0.230054 -0.081429 0.00043 1.013412 82 0.257719 0.407673 0.000715 -0.054611 0.857107 83 0.199097 0.327084 -3.376963 -6.61 E-05 4.259735 84 0.117641 0.119625 -5.220365 1.87E-05 6.120609 Mean 1.596916 0.682448 -3.366371 -0.046378 4.270279 SD 4.532553 1.198858 3.693828 0.121349 3.70827 Table D-4 - Linear model constants determined for the relaxation test performed at an instantaneous strain rate (0.32s1). Cord# Ai A 2 A 3 A 4 A 5 76 0.101253 0.051155 3.097794 7.01 E-06 -2.194471 78 0.096628 0.089525 17.02639 3.01 E-06 -16.11549 80 0.233764 1.110867 0.034914 0.00345 0.879177 82 0.098668 0.089199 1.252823 1.36E-05 -0.343865 84 0.114267 0.065544 1.321994 1.54E-05 -0.429697 Mean 0.128916 0.281258 4.546783 0.000698 -3.64087 SD 0.059014 0.464052 7.061278 0.001538 7.059054 D.2 Creep Constants The constants provided in the fo l lowing tables were determined for the fo l low ing equation (Eq. 3.3), J(t) = B^2' + B3e'Bt' + B5 166 Appendix Table D-5 rate (0.0025s1) - Linear model constants determined for the creep test performed at a quasistatic strain Cord # BA B 2 B 3 B 4 B 5 75 -0.817112 0.072338 -0.455758 -0.000449 1.490035 76 -0.324675 0.085114 0 -0.309639 1.006098 77 -1269.622 0.328978 0 -0.35178 1.001716 78 -0.254088 0.062132 0 -0.280051 1.013959 79 -0.254548 0.056472 0 -0.280051 1.014482 80 -0.260679 0.066141 0 -0.280228 1.00702 81 -0.20117 0.048814 0 -0.300002 1.013298 82 -1.673064 0.119889 0 -0.278314 1.004241 83 -0.24389 0.063196 0 -0.275512 1.012968 84 -0.343952 0.061144 0 -0.273408 1.017136 Mean -127.3995 0.0964221-0.045576 -0.262943 1.058095 SD 401.3364 0.0840931 0.144123 0.095299 0.151853 Table D-6 - Linear model constants determined for the creep test performed at strain rate (0.048s1). ^ Cord # B, B2 B 3 B 4 B 5 75 -9.417467 0.00033 -0.424869 -0.005304 10.84075 76 -0.045362 0.07164 0 -0.506594 1.030074 77 -4.087729 -6.42E-07 -0.0176 0.00015 5.105328 78 1.46E-05 0.002544 -0.000582 8.27E-05 1.000568 79 -0.101843 0.062272 1.53E-10 -0.301414 1.045438 80 -0.062348 0.100473 0 -0.494373 1.031155 81 -0.101209 0.045711 -4.62E-07 -0.161401 1.02971 82 -0.2117 0.000281 -1.98E-05 -0.082829 1.21152 83 -10.64443 3.52E-05 0 -0.493624 11.62709 84 -12.84968 7.18E-06 -1.81 E-07 -0.136658 13.8448 Mean -3.752175 0.028329 -0 0443071-0.218196 47/6643 SD 5.197216 0.038262 0 133829| 0.213717| 5.260304 Table D-7 - Linear model constants determined for the creep test performed at a high Cord# B i B 2 B 3 B 4 B 5 75 -0.046603 0.040641 0 -0.279212 1.028733 76 -0.045484 0.039038 0 -0.279212 1.028807 77 -0.043099 0.041073 0 -0.279163 1.030902 78 -0.040273 0.045642 0 -0.279188 1.02821 79 -0.041094 0.02992 0 -0.278429 1.031676 80 -0.048605 0.032721 0 -0.279168 1.033367 81 -0.040994 0.025809 0 -0.279015 1.029767 82 -0.04097 0.035654 0 -0.279212 1.031024 83 -0.044124 0.037648 0 -0.279212 1.032651 84 -0.039932 0.062458 3.14E-10 -0.286845 1.035552 Mean -0.0431181 0.03906 3 14E-111-0.279865 1.0310b9 SD 0.002987| 0.010057 9.94E-1l| 0.002464| 0.00232/ 167 Appendix Table D-8 - Linear model constants determined for the creep test performed at an instantaneous strain rate (0.17s1). Cord# B 2 B 3 B 4 B 5 75 -0.027292 0.004901 -0.033583 0.048339 1.050526 77 -0.029705 0.003712 -0.031513 0.050268 1.049914 79 -0.030433 0.003787 -0.031537 0.046667 1.052152 81 -0.028554 0.004708 -0.031422 0.043704 1.050542 83 -0.028472 0.003597 -0.022342 0.043715 1.044298 Mean -0.028891 0.004141 -0.030079 0.046539 1.049486 SD 0.001213 0.000613 0.004419 0.00288 0.003017 168 Appendix Appendix E Rectangular Specimens of QM Skin 30 E.1 Material Properties Table E-l - Dimensions of the rectangular specimens Specimen # Length Width Height (mm) (mm) (mm) 1 40.7 25.9 11.7 2 40.9 26.5 12.5 3 41.1 26.5 11.4 4 40.3 25.8 8.4 Table E-2 - Modulus of Elasticity for multiple tests performed on the rectangular specimens of QM Skin 30 Modulus of Elasticity (Pa) Specimen # 1 2 3 1 211215 165595 199075 2 241711 193735 169423 3 213315 229979 193246 4 185042 168440 175877 Mean 212820.8 189437.3 184405.3 SD 23159.79 29840.92 14030.43 E.2 Statistical Results To evaluate changes in the modulus of elasticity due to repeated testing of the rectangular specimens, a statistical analysis was performed. A repeated measures ANOVA was used to indicate whether statistical differences were present. The p-value for this test was greater than 0.05. Therefore, there were no statistical differences in the moduli of elasticity determined for the rectangular specimens due to repeated testing. Table E-3 - Statistical results for the repeated measures ANOVA Sum of Mean Squares df Square F p-level I Effect 1.84E+09 2 9.2E+08 1.972124 0.219653 I Error 2.8E+09 6 4.66E+08 169 Appendix Appendix F Load Cell Calibration F.1 LCFA-10 Load Cell A 44.5N load cell (LCFA-10, Omega Engineering Inc.) was used to test the surrogate cords in tension and compression. Several weights were supported by the load cell and the output voltage recorded. These values were used to calibrate the load cell in tension. A calibration factor of-3.0248V/kg with an R2 value of 0.9999 was determined (Figure F-la). This calibration factor was repeated for each set of tests. A similar curve was measured for the load cell with a compressive load on a different day. Seven different loads were placed on top of the load cell and its output voltage recorded (Figure F-lb). A calibration factor of 2.8206V/kg was measured with an R2 value of 0.9992. • Voltage Readings — Linear (Voltage Readings) Weight (kg) y = -3.0248x- 0.7995] R* = 0.9999 • Voltage Readings - Linear (Voltage Readings) 0.2 0.4 0.6 Weight (kg) y = 2.8206x+2.7107| R1 = 0.9992 a) Tension b) Compression Figure F-l - Calibration curve for the LCFA-10 load cell in a) tension and b) compression Repeatability of the load cell measurements were measured in two conditions. The voltage was first recorded with no weight and then recorded again with a weight of 0.228kg in tension. This sequence was repeated five times. The mean voltage was -0.86 ± 0.003V without at weight. With a 0.228kg weight hung from the load cell, the mean voltage was -1.57 ± 0.004V. Thus, the load cell had excellent repeatability. 170 Appendix F.2 SBL-10kN Load Cell A lOkN load cell set to a 100N scale was used to apply tension to the surrogate cords in Leeds, UK for the impact tests in transverse compression. To calibrate this load cell, a series of weights were hung from it and the force recorded (Figure F-2). The load cell readings were linear within 0.84%. The repeatability of the measurements output by the load cell was also measured using a 0.97N weight. An average force of 0.99 ± 0.013N was measured throughout six consecutive tests using the same weight, thus providing excellent repeatability. A p p l i e d L o a d (N) Figure F-2 - Load cell calibration for various weights mounted to the load cell 171 Appendix Appendix G Temperature Profile in the Surrogate Cord It was important to verify that the temperature of the surrogate cord at the location of impact was not affected by the dry ice in the cryogenic clamps. If the temperature in the cord dropped, this could affect the occlusion behaviour of the surrogate cord. The effect of clamping the surrogate cord into the cryogenic clamps was assessed by measuring the surface and internal temperatures of the surrogate cord while in the clamps. A thermocouple was placed in contact with the surrogate cord for 60 seconds and the temperature recorded. Internal temperature was measured by cutting a slit into the surrogate cord and placing the thermocouple at the center of the cross section of the cord. Temperature readings were taken in 10mm increments along the length of the cord starting from the base clamp. The average surface temperature of the cord was 21.4 ± 0.23°C and internal temperature was 23 ± 0.44°C before the surrogate cord was placed into the clamps. These readings were taken with a room temperature of 22.5°C. After being clamped, the surface temperature dropped to 14 + 6.21°C and the internal temperature dropped to 14.1 ± 6.55°C. At this time, the room temperature had also dropped to 19.0°C. The temperature gradient along the length of the cord was plotted (Figure G-l). 172 Appendix 30.0 - r o 25.0 -El . . re 15.0 -a> a. E 10.0 -a> I- 5.0 -0.0 i m—B-—•—Surface — a — Internal Clamped - Surface — C l a m p e d - Internal 50 100 Position (mm) Figure G - l - Temperature gradient along the length of the surrogate cord. 0mm corresponds to the temperature of the cord at the point where it exits the clamp. The temperature gradient plateaus at approximately 20 mm away from the clamps. In the range of the temperature plateau, the average temperature at the surface was 17.46 ± 0.57°C and the average internal temperature was 17.91 ± 1.47°C. The temperature of the surrogate cord was approximately 1.5°C less than the room temperature. Therefore, due to the sharp drop in temperature of the surrogate cord near the clamps, the impacts were only applied a minimum of 20mm away from the cryogenic clamps. 173 Appendix Appendix H Pressure-Velocity Calibration The pressure in the pneumatic cylinder (16mm-M134, ASCO/Joucomatic Ltd., UK) tests were performed during which the pressure was set to a predetermined level and released causing the piston to impact the bone fragment. These tests were filmed with high speed video (EktaPro 4540mx Imager, Kodak) and the images analyzed to determine the velocity of the bone fragment (Figure H-l). A velocity of 4.87 ±0.19 m/s was measured at 300kPa of pressure. Therefore, a pressure of 300kPa was chosen to cause an impact velocity of 5m/s between the bone fragment and the surrogate cord. required to induce a velocity of 5m/s for the impact fragment was evaluated. Multiple 7 o o CD E. 4 • 300 kPa A 350 kPa X 4 0 0 kPa - 4 5 0 k P a 3 > 2 0 200 250 300 350 400 450 500 Pressure(kPa) Figure H-l - The relationship between the impact fragment and the pressure in the pneumatic cylinder 174 Appendix Appendix I Matlab Code 1.1 Normalize the Image function In=normImgO 1(1); %return a new normalized image such that: %min(I(:)) —> 0 %max(I(:)) —> 1 mn=min(I(:)); mx=max(I(:)); In=(l/(mx-mn))*(I-mn); 1.2 Process Images clear all close all % CD serves to change the working directory to the directory containing all % the image files. This needs to be updated for each set of images, cd C:\Users\ 59D2; % UPDATE % GET_DATA function serves to input a data or image file into Matlab. [F,P]=uigetfile('*.tif,'Choose Image'); % User inputs for contrast, the number of images to be read and the ruler % dimension which will be selected for converting between pixels and mm. % % The cutoff to black will be removed such that 0.5 is remapped to 1.0 % (black). This linear function (with gamma = 1) alters the intensity of % the image and essentially "brightens it". With gamma equal to 1, a % linear transformation occurs, where with gamma < 1 you have the % equivalent of remapping the original data with a log plot, while gamma > % 1 is equivalent to remapping with an inverse log plot. % % The num_images variable is included so that the user can select how many % images he/she wants to examine at a time (i.e., 1000 or 50). % % The ruler variable is included for converting between pixels and physical % dimensions; millimeters in this case. A default value of 20 is picked, % so be sure to pick either 30 and 50 or 20 and 40 when selecting points % from the ruler in the first image. % 175 Appendix cutoff = 0.5; %Update for each batch of images depending on their quality gamma = 1; %Update for each batch of images depending on their quality num_images = 3; %Update for each batch of images depending on their quality ruler = 20; %Update for each batch of images depending on their quality % Sets up general format for the filenames such that we can increment the % filename and automatically open up other files (i.e., without calling out % each image). The variable vol is the volume number (i.e., 2767) of the % original filename. A conversion between strings and numbers is required % in order to increment to the next image. prefix = F( 1:4); vol = F(5:8); vol = str2num(vol); filetype = F(9:12); % Reads in image and normalizes. PF=[P,F]; ext=PF(findstr(PF,,.')+l rend); PFinf=imfinfo(PF); Im=imread(PF); Im=normlmg01(double(lm)); % Basic image setup for image viewing. figure; cla; imagesc(Im); colormap(gray); hAxis=512; % Intensity Transformation function (i.e., contrast enhancement) discussed % previously. Please adjust either the cutoff or gamma values above to % the images. Im_adj = imadjust(Im, [0 cutoff], [0 1], gamma); imagesc(Im_adj); title(vol) grid on; set(gca,'YTick',[0 25 50 75 100 125 150 175 200 225 250]); % Input function which allows the user to select points from the displayed % image. Here four points are to be selected, and must be selected in this % order: % Point 1 - Zero point on ruler (i.e., 0mm or 10mm, whatever) ZERO % Point 2 - Second point on ruler (Default: 20mm away) MEASURE % Point 3 - White vertical line on left side of image LINE % Point 4 - Point in center of moving object START [x, y] = ginput(5); 176 Appendix zero = [l,x(l),y(l)]; measure = [2, x(2), y(2)]; cord = [3, x(3), y(3)]; line = [4,x(4),y(4)]; bone = [5, x(5), y(5)]; % Sets up first line of data, to be used with the 6xnum_images motion % matrix determined below via looping pointl' = [4, line(2), line(3), bone(2), bone(3), vol]; % Basic loop which reads in the next image in a series and allows the user % to select a point on the moving object on the right side of the image. % A 3xnum_images matrix is called out at the beginning of the loop % NOTE: When going through the images, select the same point used to select % Point 4 from the first image (i.e., START). motion = [(1 :num_images-l)' (l:num_images-l)' (l:num_images-l)' (l:num_images-l)' (1 :num_images-1)' (1 :num_images-1)']; for i = 1 :num_images-l; vol = vol + 1; vol = int2str(vol); new_vol = [prefix, vol, filetype]; eval(['Im = imread(new_vol);']); Im=normImgO 1 (double(Im)); Im_adj = imadjust(Im, [0 cutoff], [0 1], gamma); imagesc(Im_adj); title(vol) grid on; set(gca,'YTick',[0 25 50 75 100 125 150 175 200 225 250]); [xl,yl] = ginput(l); [x2, y2] = ginput(l); vol = str2num(vol); motion(i,:,:,:,:,:) = [i+4, xl, yl, x2, y2, vol]; end % Simple data reordering which can be used in excel to get motions and % conversions, etc. output = [zero 0 0 0 measure 0 0 0 cord 0 0 0 pointl motion]; % Determines first and last files uploaded for the analysis. This is to be % used in the filename for the excel output. vol_start = num2str(output(4,6)); vol_end = num2str(output(end,6)); 177 Appendix % Writes data to output file, which is saved in the working directory fout = ['resultsj vol_start '_thru_' vol_end '.xls']; eval(['save ' fout' output -ascii']); 178 Appendix Appendix J Transverse Compression of the Surrogate Cord Q l = First quasistatic strain rate test (0.0025s"1) M l = First intermediate strain rate test (8s"1) Cord 77 -3 -2 Compression (mm) Cord 78 Compression (mm) Cord 79 Compression (mm) Cord 75 en An 30-Z Q1 o .n M1 -fi -i -3 -2 1 10J Compression (mm) Cord 76 cn 10 ^•v- -in Z Q1 o m M1 -5 -4 -3 -2 1 10 Compression (mm) Cord 80 40-, 30-^^^^^^^ -5 -4 -3 -2 Compression (mm) 1 Cord 81 -3 -2 Compression (mm) Cord 82 Compression (mm) Cord 83 46-z o • p An -5 -4 -3 -2 — ^ ! Compression (mm) -3 -2 Compression (mm) -Q1 - M1 -Q1 - M t -Q1 -M1 -Q1 -M1 179 Appendix Appendix K Stiffness of the Surrogate Cord in Transverse Compression Transverse compression was applied to the surrogate cord at a quasistatic (0.0025s" 1) and intermediate (8s"1) strain rate. The secant modulus o f the force-displacement curves was calculated to determine the stiffness o f the surrogate cords at these strain rates. The fol lowing figure depicts the stiffness curves for the quasistatic and intermediate strain rate tests. 180 

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