Initiation and Progression of Lumbar Disc Degeneration under Cyclic Loading: A Finite Element Study

Transcription

1 Initiation and Progression of Lumbar Disc Degeneration under Cyclic Loading: A Finite Element Study By Muhammad Qasim BSc. Mechanical Engineering University of Engineering and Technology, Lahore, Pakistan, 2003 THESIS Submitted as partial fulfillment of the requirements for the degree of Doctor of Philosophy in Bioengineering in the Graduate College of the University of Illinois at Chicago, 2012 Chicago, Illinois Defense Committee: Richard L Magin, Chair Raghu N Natarajan, Advisor James Patton Ahmed A Shabana, Mechanical and Industrial Engineering Gunnar BJ Andersson, Rush University Medical Center

2 ACKNOWLEDGEMENTS I would like to thank my advisor Dr. Natarajan for his guidance and support over the last four years without which this work would not have been possible. I would also like to thank the committee members, Dr. Magin, Dr. Andersson, Dr. Patton and Dr. Shabana who, on those occasions when we met, provided keen insight on both intellectual and organizational matters. I am grateful to my parents for investing all their attention, time and money towards my education since my childhood. Without their love and support, I would not have had the courage to begin this adventure, or the strength to finish it. I would also like to thank my brothers, sisterin-law and nephew for their continuous support during my years at University of Illinois at Chicago. I would like to recognize my cousin Dr. Ali Iftikhar Raja for encouraging me to pursue higher education and offering his advice and help at every step from applying to the graduate schools to writing and defending this thesis. I would also like to mention my uncle Dr. Iftikhar Ali Raja (Late) who inspired us to dream big and showed through his own footsteps that anything is achievable through persistence and hard work. I would also like to thank my friends Bianca, Peter, David, Aman, Minos, Wei, Pang-yu, Julia, Diego, Valentina, Rodolfo, Rebecca, Daniel and all other class fellows and colleagues during my time at UIC and Rush for their company and support without which this journey would not have been so delightful. ii

3 TABLE OF CONTENTS CHAPTER PAGE I. INTRODUCTION...1 A. Aims Aim Aim Aim II. BACKGROUND...6 A. Anatomy of the Spine Spinal Column Lumbar Spine Vertebral Anatomy Intervertebral Disc Ligaments of the Lumbar Spine...10 B. Disc Degeneration Disease...11 III. IV. EFFECT OF ANNULAR LESIONS ON THE BIOMECHANICAL BEHAVIOR OF LUMBAR MOTION SEGMENT...15 A. Introduction...15 B. Materials and Methods Finite Element Model of L4/L5 Lumbar Motion Segment Finite Element Model Validation Inclusion of Annular Lesions...30 a. Annulus Ground Substance...32 b. Annulus Fibers Damage Loading Conditions...40 C. Results Global Models Local Models LoadCap Models Radial Fissure, Concentric Tear and Rim Lesion Occurring Simultaneously...50 D. Discussion...51 BIOMECHANICAL CHARACTERISTICS OF L4/L5 LUMBAR MOTION SEGMENTS WITH DEGENERATED INTERVERTEBRAL DISC A. Introduction...54 B. Materials and Methods Biochemical Changes Morphological Changes Loading Conditions Data Analyses...61 iii

4 TABLE OF CONTENTS (continued) CHAPTER PAGE 5. Validation of Finite Element Models...62 a. Healthy Disc Finite Element Model...62 b. Grade III Disc Degeneration Finite Element Model...63 c. Grade IV Disc Degeneration Finite Element Model...63 d. Grade V Disc Degeneration Finite Element Model...63 C. Results Angular Rotation Annulus Fibrosus Stress Nucleus Pressure Facet Joints Load Endplates Stress...85 D. Discussion...91 V. FAILURE INITIATION AND PROGRESSION IN INTERVERTEBRAL DISC UNDER CYCLIC LOADING A. Introduction B. Materials and Methods Continuum Damage Mechanics Incorporation of Continuum Damage Mechanics Methodology into Finite Element Model Stress-Failure Curve for Annulus Fibrosus Elastic Modulus and Damage Parameter at Failed Integrating Points Validation of Finite Element Model Incorporated with Damage Accumulation Formulation Loading Condition C. Results Number of Load Cycles to Failure Damage Accumulation Location Endplates Stress Nucleus Pressure D. Discussion VI. CONCLUSION AND FUTURE STUDIES VII. CITED LITERATURE VIII. VITA iv

5 LIST OF TABLES TABLE PAGE I. THOMPSON DISC DEGENERATION GRADING SCHEME II. III. IV. SUMMARY OF STUDIES REPORTING OCCURRENCE OF ANNULAR LESIONS IN DIFFERENT AGE GROUPS MATERIAL PROPERTIES FOR L4/L5 LUMBAR MOTION SEGMENT FINITE ELEMENT MODEL MATERIAL PROPERTIES FOR ANNULUS GROUND SUBSTANCE USED FOR HEALTHY AND DIFFERENT GRADES OF DISC DEGENERATION FINITE ELEMENT MODELS V. MATERIAL PROPERTIES FOR NUCLEUS PULPOSUS USED FOR HEALTHY AND DIFFERENT GRADES OF DISC DEGENERATION FINITE ELEMENT MODELS VI. VII. L4/L5 INTERVERTEBRAL DISC HEIGHT AND NUCLEUS PULPOSUS AREA USED FOR HEALTHY AND DIFFERENT GRADES OF DISC DEGENERATION FINITE ELEMENT MODELS COMPARISON OF IN VITRO CYCLIC TESTING AND FINITE ELEMENT MODEL LOADING CONDITIONS AND NUMBER OF CYCLES TO FAILURE VIII. SIMPLE AND COMPLEX LOADING CONDITIONS FOR FAILURE ANALYSES UNDER CYCLIC LOADING v

6 LIST OF FIGURES FIGURE PAGE 1. Spinal column Cross-sectional view of an intervertebral disc The annulus fibrosus with the central nucleus pulposus removed. The collagen fibers are arranged in multiple concentric layers with consecutive rings running in alternating directions. Fibers are inclined at an angle of approximately 30 to the horizontal. Image borrowed from neumann, Ligaments of the lumbar spine Sagittal cryomicrotome sections demonstrating a normal disc (upper left), a disc with a rim lesion (upper right), a disc with a radial fissure (lower left) and a segment with collapsed intervertebral disc. Image borrowed from haughton et al Different stages of disc degeneration disease. First column shows the midsagittal cross-sectional view of the motion segment. Second and third columns show the radiograph and mri images of the same specimens. (a) grade i (b) grade ii (c) grade iii (d) grade iv (e) grade v. Images borrowed from benneker et al Finite element model of l4/l5 motion segment consisting of l4 vertebra, l5 vertebra, l4/l5 disc and the endplates Compressive load magnitude simulating 16 hours of normal day activities and 8 hours of sleep Diurnal changes in stature as observed in vivo and predicted by the l4/l5 lumbar motion segment finite element model Compressive load magnitude for short term creep testing Changes in stature as observed in vivo and predicted by the l4/l5 lumbar motion segment finite element model during short term creep loading Compressive load and flexion moment magnitudes during one cycle of cyclic load testing Changes in stature as reported in vivo and predicted by the l4/l5 lumbar motion segment finite element model during cyclic load testing Location of radial fissure, concentric tear and rim lesion in the annulus fibrosus Progression of radial fissure. Fissure initiated at the inner boundary of the annulus and progressed outward towards its periphery. Blue color represents the healthy annulus while red color represents the fissure volume. Fissure volume as a percentage of total annulus volume is given below each step vi

7 LIST OF FIGURES (continued) FIGURE PAGE 16. Progression of concentric tear. Tear initiated in the anterior region of the disc and progressed towards the lateral region. Blue color represents the healthy annulus and red color represents the tear volume. Tear volume as a percentage of total annulus volume is given below each step Progression of rim lesion. Lesion initiated at the outer periphery of the anterior annulus and progressed inward towards the nucleus. Blue color represents the healthy annulus and red color represents the lesion volume. Lesion volume as a percentage of total annulus volume is given below each step Annulus collagen fibers damage for global model (radial fissure). Collagen fibers (green) were modeled using concentric rings of rebar elements, embedded in the annulus matrix. Collagen fibers in the surrounding of the lesion were deactivated to model the fiber damage and can be seen missing in the picture Annulus collagen fibers damage for local model (radial fissure). Collagen fibers passing through the lesion volume only, were deactivated and can be seen missing in the picture. Only the fibers in the region of interest are shown for clarity Annulus collagen fibers damage for lodcap model (radial fissure). The load capacity of the fibers in the vicinity of the lesion was reduced by half. The fibers with the reduced load capacity can be identified with orange color in the picture Increase in rom under axial rotation with increasing size of rim lesion, radial fissure and concentric tear as predicted by global models Increase in rom under flexion / extension with increasing size of rim lesion, radial fissure and concentric tear as predicted by global models Increase in rom under later bending with increasing size of rim lesion, radial fissure and concentric tear as predicted by global models Increase in rom under axial rotation with increasing size of rim lesion, radial fissure and concentric tear as predicted by local models Increase in rom under flexion/extension with increasing size of rim lesion, radial fissure and concentric tear as predicted by local models Increase in rom under lateral bending with increasing size of rim lesion, radial fissure and concentric tear as predicted by local models Increase in rom under axial rotation with increasing size of rim lesion, radial fissure and concentric tear as predicted by loadcap models Increase in rom under flexion / extension with increasing size of rim lesion, radial fissure and concentric tear as predicted by loadcap models vii

8 LIST OF FIGURES (continued) FIGURE PAGE 29. Increase in rom under lateral bending with increasing size of rim lesion, radial fissure and concentric tear as predicted by loadcap models Increase in rom due to occurrence of annular lesions (radial fissure, concentric tear and rim lesion) under different loading modes. The increase in flexibility under axial rotation was considerably higher than under flexion/extension or lateral bending Finite element models of l4/l5 lumbar intervertebral disc showing progressive changes in disc height and nucleus area with increasing disc degeneration. Inner white core represents the nucleus pulposus while the outer blue region is annulus fibrosus, (a) healthy disc (b) grade iii disc degeneration (c) grade iv disc degeneration (d) grade v disc degeneration Finite element model and fujiwara et al in vitro segmental angular rotation values for healthy disc l4/l5 lumbar motion segment Finite element model and tanaka et al in vitro segmental angular rotation values for healthy disc l4/l5 lumbar motion segment Finite element model and fujiwara et al in vitro segmental angular rotation values for thompson grade iii disc degeneration l4/l5 lumbar motion segment Finite element model and tanaka et al in vitro segmental angular rotation values for thompson grade iii disc degeneration l4/l5 lumbar motion segment Finite element model and fujiwara et al in vitro segmental angular rotation values for thompson grade iv disc degeneration l4/l5 lumbar motion segment Finite element model and tanaka et al in vitro segmental angular rotation values for thompson grade iv disc degeneration l4/l5 lumbar motion segment Finite element model and fujiwara et al in vitro segmental angular rotation values for thompson grade v disc degeneration l4/l5 lumbar motion segment Finite element model and tanaka et al in vitro segmental angular rotation values for thompson grade v disc degeneration l4/l5 lumbar motion segment Inter-segmental rotations predicted by the finite element models for l4/l5 lumbar motion segments with healthy and degenerated discs Maximum von mises stress in the annulus ground substance of the l4/l5 intervertebral disc under flexion, extension, axial rotation and lateral bending for different grades of disc degeneration viii

9 LIST OF FIGURES (continued) FIGURE PAGE 42. Maximum shear stress between annulus lamellae of the l4/l5 intervertebral disc under flexion, extension, axial rotation and lateral bending for different grades of disc degeneration Maximum principal tensile stress in the annulus ground substance of the l4/l5 intervertebral disc under flexion, extension, axial rotation and lateral bending for different grades of disc degeneration Principal stress in the annulus fibrosus for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under flexion. P represents the posterior side Principal stress in the annulus fibrosus for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under extension. P represents the posterior side Principal stress in the annulus fibrosus for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under right axial rotation. P represents the posterior side Principal stress in the annulus fibrosus for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under right lateral bending. P represents the posterior side Maximum shear stress in the annulus fibrosus for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under flexion. P represents the posterior side Maximum shear stress in the annulus fibrosus for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under extension. P represents the posterior side Maximum shear stress in the annulus fibrosus for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under axial rotation. P represents the posterior side Maximum shear stress in the annulus fibrosus for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under lateral bending. P represents the posterior side Maximum pressure in the nucleus pulposus of the l4/l5 intervertebral disc under flexion, extension, axial rotation and lateral bending for different grades of disc degeneration Average facet joint contact forces at l4/l5 lumbar motion segment during extension, axial rotation and lateral bending for different grades of disc degeneration ix

10 LIST OF FIGURES (continued) FIGURE PAGE 54. Maximum principal tensile stress in the endplates of the l4/l5 intervertebral disc under flexion, extension, axial rotation and lateral bending for different grades of disc degeneration Principal stress in the endplates for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under flexion Principal stress in the endplates for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under extension Principal stress in the endplates for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under axial rotation Principal stress in the endplates for (a) healthy (b) grade iii (c) grade iv (d) grade v disc degeneration finite element models under lateral bending Continuum damage mechanics formulation for tracking the damage accumulation in the annulus fibrosus incorporated into l4/l5 lumbar motion segment finite element model. I is for integrating point, e is the young s modulus Stress-failure (s-n) curve for annulus fibrosus. Annulus specimens from different discs were cyclically loaded in tension for up to 10,000 cycles by green et al 120. Stress level and the numbers of load cycles to failure are plotted for each specimen. A trend line based on power function represents the fatigue behavior of the annulus ground material Failure progression for different values of elastic modulus at failed integrating points. Elastic modulus at failed integrating points was reduced by one tenth, one hundredth and one thousandth of its normal magnitude. Integrating point was considered failed when its damage parameter reached a value of Failure progression for different values of elastic modulus at failed integrating points. Elastic modulus at failed integrating points was reduced by one tenth, one hundredth and one thousandth of its normal magnitude. Integrating point was considered failed when its damage parameter reached a value of Failure progression for different values of elastic modulus at failed integrating points. Elastic modulus at failed integrating points was reduced by one tenth, one hundredth and one thousandth of its normal magnitude. Integrating point was considered failed when its damage parameter reached a value of x

11 LIST OF FIGURES (continued) FIGURE PAGE 64. Failure progression for different values of damage parameter d at which integrating points were declared failed. A value of zero for d represents the normal state of the annulus with no damage. Analyses was carried out for three values of d i.e. 0.80, 0.90, Elastic modulus at the failed integrating points was reduced by one tenth of its normal magnitude Failure progression for different values of damage parameter d at which integrating points were declared failed. A value of zero for d represents the normal state of the annulus with no damage. Analyses was carried out for three values of d i.e. 0.80, 0.90, Elastic modulus at the failed integrating points was reduced by one hundredth of its normal magnitude Failure progression for different values of damage parameter d at which integrating points were declared failed. A value of zero for d represents the normal state of the annulus with no damage. Analyses was carried out for three values of d i.e. 0.80, 0.90, Elastic modulus at the failed integrating points was reduced by one thousandth of its normal magnitude Cyclic compressive loading with three different magnitudes of peak compressive load Cyclic bending moment loading during one load cycle. Same peak bending moment magnitude was simulated in the three principal directions Cyclic bending in the three principal directions along with the cyclic compressive load Cyclic flexion bending with a peak moment of 12nm in concert with the cyclic compressive loading Cyclic flexion bending along with static compressive load Damage accumulation in the annulus fibrosus under simple loading conditions Damage accumulation in the annulus fibrosus under different cyclic loading conditions. Failure cycle is identified by sharp increase in the failure volume against a small increment in the number of load cycles Damage accumulation in the annulus fibrosus under cyclic compressive loading for three different magnitudes of peak compressive load Damage accumulation in the annulus fibrosus under cyclic flexion for two different magnitudes of peak flexion moment Damage accumulation in the annulus fibrosus under cyclic flexion in concert with cyclic and static compression xi

12 LIST OF FIGURES (continued) FIGURE PAGE 77. Damage accumulation in the annulus fibrosus in grade iii disc degeneration model under cyclic compressive loading and cyclic flexion in concert with cyclic compressive load. Results for healthy disc model are also plotted for comparison purpose Stress failure curves for degenerated annulus fibrosus Damage accumulation in the annulus fibrosus in grade iii disc degeneration model under cyclic compressive loading for three different stress failure curves Damage accumulated in the annulus until 201,216 cycles under cyclic compressive loading with a peak load of 400 n (load case 1). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face Damage accumulated in the annulus until 129,014 cycles under cyclic flexion loading with a peak moment of 6nm (load case 3). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face Damage accumulated in the annulus until 255,326 cycles under cyclic axial rotation with a peak moment of 6nm (load case 4). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face Damage accumulated in the annulus until 145,250 cycles under cyclic lateral bending with a peak moment of 6nm (load case 5). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face Damage accumulated in the annulus up to the failure cycle under cyclic compressive loading with a peak load of 800 n (load case 2). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face : damage accumulated in the annulus up to the failure cycle under cyclic flexion loading in concert with cyclic compressive load (load case 6). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face Damage accumulated in the annulus up to the failure cycle under cyclic axial rotation in concert with cyclic compressive load (load case 7). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face xii

13 LIST OF FIGURES (continued) FIGURE PAGE 87. Damage accumulated in the annulus up to the failure cycle under cyclic lateral bending in concert with cyclic compressive load (load case 8). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face Damage accumulated in the annulus up to the failure cycle under cyclic moment loading (flexion, axial rotation and lateral bending) in concert with cyclic compressive load (load case 10). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face Damage accumulated in the annulus up to the failure cycle under cyclic compressive loading with a peak load magnitude of 800 n (load case 2) in grade iii disc degeneration finite element model. White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face Damage accumulated in the annulus up to the failure cycle under cyclic flexion loading in concert with cyclic compressive load (load case 6) in grade iii disc degeneration finite element model. White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face Damage accumulated in the annulus up to the failure cycle under cyclic compressive loading with a peak load magnitude of 800 n (load case 2) in grade iv disc degeneration finite element model. White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) superior face (b) inferior face : damage accumulated in the annulus up to the failure cycle under cyclic flexion loading in concert with the cyclic compressive load (load case 6) in grade iv disc degeneration finite element model. White color shows the volume of the annulus that has failed while the black color represents the normal annulus Von mises stress in the endplates after (a) first cycle and (b) 201,216 cycles under cyclic compressive loading with a peak load of 400 n (load case 1) Von mises stress in the endplates after (a) first cycle and (b) 126,014 cycles under cyclic flexion loading with a peak moment of 6nm (load case 3) Von mises stress in the endplates after (a) first cycle and (b) 255,326 cycles under cyclic axial rotation with a peak moment of 6nm (load case 4) Von mises stress in the endplates after (a) first cycle and (b) 145,250 cycles under cyclic lateral bending with a peak moment of 6nm (load case 5) xiii

14 LIST OF FIGURES (continued) FIGURE PAGE 97. Von mises stress in the endplates after (a) first cycle and at (b) failure cycle under cyclic compressive loading with a peak load of 800n (load case 2) Von mises stress in the endplates after (a) first cycle and at (b) failure cycle under cyclic flexion bending in concert with cyclic compressive loading (load case 6) Von mises stress in the endplates after (a) first cycle and at (b) failure cycle under cyclic axial rotation in concert with cyclic compressive loading (load case 7) Von mises stress in the endplates after (a) first cycle and at (b) failure cycle under cyclic lateral bending in concert with cyclic compressive loading (load case 8) Von mises stress in the endplates after (a) first cycle and at (b) failure cycle under cyclic moment loading (flexion, axial rotation and lateral bending) in concert with cyclic compressive loading (load case 10) Von mises stress in the posterior region of the inferior endplate during the first load cycle and the failure load cycle under different loading conditions Nucleus pressure after (a) first cycle and (b) 201,216 cycles under cyclic compressive loading with a peak load of 400 n (load case 1) Nucleus pressure after (a) first cycle and (b) 126,014 cycles under cyclic flexion loading with a peak moment of 6nm (load case 3) Nucleus pressure after (a) first cycle and (b) 255,326 cycles under cyclic axial rotation with a peak moment of 6nm (load case 4) Nucleus pressure after (a) first cycle and (b) 145,250 cycles under cyclic lateral bending with a peak moment of 6nm (load case 5) Nucleus pressure after (a) first cycle and at (b) failure cycle under cyclic compressive loading with a peak load of 800n (load case 2) Nucleus pressure after (a) first cycle and at (b) failure cycle under cyclic flexion in concert with cyclic compressive loading (load case 6) Nucleus pressure after (a) first cycle and at (b) failure cycle under cyclic axial rotation in concert with cyclic compressive loading (load case 7) Nucleus pressure after (a) first cycle and at (b) failure cycle under cyclic lateral bending in concert with cyclic compressive loading (load case 8) xiv

15 LIST OF FIGURES (continued) FIGURE PAGE 111. Nucleus pressure after (a) first cycle and at (b) failure cycle under cyclic moment loading (flexion, axial rotation and lateral bending in concert with cyclic compressive loading (load case 10) xv

16 SUMMARY Back pain is one of the most prevalent and costly work related injuries in the United States. Disc degeneration disease is considered to be one of the causes associated with the low back pain in addition to the other factors. Intervertebral disc degeneration is characterized by the progressive changes in the biochemistry and morphology of the nucleus and the annulus. Disc degeneration is prevalent among older population but its occurrence is often reported in the young adults. The purpose of this study was to investigate the effect of disc degeneration on the biomechanical behavior of the lumbar motion segment using computational method of finite element analyses. Annular lesions are suggested to be the first marker of the disc degeneration process and have been reported in subjects as young as ten year old. The first aim of the thesis was to investigate the influence of radial fissure, concentric tear and rim lesion on the disc kinematics. An already validated poroelastic finite element model of L4/L5 lumbar motion segment which includes biological parameters like osmotic pressure and strain dependent permeability was employed. Annular lesions were introduced in the finite element model by altering the properties of annulus ground substance. Atrophy of the annulus fibers due to the tears was also included in the models. Finite element models predicted an increase in the flexibility of the lumbar motion segment with the occurrence of the annular lesions in the three principal directions. The increase in the flexibility predicted under axial rotation was considerably larger than the corresponding increase under flexion/extension and lateral bending. Occurrence of rim lesion caused a larger percentage increase in the angular motions as compared with the incidence of the concentric tear or the radial fissure. Increase in the flexibility means that disc will be subjected to higher levels xvi

17 of stresses thus accelerating the degeneration process. The findings from this study emphasized the importance of considering the role of annular lesions on the disc biomechanics while modeling the disc degeneration process. In addition to the annular lesions, disc degeneration is accompanied with biochemical and morphological changes. The second part of the study dealt with the development of finite element models representing different grades of disc degeneration. Morphological changes were introduced by decreasing the disc height and increasing the annulus area on the expense of the nucleus with increasing disc degeneration. Biochemical changes were included by altering the material properties of the annulus and the nucleus. The L4/L5 lumbar motion segment finite element model with healthy disc (grade I) was modified to develop three new models representing Thompson grade III, IV and V disc degeneration. The biomechanical characteristics of the degenerated disc models were then compared with the healthy disc finite element model. The finite element models predicted an increase in the flexibility of the lumbar motion segment with progressive disc degeneration in the three principal directions. The lumbar motion segment flexibility exhibited an increasing trend up to grade III disc degeneration and then a decreasing trend with further disc degeneration was observed. Annulus fibrosus was exposed to higher levels of tensile and shear stresses with increasing disc degeneration. Intradiscal nucleus pressure dropped with disc degeneration. Larger facet joint loads were found in the degenerated disc models than in the healthy disc models. These changes in the nucleus pressure, annulus stresses and the facet joint forces suggested a change in the load distribution in the disc from nucleus to the annulus and the facet joints as disc degenerates. Endplates were exposed to higher principal stresses with increasing disc degeneration making the motion segment vulnerable to failure by endplate fracture. xvii

18 The structural failures in the disc are considered to be the result of damage accumulated over a long period of time rather than a traumatic injury. Experimental studies have identified repetitive loading as a risk for disc prolapse. It is difficult to study the breakdown of disc tissue over several years of exposure to bending and lifting by experimental methods. There is no finite element model that elucidates the failure mechanism due to repetitive loading of the lumbar motion segment. The third aim of the thesis was to investigate the initiation and progression of mechanical damage in the disc under cyclic loading. Continuum damage mechanics methodology was incorporated into the finite element model of the lumbar motion segment to predict damage accumulation in the disc. The analyses showed that the damage initiated at the posterior inner annulus adjacent to the endplates and propagated outwards towards its periphery under all loading conditions simulated. With disc degeneration the location of the disc failure shifted from the inner annulus layers in the healthy disc to the outer periphery of the annulus in grade IV disc degeneration model. The analyses predicted that the disc failure is unlikely to happen with repetitive bending in the absence of compressive load. The number of load cycles to disc failure decreased as the disc was subjected to complex loading rather than single axis compression or bending. The finite element model results were consistent with the experimental and clinical observations in terms of the region of failure, magnitude of applied loads and the number of load cycles survived. The degenerated discs and fatigue failure models presented in this thesis can be extended to the whole lumbar spine and can help understanding the spine biomechanics in a much better manner. xviii

19 1 I - INTRODUCTION Low back pain is a major health condition that affects every population worldwide 1. It can lead to diminished physical function, decreased quality of life, and psychological distress 1-4. It is one of the most common conditions for which to seek medical consultation in the United States 3, 4. Although low back pain is a multifactorial condition, disc degeneration disease has been indicated to be a strong etiologic factor Intervertebral disc degeneration disease is a progressive pathological condition that alters the biochemistry and morphology of the disc. The prevalence of disc degeneration increases with age and it is estimated that by the sixth decade almost everyone experience disc degeneration 12. However the disc degenerative process is not linearly related to the age and it has been reported in young individuals 13, 14. The spinal column is a complex three dimensional structure in which the intervertebral discs play an important role in supporting the body weight while allowing physiological motions. The integrity of the different spinal structures is required to perform the daily life activities smoothly. It is important to investigate how the degenerative changes in the intervertebral disc alter the biomechanical behavior of the lumbar spine. Occurrence of annular lesions has been suggested as the first marker of the disc degeneration disease Annular lesions are defined as the structural disruption to the annulus and are reported in subjects as young as ten year old with occurrence increasing in the older population 14. Concentric tears, radial fissures and rim lesions are the most commonly observed annular lesions in the human lumbar discs. Incidences of annular lesions in the intervertebral discs have been shown to initiate cell-mediated chemical changes that are characteristics of a degenerated disc Increase in the flexibility of the motion segment with occurrence of annular lesions has been reported in the in vitro studies It is difficult to investigate the

20 2 annular lesions in isolation in vitro because of the cadaveric specimens exhibiting multiple characteristics of disc degeneration. Finite element models of the lumbar spine lack the detailed description of different types of annular lesions. The atrophy of the collagen fibers in these models has not been explained 27, 28. There is a need for developing the finite element models that can be used to understand the effects of different types of annular lesions on the biomechanics of the spine. In addition to the annular lesions the degenerative process in the disc is accompanied by the dehydration of the nucleus and the annulus, loss of proteoglycans content, decrease in the disc height and expansion of the annulus on the expense of the nucleus These biochemical and morphological changes in the disc progress with the increasing disc degeneration. Grading schemes based on the radiological, morphological and biochemical assessment have been proposed to classify the severity of the disc degeneration disease 30, 34, 36, 37. Dysfunction, instability and stabilization were proposed as three biomechanical stages of spinal degeneration This biomechanical behavior of the motion segments with progressive degeneration has been supported 39, 40 and contradicted 41, 42 by the experimental studies. Finite element models have been used to understand the effect of individual changes in the geometry and the material properties of the disc on its biomechanical behavior However, there is a need for finite element models of the lumbar spine simulating different grades of disc degeneration that include all the features of the disc degeneration simultaneously to understand the effects of disc degeneration disease on the biomechanical characteristics of the spine. The structural failures in the disc are considered to be the result of accumulated damage over a long period of time rather than a traumatic injury. Epidemiological studies have identified frequent bending and lifting as a major risk for disc prolapse 48, 49. Damage to discs structure in

21 3 response to the cyclic loading of the motion segments has been reported by a number of in vitro studies involving human cadavers and animal models However, in case of the human cadaver studies it is difficult to obtain a large number of specimens without prior disruptions in the disc structure. Also with current imaging techniques it is not possible to identify the location and extent of damage during different stages of testing without interruptions. Finite element models of the lumbar spine have predicted different loading conditions that are suggested to cause structural failure However, there is no finite element model of lumbar spine that investigates the degradation of the intervertebral disc under cyclic loading. The purpose of this thesis is to modify an existing poroelastic finite element model of L4/L5 lumbar motion segment to include the degenerative changes in the intervertebral disc. Employ the finite element models representing different stages of disc degeneration to investigate the effect of disc degeneration on the biomechanical behavior of the lumbar motion segment. Further use the finite element models to explore the initiation and progression of structural damage under different cyclic loading conditions. The specific aims of the thesis are, A. Aims 1. Aim 1 The first aim of the thesis is to investigate the effects of annular lesions on the biomechanical behavior of the lumbar motion segment. This aim will be accomplished by developing finite element models of L4/L5 lumbar motion segment that include radial fissure, concentric tear and rim lesion. Changes in the intervertebral disc kinematics with increasing size of annular lesions will be investigated. The effects of radial fissure, concentric tear and rim lesion individually and in combination with each other on the flexibility of the motion segment will be studied under different loading conditions.

22 4 This aim will test the hypothesis that the occurrence of annular lesions in the intervertebral disc will increase the flexibility of the spinal motion segment in the three principal directions. The flexibility will increase the most by the occurrence of rim lesion. Angular motion will increase the most under axial rotation in the presence of annular lesions. 2. Aim 2 The second aim of the thesis is to investigate the effects of progressive disc degeneration disease on the biomechanical characteristics of the lumbar motion segment. This aim will be accomplished by developing four finite element models of L4/L5 lumbar motion segment representing grade I/II, grade III, grade IV and grade V disc degeneration on Thompson grading scale. Morphological and biochemical changes observed with the progressive disc degeneration will be included in each model. Biomechanical behavior of the lumbar motion segments with different grades of disc degeneration will be studied under different loading modes. This aim will test the hypothesis that the flexibility of the lumbar motion segment will increase with disc degeneration in the three principal directions. Flexibility will exhibit an increasing trend up to Thompson grade IV disc degeneration. Further degeneration of the disc will result in a decrease in the flexibility of the lumbar motion segment. Annulus fibrosus will be exposed to increased levels of shear and tensile stresses with increasing severity of disc degeneration. 3. Aim 3 The third aim of the thesis is to investigate the fatigue failure of the intervertebral disc under different loading condition. This aim will be accomplished by incorporating continuum damage mechanics formulation in the finite element models of L4/L5 lumbar motion segment.

23 5 Initiation and progression of structural damage in the intervertebral disc will be tracked. Number of load cycles to disc failure will be predicted under simple and complex loading conditions. This aim will test the hypothesis that number of load cycles to disc failure will decrease as the motion segment is subjected to complex loading rather than single axis compressive or bending load. The damage will initiate and propagate preferentially in the posterior region of the intervertebral disc. With progressive degeneration of the intervertebral disc, the location of the failure initiation and propagation will shift from the inner annulus layers to the peripheral annulus layers. The chapters in this thesis are organized according to the specific aims. After a brief review of the relevant anatomy and background literature in chapter II, each specific aim is dealt with in the subsequent chapters. Chapter III presents a detailed review of the literature on the occurrence of annular lesions in the human lumbar discs and its role in the progressive disc degeneration disease. Experimental and computational work to understand the biomechanical effects of annular lesions on motion segment are discussed. A brief description of an already validated poro-elastic finite element model of L4/L5 lumbar motion segment developed by our lab is given. The modifications to the existing finite element model to introduce annular lesions are presented and the results based on the new models are discussed. In chapter IV finite element models representing different grades of disc degeneration of the disc are presented and the results are compared with the existing literature. Chapter V deals with the development of a finite element model to investigate the fatigue failure in the lumbar disc under different loading conditions. The last chapter summarizes the conclusions reached and recommendations for future research are suggested.

24 6 II - BACKGROUND A. Anatomy of the Spine 1. Spinal Column The spinal column is composed of series of vertebrae stacked one upon the other separated by the intervertebral discs. There are five regions of the spine: cervical, thoracic, lumbar, sacrum and coccyx as shown in Figure 1. Load-bearing, provision of movement, and protection of neural elements are the basic functional roles of the spine. Spinal motion segment is the smallest functional unit of the spine that contains all the components of the rest of the spine and demonstrates the characteristics of the entire spine. The motion segment consists of two vertebrae, two posterior joints, an intervertebral disc and the soft tissue structures including joint capsules, ligaments and muscles. Figure 1: Spinal column

25 7 2. Lumbar Spine The lumbar spine is the lower region of the spinal column as shown in Figure 1. In a human spine there are five lumbar vertebrae connecting proximally to the thoracic spine and distally to the sacrum. The individual vertebrae are often mentioned as L1, L2, L3, L4 and L5 where L refers to the lumbar spine and number specifies the level. L1 and L5 being the most proximal and distal vertebrae respectively. 3. Vertebral Anatomy Each vertebra consists of an anterior portion called vertebral body and a posterior ring known as the neural arch. The vertebral body is the main load bearing structure of the vertebra. It is formed by an external cortical shell surrounding the inner cancellous bone. The posterior element consists of the spinous process, laminae, superior and inferior articulating processes of the zygapophysial joints and the left and right transverse processes. Laminae connect the spinous process to the rest of the posterior element while pedicles connect the posterior element to the vertebral body. The superior and inferior articulating surfaces mate respectively with the inferior articulating process of the superior vertebra and the superior articulating process of the inferior vertebra forming the facet joints. 4. Intervertebral Disc The intervertebral disc is the soft tissue that lies between the adjacent vertebral bodies. It binds the adjacent vertebrae, transfers load from one vertebra to the other and allows the movement of vertebrae. Intervertebral disc is comprised of three distinct areas: the nucleus pulposus, annulus fibrosus and cartilaginous endplate as shown in Figure 2. The nucleus pulposus is the central fluid like mass. Water molecules make up 65-88% weight of the nucleus 64, 65, 65, 66 which is

26 8 responsible for its fluid like properties. It is rich in proteoglycans, contributing 65% of the dry weight 64, 65, 67. Proteoglycans have the ability to attract and retain water thus creating osmotic pressure. Collagen type II constitutes 15-20% of the dry mass of the nucleus 66, 68, 69. The annulus fibrosus surrounds the nucleus pulposus laterally, anteriorly and posteriorly. It is composed of fibrous tissue in discontinuous concentric laminated bands 70.Water amounts to 70-78% of annulus. Collagen type I and proteoglycans make up 50-60% and 20% of dry weight of the annulus respectively The collagen content increases while the water and the proteoglycans content decreases from the inside to the peripheral layers of the annulus 66. The collagen fibers within each lamella of the annulus fibrosus are arranged parallel to each other and inclined at an angle of 30 to the horizontal 70. In consecutive lamellae, this inclination alternates from positive to negative with respect to the vertical axis 69, 70 as shown in Figure 3. Endplates are composed of hyaline cartilage and sit on the superior and inferior faces of the discs, separating them from the vertebrae. The permeable central portion of the endplates allows the diffusional transport of water and nutrients to the disc. The peripheral rings of the annulus insert directly into the bone of the adjacent vertebral bodies.

27 9 Endplate Annulus Nucleus Annulus Endplate Figure 2 Cross-sectional view of an intervertebral disc. Figure 3: The annulus fibrosus with the central nucleus pulposus removed. The collagen fibers are arranged in multiple concentric layers with consecutive rings running in alternating directions. Fibers are inclined at an angle of approximately 30 to the horizontal. Image borrowed from Neumann,

28 10 5. Ligaments of the Lumbar Spine Spinal ligaments act as static stabilizers and limit the range of motion of the motion segment. The major ligaments of the lumbar spine are shown in Figure 4. Anterior longitudinal ligament is a multisegmental ligament that attaches to the anterior and medial surfaces of the vertebral bodies and IVDs along the entire spinal column. Its major role is in limiting the rotation under extension. Posterior longitudinal ligament is also a multisegmental ligament located in the vertebral canal and attaches to the posterior surfaces of the vertebral bodies and IVDs along the entire spinal column. It restricts the flexion motion. Ligamentum flavum is a highly elastic intersegmental ligament that attaches to the posterior elements, connecting the laminae of the adjacent vertebrae. It minimizes the likelihood of spinal cord impingement. The interspinous and supraspinous ligaments connect the spinous processes of the adjacent vertebrae and limits movement during flexion. Interspinous ligaments are intersegmental while supraspinous ligament spans along the entire vertebral column. The capsular ligaments are oriented perpendicular to the plane of the facets joints, resisting the axial rotation in the lumbar spine. Figure 4: Ligaments of the lumbar spine.

29 11 B. Disc Degeneration Disease Disc degeneration is a progressive pathological condition that alters the biochemistry and morphology of the IVD. The most notable change is the reduction of water and proteoglycans content of the nucleus pulposus. The water content in the healthy disc is up to 88%, while in a degenerated disc it can be as low as 65% The proteoglycans concentration decreases from 65 % of the dry weight in the healthy nucleus to 16% in a degenerated disc The collagen content in the nucleus increases with disc degeneration 68. Similar changes are observed in the annulus fibrosus. Water content in the annulus fibrosus decreases from 78% in the healthy disc to 70% in the degenerated disc 65, Disc degeneration is classified based on radiographical, morphological and biochemical assessment 30, 34, 36, 37. The most commonly used classification schemes are proposed by Thompson et al 34 and Pfirrmann at al 36. The system proposed by Thompson et al 34 is based on the gross morphology and describes discs in terms of epidemiological changes. The grading scheme classifies disc degeneration process into five stages 34. Grade I represents a healthy intervertebral disc with a bulging gelatinous nucleus that can be easily distinguished from the lamellas of the annulus fibrosus and a uniformly thick endplate. Grade II disc degeneration is identified by the presence of white fibrous tissue in the peripheral nucleus and mucinous material between the annulus layers. Endplates are presented with irregular thickness. Grade III represents the presence of fibrous tissue in the nucleus, loss of annular-nuclear demarcation and a slightly decreased disc height. Focal defects are observed in the endplates. Grade IV discs exhibit clefts in the nucleus, focal disruptions in the annulus and further decrease in the disc height. Grade V represents a severely degenerated disc with complete collapse of the intervertebral disc space, clefts expanding through the nucleus and annulus, diffuse sclerosis in the endplate and large

30 12 osteophytes. Figure 5 shows the sagittal cross-sections of the lumbar motion segments with healthy disc, disc with rim lesion and a collapsed disc. Figure 6 shows the morphological, radiological and MRI images of different stages of disc degeneration. Table 1 summarizes the description of changes in the intervertebral disc for five grades of disc degeneration as defined by Thompson et al 34. ` Figure 5: Sagittal cryomicrotome sections demonstrating a normal disc (upper left), a disc with a rim lesion (upper right), a disc with a radial fissure (lower left) and a segment with collapsed intervertebral disc. Image borrowed from Haughton et al 23

31 Figure 6: Different stages of disc degeneration disease. First column shows the mid-sagittal cross-sectional view of the motion segment. Second and third columns show the radiograph and MRI images of the same specimens. (a) Grade I (b) Grade II (c) Grade III (d) Grade IV (e) Grade V. Images borrowed from Benneker et al 30 13

32 14 Table I: Thompson Disc Degeneration Grading Scheme 34. Degeneration Grade Nucleus Annulus Endplate Vertebral Body I Bulging gel Discrete fibrous lamellas Hyaline, uniformly thick Margins rounded II White fibrous tissue Peripherally Mucinous material between Lamellas Thickness irregular Margins pointed III Consolidated fibrous tissue Extensive mucinous infiltration; loss of annular-nuclear demarcation Thickness irregular Early chondrophytes or osteophytes at margins IV Horizontal clefts parallel to end plate Focal disruptions Fibrocartilage extending from subchondral bone; irregularity and focal sclerosis in subchondral bone Osteophytes less than 2 mm V Clefts extend through nucleus and annulus Clefts extend through Diffuse sclerosis Osteophytes greater than 2 mm

33 15 III - EFFECT OF ANNULAR LESIONS ON THE BIOMECHANICAL BEHAVIOR OF LUMBAR MOTION SEGMENT A. Introduction Intervertebral disc degeneration is considered to be a cause for low back pain in addition to other factors Occurrence of annular lesions has been suggested as the first marker of the disc degeneration process 14, 15, 17, 19. Annulus lesions are defined as the disruptions to the annulus structure and can be categorized into concentric tears, radial fissures and rim lesions 72. Concentric tears are defined as the delamination of the annular lamellae circumferentially. Radial fissures are annulus disruptions that initiate from the nucleus and propagate in radial direction towards the outer annulus. Rim lesions are the separation of the peripheral annulus from the rim of the adjacent vertebral bodies. Annular lesions have been reported in subjects as young as ten years old and their occurrence increases in the older population. Sharma et al 14 studied the occurrence of annular tears and nuclear degeneration in 26 children aged between 9-21 years. Annular lesions were reported in 60% of the discs. Their analysis of disc degeneration progression suggested that annular tears preceded nuclear degeneration. Osti et al 16 examined 135 cadaveric lumbar discs from 27 spines aged between years. They reported annular tears in 50% (45) of the specimens less than 35 years of age while 73% (33) of the discs in the years age group had incidence of annular tears. 91% of radial tears were located in the posterior annulus while 69% of rim tears were observed in the anterior annulus. Concentric tears were distributed as 44% and 56% among the anterior and posterior annulus respectively. Haefeli et al 15 examined 41 cadaveric human lumbar spines aged 7 months to 88 years. Radial tears were observed in 5% of specimens until the age of 20 years however its occurrence increased to 25% by the third decade and to 60% by the sixth decade. Concentric tears were not found in the

34 16 first two decades but its prevalence increased to 34% between third and fifth decade and to 69% after the age of 48 years. Rim lesions were reported in 22% of specimens older than 50 years. Sharma et al 19 used MRI to study the occurrence of annular tears in the disc. Annular tears were identified by the presence of hyper-intense signal intensity within the annulus. They examined 276 disks (T12-S1) from 46 patients aged between years. Annular tears were reported in 203 of 276 discs. Discs were graded based on the degeneration scale of Pfirrmann et al % (22) of the grade-i discs and 70% (61) of the grad-ii discs had annular tears. Annular tears were reported in 97% (120) of the discs with degeneration grade greater than II. Roberts et al 17 examined 70 cadaveric human L4/L5 discs aged between 13 to 79 years for structural failures. Radial tears were reported in 68% of discs aged between years and increased to 90% in age group years. Concentric tears were reported in all the discs. Rim lesions were infrequent in early age with only 20% of discs in age group years but increasing to 40% in age group years and 90% in age group years. Table II summarizes the findings of the in vivo and in vitro studies investigating the occurrence of annular lesions in different age groups and discs of different degeneration grade.

35 17 Table II: Summary of studies reporting occurrence of annular lesions in different age groups. Study Discs Examined Age Group Annular Lesions Occurrence Radial Concentric Rim Haefeli et al 15 Roberts et al Cadaveric Lumbar Spine 70 Cadaveric L4/L5 Discs Until 30 years 25 % Over 30 years 60 % years 34 % Over 50 years 69 % 22 % years 68 % 100 % 20 % years 73 % 100 % 40 % years 90 % 97 % 90 % Osti et al Cadaveric Lumbar Discs Until 35 years 50 % Over 35 years 73 % Sharma et al Patients 276 Discs MRI Grade I 31 % Grade II 70 % Grade > II 97 %

36 18 Occurrences of annular lesions in the discs have been shown to cause cell-mediated biochemical changes that are characteristics of a degenerated disc. Sharma et al 19 imaged 46 patients twice with a mean duration of at least 2.5 years between the two MRI scans. They reported a mean increase of 0.31 in the degeneration grade of the discs with annulus tears as compared to a mean increase of 0.15 in the discs without annulus tears. Yoon et al 18 studied the effect of annular injury in porcine discs. Annular lesions (2-3mm incision) on the left dorsal side were created in 22 discs while 13 discs were used as a control group. Both the lesion and the control group discs were evaluated as degeneration grade-i preoperatively. The mean degeneration grade for lesion group increased to 3.5 by the 5 th week of the study while no change in control group was reported. They also reported a decrease in preoperative mean disc height of 0.43cm to 0.39cm by the 5 th week and to 0.36cm by the 39 th week of the study while no significant change in disc height was noted in the control group. Kaigle et al 20 reported disruption in the inner annulus, fibrous nucleus and disc height reduction three months after the introduction of outer annulus tears in the porcine discs. Latham et al 21 introduced outer annulus injury in the ovine discs. They observed mild to moderate degeneration in the inner annulus and the nucleus six months after the intervention. It is important to understand that how annular lesions change the disc kinematics and stress distribution pattern resulting in an accelerated disc degeneration process. Different studies have reported changes in disc biomechanics with the occurrence of annular lesions. Schmidt et al 24 reported a decrease in rotational stiffness under different loading modes in cadaveric human lumbar discs with occurrence of radial fissures. Haughton et al 22, 23 observed increase in ROM under axial rotation for cadaveric lumbar motion segments with rim lesions or radial fissures. Thompson et al 26 encountered larger motion under axial rotation for cadaveric human lumbar

37 19 motion segments with annular lesions. Przybyla et al 73 studied the effect of annular tears and endplate fractures on the intradiscal stress in the human intervertebral discs under compressive load. They concluded that peripheral annulus tears have no significant effect on the intradiscal stress. In vitro studies involving cadaveric human spine have their limitations in terms of understanding the effects of different types of annulus lesions on the biomechanical behavior of the motion segment. Cadaveric motion segments normally exhibit multiple characteristics of disc degeneration (fibrotic nucleus, annulus disruptions, reduced disc height, osteophytes and facet joints degeneration) rather than just the annular lesions. Thus, the observations reported by in vitro studies were the result of the overall degeneration state of the motion segment not just the occurrence of annular lesions. Thompson et al 25 introduced radial fissures, concentric tears and rim lesions in healthy ovine discs. Their protocol made it possible to study the effect of different types of annular lesions on disc kinematics in isolation. They reported increase in the flexibility of the motion segments with the occurrence of the rim lesion. However, no significant changes were observed with the presence of radial fissure or concentric tear. In vitro testing involving animal models helps in understanding the effect of annular disruptions on the motion segment s kinematics. However, it is difficult to introduce inner annulus lesions (radial fissure & concentric tear) without disrupting the endplate or the outer annulus in the experimental setup. Also there is always the difficulty of interpreting the conclusions reached using animal models to correlate to the corresponding changes in human motion segments. Finite element modeling has been used extensively to understand the biomechanics of the spine. It is easy to introduce different types of annular lesions in the finite element models without damaging other components of the motion segment. Goel et al 27 introduced radial fissure and concentric tear in the finite element model of L3/L4 motion

38 20 segment. They reported an increase in the disc bulge and axial displacement due to annular lesions. However, analyses were performed under compressive loading only with no bending moments applied. Little et al 28 developed a non-linear finite element model of L4/L5 disc to investigate the effect of annular tears on disc biomechanics. They concluded that nucleus degeneration reduced the peak moment of the disc but annular lesions did not have a considerable effect. Collagen fibers atrophy was not mentioned by both computational studies while modeling different types of annular lesions. The purpose of this study was to develop a finite element model of L4/L5 lumbar motion segment that includes different types of annular lesions. Effect of different types and sizes of annular lesions on the lumbar motion segment biomechanics was analyzed. It was hypothesized that (a) Introduction of annular lesions will result in an increase in the flexibility of the lumbar motion segment in the three principal directions (b) Rim lesion will increase the flexibility of the motion segment the most followed by the radial fissure and concentric tear respectively (c) Angular motion will increase the most under axial rotation in the presence of annular lesions. B. Materials and Methods 1. 3D Finite Element Model of L4/L5 Lumbar Motion Segment A previously validated 74, 75 three dimensional non-linear poroelastic finite element model of a healthy lumbar L4/L5 motion segment developed by our research team was employed for the current study. It included biological parameters such as porosity, osmotic pressure and the strain dependent permeability. Detailed description of the finite element model in terms of types of elements used and description of properties of materials associated with various components in the motion segment have already been published 74, 75 and hence only a brief summary will be

39 21 presented here. Analyses were carried out using a commercially available software package ADINA 76. The geometric shape of the lumbar motion segment was generated from a serial computed axial tomographic scan (CT) of an L4/L5 disc body unit. Using this CT scan a 3- dimensional finite element model was generated for the motion segment consisting of vertebradisc-vertebra unit using a CAD station. The cortical bone, cancellous bone, posterior elements, endplates, facet cartilage, and nucleus pulposus were modeled as 8-node, 3-dimensional, isoparametric elements. The left and right superior and inferior articulating surfaces of the facet cartilage were approximated by flat trapezoidal moving frictionless contact surfaces. In the intervertebral disc, the annulus matrix was assumed as a composite material consisting of fibers embedded in a homogenous matrix material. The annulus ground matrix was discritized by 8- node, 3-dimensional solid elements. The annular fibers were assembled in a criss-cross fashion at an angle approximately 30 to the transverse plane. Annular fibers were modeled as the truss elements connected to the 3-dimensional solid elements of the annulus ground substance using rebar option. Nodes were generated at the intersections of the rebar lines representing the annular fibers and the faces of the 3-dimensional solid elements of the annulus ground substance. Constraint equations between the generated nodes and the three corner nodes of the 3- dimensional element faces ensured that annular fibers deform with the annulus ground substance. The normal nucleus, which is a gelatinous material, was represented by 3-dimensional fluid elements. The seven major ligaments were modeled by 2-node nonlinear cable elements and their attachment points were taken from the literature.

40 22 Table III: Material properties for L4/L5 lumbar motion segment finite element model Structure Elastic Modulus Poisson s ratio Type of element No. of Elements Material Model Cortical bone 12 GPa D Solid (8 node) 1759 User Supplied (Soil Consolidation) Cancellous bone 100 MPa D Solid (8 node) 3112 User Supplied (Soil Consolidation) Posterior elements 3.5 GPa D Solid (8 node) 2112 User Supplied (Soil Consolidation) Endplate 20 MPa D Solid (8 node) 264 User Supplied (Soil Consolidation) Nucleus 1.0 MPa D Solid (8 node) 720 User Supplied (Soil Consolidation) Annulus 4.2 MPa D Solid (8 node) 1920 User Supplied (Soil Consolidation) Annular fibers - - Rebar Elements 1760 Non-linear Elastic Ligaments - - Truss 32 Non-linear Elastic Facet cartilage 11 MPa D Solid (8 node) 192 User Supplied (Soil Consolidation) Facet contacts - - Contact 24 -

41 23 The effect of the change in the concentration of proteoglycans contained within the nucleus was modeled by incorporating a pressure, referred to as the swelling pressure (p swell ), which is dependent on the fixed charge density. The swelling pressure was calculated using an equation proposed by Broberg 82 : p swelli f 1 Pfi f 1 2 i 2 i Where f i is the fixed charge density at time t i and P and are constants. Similarly, the effect of the change in permeability resulting from the axial strain in the tissue was modeled by including internal pressure acting on the disc. This pressure (Pstrain) was calculated using the equation 83 : p straini 2 1 ei Eei H exp A 2 1 ei ei 1 Where E is the Young s modulus, H A is the aggregate modulus, e is the axial strain in the disc tissue, is the porosity at any time t and is the nonlinear stiffness coefficient. Regional variations in the elastic and poroelastic material properties and water content of the various disc tissues (outer annulus, inner annulus and nucleus pulposus) were also incorporated in the model 75. These variations allowed the swelling pressure and strain pressure to vary regionally throughout the disc as known to occur in vivo. i

42 24 Posterior L4 Vertebra L4/L5 Disc Endplate L5 Vertebra Figure 7: Finite Element model of L4/L5 motion segment consisting of L4 vertebra, L5 vertebra, L4/L5 disc and the endplates

43 25 2. Finite Element Model Validation In order to validate the finite element model studies were conducted to predict the percent change in the total stature in response to three different loading conditions 75. The results predicted by the finite element model were then compared to the results collected in vivo reported by Tyrrell et al 84. The first study was related to the diurnal change in the total stature. Tyrell et al 84 measured the change in stature of eight young adults. The subjects were not allowed to do any physical work or exercise during the day. Height measurements were made with the subjects standing upright in a relaxed posture. They were allowed to sleep for 8 hours. Measurements were made over the period of 24 hours for each subject. The mean and the standard deviation of the observations were reported. To predict the diurnal changes in stature using the finite element model, the motion segment was subjected to a static compressive load of 850 N for 16 hours, which was reduced to 440 N to simulate loading during 8 hours of sleep as shown in Figure The diurnal changes in the stature predicted by the finite element model over the 24 hours period were within one standard deviation of the mean stature changes reported in vivo as shown in Figure 9 75.

44 26 Figure 8: Compressive load magnitude simulating 16 hours of normal day activities and 8 hours of sleep. Figure 9: Diurnal changes in stature as observed in vivo and predicted by the L4/L5 lumbar motion segment finite element model 75.

45 27 The second study investigated the change in the total stature due to creep loading over a short period of time. Tyrell et al 84 measured changes in stature for subjects who held a 40 kg barbell across their shoulders for 20 minutes followed by a 10 minutes recovery period. The loading was simulated in the finite element model by applying a compressive load of 800 N for 20 minutes, after which the load was reduced to 440 N as shown in Figure The change in the disc height was calculated during the creep loading and until ten minutes after unloading. The stature changes predicted by the finite element model in response to short term creep loading were within 4% of those reported in vivo as shown in Figure The third study conducted to validate the finite element model measured the stature changes in response to cyclic loading of the spinal column. The lumbar motion segment was subjected to 12 loading cycles per minute for 20 minutes. The loading protocol consisted of a compressive preload of 400 N in conjunction with a peak to peak cyclic compressive load of 400 N and a 5 Nm peak to peak cyclic flexion moment as shown in Figure 12. Changes in disc height were recorded during the cyclic loading duration and until ten minutes after unloading. The stature changes predicted by the finite element model under cyclic loading were within 3% of those reported by Tyrell et al 84 as shown in Figure

46 28 Figure 10: Compressive load magnitude for short term creep testing. Figure 11: Changes in stature as observed in vivo and predicted by the L4/L5 lumbar motion segment finite element model during short term creep loading 75.

47 29 Figure 12: Compressive load and flexion moment magnitudes during one cycle of cyclic load testing. Figure 13: Changes in stature as reported in vivo and predicted by the L4/L5 lumbar motion segment finite element model during cyclic load testing 75.

48 30 3. Inclusion of Annular Lesions Annular lesions were introduced in the L4/L5 finite element model (Figure 7) with geometry and material properties of the healthy disc. Radial fissure, concentric tear and rim lesion were introduced in the finite element model one at a time. The location of annular lesions was selected from the information available in the literature Radial fissure was introduced in the left lateral posterior region near the superior end of the disc. It initiated in the inner annulus layer next to the nucleus and propagated outward towards the periphery of the annulus. Concentric tear was introduced in the anterior region of the annulus. It initiated at the anterior region of the disc and progressed towards the lateral side. Rim lesion was introduced in the anterior annulus next to the superior endplate. It extended from the outer rim to a few outer layers of annulus. Figure 14 shows the location of the three types of annular lesions within the annulus. Radial fissure, concentric tear and rim lesion occupied a maximum of 0.31%, 0.37% and 0.28% of the volume of the annulus respectively

49 31 Radial Posterior Rim Anterior Concentric Figure 14: Location of Radial fissure, Concentric Tear and Rim Lesion in the annulus fibrosus.

50 32 a. Annulus Ground Substance The annular lesions were modeled by modifying the material properties of the annulus ground substance to that of the nucleus. Each finite element representing the annulus was characterized by eight integrating points distributed in a symmetric fashion within the element. The size of the lesion was increased in increments using the user defined material routine available in the finite element package ADINA. The routine enabled to change the material property associated with each integrating point. Propagation of the annular lesion was modeled by progressively changing the material properties at appropriate integrating points in the elements along the assumed progression direction. Size of radial fissure was increased in small steps with the smallest fissure initiating at the inner annulus layer and the largest fissure extending up to the outer annulus periphery as shown in Figure 15. Similarly, concentric tear initiated by occupying 0.02% of the annulus volume and propagated circumferentially in five steps occupying 0.37% of the annulus volume as shown in Figure 16. Rim lesion initiated at the annulus rim and progressed circumferentially and radially in small increments as depicted in Figure 17.

51 % 0.02% 0.04% 0.10% 0.15% 0.21% 0.26% 0.31% Figure 15: Progression of radial fissure. Fissure initiated at the inner boundary of the annulus and progressed outward towards its periphery. Blue color represents the healthy annulus while red color represents the fissure volume. Fissure volume as a percentage of total annulus volume is given below each step.

52 % 0.02% 0.09% 0.18% 0.29% 0.37% Figure 16: Progression of concentric tear. Tear initiated in the anterior region of the disc and progressed towards the lateral region. Blue color represents the healthy annulus and red color represents the tear volume. Tear volume as a percentage of total annulus volume is given below each step.

53 % 0.05% 0.14% 0.22% 0.28% Figure 17: Progression of rim lesion. Lesion initiated at the outer periphery of the anterior annulus and progressed inward towards the nucleus. Blue color represents the healthy annulus and red color represents the lesion volume. Lesion volume as a percentage of total annulus volume is given below each step.

54 36 b. Annulus Fibers Damage The damage to annulus fibers caused by the lesion was modeled in three different ways. In the first method all the fibers in the vicinity of the lesion volume were assumed to be nonfunctional and were deactivated. This model will be referred as Global. In the second method only the fibers within the lesion volume were deactivated. This model will be referred as Local. In the third method the loading capacity of the fibers in the vicinity of the lesion was reduced by half by modifying the fiber s stress-strain curves. This case will be referred as LoadCap. Thus in total nine models were created, three for each type of annular lesion. Figure 18, Figure 19 and Figure 20 show the three scenarios (Global, Local, and LoadCap) of annulus fibers damage for the full extent of the radial fissure. Finally a finite element model was created with the three types of annular lesions occurring simultaneously in the disc. The location and the size of the lesions were same as in the previous models. Annular lesions occupied a total of 0.96% of the annulus volume. The damage to annulus fibers was modeled by deactivating the fibers passing through the lesions and reducing the load capacity of surrounding fibers by half.

55 Figure 18: Annulus collagen fibers damage for Global model (Radial fissure). Collagen fibers (Green) were modeled using concentric rings of rebar elements, embedded in the annulus matrix. Collagen fibers in the surrounding of the lesion were deactivated to model the fiber damage and can be seen missing in the picture. 37

56 Figure 19: Annulus collagen fibers damage for Local model (Radial fissure). Collagen fibers passing through the lesion volume only, were deactivated and can be seen missing in the picture. Only the fibers in the region of interest are shown for clarity. 38

57 Figure 20: Annulus collagen fibers damage for LodCap model (Radial fissure). The load capacity of the fibers in the vicinity of the lesion was reduced by half. The fibers with the reduced load capacity can be identified with orange color in the picture. 39

58 40 4. Loading Conditions In order to investigate the effect of annular lesions on the disc kinematics, models were pre-loaded with a 400 N static compressive load followed by moments of 7.5 Nm in flexion, extension, axial rotation and lateral bending respectively. The applied static compressive load represented the body weight on the L4/L5 lumbar motion segment while the applied moments allowed the angular motions in the three principal directions within the physiological range 85. C. Results Rotation under flexion, extension, axial rotation and lateral bending was calculated for each step increase in the size of the annular lesions. ROM for the lesion models was compared with the corresponding results from an intact motion segment to determine the effect of lesions on the flexibility of the lumbar disc. ROM of the motion segment increased by the occurrence of the annular lesion in the disc in the three principal directions. Results for each type of annular lesion are discussed below. 1. Global Models Figure 21, Figure 22 and Figure 23 show the percentage increase in ROM with increasing size of radial fissure, concentric tear and rim lesion under different loading modes as predicted by the Global models. ROM increased non-linearly with the progression of the tears under all loading modes. Axial rotation increased by 4.6%, 1.4% and 0.6% by the occurrence of rim lesion, radial fissure and concentric tear respectively (Figure 21). Flexion/extension increased by 1.1%, 0.6% and 0.2% by the occurrence of rim lesion, radial fissure and concentric tear respectively (Figure 22). Lateral bending increased by 0.5%, 0.8% and 0.2% by the occurrence of rim lesion, radial fissure and concentric tear respectively (Figure 23). Flexibility of the motion segment increased the most under axial rotation for each type of annular lesion. Rim

59 41 lesion caused the largest increase in the motion under axial rotation and flexion/extension and concentric tear had the least effect on the stiffness under all loading modes. In case of radial tear, a sharp increase in rotation was observed as it reached the periphery of the annulus. This was especially true for the lateral bending, which can be attributed to the location of the radial fissure in the lateral region of the disc.

60 42 Figure 21: Increase in ROM under axial rotation with increasing size of rim lesion, radial fissure and concentric tear as predicted by Global models. Figure 22: Increase in ROM under flexion / extension with increasing size of rim lesion, radial fissure and concentric tear as predicted by Global models.

61 Figure 23: Increase in ROM under later bending with increasing size of rim lesion, radial fissure and concentric tear as predicted by Global models. 43

62 44 2. Local Models Figure 24, Figure 25 and Figure 26 show the percentage increase in ROM with increasing size of annular lesions under different loading modes as predicted by the Local models. ROM increased non-linearly with the progression of the tears under all loading modes. Axial rotation increased by 1.4%, 0.4% and 0.4% by the occurrence of rim lesion, radial fissure and concentric tear respectively (Figure 24). Flexion/extension increased by 0.2%, 0.1% and 0.1% by the occurrence of rim lesion, radial fissure and concentric tear respectively (Figure 25). Lateral bending increased by 0.2%, 0.2% and 0.1% by the occurrence of rim lesion, radial fissure and concentric tear respectively (Figure 26). Local models also demonstrated that the flexibility increased the most under axial rotation for each type of annular lesion. Rim lesion caused the largest increase in the motion under axial rotation and flexion/extension. Local models predicted a much smaller increase in the rotation as compared to the Global models under all loading modes.

63 45 Figure 24: Increase in ROM under axial rotation with increasing size of rim lesion, radial fissure and concentric tear as predicted by Local models. Figure 25: Increase in ROM under flexion/extension with increasing size of rim lesion, radial fissure and concentric tear as predicted by Local models.

64 Figure 26: Increase in ROM under lateral bending with increasing size of rim lesion, radial fissure and concentric tear as predicted by Local models. 46

65 47 3. LoadCap Models Figure 27, Figure 28 and Figure 29 show the percentage increase in ROM with increasing size of radial fissure, concentric tear and rim lesion under different loading modes as predicted by the LoadCap models. ROM increased non-linearly with the progression of the tears under all loading modes. Axial rotation increased by 0.3%, 0.2% and 0.3% by the occurrence of rim lesion, radial fissure and concentric tear respectively (Figure 27). Flexion/extension increased by 0.2%, 0.1% and 0.2% by the occurrence of rim lesion, radial fissure and concentric tear respectively (Figure 28). Lateral bending increased by 0.1%, 0.1% and 0.1% by the occurrence of rim lesion, radial fissure and concentric tear respectively (Figure 29). Again the flexibility increased the most under axial rotation for each type of annular lesion and rim lesion caused the largest increase in the motion under axial rotation and flexion/extension.

66 48 Figure 27: Increase in ROM under axial rotation with increasing size of rim lesion, radial fissure and concentric tear as predicted by LoadCap models. Figure 28: Increase in ROM under flexion / extension with increasing size of rim lesion, radial fissure and concentric tear as predicted by LoadCap models.

67 Figure 29: Increase in ROM under lateral bending with increasing size of rim lesion, radial fissure and concentric tear as predicted by LoadCap models. 49

68 50 4. Radial Fissure, Concentric Tear and Rim Lesion Occurring Simultaneously Figure 30 shows the percentage increase in the ROM under different loading directions due to occurrence of radial fissure, concentric tear and rim lesion simultaneously in the disc. ROM increased by 3.3%, 0.9% and 1.3% under axial rotation, flexion/extension and lateral bending respectively. Figure 30: Increase in ROM due to occurrence of annular lesions (radial fissure, concentric tear and rim lesion) under different loading modes. The increase in flexibility under axial rotation was considerably higher than under flexion/extension or lateral bending.

69 51 D. Discussion The finite element models presented, helped to understand the effect of annular lesions on the lumbar spine biomechanics. The ROM increased with increasing size of the annular lesions under all loading modes thus validating the first hypothesis. The increase in ROM due to rim lesion as predicted by the finite element models was two to four times that of radial fissure or concentric tear under different loading modes supporting the second hypothesis. The Increase in ROM predicted under axial rotation was two to ten times greater than that under flexion/extension or lateral bending validating the third hypothesis. The increase in the flexibility of the motion segment due to annular lesions depended strongly on the manner in which the damage to annulus fibers was modeled. A larger increase in ROM was observed when all the fibers in the vicinity of the lesion were non-functional(global) than the cases when only the fibers within the lesion volume were deactivated (Local) or the loading capacity of the surrounding fibers was reduced by half (LoadCap). Thus, it is important to include the annulus fibers damage while modeling annulus lesions. Thompson et al 25 studied the effect of different types of annulus tears on the joint mechanics using ovine lumbar spinal motion segments. Their protocol allowed examining the effect of each type of tear in isolation. Introduction of the rim lesion decreased the peak moments by 25.8%, 17.1% and 13.3% under axial rotation, flexion/extension and lateral bending respectively. They concluded that concentric tear and radial fissure did not have significant effect on the stiffness of the motion segment. The current finite element models also predicted a larger increase in the flexibility due to rim lesion as compared with the concentric tear and radial fissure. Larger increase in ROM was predicted under axial rotation than under flexion/extension or lateral bending. Difference in the magnitude of the results between the current study and the

70 52 experimental study could be due to the use of ovine samples and difference in the exact sizes and locations of the annular lesions. Haughton et al 23 reported the ROM in the three principal directions for 68 cadaveric human lumbar motion segments with healthy discs, discs with radial fissures and discs with rim lesions. The motion under axial rotation and flexion/extension was significantly larger in the motion segments with the annulus tears than the one with the healthy discs. The mean ROM increased by 136% and 132% under axial rotation in the motion segments with rim lesions and radial fissures respectively. Thompson et al 26 tested lumbar motion segments from 30 cadaveric human lumbar spines under flexion/extension and axial rotation. Larger motion was observed under axial rotation for motion segments with annulus tears than those without tears. Haughton et al 22 tested 82 cadaveric human lumbar motion segments under an axial rotational moment of 6.6Nm. Average stiffness of 7.0Nm/deg was reported for motion segments with normal discs which decreased to 1.9Nm/deg and 1.7Nm/deg by the occurrence of rim lesion and radial fissure respectively. Schmidt et al 24 tested 20 cadaveric human lumbar motion segments under flexion, extension, axial rotation and lateral bending. They reported a 71% and 39% reduction in stiffness under axial rotation and flexion respectively with the incidence of annular lesions. The current finite element analyses showed that annular lesions occupying only one percent of annulus volume could result in one to three percent increase in rotation under different loading modes. Cadaver studies reported much larger increase in the flexibility which could be due to occurrence of multiple annular lesions, large size of the tears and other degenerative changes in the motion segment. The increase in flexibility of the motion segment due to occurrence of annular lesions suggests that the disc will be subjected to higher stresses. Abnormal stresses in the disc can

71 53 promote the cell mediated degenerative changes which would alter the load distribution pattern and accelerate the degeneration process. The purpose of this study was to investigate the effects of annular lesions on the disc kinematics in isolation. So other disc degenerative changes like dehydration of the nucleus and the annulus, reduced disc height, expansion of the annulus and altered material properties were not included in the finite element models. The effects of annular lesion on disc biomechanics will be incorporated while developing the finite element models representing different grades of disc degeneration.

72 54 IV - BIOMECHANICAL CHARACTERISTICS OF L4/L5 LUMBAR MOTION SEGMENTS WITH DEGENERATED INTERVERTEBRAL DISC A. Introduction Disc degeneration is characterized by the progressive changes in the morphology and the biochemistry of different components of the disc. Morphological changes include appearance of the annular lesions, expansion of the inner annulus on the expense of the nucleus and reduction in the disc height 29-31, 34. Biochemical changes result in decrease in the water content in the nucleus and the annulus, decrease in the proteoglycans concentration in the nucleus and increase in the collagen fibers in the nucleus The dehydrated nucleus transitions from its fluid-like behavior to a solid like behavior making it hard to distinguish it from the annulus fibrosus 86. Decrease in swelling stress and effective aggregate modulus accompanied by an increase in permeability has been reported in the nucleus with progressive degeneration 87. Stress profilometry of the degenerative discs showed a 30% reduction in the intra-discal pressure and a decrease in the nucleus sagittal diameter by half accompanied with increase in annulus stress by 160% 29. Elastic material properties such as Poisson ratio, failure stress and strain energy density of the annulus have been shown to be strongly influenced by the disc degeneration 33, Iatridis et al 83 suggested a shift in load bearing in the disc from fluid pressurization to compressive deformation due to changes in the material properties of the annulus with degeneration. The chemical and geometrical changes characteristic of disc degeneration alter the biomechanical behavior of the motion segment. Abnormal mechanics in terms of magnitude and asymmetry of motion, transverse and sagittal translation, location of the instantaneous axis of rotation and patterns of coupled motion have been reported with disc degeneration 91, 92. Pollintine et al 93 observed increased load bearing in the facet joints with disc degeneration.

73 55 Kirkaldy-Willis and Farfan 38 suggested three biomechanical stages of spinal degeneration: dysfunction, instability and stabilization. This behavior has also been reported by Fujiwara et al 39 who tested 110 cadaveric lumbar motion segments under bending moments in the three principal directions. They found that segmental flexibility increased with increasing severity of disk degeneration to grade IV, but decreased when the disk degeneration advanced to grade V. Such segmental motion changes were greater in axial rotation compared with those in lateral bending, flexion, and extension. Tanaka et al 40 also reported increase in flexibility with moderate disc degeneration but a decrease with further degeneration in 114 cadaveric lumbar motion segments. Again the increase was more under axial rotation than lateral bending and flexion/extension. Decrease in lumbar motion segment stiffness with occurrence of annular lesions a feature of early stage disc degeneration was also reported 22, 23. Mimura et al 41 reported an increase in flexibility under axial rotation with moderate degeneration and drop with further degeneration. But they reported a decrease in motion under flexion/extension and lateral bending with disc degeneration. Recently Kettler et al 42 reviewed kinematics data and classified it according to disc degeneration grades for 203 lumbar motion segments. They concluded that ROM decreased under flexion/extension and lateral bending with increasing disc degeneration. Increase in flexibility under axial rotation was reported with increasing disc degeneration but without any stabilization step with advanced degeneration. Finite element models of lumbar spine have been used to investigate the disc degeneration disease. Earlier models represented the vertebral body and the disc using linear elastic material properties 7, 44. Disc degeneration was simulated by removing the hydrostatic characteristics of the nucleus 44. Changes in disc height, material properties of the annulus and structural disruptions such as annular lesions were not considered 7, 43, 44. More recent finite element models of spine have introduced hyperelastic

74 56 material properties to simulate the nonlinear behavior of the disk 45, 94. Changes in the disk height and the material properties of the nucleus were included to study the effects of degeneration on the biomechanical characteristics of the disc. These finite element models did not consider the viscoealastic behavior of the nucleus and the annulus by representing the disc components with single phase material model 45. Poroelastic finite element models can better predict the biomechanical behavior of the disk by considering both the solid and fluid phases 46, 47, 63, 74, 75, However such finite element models have not been used to study the disc degeneration process. Effect of disc degeneration on the creep characteristics was investigated by altering the permeability and the stiffness of the annulus and nucleus in a poroelastic finite element model 46. Role of static compression in inducing disc degeneration was studied using a poroelastic finite element and in vivo mouse model. However, collagen fibers and strain dependent permeability were not considered in the finite element model 47. Natarajan et al 74 investigated the effects of disc degeneration on the biomechanical behavior of the lumbar motion segment using a poroelastic finite element model. Disc degeneration was modeled by changing the material properties of the annulus and the nucleus. However, changes in the disc geometry were not introduced. Finite element models of the lumbar spine that include both the morphological and the biochemical changes with disc degeneration are required to have a thorough understanding of the effects of degenerative process on the biomechanical behavior of the spine. The aim of this study was to modify the existing finite element model of L4/L5 lumbar motion segment with healthy disc described in the previous chapter to develop finite element models representing different grades of disc degeneration. These models were then employed to investigate the effects of progressive disc degeneration on the biomechanical characteristics of the lumbar motion segment. It was hypothesized that (a) the flexibility of the lumbar motion

75 57 segment will increase with disc degeneration in the three principal directions (b) flexibility will exhibit an increasing trend up to grade IV disc degeneration in the three principal directions (c) further degeneration of the disc will result in a decrease in the flexibility of the lumbar motion segment (d) annulus fibrosus will be exposed to increased levels of shear and tensile stresses with increasing severity of the disc degeneration. B. Material and Methods The poroelastic finite element model of L4/L5 lumbar motion segment described in the previous chapter was modified to include the degenerative changes in the disc representing different stages of disc degeneration. Morphological and biochemical changes reported in the degenerated discs were introduced simultaneously. Three finite element models of L4/L5 lumbar motion segment representing Thompson s disc degeneration grades III, IV and V were created and their biomechanical characteristics were compared with that of the healthy disc model. 1. Biochemical Changes Biochemical changes in the disc were simulated by altering the drained elastic material properties and the poroelastic properties of the annulus and the nucleus. Effect of annular lesions in the degenerated discs was accounted for while assigning the Young s modulus to the degenerated annulus. Material properties were adopted from the literature 83, Table IV and Table V list the Young s modulus, Poisson s ratio, water content and permeability for annulus and nucleus assigned for different grades of disc degeneration.

76 58 Table IV: Material properties for annulus ground substance used for healthy and different grades of disc degeneration finite element models 83, 86, 88, 98, Degeneration Grade Young s Modulus (MPa) Poisson s Ratio Water Content (%) Permeability (m 4 /Ns) k x k y k z Healthy E E E-15 Grade III E E E-15 Grade IV E E E-15 Grade V E E E-15 Table V: Material properties for nucleus pulposus used for healthy and different grades of disc degeneration finite element models 69, 83, 86, Degeneration Grade Young s Modulus (MPa) Poisson s Ratio Water Content (%) Permeability (m 4 /Ns) k x k y k z Healthy E E E-15 Grade III E E E-15 Grade IV E E E-15 Grade V E E E-15

77 59 2. Morphological Changes The geometry of the disc corresponding to different grades of degeneration was simulated by decreasing the disc height and the nucleus area. The disc height was reduced by 15%, 33% and 70% as compared to healthy disc height (12.0mm) to represent disc degeneration grades III, IV and V respectively. These values were assumed according to the scheme of Banneker et al 30. Nucleus pulposus area for the grade III degeneration model was kept the same as for healthy disc model, but it was reduced by 67% to represent grade IV and V disc degeneration according to the stress profilometry studies of Adams et al 29.The decreased nucleus area was replaced with elements representing the annulus ground substance so as to maintain the same disc area. Table VI lists the height and nucleus area for healthy and degenerated disc models. Loss of disc height causes the laxity in the ligaments and the annular fibers. This phenomenon was simulated in the finite element models by offsetting the non-linear stress-strain curves of the annular fibers and the surrounding ligaments so that they would become active once they reached their original length 104, 105.

78 60 Table VI: L4/L5 Intervertebral disc height and nucleus pulposus area used for healthy and different grades of disc degeneration finite element models 29, 30. Disc Degeneration Grade Disc Height (mm) Nucleus Area (mm 2 ) Healthy Grade III Grade IV Grade V (a) (b) (c) (d) Figure 31: Finite element models of L4/L5 lumbar intervertebral disc showing progressive changes in disc height and nucleus area with increasing disc degeneration. Inner white core represents the nucleus pulposus while the outer blue region is annulus fibrosus, (a) Healthy disc (b) Grade III disc degeneration (c) Grade IV disc degeneration (d) Grade V disc degeneration

79 61 3. Loading Conditions In order to investigate the biomechanics of disc degeneration finite element models were subjected to bending moments under flexion, extension, axial rotation and lateral bending. Fujiwara et al 39 carried a biomechanical study on cadaveric lumbar motion segments. They subjected the specimens to pure bending moments of 6.6 Nm in the three principal directions. The same magnitude of bending moments (6.6 Nm) was applied in the current study so that the finite elements models of degenerated discs can be validated against the available in vitro experimental results. 4. Data Analyses The effect of disc degeneration on the lumbar motion segment s biomechanical behavior was analyzed by comparing the angular rotation in the three principal directions for different grades of disc degeneration finite element models with the corresponding results from the healthy disc finite element model. Maximum von Mises stress, shear stress and tensile principal stress in the annulus fibrosus of the healthy and degenerated disc models were obtained under all loading modes. Maximum nucleus pressure in the degenerated disc models were compared with that in the healthy disc model. Maximum tensile principal stress in the endplates was analyzed for different grades of disc degeneration under all loading modes. Maximum values of stresses in different component of the disc were calculated by performing histogram analyses of the stress and pressure values in annulus, endplate and nucleus elements. The reported values of stresses were exhibited by at least ten integrating points in the given disc component. Facet contact loads were analyzed during extension, lateral bending and axial rotation. Facet loads reported during extension were the average values for the contacting surfaces on the

80 62 right and left side. Facet loads under lateral bending were the average values of the contacting surfaces on the same side as the direction of motion. Facet loads for axial rotation were the average values of the contacting surfaces on the contra-lateral side to the direction of motion. 5. Validation of Finite Element Models The finite element models with healthy and degenerated discs were validated by comparing the ROM results with the cadaveric human lumbar motion segment studies carried out by Fujiwara et al 39 and Tanaka et al 40. Fujiwara et al 39 tested 110 cadaveric lumbar motion segments under pure bending moments of 6.6 Nm in the three principal directions. The ROM results were classified based on the Thompson scheme for disc degeneration grading. Tanaka et al 40 tested 114 cadaveric lumbar motion segments under pure bending moments of 5.7 Nm in the three principal directions. They grouped the ROM results according to disc degeneration grades based on morphological and magnetic resonance imaging assessment. a. Healthy Disc Finite Element Model Healthy disc finite element model was validated against the in vitro results reported for Grade II disc degeneration motion segments by Fujiwara et al 39 and Tanaka et al 40. Only two lumbar motion segments were reported to have Thompson disc degeneration grade I by Fujiwara et al and were excluded from the data analyses 39. Similarly, Tanaka et al reported only one lumbar motion segment with grade I disc degeneration based on the morphological and the magnetic resonance imaging assessment 40. The angular rotations predicted by the healthy disc finite element model fell within one standard deviation of the mean ROM in the three principal directions reported by Fujiwara et al 39 (Figure 32). The finite element model ROM matched well with the results reported by Tanaka et al 40 under flexion, extension and axial rotation (Figure 33). However, rotation under lateral bending

81 63 predicted by the finite element model was below one standard deviation of the mean rotation reported by Tanaka et al 40. The largest angular rotation was predicted under lateral bending followed by flexion, extension and axial rotation respectively. b. Grade III Disc Degeneration Finite Element Model Grade III disc degeneration finite element model was validated against the in vitro results reported for Grade III disc degeneration motion segments by Fujiwara et al 39 and Tanaka et al 40. The ROM predicted by the finite element model fell within one standard deviation of the in vitro mean ROM under all loading conditions (Figure 34 & Figure 35). The largest angular rotation was predicted under lateral bending followed by flexion, extension and axial rotation respectively. c. Grade IV Disc Degeneration Finite Element Model Grade IV disc degeneration finite element model was validated against the in vitro results reported for Grade IV disc degeneration motion segments by Fujiwara et al 39 and Tanaka et al 40. The angular rotation predicted by the finite element model fell within one standard deviation of the in vitro mean ROM under flexion, extension and lateral bending (Figure 36 & Figure 37). The ROM under axial rotation predicted by the finite element model fell within two standard deviation of the in vitro mean ROM (Figure 36 & Figure 37). The largest angular rotation was predicted under lateral bending followed by flexion, extension and axial rotation respectively. d. Grade V Disc Degeneration Finite Element Model Grade V disc degeneration finite element model was validated against the in vitro results reported for Thompson Grade V disc degeneration motion segments by Fujiwara et al 39 and Tanaka et al 40. The ROM predicted by the finite element model fell within one standard

82 64 deviation of the in vitro mean ROM under all loading conditions (Figure 38 & Figure 39). The largest angular rotation was predicted under lateral bending followed by flexion, extension and axial rotation respectively.

83 65 Figure 32: Finite element model and Fujiwara et al in vitro segmental angular rotation values for healthy disc L4/L5 lumbar motion segment. Figure 33: Finite element model and Tanaka et al in vitro segmental angular rotation values for healthy disc L4/L5 lumbar motion segment.

84 66 Figure 34: Finite element model and Fujiwara et al in vitro segmental angular rotation values for Thompson grade III disc degeneration L4/L5 lumbar motion segment. Figure 35: Finite element model and Tanaka et al in vitro segmental angular rotation values for Thompson grade III disc degeneration L4/L5 lumbar motion segment.

85 67 Figure 36: Finite element model and Fujiwara et al in vitro segmental angular rotation values for Thompson grade IV disc degeneration L4/L5 lumbar motion segment. Figure 37: Finite element model and Tanaka et al in vitro segmental angular rotation values for Thompson grade IV disc degeneration L4/L5 lumbar motion segment.

86 68 Figure 38: Finite element model and Fujiwara et al in vitro segmental angular rotation values for Thompson grade V disc degeneration L4/L5 lumbar motion segment. Figure 39: Finite element model and Tanaka et al in vitro segmental angular rotation values for Thompson grade V disc degeneration L4/L5 lumbar motion segment.

87 69 C. Results 1. Angular Rotation Degeneration of the intervertebral disc resulted in an increase in the segmental rotation in the loading plane under all loading directions considered. Figure 40 shows the ROM for L4/L5 motion segments with healthy and degenerated discs under different loading modes. The ROM under flexion bending increased with grade III disc degeneration but it decreased with further degeneration. However, ROM under flexion for grade IV and V disc degeneration were larger than the healthy disc motion segment. Flexion ROM increased by a maximum of 38% with disc degeneration as compared to the healthy disc. Angular rotation under extension loading increased with grade III and IV disc degeneration and decreased with further degeneration. ROM under extension for grade V disc degeneration model was larger than the healthy disc model. Extension ROM increased by a maximum of 29% with disc degeneration as compared to the healthy disc. Under axial rotation and lateral bending the ROM increased with grade III disc degeneration and then decreased with further degeneration. However, angular motion under axial rotation and later bending for grade IV and V disc degeneration models were larger than the respective angular motions for healthy disc model. The ROM increased by a maximum of 51% and 45% with disc degeneration as compared to the healthy disc under axial rotation and later bending respectively. The largest percentage increase in ROM was predicted under axial rotation followed by lateral bending, extension and flexion respectively.

88 Figure 40: Inter-segmental rotations predicted by the finite element models for L4/L5 lumbar motion segments with healthy and degenerated discs. 70

89 71 2. Annulus Fibrosus Stresses Shear stress, von Mises stress and principal tensile stress were calculated in the annulus under all loading modes for different grades of disc degeneration. Stress levels increased with disc degeneration under all loading directions (Figure 41, Figure 42 and Figure 43). Maximum von Mises stress in the annulus fibrosus increased with grade III disc degeneration and then decreased with further degeneration under flexion and axial rotation (Figure 41). However, under extension and lateral bending von Mises stress increased up to grade IV disc degeneration and then decreased with advanced degeneration (Figure 41). The maximum von Mises stress in the grade IV and V degenerated discs were greater than those in the healthy disc under all loading conditions except under axial rotation (Figure 41). Maximum shear stress in the annulus fibrosus increased with grade III disc degeneration and then decreased with further degeneration under axial rotation (Figure 42). However, under flexion, extension and lateral bending maximum shear stress increased up to grade IV disc degeneration and then decreased with advanced degeneration (Figure 42). The maximum shear stress in the grade IV and V degenerated discs were greater than those in the healthy disc under all loading conditions except under axial rotation (Figure 42). Maximum principal tensile stress in the annulus showed an increasing trend with increasing degeneration under all loading modes (Figure 43). Percentage increase in the maximum principal tensile stress (132% - 312%) in the annulus with disc degeneration under different loading conditions was considerably larger than the corresponding increase in the maximum shear stress (13% - 38%) and the maximum von Mises stress (39% - 51%) in the three principal directions (Figure 41, Figure 42 and Figure 43).

90 72 Figure 41: Maximum von Mises stress in the annulus ground substance of the L4/L5 intervertebral disc under flexion, extension, axial rotation and lateral bending for different grades of disc degeneration. Figure 42: Maximum shear stress between annulus lamellae of the L4/L5 intervertebral disc under flexion, extension, axial rotation and lateral bending for different grades of disc degeneration.

91 Figure 43: Maximum principal tensile stress in the annulus ground substance of the L4/L5 intervertebral disc under flexion, extension, axial rotation and lateral bending for different grades of disc degeneration. 73

92 74 In addition to the maximum stress values in the annulus fibrosus, tensile and shear stress distribution patterns were analyzed for different grades of disc degeneration under all loading conditions. With increasing disc degeneration the larger annulus volumes were exposed to higher tensile stresses as evident from Figure 44, Figure 45, Figure 46 and Figure 47. Under flexion bending the posterior annulus experienced tensile stresses while under extension loading it was the anterior annulus was exposed to tensile stresses as expected (Figure 44 & Figure 45). Under axial rotation and lateral bending the higher tensile stresses were found to be in the lateral annulus (Figure 46 and Figure 47). The maximum shear stress also increased with increasing degeneration. The annulus volume exposed to higher shear stresses also increased with increasing degeneration as shown in Figure 48 to Figure 51. Higher shear stresses were observed in the anterior annulus in the healthy disc under flexion bending. With increasing disc degeneration the posterior region of the annulus was exposed to high shear stresses also. This phenomenon is especially evident with grade III and V disc degeneration (Figure 48). Under extension loading posterior annulus was exposed to high shear stresses in the healthy disc. With increasing disc degeneration the anterior annulus experienced high shear stresses also (Figure 49). In healthy disc high shear stresses were observed in the anterior annulus. With progressive disc degeneration high shear stresses encompassed the anterior and the lateral regions of the annulus (Figure 50). Under lateral bending higher shear stresses were concentrated in the lateral region of the annulus on the same side as the bending direction in the healthy disc. With disc degeneration both the right and the left lateral annulus regions were exposed to high shear stresses (Figure 51).

93 75 P P (a) (b) P P (c) (d) Figure 44: Principal stress in the annulus fibrosus for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under flexion. P represents the posterior side.

94 76 P P (a) (b) P P (c) (d) Figure 45: Principal stress in the annulus fibrosus for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under extension. P represents the posterior side.

95 77 P P (a) (b) P P (c) (d) Figure 46: Principal stress in the annulus fibrosus for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under right axial rotation. P represents the posterior side.

96 78 P P (a) (b) P P (c) (d) Figure 47: Principal stress in the annulus fibrosus for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under right lateral bending. P represents the posterior side.

97 79 P P (a) (b) P P (c) (d) Figure 48: Maximum shear stress in the annulus fibrosus for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under flexion. P represents the posterior side.

98 80 P P (a) (b) P P (c) (d) Figure 49: Maximum shear stress in the annulus fibrosus for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under extension. P represents the posterior side.

99 81 P P (a) (b) P P (c) (d) Figure 50: Maximum shear stress in the annulus fibrosus for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under axial rotation. P represents the posterior side.

100 82 P P (a) (b) P P (c) (d) Figure 51: Maximum shear stress in the annulus fibrosus for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under lateral bending. P represents the posterior side.

101 83 3. Nucleus Pressure Intradiscal pressure in the nucleus decreased with the increasing disc degeneration under all loading conditions (Figure 52). Maximum nucleus pressure in the grade III disc degeneration model was about 10% less than in the healthy disc model and reduced to almost half with further disc degeneration under flexion, extension and lateral bending. Under axial rotation the maximum pressure in the nucleus decreased by 25% and 75% in grade III and IV disc degeneration models respectively and dropped to negative pressure in grade V disc degeneration model (Figure 52). 4. Facet Joint Load Facet joint contact forces were calculated under extension, axial rotation and lateral bending. The largest forces were observed under axial rotation followed by extension and lateral bending respectively (Figure 53). Facet joint load decreased with the progressive degeneration of the disc under extension moment. Under axial rotation a gradual increase in the contact forces was observed with progressive disc degeneration (Figure 53). Contact forces increased by a maximum of 17 % with disc degeneration as compared to the healthy disc. Under lateral bending, the facet joint forces followed an increasing trend with grade III and IV disc degeneration but decreased with further disc degeneration. Contact forces increased by a maximum of 120 % with disc degeneration as compared to the healthy disc. Facet joint forces in grade V disc degeneration model were higher than in the healthy disc model (Figure 53).

102 84 Figure 52: Maximum pressure in the nucleus pulposus of the L4/L5 intervertebral disc under flexion, extension, axial rotation and lateral bending for different grades of disc degeneration. Figure 53: Average facet joint contact forces at L4/L5 lumbar motion segment during extension, axial rotation and lateral bending for different grades of disc degeneration

103 85 5. Endplates Stress The maximum tensile principal stress was calculated in the endplates under all loading modes with increasing severity of the disc degeneration. Tensile stress followed an increasing trend with the progressive disc degeneration under all loading modes except under axial rotation (Figure 54). The maximum percentage increase in the tensile stress in the endplates was observed under extension (109%) followed by lateral bending (93%) and flexion (53%) respectively. The percentage decrease in the endplate stress under axial rotation was less than 14%. In addition to the maximum stress values in the endplates, the stress distribution patterns were also analyzed for different grades of disc degeneration. Under flexion and extension the higher tensile stresses were observed in the posterior and anterior regions respectively. With increasing disc degeneration the volume of the endplates exposed to high tensile stresses increased under flexion and extension as evident in Figure 55 & Figure 56. Maximum value of the tensile stress in the endplates decreased with disc degeneration under axial rotation but larger areas of the endplates experienced high tensile stresses in the degenerated discs as depicted in Figure 57. Under lateral bending the posteriolateral region of the endplates were exposed to high tensile stresses with increasing disc degeneration (Figure 58). The central regions of the endplates were exposed to higher tensile stresses in the degenerated discs as compared with the healthy discs under all loading modes.

104 Figure 54: Maximum principal tensile stress in the endplates of the L4/L5 intervertebral disc under flexion, extension, axial rotation and lateral bending for different grades of disc degeneration. 86

105 87 P P (a) (b) P P (c) (d) Figure 55: Principal stress in the endplates for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under flexion.

106 88 P P (a) (b) P P (c) (d) Figure 56: Principal stress in the endplates for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under extension.

107 89 P P (a) (b) P P (c) (d) Figure 57: Principal stress in the endplates for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under axial rotation.

108 90 P P (a) (b) P P (c) (d) Figure 58: Principal stress in the endplates for (a) Healthy (b) Grade III (c) Grade IV (d) Grade V disc degeneration finite element models under lateral bending.

109 91 6. Discussion A three dimensional poroelastic finite element model of the L4/L5 motion segment with healthy intervertebral disc was modified to simulate grade III, IV and V disc degeneration stages. Morphological and biochemical changes were introduced by altering the geometry and the material properties of the disc components in the finite element models. The finite element models were subjected to pure bending moments in the three principal directions. The healthy and degenerated disc models were validated against the in vitro cadaveric human lumbar motion segments results available in the literature. Influence of progressive disc degeneration disease on the biomechanical characteristics of the lumbar motion segment was studied. The current finite element models predicted a substantial increase (29% - 51%) in the angular motion with disc degeneration in the three principal directions supporting the first hypothesis of increase in the flexibility of lumbar motion segment with disc degeneration. The finite element models predicted an increasing trend in the flexibility of the lumbar motion segment up to grade III disc degeneration and a decrease with further degeneration of the disc under flexion, axial rotation and lateral bending. Under extension loading an increasing trend was observed up to grade IV disc degeneration with a decreasing trend with advanced disc degeneration. These findings do not fully support the second hypothesis of an increasing trend in flexibility up to grade IV disc degeneration and a decrease with further degeneration. A considerable increase in the shear and tensile stresses was predicted with disc degeneration validating the third hypothesis. The changes in the angular rotations in the three principal directions with increasing disc degeneration predicted by the finite element models are consistent with the observations of Kirkaldy-Wallis and Farfan 38 who proposed the three stages of disc degeneration: dysfunction,

110 92 instability and stabilization. The finite element models results are also in agreement with the findings reported by Fujiwara et al 39 and Tanaka et al 40. Axial rotation predicted by grade IV disc degeneration finite element model is less than those reported in the two in vitro studies 39, 40. The larger motions experienced in the experimental studies could be due to the facet joint degeneration observed in the grade IV disc degeneration specimens. Haughton et al 22 tested 82 cadaveric human lumbar motion segments under axial rotation. Average stiffness of 7.0 Nm/deg, 1.9 Nm/deg, 1.7 Nm/deg and 3.1 Nm/deg were reported for motion segments with healthy discs, discs with rim lesions, discs with radial fissures and collapsed discs respectively. Motion segments with annular lesions had mild to moderate disc degeneration while collapsed discs represented severe disc degeneration. Thus, the experimental results support the finite element models predictions of increased flexibility with early disc degeneration and then a stabilization step with severe disc degeneration. Thompson et al 26 tested lumbar motion segments from 30 cadaveric human lumbar spines under flexion/extension and axial rotation. Larger motion was observed under axial rotation for motion segments with annular tears (feature of disc degeneration) than those with healthy discs. Haughton et al 23 reported an increase in the flexibility of cadaveric human lumbar motion segments with occurrence of annular lesions (feature of disc degeneration) under axial rotation and flexion/extension. Schmidt et al 24 tested 20 cadaveric human lumbar motion segments under flexion, extension, axial rotation and lateral bending. A decrease in stiffness was reported in the three principal directions for specimens exhibiting nucleus degeneration and radial fissures as compared with healthy disc motion segments. These in vitro studies support the finite element models predictions. The current finite element models results are also consistent with the experimental results reported by Mimura et al 41 and Kettler et al 42 under axial rotation. However, both studies reported a decrease in the

111 93 flexibility under flexion/extension and lateral bending with disc degeneration which do not support the finite element models predictions. Shear and tensile stresses in the annulus have been suggested as the failure mechanism of the intervertebral disc 58, 106, 107. Shear causes the delamination of the annulus layers while the annulus fibers are known to fail under tension. It is not possible to measure the stresses in the experimental setup. The finite element models predicted an increase in the shear and tensile stresses in the annulus with disc degeneration. Increase in the tensile stresses was found to be much larger than the corresponding increase in the shear stress under different loading modes. The increase in the tensile and shear stress levels in the annulus raises the chances of structural disruptions in the annulus and disc herniation. The decrease in the nucleus pressure with degeneration predicted by the finite element models is in agreement with the results of the in vitro studies 108, 109. Increase in the stresses in the annulus and a corresponding decrease in the nucleus pressure suggest the change in the load sharing pattern between the nucleus and the annulus with progressive disc degeneration disease. Endplates were exposed to higher levels of tensile principal stresses with increasing disc degeneration. Higher stresses were found in the central region of the endplates in the degenerated discs. This could be due to the dehydration of the nucleus with disc degeneration. Higher stresses in the endplates could increase the vulnerability of intervertebral disc to failure by endplate fracture. The facet joints contact forces increased with the progressive disc degeneration under axial rotation and lateral bending. This behavior suggests the transfer of load from the disc to the facet joints with increasing disc degeneration. This exposes the facet joints to higher stresses and could cause the degeneration of the joints.

112 94 V - FAILURE INITIATION AND PROGRESSION IN INTERVERTEBRAL DISC UNDER CYCLIC LOADING A. Introduction The structural failures in the disc are considered to be the result of accumulated damage over a long period of time rather than a traumatic injury. Epidemiological studies have identified frequent bending and lifting as a major risk for disc prolapse 48, 49. Research has been carried out to understand the behavior of the motion segment during repetitive loading. Damage to disc structure has been reported in response to cyclic loading of the motion segment by a number of studies involving human cadavers and animal models. Yu et al 59 reported presence of irregular fibers, buckling and bleeding in the porcine annulus in response to compressive cyclic loading. Gordon et al 54 reported disc herniation in 14 cadaveric lumbar motion segments, subjected to combination of flexion, axial rotation and compression for an average duration of 36,750 cycles. Goel et al 53 tested 11 cadaveric lumbar spines under cyclic pure flexion/extension for up to 9600 loading cycles. They observed disc failure in none of the spines. Liu et al 57 subjected cadaveric lumbar motion segments to cyclic axial loads ranging from 37-80% of their failure load limit for up to 10,000 cycles. Disc injury was reported in 2 of 11 specimens while all the specimens experienced endplate or vertebral bone cracking. Adams et al 51 subjected 41 cadaveric human lumbar motion segments, in flexed position, to cyclic compressive loads for up to 9600 cycles. Peak load values ranged between 1500N to 6000N. The motion segments were flexed to one degree less than their physiological limits. Eleven specimens failed either by the fracture of the endplate or the crushing of the vertebral body. Slight to severe distortion of the annulus was reported in 14 discs. Another 9 discs were observed to have radial fissures in the posterior or the posterior-lateral region of the disc. Parkinson and Callaghan 110 conducted a series of in-vitro

113 95 fatigue testing on porcine motion segments to understand the failure mechanism. They concluded that cyclic flexion/extension bending results in the failure of the disc while large cyclic compressive loading fractures the vertebral body. Average numbers of load cycles for disc injury were reported to be 9,000 as compared to 930 for vertebral bone fracture. Marshall and McGill 58 showed that cyclic flexion/extension bending of porcine motion segments caused nucleus tracking through the posterior annulus, while cyclic axial rotation resulted in the radial delamination of the annulus. In case of the human cadaver studies, it is difficult to obtain a large number of specimens without disc degeneration or pre-existing annular disruptions. With current imaging techniques it is not possible to identify the location and extent of damage during different stages of testing without interruptions. Most of the experimental studies involve the application of cyclic compressive loading alone or in combination with flexion or extension moment. It is difficult if not impossible to apply complex loadings that are representative of daily life activities in the cadaver testing setup. These limitations make it hard to track the initiation and progression of structural damage in the intervertebral disc under complex loading conditions in the experimental setup. Finite element modeling has been used extensively to explore the spine biomechanics. However most of the finite element models of the spine are employed to elucidate the spine kinematics under single load cycle. Riches et al 111 presented a one dimensional mathematical model to study the disc mechanics under cyclic loading. Only five load cycles of 20 min compression followed by 40 min of expansion were simulated. Natarajan et al 112 investigated the development and progression of annular tears, nuclear clefts and endplate fractures. The analyses showed that endplates were the weakest link in the intervertebral disc and were the first to fail. However, numbers of load cycles required to cause the damage were not calculated. Lu et

114 96 al 113 investigated the initiation and progression of failure in the annulus under compression, flexion and axial rotation using viscoealastic finite element model. The analyses simulated failure under a single load cycle and did not consider damage accumulation under repetitive loading conditions. Loss of disc height at the peak load with increasing number of compressive load cycles was studied by Natarajan et al 114 using a poroelastic finite element model. Analyses were carried out for grade I and grade IV disc degeneration models. However, only 240 load cycles were simulated and damage accumulation in the disc with increasing number of load cycles was not included. There is no finite element model for lumbar spine that looks into the degradation of the intervertebral disc due to cyclic loading to the best of the author knowledge. It is difficult to simulate large number of load cycles using detailed finite element models due to high computational and time expense. The purpose of this study is to develop a poroelastic finite element model of a lumbar motion segment that can predict the initiation and progression of structural failure in the disc under cyclic loading. Initiation and progression of structural damage can be tracked in a motion segment by employing User supplied routines in conjunction with the finite element model. It is hypothesized that the (a) number of load cycles to disc failure will decrease as the motion segment is subjected to complex loading rather than single axis compressive or bending load (b) damage will initiate and propagate preferentially in the posterior region of the intervertebral disc under all loading conditions (c) progressive degeneration of the intervertebral disc will shift the location of the disc failure from the inner annulus layers to the peripheral annulus layers.

115 97 B. Materials and Method 1. Continuum Damage Mechanics Kachanov 115 introduced the concept of damage being continuously distributed throughout the solid and proposed a damage variable as an internal state variable describing the state of degradation of the material. A computational methodology for the prediction of degradation of materials under cyclic loading 116 based on Kachanov s concept was employed in the current study to investigate the failure progression in the annulus. Continuum damage mechanics formulation along with the finite element modeling has been employed to simulate the fatigue behavior of the human cortical bone 117. Jeffers at al 118 and Lennon et al 119 also used it to investigate the cement mantle failure and loosening of femoral components in total hip arthroplasty respectively. Application of continuum damage mechanics methodology has not been reported in soft biological tissues like annulus fibrosus and nucleus. Continuum damage mechanic formulation can be a useful tool to investigate the failure initiation and progression in the lumbar motion segment under different loading conditions. This methodology can help in avoiding high computational expense normally required for cyclic loading analyses of biological tissues. 2. Incorporation of Continuum Damage Mechanics Methodology into L4/L5 Lumbar Motion Segment Finite Element Model The poroelastic finite element model of L4/L5 lumbar motion segment described in chapter III was employed for this part of the study. The continuum damage mechanics formulation was incorporated into the finite element model to investigate the initiation and progression of failure in the intervertebral disc under cyclic loading. Damage accumulation methodology is described below and is presented schematically in Figure 59.

116 98 In the finite element model, annulus was composed of 1,920 finite elements. Elemental properties were calculated at eight integrating points distributed symmetrically in each element. At the beginning of the analysis each integrating point in the elements representing annulus was assigned a value of zero for the damage variable d. The loading was applied to the finite element model in incremental steps. At the maximum load step, tensile principal stress was calculated at each integrating point in the annulus elements. The number of load cycles to failure (N) was calculated at each integrating point in the annulus using a Stress-Failure (S-N) curve. The lowest number of cycles to failure (N min ) corresponded to the integrating point with the highest stress value. Damage d at each integrating point was incremented as d i = d i + (N min / N i ), where i represented the integrating point. When damage d for an integrating point reached a predefined limit, the corresponding integrating point in the element was assumed unable to share any load. The elastic modulus at the failed integrating point was reduced by a predetermined value thus introducing the degradation of the material at that location in the annulus. The numbers of loading cycles simulated by this iteration were equal to the lowest number of cycles to failure (N min ) in the whole annulus. The stiffness matrix was then updated. The same loading was again applied to the motion segment and damage was incremented for each integrating point following the above procedure. The damage initiation and progression was tracked by recording the failed integrating points. The procedure was implemented by introducing a FORTRAN code in the ADINA subroutine ( User Supplied Material ) that allowed changing elastic modulus at each integrating point of the annulus.

117 99 Damage Parameter d i = 0 Apply Load in FEM Stress (S i ) Number of Cycles to Failure N i = f (S i ) d i = d i + ( N min / N i ) If d i = 0.90 E i = 0.01 * E i Figure 59: Continuum damage mechanics formulation for tracking the damage accumulation in the annulus fibrosus incorporated into L4/L5 lumbar motion segment finite element model. i is for integrating point, E is the Young s modulus.

118 Stress-Failure Curve for Annulus Fibrosus The Stress failure (S-N) curve for the annulus fibrosus was developed by using the data from a cyclic cadaver study carried out by Green at al 120. They tested 22 annulus specimens from the anterior and posterior regions of the lumbar discs (age range years) under different magnitudes of tensile stress for up to 10,000 cycles. Two matching specimens were obtained from each disc. One specimen was pulled to failure to determine its ultimate tensile strength. The other matching specimen was cyclically loaded in tension at a certain percentage of its estimated ultimate tensile strength for up to 10,000cycles. The ultimate tensile strength, number of cycles to failure and the corresponding stress level were reported for each specimen. Failure did not occur in five specimens within the maximum testing period of 10,000 cycles. Figure 60 shows the number of cycles to failure at different magnitudes of stress for individual specimens. A curve fit based on the power-law represents the S-N curve for the annulus. The logic behind using power-law model rather than a linear model as reported for other biological tissues 121, 122 was to include the effect of endurance limit observed during cyclic testing of annulus fibrosus specimens 120.

119 Figure 60: Stress-Failure (S-N) curve for annulus fibrosus. Annulus specimens from different discs were cyclically loaded in tension for up to 10,000 cycles by Green et al 120. Stress level and the numbers of load cycles to failure are plotted for each specimen. A trend line based on power function represents the fatigue behavior of the annulus ground material. 101

120 Effect of Magnitudes of Elastic Modulus and Damage Parameter at Failed Integrating Points on the Failure Progression Analyses were carried out to investigate the effect of elastic modulus and damage parameter value at the failed integrating points on the damage accumulation in the annulus fibrosus. For this the motion segment was subjected to a compressive cyclic loading with a peak load of 800 N. Analyses were conducted by reducing the elastic modulus at the failed integrating points by one tenth, one hundredth and one thousandth of its original value at three different values of damage parameter (0.99, 0.90, and 0.80). In total nine simulations were performed; three different values of damage parameter paired with three different values of elastic modulus at failed integrating points. Figure 61, Figure 62 and Figure 63 show the damage accumulation in the annulus for three different magnitudes of the elastic modulus at the failed integrating points. A much faster failure progression was observed when the elastic modulus was reduced by one hundredth than if it was reduced by one tenth of its original value (Figure 61, Figure 62 & Figure 63). However failure progression rate did not change appreciably when elastic modulus was reduced by one thousandth rather than one hundredth. Thus the magnitude of the elastic modulus at the failed integrating point had a considerable effect on the rate of damage accumulation. Figure 64, Figure 65 and Figure 66 show the damage accumulation for three different values of damage parameter d, i.e. 0.99, 0.90 and The damage accumulation was faster with a decreasing value of d and became slower with an increasing value of d (Figure 64, Figure 65 & Figure 66). However, the difference between the three cases was not appreciable. Thus the damage parameter value at which the integrating point failure was considered did not have considerable effect on the failure progression rate.

121 103 Based on the above findings it was decided to reduce the elastic modulus of the integrating point by one hundredth of its original value, if its damage parameter reached a value of 0.90 for subsequent analyses.

122 Figure 61: Failure progression for different values of elastic modulus at failed integrating points. Elastic modulus at failed integrating points was reduced by one tenth, one hundredth and one thousandth of its normal magnitude. Integrating point was considered failed when its damage parameter reached a value of

123 Figure 62: Failure progression for different values of elastic modulus at failed integrating points. Elastic modulus at failed integrating points was reduced by one tenth, one hundredth and one thousandth of its normal magnitude. Integrating point was considered failed when its damage parameter reached a value of

124 Figure 63: Failure progression for different values of elastic modulus at failed integrating points. Elastic modulus at failed integrating points was reduced by one tenth, one hundredth and one thousandth of its normal magnitude. Integrating point was considered failed when its damage parameter reached a value of

125 Figure 64: Failure progression for different values of damage parameter d at which integrating points were declared failed. A value of zero for d represents the normal state of the annulus with no damage. Analyses was carried out for three values of d i.e. 0.80, 0.90, Elastic modulus at the failed integrating points was reduced by one tenth of its normal magnitude. 107

126 Figure 65: Failure progression for different values of damage parameter d at which integrating points were declared failed. A value of zero for d represents the normal state of the annulus with no damage. Analyses was carried out for three values of d i.e. 0.80, 0.90, Elastic modulus at the failed integrating points was reduced by one hundredth of its normal magnitude. 108

127 Figure 66: Failure progression for different values of damage parameter d at which integrating points were declared failed. A value of zero for d represents the normal state of the annulus with no damage. Analyses was carried out for three values of d i.e. 0.80, 0.90, Elastic modulus at the failed integrating points was reduced by one thousandth of its normal magnitude. 109

128 Validation of the Finite Element Model Incorporated with Damage Accumulation Formulation The finite element model incorporated with the continuum damage mechanics methodology was validated by comparing the results with the human cadaver study carried out by Gordon et al 54. They studied the disc rupture mechanism using 14 human lumbar motion segments (age range years) under complex cyclic loading. Testing was carried out under displacement control. Motion segments were subjected to 7 flexion, 0.93 ± 0.56 mm compression and 1.9 ± 0.6 axial rotation simultaneously. They reported mean failure cycles of 36,750 with a standard deviation of 12,612. The current poroelastic finite element model was subjected to 7.16 flexion accompanied by 1.09 mm axial compression and 1.67 axial rotation. The finite element model predicted that the motion segment will require 31,855 cycles to fail for the given loading conditions. The current finite element model results matched well with the cadaver study observations (Table VII). Most of the human cadaver studies involving cyclic loading of the lumbar spine reported the failure of the motion segment due to cracking of the endplate or the vertebral bone 50, 51, 53, 55, 56, 56, 57, 123, 124, which is attributed to large compressive loads applied in the testing protocols. Gordon et al 54 is the only study that reports fatigue failure in the human disc (to the best of the author knowledge). Thus the finite element model was validated against this study s results.

129 111 Table VII: Comparison of in vitro cyclic testing and finite element model loading conditions and number of cycles to failure. Testing Method Compression (mm) Axial Rotation (Deg) Flexion (Deg) Number of Cycles to Failure in vitro ± ± ,750 ± 12,612 Finite Element (1 st Failure) cycle ,855

130 Loading Conditions In order to investigate the effect of different modes of loading on damage accumulation in a lumbar disc, simple and complex loadings were applied to the motion segment. Simple loading conditions involved the application of either the axial compressive load or the bending moments in one of the three principal directions (Table VIII, Load cases 1-5) as shown in Figure 67 and Figure 68. Complex loading scenarios were simulated by the application of the bending moments in single or multiple directions along with the compressive load (Table VIII, Load cases 6-10) as shown in Figure 69. In all load cases, the motion segment was subjected to twelve load cycles per minute. Effect of magnitude of compressive load on the failure propagation was analyzed by simulating cyclic compressive loading with peak load magnitudes of 400 N (Table VIII, Load case 1), 800 N (Table VIII, Load case 2) and 1600 N (Table VIII, Load case 12) as shown in Figure 67. Role of flexion bending on the failure initiation and progression was investigated by subjecting the lumbar motion segment to different magnitudes of flexion moment. Cyclic loading analyses were carried out for 6 Nm (Table VIII, Load case 6) and 12 Nm (Table VIII, Load case 11) flexion moments in concert with the cyclic compressive load with a peak magnitude of 800 N as shown in Figure 69 and Figure 70 respectively. Influence of cyclic and static compressive load on damage accumulation was explored by simulating cyclic flexion with a static compressive load of 800 N (Table VIII, Load case 13) and cyclic flexion in concert with cyclic compressive load (Table VIII, Load case 6) as shown in Figure 69 and Figure 71 respectively. In order to investigate the failure in the degenerated discs, grade III and grade IV disc degeneration finite element models developed in the previous chapter were subjected to cyclic compression (Load case 2) and cyclic flexion in concert with cyclic compression (Load case 6).

131 113 Figure 67: Cyclic compressive loading with three different magnitudes of peak compressive load. Figure 68: Cyclic bending moment loading during one load cycle. Same peak bending moment magnitude was simulated in the three principal directions.

132 114 Figure 69: Cyclic bending in the three principal directions along with the cyclic compressive load. Figure 70: Cyclic flexion bending with a peak moment of 12Nm in concert with the cyclic compressive loading.

133 Figure 71: Cyclic flexion bending along with static compressive load. 115

134 116 Table VIII: Simple and complex loading conditions for failure analyses under cyclic loading. Load Case Peak Compressive Load Peak Bending Moment (6 Nm) 400 N 800N Flexion Axial Rotation Lateral Bending 1 x 2 x 3 x 4 x 5 x 6 x x 7 x x 8 x x 9 x x x 10 x x x x 11 x 12 Nm N N Static Compression x

135 117 C. RESULTS 1. Number of Load Cycles to Failure The number of load cycles to failure decreased as the motion segment was subjected to bending moments in addition to the compressive load. The failure load cycle was identified by sharp increase in failure volume against a very small increment in number of load cycles. Figure 72 to Figure 77 show the damage accumulation in the annulus with increasing number of load cycles, under different simple and complex loading conditions. The failure volume in the annulus increased almost linearly with increasing number of load cycles until the point of failure under all loading modes. At the failure point an exponential increase in the failure volume was observed against a very small increment in the number of load cycles. Such a sharp increase in the failure volume was not observed under some loading conditions even with large number of applied load cycles. The absence of this behavior indicated that the lumbar motion segment will not collapse due to intervertebral disc failure under the given loading conditions regardless of the number of load cycles. Application of 6 Nm moments in the three principal directions without any compressive load (Load cases 3-5) did not create the failure of the disc, regardless of the large number of applied load cycles. The finite element model did not predict the failure of the disc for up to 126,014, 255,326 and 145,250 load cycles under flexion, axial rotation and lateral bending respectively as shown in Figure 72. Similarly, cyclic compressive loading with a peak load magnitude of 400 N (Load case 1) did not fail the disc for up to 201,216 load cycles (Figure 72). The finite element model predicted the failure of the disc in 50,798 load cycles under cyclic compressive loading with a peak load of 800 N (Load case 2) as shown in Figure 73. Introduction of 6 Nm moments in one of the three principal directions in concert with the cyclic

136 118 compressive load (Load cases 6-8) decreased the number of load cycles to failure by 50%(flexion), 32%(lateral bending) and 18%(axial rotation) as compared to the uni-axial cyclic compressive loading (Load case 2) as depicted in Figure 73. Subjection of the lumbar motion segment to 6 Nm moments in flexion and axial rotation in concert with the compressive load (Load case 9) decreased the number of cycles to failure by 64% as compared to the cyclic compressive loading (Figure 73). Application of 6 Nm moments in the three principal directions simultaneously along with the compressive cyclic load (Load case 10), reduced the number of load cycles to failure by 71% as compared to the cyclic compressive loading (Figure 73). Influence of compressive peak load magnitude on the failure progression in the disc was analyzed. Figure 74 compares the damage accumulation in the annulus for three different magnitudes of peak compressive load. Disc failure was not predicted under cyclic compressive loading with a peak load magnitude of 400 N for up to 201,216 load cycles. When the peak compressive load was increased to 800 N, disc failure was predicted in 50,798 load cycles. Increasing the peak compressive load to 1600 N decreased the number of load cycles to failure by 80% as compared to the peak load magnitude of 800 N (Figure 74). Magnitude of flexion moment had a strong effect on the failure progression in the annulus fibrosus. Doubling the peak flexion moment from 6Nm to 12Nm decreased the predicted number of load cycles to failure by 67% as shown in Figure 75. Choice of cyclic or static compressive load did not have a strong influence on the damage accumulation rate in the annulus under cyclic flexion bending. The number of load cycles to failure predicted under static compression was less than that predicted under dynamic compressive load but were not considerably different as shown in Figure 76.

137 119 Degenerated Disc Failure The numbers of load cycles to failure predicted for grade III disc degeneration finite element model under cyclic compressive loading (Load case 2) and cyclic flexion in concert with the compressive load (Load case 6) decreases by 53% and 92% respectively when compared with the corresponding results in the healthy disc model as shown in Figure 77. The numbers of load cycles to failure predicted for grade IV disc degeneration finite element model under cyclic compressive loading (Load case 2) and cyclic flexion in concert with the compressive load (Load case 6) dropped to 3,358 and 619 respectively. This represents a 93% and 98% decrease when compared with the corresponding results in healthy disc model. The exponential decrease in the number of load cycles to failure was due to the SN curve employed which represented mechanical behavior of the healthy annulus tissue. Based on the above results it was assumed that with disc degeneration annulus was able to survive more number of load cycles for a given stress level as compared to the annulus tissue in the healthy disc. Two SN curves were developed assuming a 10% and 25% increase in the strength of the annular tissue under cyclic loading as shown in Figure 78. The numbers of load cycles to failure under predicted for grade III disc degeneration finite element model under cyclic compressive loading (Load case 2) by employing the new SN curves are compared in Figure 79. An increase in number of load cycles to failure was observed by the introduction of new SN curves. However, the damage-number of load cycles curves were only shifted along the horizontal axis while following the same damage accumulation pattern.

138 120 Figure 72: Damage accumulation in the annulus fibrosus under simple loading conditions. Figure 73: Damage accumulation in the annulus fibrosus under different cyclic loading conditions. Failure cycle is identified by sharp increase in the failure volume against a small increment in the number of load cycles.

139 121 Figure 74: Damage accumulation in the annulus fibrosus under cyclic compressive loading for three different magnitudes of peak compressive load. Figure 75: Damage accumulation in the annulus fibrosus under cyclic flexion for two different magnitudes of peak flexion moment.

140 122 Figure 76: Damage accumulation in the annulus fibrosus under cyclic flexion in concert with cyclic and static compression. Figure 77: Damage accumulation in the annulus fibrosus in grade III disc degeneration model under cyclic compressive loading and cyclic flexion in concert with cyclic compressive load. Results for healthy disc model are also plotted for comparison purpose.

141 123 Figure 78: Stress failure curves for degenerated annulus fibrosus Figure 79: Damage accumulation in the annulus fibrosus in grade III disc degeneration model under cyclic compressive loading for three different stress failure curves.

142 Damage Accumulation Location Damage initiation location and propagation direction with increasing number of load cycles was analyzed under different simple and complex loading conditions. Figure 80 to Figure 92 show the damage accumulation in the annulus up to the failure cycle subjected to different simple and complex loading conditions. Finite element models predicted the initiation of damage at the posterior region of the inner annulus next to the endplates and propagated radially towards the outer periphery under all loading conditions except under flexion (Figure 81) and lateral bending (Figure 83). It is evident that the damage accumulation was concentrated in the posterior region of the annulus adjacent to the endplates. Inferior face of the annulus experienced more damage than the superior face. Under cyclic flexion bending without the compressive load (Load case 3) damage accumulated preferentially at the posterior outer periphery of the annulus as shown in Figure 81. Similarly, under cyclic lateral bending without the compressive load (Load case 5) damage accumulated in the posteriolateral side at the outer periphery of the annulus as shown in Figure 83. The damage propagated inwards towards the nucleus with increasing number of load cycles under both loading conditions. Under cyclic compressive loading with a peak load magnitude of 800N the damage propagated preferentially at the inferior face of the annulus and reached the out annulus layers (Figure 84). With the application of the bending moment in addition to the compressive load, the damage accumulation shifted towards the posteriolateral side especially under flexion and lateral bending (Figure 85 & Figure 87). The volume of the annulus damaged up to the failure load cycle decreased as the motion segment was subjected to complex loading conditions. This is evident by comparing the failure volumes in Figure 84 and Figure 88. In grade III disc degeneration model damage initiated in the inner posterior annulus and progressed outward towards the out periphery with increasing number of

143 125 load cycles as shown in Figure 89 and Figure 90. The failure pattern in grade III disc degeneration model was similar to the healthy disc model. In grade IV disc degeneration model the damage accumulated in the posteriolateral and posterior region under cyclic compression and cyclic flexion respectively as shown in Figure 91 and Figure 92. Failure initiated and propagated at the outer periphery of the annulus in grade IV disc degeneration model as opposed to the inner annulus layers in the healthy and grade III disc degeneration models under same loading condition.

144 126 (a) (b) Figure 80: Damage accumulated in the annulus until 201,216 cycles under cyclic compressive loading with a peak load of 400 N (Load case 1). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face (a) (b) Figure 81: Damage accumulated in the annulus until 129,014 cycles under cyclic flexion loading with a peak moment of 6Nm (Load case 3). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face

145 127 (a) (b) Figure 82: Damage accumulated in the annulus until 255,326 cycles under cyclic axial rotation with a peak moment of 6Nm (Load case 4). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face (a) (b) Figure 83: Damage accumulated in the annulus until 145,250 cycles under cyclic lateral bending with a peak moment of 6Nm (Load case 5). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face

146 128 (a) (b) Figure 84: Damage accumulated in the annulus up to the failure cycle under cyclic compressive loading with a peak load of 800 N (Load case 2). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face (a) (b) Figure 85 : Damage accumulated in the annulus up to the failure cycle under cyclic flexion loading in concert with cyclic compressive load (Load case 6). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face

147 129 (a) (b) Figure 86: Damage accumulated in the annulus up to the failure cycle under cyclic axial rotation in concert with cyclic compressive load (Load case 7). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face (a) (b) Figure 87: Damage accumulated in the annulus up to the failure cycle under cyclic lateral bending in concert with cyclic compressive load (Load case 8). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face

148 130 (a) (b) Figure 88: Damage accumulated in the annulus up to the failure cycle under cyclic moment loading (flexion, axial rotation and lateral bending) in concert with cyclic compressive load (Load case 10). White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face (a) (b) Figure 89: Damage accumulated in the annulus up to the failure cycle under cyclic compressive loading with a peak load magnitude of 800 N (Load case 2) in grade III disc degeneration finite element model. White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face

149 131 (a) (b) Figure 90: Damage accumulated in the annulus up to the failure cycle under cyclic flexion loading in concert with cyclic compressive load (Load case 6) in grade III disc degeneration finite element model. White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face (a) (b) Figure 91: Damage accumulated in the annulus up to the failure cycle under cyclic compressive loading with a peak load magnitude of 800 N (Load case 2) in grade IV disc degeneration finite element model. White color shows the volume of the annulus that has failed while the black color represents the normal annulus. (a) Superior face (b) Inferior face

150 Figure 92 : Damage accumulated in the annulus up to the failure cycle under cyclic flexion loading in concert with the cyclic compressive load (Load case 6) in grade IV disc degeneration finite element model. White color shows the volume of the annulus that has failed while the black color represents the normal annulus. 132

151 Endplates Stress The effect of fatigue failure in the annulus on the adjacent endplates was investigated by recording the von Mises stress in the endplates with increasing number of load cycles. Figure 93 to Figure 101 show the von Mises stress in the endplates at the first and the failure load cycles under different loading conditions. The loading conditions under which the disc failure was not predicted did not see a considerable change in the stress distribution pattern in the endplates as shown in Figure 93 to Figure 96. Increase in the von Mises stress in the endplates with increasing number of load cycles was observed under other loading conditions simulated. This was especially evident in the posterior region of the inferior endplate (Figure 97 to Figure 101). Stress in the posterior region of the inferior endplate increased by 50% to 84% from first load cycle to the failure load cycle under different loading conditions as shown in Figure 102.

152 134 (a) (b) Figure 93: von Mises stress in the endplates after (a) first cycle and (b) 201,216 cycles under cyclic compressive loading with a peak load of 400 N (Load case 1). (a) (b) Figure 94: von Mises stress in the endplates after (a) first cycle and (b) 126,014 cycles under cyclic flexion loading with a peak moment of 6Nm (Load case 3).

153 135 (a) (b) Figure 95: von Mises stress in the endplates after (a) first cycle and (b) 255,326 cycles under cyclic axial rotation with a peak moment of 6Nm (Load case 4). (a) (b) Figure 96: von Mises stress in the endplates after (a) first cycle and (b) 145,250 cycles under cyclic lateral bending with a peak moment of 6Nm (Load case 5).

154 136 (a) (b) Figure 97: von Mises stress in the endplates after (a) first cycle and at (b) failure cycle under cyclic compressive loading with a peak load of 800N (Load case 2). (a) (b) Figure 98: von Mises stress in the endplates after (a) first cycle and at (b) failure cycle under cyclic flexion bending in concert with cyclic compressive loading (Load case 6).

155 137 (a) (b) Figure 99: von Mises stress in the endplates after (a) first cycle and at (b) failure cycle under cyclic axial rotation in concert with cyclic compressive loading (Load case 7). (a) (b) Figure 100: von Mises stress in the endplates after (a) first cycle and at (b) failure cycle under cyclic lateral bending in concert with cyclic compressive loading (Load case 8).

156 138 (a) (b) Figure 101: von Mises stress in the endplates after (a) first cycle and at (b) failure cycle under cyclic moment loading (flexion, axial rotation and lateral bending) in concert with cyclic compressive loading (Load case 10). Figure 102: von Mises stress in the posterior region of the inferior endplate during the first load cycle and the failure load cycle under different loading conditions.

157 Nucleus Pressure The effect of damage accumulation in the annulus on the nucleus pulposus was analyzed by recording the pressure in the nucleus with increasing number of load cycles. Figure 103 to Figure 111 compare the nucleus pressure distribution at the first and the failure load cycle. A decrease in the pressure was observed on the posterior side of the nucleus with increasing number of load cycles. Such a reduction in pressure was especially evident next to the annulus and adjacent to the endplates as shown in Figure 103 to Figure 111. (a) (b) Figure 103: Nucleus pressure after (a) first cycle and (b) 201,216 cycles under cyclic compressive loading with a peak load of 400 N (Load case 1).

158 140 (a) (b) Figure 104: Nucleus pressure after (a) first cycle and (b) 126,014 cycles under cyclic flexion loading with a peak moment of 6Nm (Load case 3). (a) (b) Figure 105: Nucleus pressure after (a) first cycle and (b) 255,326 cycles under cyclic axial rotation with a peak moment of 6Nm (Load case 4).

159 141 (a) (b) Figure 106: Nucleus pressure after (a) first cycle and (b) 145,250 cycles under cyclic lateral bending with a peak moment of 6Nm (Load case 5). (a) (b) Figure 107: Nucleus pressure after (a) first cycle and at (b) failure cycle under cyclic compressive loading with a peak load of 800N (Load case 2).

160 142 (a) (b) Figure 108: Nucleus pressure after (a) first cycle and at (b) failure cycle under cyclic flexion in concert with cyclic compressive loading (Load case 6) (a) (b) Figure 109: Nucleus pressure after (a) first cycle and at (b) failure cycle under cyclic axial rotation in concert with cyclic compressive loading (Load case 7).

161 143 (a) (b) Figure 110: Nucleus pressure after (a) first cycle and at (b) failure cycle under cyclic lateral bending in concert with cyclic compressive loading (Load case 8). (a) (b) Figure 111: Nucleus pressure after (a) first cycle and at (b) failure cycle under cyclic moment loading (flexion, axial rotation and lateral bending in concert with cyclic compressive loading (Load case 10).