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Proximal junctional kyphosis following surgical treatment of global sagittal imbalance : predictive analysis… Murray, Heather Leanne 2012

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PROXIMAL JUNCTIONAL KYPHOSIS FOLLOWING SURGICAL TREATMENT OF GLOBAL SAGITTAL IMBALANCE: PREDICTIVE ANALYSIS USING MATHEMATICAL AND IN VITRO BIOMECHANICAL MODELS  by Heather Leanne Murray  B.A.Sc., Queen’s University, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  April 2012 © Heather Leanne Murray, 2012  ii Abstract Introduction: Sagittal realignment using posterior spinal fixation and fusion, with or without corrective osteotomy, is the current treatment for global sagittal imbalance. Patients may develop proximal junctional kyphosis (PJK) through failure of the uppermost instrumented or adjacent vertebra.  The effects of surgical and patient variables on the development of PJK have not been studied biomechanically. Objectives: (1) To analyze pre- and post-operative intervertebral loading and the effect of osteotomy location and extensor muscle function on intervertebral spine loading using a 2D equilibrium model of sagittally imbalanced adult spine, and (2) to characterize pure moment loading pathways of multi-segment human cadaveric spines following posterior spinal fixation and in a number of surgical conditions. Methods: (1) Pre- and post-operative lateral radiographic measurements were taken of patients (N=7) and used to predict intervertebral compressive loading patterns.  From pre-operative curves, the changes in loading behaviour due to simulated osteotomies and decreasing levels of extensor muscle function were assessed. (2) Six human cadaver five-segment spines in six surgical states were tested in pure flexion-extension bending to represent the post-operative loading of patients without extensor muscle function.  Vertebral strain, rod strain, and specimen kinematics were measured and rod loading was used to predict load-sharing between the implant and the spine. Results: (1) Predicted intervertebral compressive loads increased up to 29% after development of PJK.  Predicted compressive loads were not notably affected by the chosen level of the osteotomy but increased up to 42% after intra-operative extensor muscle loss.  (2) A force couple existed between the vertebral column and the implant, supporting the majority of the applied  iii moment.  The additional compressive force on the spine due to the applied moment was predicted based on rod load measurements, found to agree with model predictions.  Specimen condition had minimal or no significance on measurements. Discussion: The developed equilibrium model introduced a predictive tool for surgical planning and deformity progression.  Predicted intervertebral compressive loads were higher in sagitally- imbalanced spines than asymptomatic spines (96), worsened by loss of extensor muscle function. Simulating muscle loss by applying a pure moment in vitro may provide insight to the resulting additional spine loading.  iv Preface This thesis was written in its entirety by Heather Murray.  Drs. Thomas Oxland and John Street provided guidance for the development of the testing methodologies and provided revisions for the writing of this thesis. The spine simulator used for the testing described in Chapter 3 was originally designed by Goertzen et al. and reported in a previous publication1.  The original design was adapted by Dr. Juay Seng Tan and subsequent software modifications were made by Jason Chak.  Spinal rod strain gauge application was completed by UBC’s Electronic Shop Technician, Glenn Jolly. The radiographic analysis and coding were completed by Heather Murray.  Information about surgical history of patients analyzed was given by Dr. John Street. Heather Murray and Angela Melnyk completed the specimen preparation.  The testing was completed mostly by Heather Murray and Angela Melnyk and partly by Jason Chak.  All the surgical work was completed by Vancouver General Hospital spine surgeon Dr. John Street. Data analysis was performed by Heather Murray.  A combined version of both Chapters 2 and 3 will be submitted for publication, titled “Proximal Junctional Kyphosis Following Surgical Treatment of Global Sagittal Imbalance: Development of a Predictive Mathematical Model Supplemented with an In Vitro Investigation”. The radiographic study described in Chapter 2 was approved by the University of British Columbia’s Clinical Research Ethics Board (ethics certificate number: H11-03162).  The specimen testing described in Chapter 3 was approved by the University of British Columbia’s Clinical Research Ethics Board (ethics certificate number: H11-00198).  1  Goertzen DJ, Lane C, Oxland TR. Neutral zone and range of motion in the spine are greater with stepwise loading than with a continuous loading protocol. An in vitro porcine investigation. Spine 2004;37:257-61.  v Table of Contents Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iv Table of Contents .......................................................................................................................... v List of Tables ................................................................................................................................. x List of Figures ............................................................................................................................... xi Acknowledgements .................................................................................................................... xvi Chapter  1: Introduction .............................................................................................................. 1 1.1 Overview ......................................................................................................................... 1 1.2 Adult Spinal Deformity................................................................................................... 2 1.2.1 Sagittal Imbalance ....................................................................................................... 2 1.2.2 Surgical Treatment ...................................................................................................... 7 1.2.2.1 Spinal Fusions with Instrumentation .................................................................. 9 1.2.2.2 Osteotomies....................................................................................................... 10 1.2.3 Proximal Junctional Kyphosis .................................................................................. 14 1.3 Spine Loading Models, Measurements, and Calculations ............................................ 17 1.3.1 Geometric Models ..................................................................................................... 17 1.3.1.1 Two-Dimensional ............................................................................................. 17 1.3.1.2 Three-Dimensional ........................................................................................... 20 1.3.2 Spine Loading Models .............................................................................................. 20 1.3.2.1 Static Equilibrium Biomechanical Model ......................................................... 20 1.3.2.2 Two-Dimensional ............................................................................................. 23 1.3.2.3 Three-Dimensional ........................................................................................... 25  vi 1.3.3 Experimental Models and Measurements ................................................................. 27 1.3.3.1 Intradiscal Pressure Measurements ................................................................... 27 1.3.3.1.1 In Vivo Studies ............................................................................................ 28 1.3.3.1.2 In Vitro Studies............................................................................................ 29 1.3.3.2 Strain Gauge Measurements ............................................................................. 31 1.3.3.2.1 In Vivo Studies ............................................................................................ 32 1.3.3.2.2 In Vitro Studies ............................................................................................ 33 1.3.3.3 Load-Sharing Considerations............................................................................ 35 1.4 Study Relevance and Objectives ................................................................................... 36 1.4.1 Clinical Relevance .................................................................................................... 36 1.4.2 Study Objectives ....................................................................................................... 39 1.5 Scope ............................................................................................................................. 40 Chapter  2: Development of a Two-Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines...................................................................................... 42 2.1 Introduction ................................................................................................................... 42 2.2 Methods......................................................................................................................... 43 2.2.1 Patient and Radiographic Data Collection ................................................................ 43 2.2.2 Geometrical Model Development ............................................................................. 46 2.2.3 Spine Loading Model Development ......................................................................... 46 2.2.4 Patient and Surgical Variables .................................................................................. 50 2.2.4.1 Osteotomy Location .......................................................................................... 50 2.2.4.2 Extensor Muscle Function ................................................................................ 52 2.3 Results ........................................................................................................................... 54  vii 2.3.1 Geometrical Model ................................................................................................... 55 2.3.2 Spine Loading Model ................................................................................................ 56 2.3.3 Patient and Surgical Variables .................................................................................. 58 2.3.3.1 Osteotomy Location .......................................................................................... 58 2.3.3.2 Extensor Muscle Function ................................................................................ 59 2.4 Discussion ..................................................................................................................... 63 Chapter  3: In Vitro Pure Moment Loading Investigation with Instrumented Multi- Segment Adult Spines ................................................................................................................. 72 3.1 Introduction ................................................................................................................... 72 3.2 Methods......................................................................................................................... 74 3.2.1 Specimens ................................................................................................................. 74 3.2.2 Testing....................................................................................................................... 76 3.2.2.1 Loading Apparatus and Testing Software......................................................... 76 3.2.2.2 Conditions ......................................................................................................... 79 3.2.3 Measurements ........................................................................................................... 81 3.2.3.1 Vertebral Body Strain ....................................................................................... 81 3.2.3.1.1 Application of Vertebral Strain Gauges ...................................................... 82 3.2.3.1.2 Calibration ................................................................................................... 83 3.2.3.2 Rod Strain ......................................................................................................... 86 3.2.3.2.1 Application of Strain Gauges to Rods ......................................................... 88 3.2.3.2.2 Calibration ................................................................................................... 89 3.2.3.2.3 Load-sharing Calculations........................................................................... 90 3.2.3.3 Range of Motion ............................................................................................... 91  viii 3.2.4 Data Analysis ............................................................................................................ 92 3.2.5 Statistics .................................................................................................................... 93 3.3 Results ........................................................................................................................... 93 3.3.1 Vertebral Body Strain ............................................................................................... 93 3.3.2 Rod Strain ................................................................................................................. 96 3.3.2.1 Load-Sharing..................................................................................................... 99 3.3.3 Range of Motion ..................................................................................................... 101 3.4 Discussion ................................................................................................................... 102 Chapter  4: Conclusion .............................................................................................................  117 4.1 Summary of Thesis ..................................................................................................... 117 4.2 Integration of Mathematical and Experimental Studies .............................................. 118 4.3 Study Relevance and Applications of Research Findings .......................................... 121 4.4 Study Strengths and Limitations ................................................................................. 123 4.4.1 Strengths ................................................................................................................. 123 4.4.2 Limitations .............................................................................................................. 125 4.4.2.1 Equilibrium Model .......................................................................................... 125 4.4.2.2 In Vitro Investigation ...................................................................................... 127 4.5 Future Work ................................................................................................................ 131 References ..................................................................................................................................  134 Appendix A Strain Gauge Background ...................................................................................... 149 A.1 Foil Strain Gauge Background Theory ................................................................... 149 A.2 Wheatstone Bridge .................................................................................................. 151 Appendix B Patient Radiographs ................................................................................................ 154  ix Appendix C Example Radiographic Data ............................................................................... 158 Appendix D Osteotomy Calculation ....................................................................................... 159 Appendix E Equilibrium Model Results (Chapter 2) ............................................................. 162 Appendix F - Loading Apparatus and Pure Moment Verification ......................................... 170 Appendix G Preliminary Study: Vertebral Load Calibration using Matrix Method .............. 173 Appendix H Spinal Rod Drawings ......................................................................................... 177 Appendix I Rod Loading Theoretical Relationships .............................................................. 178 Appendix J Rod Accuracy and Sensitivity Tests .................................................................... 179 J.1 Accuracy Test ......................................................................................................... 179 J.2 Sensitivity Test........................................................................................................ 181 Appendix K Example in vitro Results for Specimen 4 Condition 2 (Chapter 3) ................... 187 K.1 Vertebral Strain ....................................................................................................... 187 K.2 Rod Strain ............................................................................................................... 189 K.3 Anterior Column Loads and Moments ................................................................... 194 K.4 Range of Motion ..................................................................................................... 195 Appendix L Additional Study: Diagnosis of Rod Bending Strain Results ............................. 197         x List of Tables Table 1-1: Predicted compressive loads for L4-L5 level in various 2D and 3D studies .............. 27 Table 1-2: In vivo intradiscal pressure measurements in healthy subjects ................................... 29 Table 2-1: Demographic data for patients used in this study ........................................................ 45 Table 2-2: Magnitude and location of external forces used in this study ..................................... 49 Table 2-3: Peak predicted compressive loads and muscle forces for each patient. ...................... 57 Table 2-4: Percent increase in predicted compressive loads after muscle loss............................. 63 Table 2-5: Spinal parameters in patients from current study and in asymptomatic adults ........... 64 Table 3-1: Summary of specimen data ......................................................................................... 75 Table 3-2: Summary of surgical conditions performed ................................................................ 79 Table 3-3: Specimen images and schematics of surgical conditions ............................................ 80 Table 3-4: Median calculated anterior column moments ........................................................... 101 Table 3-5: Median calculated anterior column loads .................................................................. 101 Table 3-6:  Peak measured in vitro vertebral strains from current study and literature. ............. 111 Table 4-1: Peak predicted anterior column compressive loads from model and in vitro study. . 119 Table B-1: Three foot standing x-rays for Patients 1 through 7 …………………….…………154 Table C-1: Radiographic measurements collected in current study…..…………………..……158 Table J-1: Accuracy (percent error) of calculated rod moments compared to applied moment..181 Table J-2: Accuracy and sensitivity of calculated rod moments in two orientations…………..186      xi List of Figures Figure 1-1: Relevant Spine Anatomy. ............................................................................................ 4 Figure 1-2: Lateral radiographs of healthy (neutral) and sagittally imbalanced spines .................. 5 Figure 1-3: Quantification of sagittal alignment using the C7 plumb line method. ....................... 6 Figure 1-4: Neutral standing sagittal profiles of healthy subjects .................................................. 7 Figure 1-5: Radiographs showing anterior translation after instrumented fusion surgery ............. 8 Figure 1-6: Posterior instrumented fusion with pedicle screws and hooks. ................................... 9 Figure 1-7: Schematic of a pedicle subtraction osteotomy ........................................................... 11 Figure 1-8: Kyphotic deformity treated with pedicle subtraction osteotomy ............................... 11 Figure 1-9: Mathematical calculation of osteotomy size based on desired correction ................. 12 Figure 1-10: Mathematical calculation of osteotomy height ........................................................ 13 Figure 1-11: Radiographic evidence of PJK ................................................................................. 15 Figure 1-12: Schematic of elliptical model used to construct spinal curvature ............................ 18 Figure 1-13: Construction of spine geometry using a polynomial ............................................... 19 Figure 1-14: 2D equilibrium calculations used to predict lumbar intervertebral loads. ............... 22 Figure 1-15: Intradiscal compressive stress profiles for healthy and degenerated discs .............. 30 Figure 1-16: Moment distribution across spinal structures under an applied pure moment ......... 36 Figure 2-1: Radiographic measurements taken for the current study. .......................................... 46 Figure 2-2: Development of a 2D equilibrium model to predict intervertebral loading. .............. 48 Figure 2-3: Schematic demonstrating vertical drop in vertebrae resulting from an osteotomy. ... 52 Figure 2-4: T Free-body diagrams of two equilibrium scenarios after muscle loss ..................... 54 Figure 2-5: Pre-operative sagittal profiles of patients from current study using model. .............. 55 Figure 2-6:  Sagittal profiles of Patient 2 in four pre- and post-operative stages, using model ... 56  xii Figure 2-7: Predicted intervertebral compressive loads of Patient 2, calculated using model ..... 57 Figure 2-8: Sagittal profiles of Patient 2 pre-operatively and after simulated osteotomies……..58 Figure 2-9: Predicted intervertebral compressive loads of Patient 2 after simulated osteotomies ... ....................................................................................................................................................... 59 Figure 2-10: Percent difference in median predicted compressive load after an osteotomy at three different levels compared to the pre-operative scenario. .............................................................. 59 Figure 2-11:  Predicted moment transferred to the spine with decreasing muscle functionality. . 60 Figure 2-12: Predicted intervertebral compressive loads with and without muscle function. ...... 62 Figure 2-13: Percent difference in mean predicted compressive load with and without muscle function ......................................................................................................................................... 62 Figure 2-14: Intervertebral loading results from two published equilibrium models ................... 66 Figure 2-15: Predicted compressive intervertebral loads from current study and literature. ........ 67 Figure 3-1: Specimen prepared for potting. .................................................................................. 75 Figure 3-2: S Schematic and image of spine simulator used to apply pure moment. ................... 78 Figure 3-3: Vertebra strain gauges on specimen ........................................................................... 82 Figure 3-4: Image of prepared specimen in loading apparatus ..................................................... 83 Figure 3-5: Image of specimen in loading apparatus, prepared for calibration test ..................... 85 Figure 3-6: Schematic of orientation of strain gauges on spinal rod. ........................................... 87 Figure 3-7: Posterior view of specimen with strain-gauged rods ................................................. 88 Figure 3-8:  Free-body diagram used for published intervertebral loading calculations .............. 91 Figure 3-9: Image of specimen in loading apparatus with optoelectric markers .......................... 92 Figure 3-10: Vertebral strain time trace and load data for one gauge from Specimen 4 .............. 94 Figure 3-11: Median (and range) vertebral strain across specimens in each condition ................ 95  xiii Figure 3-12: Rod strain time trace for one gauge from Specimen 4 ............................................. 96 Figure 3-13: Calculated rod moment and load in flexion loading cycle ....................................... 97 Figure 3-14: Median (and range) calculated rod moment and load across specimens in each condition ....................................................................................................................................... 98 Figure 3-15: Median (and range) predicted anterior column moments and loads across specimens in each condition ......................................................................................................................... 100 Figure 3-16: Sagittal plane kinematic data during flexion-extension loading ............................ 102 Figure 3-17:  Vertebral strain for each specimen in each condition. …………………………...108 Figure 3-18: Published resultant axial force and bending moment in flexion and extension. ….113 Figure 3-19: Intradiscal pressure profiles for degenerated discs in neutral and scoliotic postures …………………………………………………………………………………………………..116 Figure 4-1:  Summary of published segmental trends in vertebral compressive strength ……...121 Figure A-1: Strain gauge theory: change in wire length under an applied load………………..149 Figure A-2: Wheatstone Bridge circuit in simple and quarter-bridge configurations………….151 Figure A-3: Three-wire quarter-bridge circuit used in current study…………………………..153 Figure D-1: Schematic illustrating geometry used for osteotomy calculation………………....159 Figure D-2: Schematic of vertebral level above osteotomy before and after subtraction……...161 Figure D-2: Schematic of vertebral level above osteotomy before and after subtraction……...161 Figure E-1:  Model results for Patient 1 ………………………………………………………..163 Figure E-2:  Model results for Patient ………………………………………………………….164 Figure E-3:  Model results for Patient 3 ………………………………………………………..165 Figure E-4:  Model results for Patient 4 ………………………………………………………..166 Figure E-5:  Model results for Patient 5 ………………………………………………………..167  xiv Figure E-6:  Model results for Patient 6 ………………………………………………………..168 Figure E-7:  Model results for Patient 7………………………………………………………...169 Figure F-2: Articulating arm of loading apparatus…………………………………………..…170 Figure F-3: Image of loading apparatus setup for pure moment loading test………………..…171 Figure F-4:  Results from pure moment loading test …………………………………………...172 Figure G-1: Schematic of loading setup for vertebral strain calibration tests……………….…173 Figure G-2: Results from vertebral strain calibration tests………………………………….….175 Figure G-3: Measured vertebral strain as a function of applied moment and load………….….176 Figure H-1:  Posterior spinal fusion rod drawing (short length)………………………………..177 Figure H-2:  Posterior spinal fusion rod drawing (long length)………………………………...177 Figure J-1: Images of rod loading accuracy test preparation…………………………………...179 Figure J-2: Images of rod strain gauge orientation and loading during accuracy test………….180 Figure J-3: Results from rod loading accuracy test…………………………………………….181 Figure J-4: Images of rod loading sensitivity (pedicle position) test preparation………….…...182 Figure J-5: Calculated moments from rod loading sensitivity (pedicle position) test……....….183 Figure J-6: Schematics of strain gauge orientation in sensitivity (circumferential position) test. …………………………………………………………………………………………………..184 Figure J-7: Rod strain time traces for three strain gauge orientations………………………….184 Figure J-8: Calculated moments from loading sensitivity (circumferential position) test….......185 Figure K-1.1: Raw vertebral strain and linearity data.……………………………………...…..187 Figure K-1.2: Adjacent Vertebra strain magnitudes at maximum loading across conditions.....187 Figure K-1.3: Uppermost Instrumented Vertebra strain magnitudes at maximum loading across conditions. ………………………………………………………………………………………188  xv Figure K-2.1: Raw rod strain data for each gauge set.……………………………………...…..189 Figure K-2.2: Raw rod linearity for each gauge set.……………………………………………190 Figure K-2.3: Calculated rod bending moments for flexion and extension loading……………191 Figure K-2.4: Calculated rod loads for flexion and extension loading…………………………192 Figure K-2.5: Calculated rod moment magnitudes at maximum loading across conditions.…..193 Figure K-2.6: Calculated rod load  magnitudes at maximum loading across conditions.……...193 Figure K-3.1: Predicted anterior column moment magnitudes at maximum loading across conditions. …………………………………………...……………………………………...…..194 Figure K-3.2: Predicted anterior column load magnitudes at maximum loading across conditions. ……………………………………………………….……………………………………...…..195 Figure K-4.1: Flexibility curve for 5th loading cycle. ……………………………………...…..195 Figure K-4.2: Range of motion magnitudes at maxmim loading across conditions...……...…..196 Figure L-1: Specimen prepared for subsequent testing to explain rod strain results. …………..197 Figure L-2: Rod strain time traces for each subsequent test ....................................................... 199 Figure L-3: Calculated moments from rod strains measured during flexion loading ................. 200   xvi Acknowledgements I would like to thank Dr. Tom Oxland for his guidance and support for the duration of my thesis project.  He kept a solid focus on the long term objectives of our research which helped me keep perspective despite frequent obstacles.  I also would like to thank Dr. Cripton for his assistance in making decisions related to the in vitro investigation. Dr. John Street contributed not only his clinical perspective when defining our research questions but also his expertise in performing surgeries on cadaver specimens.  He was extremely accommodating and flexible, always making time for my project despite his demanding work schedule, and remained positive and entertaining through long testing days. I would like to acknowledge my funding sources and collaborators: Natural Sciences and Engineering Research Council of Canada (NSERC), The George Bagby Fund, International Collaboration on Repair Discoveries (ICORD), Vancouver Coastal Health Research Institute, and The University of British Columbia. I would like to especially thank Angela Melnyk for all the hours she put into my project: helping me with every cadaver test, meeting with me on a whim, and acting as my sounding board.  I could not have completed my Masters without her.  Thank you to Jason Chak for fixing all the software kinks during my testing and providing impressive experience and knowledge. Also continually supporting me were my friends and lab mates who helped me work through numerous questions and problems: Chris Dart, Erin Lucas, Katharine Wilson, Claire Jones, Hannah Gustafson, Robyn Newell, Carolyn Van Toen, Dan Dressler, Tim Bhatnagar, and Kurt McInnis. Finally I would like to thank my family for their continuing support throughout my studies, encouraging me to follow my passion even if it means moving across the country.  xvii Dedication To everyone living with and affected by disease and deformity.    Chapter 1: Introduction  1 Chapter  1: Introduction 1.1 Overview The average age of the population in North America is quickly increasing (1; 2) and with it, the prevalence of adult spinal deformity (3).  The aging process and deformity of the spinal column can lead to altered sagittal plane alignment.  Positive sagittal alignment is associated with an anterior shift of the body-weight loads of the head, arm, and trunk with respect to the pelvis, causing an overall imbalance of the spine. The common surgical correction involves sagittal realignment using long posterior spinal fixation and fusion, with or without corrective osteotomy.  However, up to 46% of patients who receive instrumented posterior spinal fusion develop proximal junctional kyphosis (PJK) (4; 5; 6).  Failure of the uppermost instrumented vertebra (UIV) or of the vertebra adjacent to the instrumentation occurs by means of vertebral fracture, disc failure, implant-bone interface failure, or intervertebral motion.  Several risk factors have been suggested but it is generally accepted that the transition between fused and unfused spinal segments causes accelerated degeneration at this junction and a higher likelihood of thoracic kyphosis progression and UIV fracture (7; 8). There has been a limited number of studies that have used biomechanics to explain how and why these post-surgical problems occur; specifically it is not known how the proximal junction is loaded after correction of a deformed spine.  Further, most of the extensor muscles are removed or damaged throughout the length of the construct intra-operatively.  The resulting additional compressive loads placed on the spine due to muscle loss are unknown.  To help predict clinical outcome, it is also of interest to investigate how loading patterns are affected by patient and surgical variables such as sagittal profile, construct length, and osteotomy location.   Chapter 1: Introduction  2 The following sections include a review of the literature with discussion of the findings of relevant studies regarding sagittal imbalance, surgical treatment, and spine loading models and experiments, from which the objectives of this thesis are drawn. 1.2 Adult Spinal Deformity The elderly population in industrialized countries is growing every year.  Between 2001 and 2006, the proportion of the Canadian population aged 65 and over increased 11.5% and that aged 80 and over increased 25.2% (1).  Similarly, the United States saw a 21.1% increase in the population aged 62 years and over between 2000 and 2010 (2).  Overall, the population worldwide is growing at a faster rate in the older ages than in the younger ages, a phenomenon that has led to the increase in prevalence and severity of adult spinal deformities (3).  Spinal deformity consists of coronal and sagittal plane deformations (9), the latter of which results in kyphosis and was found to be more significantly associated with pain and disability than curve magnitude, curve location, or coronal imbalance (10). 1.2.1 Sagittal Imbalance The human spine is composed of three regions that, when sagittally-aligned and asymptomatic, have the following curvatures: cervical lordosis (C1-C7) of 20 to 40 degrees, thoracic kyphosis (T1-T12) of 20 to 45 degrees, and lumbar lordosis (L1-L5) of 40 to 60 degrees (Figure 1-1a) (11), though specific angles vary across age groups (12; 13; 14; 15). Each vertebral level consists of a vertebral body, intervertebral disc, posterior elements, and supporting ligaments (Figure 1-1b and c); the vertebral body, intervertebral disc and supporting ligaments make up the anterior column of the spine.  Clinically, it is believed that proper alignment is achieved when the lordotic regions balance the kyphotic region, placing the body’s centre of   Chapter 1: Introduction  3 gravity over the hips and pelvis.  When this alignment is achieved, it is expected to minimize the energy expenditure and muscular effort required to maintain an erect posture (7). The influence of positive sagittal balance on the development and progression of spinal deformities and diseases has become increasingly recognized (16; 17; 18).  Disruption of normal sagittal alignment can occur from a number of spinal deformities, trauma, or surgical interventions, including but not limited to: post-traumatic kyphosis causing kyphotic decompensation syndrome, degenerative disc disease, spondylosis, spondylolisthesis, ankylosing spondylitis, scoliosis, iatrogenic flatback, spine injury, spinal fusion, and overall spine degeneration (19; 20; 21).  Any one of these abnormalities, or combination thereof, can result in a loss of lumbar lordosis (lumbar flatback) (Figure 1-2b) or excessive thoracic kyphosis (Figure 1-2c), both of which ultimately shift the spine’s centre of gravity anteriorly relative to the hips and pelvis and create an overall sagittal imbalance.  In the case of lumbar flatback, patients generally compensate with pelvic retroversion, hip extension, and knee flexion, and subsequent disc degeneration (22), muscle fatigue, and hip and pelvic disease (23) result in an imbalanced spine.      Chapter 1: Introduction  4    Figure 1-1: Relevant Spine Anatomy. (a) Lateral view of the human spine showing curvature of the three main regions: cervical (20 to 40 degrees) (11), thoracic (20 to 40 degrees) (15; 16; 11), and lumbar (40 to 60 degrees) (16; 11), as well as the sacral and coccyx regions, (b) relevant anatomical structures of a thoracic vertebra, and (b) relevant spinal ligaments.  The interspinous and supraspinous ligaments connect the length and apices of the spinous processes of adjacent vertebrae, respectively, while the anterior longitudinal ligament runs along the length of the spine attaching to the anterior vertebral bodies and discs.  All drawings reprinted from Drake et al., 2010 (24) with permission from Elsevier ©Elsevier Ltd., 2005. (a) Cervical (lordosis) Thoracic (kyphosis) Lumbar (lordosis) Sacral and coccyx Gravity line (b) Body Vertebral foramen Superior and Inferior Facet Articular Processes Spinous process Pedicle (c) Intervertebral Disc Facet joint Interspinous Ligament Supraspinous Ligament Anterior Longitudinal Ligament Posterior Longitudinal Ligament  Figure 1-2: Lateral spine radiographs with lumbar flatback (spinal deformity patient of Dr. John Street), and (c) a spine with severe kyphosis The red star marks the location of the sacrum, the red arrow the acting location of the bodyweight load, and the black dashed line the moment arm created by the body anterior displacement of the body-weight load, causing an overall sagittal imbalance. The spine’s sagittal profile can be quantified in terms of regional or g The Cobb method, modified for the sagittal plane, is most often used to describe the degrees of cervical lordosis (27), thoracic kyphosis segmental angulation (16; 33; 34) radiographs and, although the gold standard, tends to neglect regional curvature changes An accepted measure of global sagittal balance is the C7 plumb line other methods using pelvic parameters have also been developed. With the C7 plumb line method, the difference between the posterior-superior corner of the S1 vertebra describes the balance of the spine ( (10).  If the C7 plumb line falls anterior to S1, the spine is said to (a)  Chapter 1: Introduction  of (a) a neutral spine curvature (25), (b) a sagittally -weight load.  Spines in both (b) and (c) have  lobal parameters. (28; 29; 30; 31), and lumbar lordosis (32; 31) .  It uses vertebral endplate lines to construct angles on sagittal (10; 12; 13; 36) (37; 38; 39; 40)  and segmental vertebral positions the centre of the C7 vertebra and  have positive sagittal balance (c) (b)  5  -imbalanced spine (26).  as well as (35). , though (41) Figure 1-3)   Chapter 1: Introduction  6 while if it falls posterior to S1, it is said to have negative sagittal balance.  A normal erect spine has a C7 plumb line between ± 4 cm from S1 (Figure 1-4) (22; 41; 42; 43). Anterior deviation of the C7 plumb line can cause increased loading on the spine and ensuing pain and debilitation, resulting in the reduction of quality of life of those affected. Conservative methods exist as treatment for such deformities, such as physical therapy (19; 44), use of non-steroidal anti-inflammatory medications (45), braces (46), and modifications of lifestyle (44), but should pain remain or worsen, invasive intervention often follows.  Figure 1-3: Quantification of sagittal alignment using the C7 plumb line method. The difference between the sagittal positions of the centre of C7 (B) and S1 (A) is positive for positive sagittal balance, negative for negative sagittal balance, and zero for neutral sagittal balance. Reprinted from Glassman et al., 2005 (10) with permission from Wolters Kluwer Health.   Chapter 1: Introduction  7  Figure 1-4: Neutral standing sagittal profiles derived from vertebral body centroids of 67 healthy subjects. Sagittal balance parameters, T1-T12 and C7-S1 are shown illustrating the vertical alignment of these segments in the upright posture. Reprinted from Keller et al., 2005 (43) with permission from Elsevier. 1.2.2 Surgical Treatment In cases where non-surgical, conservative treatment fails, surgical intervention is sought. Surgical indications in these cases are pain, neurologic deterioration, deformity progression, cosmetic issues, and prophylaxis (42).  The overall goals of spinal deformity surgery include reasonable correction of curvature, improvement of sagittal balance, prevention of further deformation, and ultimately, restoration of function with decreased pain (47). No consensus exists as to what surgical method should be used to correct a kyphotic deformity.  Due to the range of causes, clinical indications, medical histories and complications amongst the affected patients, the ideal method of correction remains in the discretion of the surgeon, decided on a case-by-case basis.  Some common guidelines  include restoring segmental sagittal lordosis and kyphosis to normal degrees of curvature (44), restoring lumbar Anterior Posterior   Chapter 1: Introduction  8 lordosis to 10° – 30° greater than thoracic kyphosis (44), centering the C7 vertebral body over the sacrum (44; 48), or centering L1 over the sacrum (49). Currently, the most common surgical correction techniques for positive sagittal balance include single or multi-level posterior instrumented fusion often in combination with at least one osteotomy, though no procedure has been proven to completely prevent further progression of kyphotic deformity (Figure 1-5) (3).  Two studies reported 90% (23) and 86% (44) of patients treated for sagittal imbalance with posterior instrumented fusion to be satisfied with the results, though only 50% reported increased function (44).  Alternatively, LaGrone et al. (50) found that 36% of patients who received subsequent corrective osteotomies following initial spinal fusion complications reported moderate to severe pain at follow-up.   Similarly, there was a 25% complication rate in osteotomy revision surgeries following previous instrumented fusions (19). This trend marks the importance of successful long-term outcome of the initial spinal fusion surgery as that of any subsequent revision surgery is markedly lower.  Also crucial to successful and retained correction is adequate restoration of sagittal balance as one study found a 71.5% failure rate in cases that did not achieve this result (48).  Figure 1-5: Radiographs showing anterior translation of a spine after three-level posterior instrumented fusion surgery. (a) Pre-operative x-ray showing marked positive sagittal balance, (b) the 8 week follow-up x- ray after a PSO was performed, showing improved sagittal balance, and (c) 2 year, 10 month follow-up x-ray showing progression of positive sagittal balance.  Reprinted from Rose et al., 2009 (51) with permission from Wolters Kluwer Health.  (b) (a) (c)  1.2.2.1 Spinal Fusions with Instrumentation Spinal fusion is an invasive opera with a bone graft to eliminate mot initially high after this procedure should be minimized to allow more segments to accommodate the spine’s normal range of motion (52). Most spinal fusion surgeries today use stabilizing instrumentation, fixed to the vertebrae with either pedicle screws or hook constructs, to stabilize and immobilize the affected levels during bone growth (Figure 1-6). Figure 1-6: Posterior instrumented fusion for s screws with a distal hook.  Reprinted from Corenman, 2011 Fluoroscopy or computer-assisted guidance is often used to localize the pedicles within the fusion mass to ensure accurate placement constructs are the creation of a three (a)  Chapter 1: Introduction  tion; in the case of interbody fusion, the disc is ion at any level causing pain.  Pseudarthrosis rates were  and it became clear that the number of motion segments fused pinal deformity using (a) pedicle screws only and (b) pedicle (53) with permission from SpineUniverse. (44).  The advantages of pedicle screw ove -column fixation (54; 55), better correction with a smaller (b)  9  replaced   r hook   Chapter 1: Introduction  10 number of fusion segments (54; 56), improved pulmonary function (56), and the facilitation of performing osteotomies (54).  Pedicle screw fixation can, however, place higher stress on the adjacent segments due to the rigid fixation (54) and is a more expensive procedure (56).  Studies have shown that the addition of pedicle-screw-based fixation increases the rate of fusion (57; 58; 59), ultimately shortening the recovery period after surgery, and there has been high patient satisfaction in those treated for many deformities (7; 18; 60; 61; 62).  To attain desired results with pedicle screw constructs, proper load-sharing between the spinal column and the implant is essential, especially during fusion healing (63). 1.2.2.2 Osteotomies In cases where substantial correction is required, posterior instrumented fusion is often supplemented with an osteotomy which involves a resection of bone to adjust the placement or alignment of adjacent bony structures, ultimately restoring sagittal balance to reduce pain and enable an erect posture (64).  The three main types of osteotomies are Smith-Petersen osteotomy (65), pedicle subtraction osteotomy, and vertical column resection, differing by the amount of posterior and anterior bony elements that are removed. Pedicle subtraction osteotomy involves a V-shaped resection through the posterior elements, pedicles, and vertebral body with the apex at the anterior border of the vertebral body (Figure 1-7).  When closed, there is bone-on-bone contact in the posterior, middle, and anterior columns (66).  It is performed most often in the lumbar spine (L2 to L4) in cases where the required correction is approximately 30° (44; 64), sagittal imbalance is greater than 10 to 12 cm, or there is a sharp, angular kyphosis (66).  It is advantageous because correction can be achieved through a single approach that does not cause anterior gapping, thereby maximizing the healing potential (44; 64).  Successful sagittal correction of a number of kyphotic deformities (fixed sagittal   Chapter 1: Introduction  11 imbalance, rigid thoracolumber hyperkyphosis) can be attained with a pedicle subtraction osteotomy in the lumbar or thoracolumbar region (42; 67; 68; 69; 70) (Figure 1-8), achieving improved realignment when compared to using three or more Smith-Peterson osteotomies (71).  Figure 1-7: Schematic of a pedicle subtraction osteotomy.  This osteotomy closes the posterior and middle columns, hinging on the anterior column (66).  Reprinted from Kim et al., 2009 (64) with permission from Open Access under the terms of Creative Commons Attribution Non-Commerical License.  Figure 1-8: Kyphotic deformity (caused by ankylosing spondylitis) treated with pedicle subtraction osteotomy. (a) Pre-operative x-ray showing global kyphosis with lumbar flatback, (b) Post-operative x-ray showing significant improvement of sagittal imbalance, (c) close-up x-ray showing a PSO at L3. Reprinted from Kim et al., 2009 (64) with permission from Open Access under the terms of Creative Commons Attribution Non-Commerical License.  Given the amount of surgical correction attained and the possible complications, it is important to plan and execute the osteotomy procedure carefully (42; 72; 70; 73).  Ondra et al. (a) (b) (c) PSO   Chapter 1: Introduction  12 (42) and Chou-kuan et al. (72) reported the need for a quantitative method of predicting the required osteotomy size for a desired correction to replace past methods that involve estimation and radiograph traces and cutouts only (44; 70).  By choosing the desired vertebral level for the osteotomy, trigonometry can be used to calculate the required osteotomy angle (42) (Figure 1-9), and height (72) (Figure 1-10) pre-operatively, eliminating guesswork during the surgery.  Figure 1-9: Mathematical calculation of pedicle subtraction osteotomy size based on desired correction, given a specified osteotomy location. Two parallel lines are drawn from the measured pre-operative locations of each C7 and S1, representing the plumb line (PL) and posterior sacral perpendicular line (PSPL), respectively.  The correction distance (CD) is the horizontal location of C7 with respect to S1, ie. the distance between PL and PSPL.  An oblique line is then drawn from C7 to S1.  The angle α represents the desired angle of correction for this patient’s spinal imbalance, and its magnitude is found from α = tan-1(CD/PL). This particular sagittal profile is such that the tip of the osteotomy is in line with PSPL but this is not always the case, based on different osteotomy locations of interest in this study. Reprinted from Ondra et al., 2006 (42) with permission from Wolters Kluwer Health. Ondra et al. determined the osteotomy angle (α) required to bring the C7 plumb line in line with the sacrum, knowing the horizontal correction distance (CD) and the vertical distance between C7 and the osteotomy level (PL) (Eq. 1-1).   tan  
 (Eq. 1-1)   Chapter 1: Introduction  13  Figure 1-10: Mathematical calculation of osteotomy height using a geometrical model (71).  (a) Measurements from vertebral levels involved in a posterior closing wedge osteotomy, where C is the pre-operative kyphotic angle, H1, H3, and H2 are the pre-operation heights of the superior vertebra, inferior vertebra, and the difference between them, respectively, and H1’ and H2’ are the post-operative heights of the superior and inferior vertebrae, respectively.  (b) Simplified geometry to calculate posterior closing wedge osteotomy size, where the osteotomy angle (A) is the difference between the pre-operative kyphotic angle (C) and post- operative kyphotic angle (C’).  Reprinted and modified from Chou-kuan et al., 2008 (72) with permission from Open Access under the terms of Creative Commons Attribution Non-Commerical License.  Chou-kuan et al. determined a relationship between the osteotomy angle (A) and height (L), given the length along the superior and inferior vertebrae that are being cut (D1 and D2), using the Cosine Rule (Eq.1-2).   1  2  2 · 1 · 2 · cos  And since the superior and inferior vertebrae align when the osteotomy is closed, D=D1=D2, and Eq.1-2 can be re-arranged to solve for A:   cos 1  2 The post-operative kyphotic angle (C’) then can be calculated by subtracting the osteotomy angle (A) from the pre-operative kyphotic angle (C). Both studies implemented their respective mathematical relationships to a cohort of retrospective cases to determine their efficacy in a clinical setting and found that the percent difference between calculated osteotomy parameters compared to those actually attained for a given desired correction were 9% and 15% for Ondra et al. and Chou-kuan et al.’s models, respectively.  It must be noted that the calculations made by Ondra et al. relate to a pedicle subtraction osteotomy while those made by Chou-kuan et al. relate to a posterior closing wedge L (Eq.1- 2) (Eq. 1-3) (a) (b)   Chapter 1: Introduction  14 osteotomy where the wedge is taken from two vertebrae and the disc.  Both methods provide means to estimate the osteotomy size required to achieve a desired correction, ultimately affecting the loading of the spine. 1.2.3 Proximal Junctional Kyphosis While sagittal realignment using long posterior spinal fixation and fusion, with or without corrective osteotomy, is the treatment of choice for global sagittal imbalance, patients often develop proximal junctional kyphosis (PJK) through failure of the uppermost instrumented or adjacent vertebra (Figure 1-11).  In addition to failure at these levels, PJK is considered abnormal when the proximal junctional angle is more than 10° and at least 10° greater than the corresponding pre-operative measurement (6; 60; 74; 75).  Common mechanisms of failure at the uppermost instrumented level are superior endplate fracture or screw pull-out while at the adjacent level they are vertebra fracture or listhesis (76). It has been found that uppermost instrumented vertebra collapse tends to occur within months of surgery and often results in subsequent adjacent vertebra listhesis, while adjacent vertebra compression fracture generally occurs years after surgery (54; 76).  Disc and ligamentous failure was the cause of PJK in 81% of thirty-two adult idiopathic scoliosis patients from another study (75).   Chapter 1: Introduction  15  Figure 1-11: Radiographic evidence of proximal junctional kyphosis (PJK) occurring by adjacent vertebra (T8) fracture two months post-operative showing (a) pre-operative and (b) two months post-operative postures.  X-rays were courtesy of Dr. John Street from Vancouver General Hospital. Glattes et al. (6) found 26% of 81 adult spinal deformity patients (scoliosis, sagittal imbalance, or both) treated with long instrumented posterior spinal fusion developed PJK, while other researchers found failure rates at the proximal junction of 31% (77) and 43% (74) in cohorts of thirty-two and fourteen, respectively.  Amongst 67 adult Scheuermann Kyphosis patients, 30% developed PJK by five-year follow-up (60) while up to 46% of patients corrected for adolescent idiopathic scoliosis developed PJK 7.3 years (5) and 2 years (4) after operation, respectively.  Sagittal thoracic decompensation, defined as progressive kyphotic deformity of the thoracic spine resulting in a C7 plumb line  8 cm, was found to be an indication of PJK and occurred in 23% of lumbar deformity patients (78). Risk factors for PJK include age (54; 78), osteopenia (54), severe pre-operative global sagittal imbalance (54; 75) pre-operative sagittal thoracic Cobb angle (T5-T12) larger than (a) (b)   Chapter 1: Introduction  16 40° (5), disruption of junctional ligaments (60), unsuccessful fusion of the uppermost instrumented vertebra (60), inappropriate upper end vertebra selection (60), and more than eleven levels fused (5).  The amount of sagittal correction restored during surgery was also found to correlate with PJK occurrence as a C7 plumb line shift of over 50 mm occurred in 84% of PJK patients and only 6.4% of non-PJK patients (75; 79). Although it remains impossible to conclude whether PJK is a result of an iatrogenic effect of the surgery, natural age-related degeneration or a combination thereof (6), it is generally accepted that fixed segments following instrumentation and fusion increase stress on unfused spinal segments causing accelerated degeneration at this junction and a higher likelihood of thoracic kyphosis progression and UIV fracture (7; 8). Revision surgery for PJK involves removing the screws from fractured vertebrae and extending the instrumentation past the failed level to increase the number of fixation points while maintaining the largest range of motion possible.  The reoperation rate after PJK varies based on severity of failure and patient medical history and preference.  Of two different PJK populations, only 20% (60) and 12.5% (75) of patients had revision surgeries while other patients refused revision due to lengthened follow-up periods and the chances of a further increase in reoperation rate (77). Due to the poor surgical outcome of revision surgeries (19; 50), it is crucial to be aware of the indications to predict the likelihood of PJK on a case-by-case basis.  To facilitate this, consideration of loads imposed on the spine is important and how they are affected by surgical variables including but not limited to: pre-op and post-op sagittal balance, osteotomy size and location, length of fixation, type of fixation, muscle function, load sharing between vertebra and implant, bone density, and surgical history.  Although many researchers have studied the loading of the natural and instrumented spine (80; 81; 82; 83; 84; 85; 86) and its natural strength (87; 88;   Chapter 1: Introduction  17 89; 90; 91; 92), no literature is available for the effect of spine geometry and the aforementioned surgical variables on the loads seen at the proximal junction. 1.3 Spine Loading Models, Measurements, and Calculations Quantitative evaluation and graphical representation of the spine allows for surgical planning and monitoring deformity progression and provides a means of comparison to reference values in normal and pathological conditions (61).  Medical images are used as a basis of spinal curvature development, including two-dimensional radiography (x-ray) and three-dimensional computed tomography (CT) and magnetic resonance (MR) modalities.  Technological advancements continue to improve the accuracy and utility of spinal curvature quantification, methods for which range from simplified two-dimensional geometric models to complex three-dimensional finite element models that take into account surrounding tissues and the behaviour of each anatomic structure.  These models are then used to predict loading patterns along the spine in a variety of static postures and during activities of daily living, both of which provide valuable information for conservative and surgical treatment strategies for spinal deformity patients. 1.3.1 Geometric Models 1.3.1.1 Two-dimensional Many researchers have taken sagittal alignment measurements directly from patient radiographs to develop models of spine curvature using a number of geometric shapes and techniques including an ellipse (93; 94; 95), circle (93), polynomial (29), and spline (41).  These models all aim to provide a more comprehensive representation of the global sagittal profile than can standard radiographic measurements alone.  Vertebral body corners (41; 43; 93; 94; 95; 96; 97; 98), anterior and posterior vertebral contours (29), posterior vertebral body heights (95), or   Chapter 1: Introduction  18 posterior disc heights (95) were digitized from lateral radiographs of normal subjects and geometric shapes were constructed for various components of the curves. Using a least-squares method to determine the best fit, both Harrison et al. (93) and Janik et al. (95) concluded that an elliptical model (Eq. 1-4; Figure 1-12), more closely fit thoracic and lumbar curvature compared to a circular model. Curve predictions from both models show good agreement with reported radiographic measurements for normal curves (16; 99; 100).  ⁄ !  " #⁄ !  1  Figure 1-12: Schematic of elliptical model used to construct spinal curvature , assuming uniform disc and vertebral body heights.  The lumbar lordosis is measured from the posterior endplate of T12 to the superior endplate of S1 and each posterior body corner was given a percentage of the lumbar ellipse.  Reprinted from Harrison et al., 2002 (93)  with permission from Wolters Kluwer Health. Elliptical models are a good approximation of regional curves but it becomes more difficult to fully represent global sagittal curvature. A polynomial function, used by Singer et al. (29) to represent the thoracic curve from lateral chest x-rays, has the advantage of running smoothly along the full length of the spine, incorporating all regional curves. A seventh order polynomial was fit to a representative curve constructed from digitized points along the posterior vertebral margin and the thoracic curve apex and inflexion between thoracic kyphosis and lumbar lordosis were derived from its first and second derivatives, respectively (Figure 1-13).  Unlike the Cobb method, this method was not affected by the poor visibility in x-rays and variability of (Eq. 1-4)   Chapter 1: Introduction  19 orientation of the upper and lower vertebrae.  It is expected that thoracic angles calculated from the polynomial model more accurately describe the full thoracic curve as opposed to only the relative angulation between T3 and T11. Moreover, polynomials are computationally efficient because they can be integrated and differentiated easily in a finite number of steps using basic arithmetic operations.  Figure 1-13: Construction of spine geometry using a polynomial to derive the T3 to T11 thoracic kyphosis from lateral chest radiographs. (a) A modified Cobb technique was used as a baseline, (b) then the anterior and posterior contours of all visualized segments were digitized and (c) a smoothed curve was constructed to which a seventh order polynomial was fit.  The short lines represent the locations of T3 and T11, used for the calculation of thoracic kyphosis, the x represents the thoracic curve apex and the x with a line represents the thoracolumbar inflexion point, calculated with first and second derivatives of the polynomial function, respectively.  Reprinted from Singer et al., 1990 (29) with permission from SpringerLink.   Yang et al. (41) derived a spline, a piecewise-polynomial function constructed from a number of low-order polynomials, from digitized vertebral coordinates.  A spline passes through each vertebra error free thereby retaining segmental deviations of the spinal curve (41).  It eliminates the error associated with selecting a polynomial of the appropriate degree to represent a curvature that may change shape along the length of the spine.  In a follow-up study, the spline model was applied to a cohort of 34 patients who underwent pedicle subtraction osteotomy for correction of fixed sagittal imbalance and C7 plumb line measurements were compared to (a) (b) (c)   Chapter 1: Introduction  20 normal subjects (101).  This analysis has not yet been extended for use as a pre-operative surgical planning tool for sagittal deformity patients. 1.3.1.2 Three-dimensional  Similar techniques of defining spinal curvature can be used with landmarks taken from three-dimensional (3D) images that more accurately represent the complex anatomical structure of the spine.  A number of studies have modeled the curvature of normal and pathological spines imaged from CT scans with spline (102; 103) and polynomial (104; 105) functions or from MR images with polynomial functions (106; 107) fit to the 3D coordinates of vertebral body centers, corners, or intervertebral discs. As new means of imaging are developed and adopted clinically, three-dimensional spinal curvature construction will become increasingly effective and superior to its two-dimensional counterpart as it can offer a more comprehensive depiction of the spine.  An example of such means is video rasterstereographic (ie. topographic) imaging which takes radiation-free surface contours of the back that can be used to detect the spinal profile for the diagnosis of spinal deformity (108).  However, these analyses are currently limited by the cost and availability of 3D images and their added complexity may not be required for robust curvature development. Regardless of the complexity of the geometric model, the end goal is often to use the constructed curvature as a baseline for spine loading predictions, avoiding the added complications of experimental measurements. 1.3.2 Spine Loading Models 1.3.2.1 Static Equilibrium Biomechanical Model The simplest, and often sufficiently insightful, load calculation method is a statically- determinate two-dimensional (2D) biomechanical model that assumes the spine is in a state of   Chapter 1: Introduction  21 equilibrium, described by Schultz and Andersson in 1981 (81).  An imaginary transverse cutting plane is passed through the level of interest and Newton’s Laws are applied to the upper part by first calculating the net reaction and then estimating internal forces.  Three net force and three net moment components, equal to the vector sum of all the internal forces and moments caused by those forces, respectively, are generated from the lower part and act on the upper part.  The sum of the net force and any external forces, and the sum of the moments these forces generate about a point of interest, must equal zero in each direction. External loads are those from body segments or those applied in the execution of a task.  The loads and locations of centres of mass of different body segments are reported in the literature (109; 110; 111; 112; 113; 114), assuming that each body has uniform density (81).  The net reaction is not affected directly by anything below the cutting plane nor the material properties of the surrounding tissues. Anatomical variables affect only the mass distribution and moment arms of body segments (81). For a determinate model, the extensor musculature is combined into one functional group that acts at an assumed line of action with respect to the vertebral body and that maintains equilibrium with the body-weight loads.  When the forces acting by individual muscles are considered, it creates a condition of indeterminacy where an infinite number of possible force- producing options are available to balance external loads, making equilibrium calculations alone inadequate.  Optimization provides a unique set of muscle forces within certain constraints and according to a specified criterion (115; 116; 117; 118), such as minimizing muscle fatigue (98) or minimizing the compressive load on the vertebral level of interest (82).  Although taking into account the complexity of musculature may give a more accurate representation of spinal loads, it is limited by having to approximate muscle recruitment and behaviour, and different optimization constraints have been found to change spine load predictions (118).  Further, large  variation exists between muscle forces calculated with optimization methods and those measured through electromyography (method of recording the electrical activity of muscles) Equilibrium calculations have been use (LBP) analyses and the loads were often calculated at L3 121; 122) (Figure 1-14).  These load calculations can for other applications such as spine loading during activities of daily living various spinal deformities (96; 97; 98; Figure 1-14: 2D equilibrium calculations used to predict lumbar intervertebral loads during a static lift mass, m, a distance of (H), arm (A), and trunk (T) act at distances reaction force, R, (red) acting at the disc, and unknown muscle force, the disc centre (5 cm is a common approximation of the moment arm of a grouped extensor muscle force) can be calculated with static equilibrium calculations, – F + R = 0 and b) ΣMO = F·LF – m·L Due to the variability in anthropometry and activity execution across humans, a wide range of loads have been calculated during different postures and activities quiet standing (81; 124) to ~5,000 N in lifting tasks  Chapter 1: Introduction d in Manual Materials Handling and l -L4 or L4-L5 disc levels  be extended along the length of the spine (81; 118) 123).   for the L4 Lm from the disc centre.  The body-weight loads (blue) of the head LH, LA, and LT from disc centre, respectively F, (green) acting at a di given the coordinate system shown: a) ΣF m – (H·LH + A·LA + T·LT) = 0. (ie. ~300 (121; 122)).  It is therefore often unnecessary z y x LF O H A m T R F LA Lm LT LH LF O  22 (119). ower back pain  (81; 82; 120;  or with -L5 disc level .  The unknown stance LF from y = -(H+A+T) – m -500 N in    Chapter 1: Introduction  23 to collect precise three-dimensional coordinate data to describe spine geometry and loading as even a rough estimate of the loads generated by an activity will have clinical utility (81). However, even if the use of a more complex model is deemed suitable for a given research question, intervertebral equilibrium equations are still used as a basis for analysis. 1.3.2.2 Two-Dimensional Two-dimensional loading models developed to predict approximate loads along the length of the spine based on a given sagittal profile and activity vary by external loading assumptions and the anatomic structures and material properties used in the model. Keller and Nathan (123) were concerned with the height change caused by intervertebral disc degeneration during aging and created a three-parameter model to represent the disc as a deformable element with viscoeleastic behaviour.  However, sagittal profiles were built from ideal dimensions and postures taken from the literature (100; 125; 126), limiting clinical utility. A later study adapted this upright posture model to predict kyphotic spine deformities associated with osteoporosis using digitized points from twenty patient x-rays and manipulating the equilibrium loading model to include vertebral stiffness to determine its deformation (97). Keller et al.’s (43) most recent study used this model to investigate the interaction between spinal morphology, specifically sagittal curvature and balance, and intervertebal disc loading using sagittal profiles of sixty-seven young asymptomatic subjects, without consideration of disc deformation and other material parameters. These studies are limited as they do not include contributions of individual spinal muscles or the ribcage, both found to change the spine’s loading response, adding stiffness and thus stability to the spine (127; 128; 129).  McGill et al (122). developed a model that included contributions of disc deformation, intra-abdominal pressure, and twenty-six ligaments and muscles.  The   Chapter 1: Introduction  24 reactive L4-L5 moment and forces were calculated by considering the partitioning that takes place between the muscle, ligament, and disc.  Muscle attachment points and lines of action were modeled anatomically and muscle forces were estimated from EMG activity.  They predicted compressive disc loads 16.2% lower than those calculated from a simple model using a grouped extensor muscle with a 5 cm extensor moment arm (130).  They also found that, during lifting, the sacrospinalis muscle dominated the counteraction of body-weight loads when compared to ligaments and discs.  These findings justify the assumption of static equilibrium based on one extensor muscle but suggest that these models may overestimate intervertebral compressive loading. Iyer et al. (118) developed a quasi-static model that, in addition to incorporating eleven spinal muscles, considered the ribcage and sternum to act as load-bearing elements that contributed based on experimental data (128).  Using this model, the increase in loading that occurred from a neutral to a flexed posture was reduced in thoracic compared to lumbar regions. All models discussed thus far have considered only neutral postures of normal spines but it is expected that loading changes with posture and deformity.  Legaye et al. (40) justified this theory by demonstrating that sagittal balance requires compensatory activity of posterior spinal musculature which increases with smaller moment arms in torso flexion (131) and in uneconomical or pathological postures (82; 111; 132), a phenomenon that leads to increased vertebral column loads.  To characterize the changes in disc loads and muscle forces following anterior translation of the thoracic spine, and thus the gravity line, Harrison et al. (96) took vertebral body geometries from lateral x-rays of eighteen young normal spine subjects in two postures: neutral, and with anterior translation of the thorax relative to the pelvis.  From a neutral to anterior-   Chapter 1: Introduction  25 translated posture, disc loads at L5-S1 increased up to 92.2%, 223%, and 80.8% at the centroid, anterior, and posterior edges, respectively, while muscle forces increased 54.6% and 942% in thoracic and lumbar regions, respectively (96).  The body-weight loads were assumed to act at a line of gravity 10 mm anterior of T4. Due to the limitations of simulating postural (96) and degenerative (97) changes using young healthy spines, Briggs et al. (98) based their model on a cohort of forty-four elderly subjects grouped into high and low kyphosis groups, sagittal profiles of which were each fit to a polynomial curve.  Comparisons between groups showed strong positive associations between normalized net segmental load parameters and thoracic curvature (98).  Modeling elderly subjects added authenticity to their study but the mean kyphosis angle of the high kyphosis group still only reached 37.6° whereas other studies found kyphosis angles of 77° and  51° - 121° for healthy elderly (13) and kyphotic deformity (10) subjects, respectively.  No known study has been conducted to determine loading behaviour of spines with significant natural positive sagittal balance. 1.3.2.3 Three-Dimensional Three-dimensional models have been used to improve the validity of loading models, accounting for the three-dimensional nature of spinal curvature, especially when deformed.  The finite element models described by Arjmand et al. (116; 133),  Bazrgari et al. (115) and El-Rich et al. (117) used seven rigid elements to describe the T12-S1 vertebrae, non-linear beam elements to represent the stiffness of T12-S1 (produced from a combination of vertebral, disc, facet, and ligamentous structures), and a single rigid body element to represent T1-T12 and the thorax-neck-head assembly.  The insertion points and lines of action of ten muscles, assumed to run straight in all but Arjmand et al.’s latest study (133), were included and an optimization   Chapter 1: Introduction  26 approach was used to estimate muscle forces and ultimately spinal loads.  Including more physiologic curved paths for global extensor muscles during forward flexion decreased the predicted muscle forces and spinal compressive loads at all levels (133).  As all of these studies were concerned with the whole trunk response to different movements, relatively simple models with limited material properties were used for the individual segments. To further consider the response of various spinal structures to loading, a number of more complex finite element models have been constructed of functional spinal units or single vertebral bodies, dimensions and relative positioning taken from computed tomography (CT) scans (89; 134), x-rays (135; 136), or in vitro measurements (100; 126; 137). Some groups have used finite element models of vertebral segments to investigate the effect of a spinal fixation device and the interaction between the pedicle screw-vertebra complex (134; 136; 137).  Calisse et al. (136) simulated three groups of muscle forces, magnitudes for which were chosen based on the combination that produced similar fixator loads in their model as those determined in vivo.  They found that the global dorsal muscle force was predominant in both neutral and flexed postures, increasing over 200% from one to the other, but did not address vertebral loading. With a simpler instrumented multi-segment finite-element model, Hato et al. (137) made clinically important findings by looking at the effect of bone quality, kyphosis, and compensatory mechanisms often adopted by kyphotic deformity patients.  With an applied load to the superior segment along the line of gravity, the maximum vertebral compressive stress was found to increase with severity of both osteoporosis and kyphosis and decrease with compensation, while the maximum rod stress was consistently found directly under the inferior pedicle screw, increasing with kyphosis (137).   Chapter 1: Introduction  27 The use of a more complex three-dimensional model is not always worthwhile as, in many cases, simple two-dimensional models provide similar predictions, subject to variation in load application (Table 1-1). Table 1-1: Predicted compressive loads for L4-L5 level in various 2D and 3D studies Study Model Predicted Compressive Load [N] El-Rich, 2004 (114) 3D 534 Arjmand, 2009 (113) 3D 420 Schultz, 1981 (78) 2D 400 Keller and Nathan, 1999 (123) 2D 400 Keller, 2003 (94) 2D 620 Keller, 2005 (43) 2D 320 Iyer, 2010 (115) 2D 320  Attempting to represent physiologic muscle activation has proven to be a daunting task as even moderate changes in assumed lines of action or optimization objective functions could substantially alter the magnitudes of predicted muscle and spinal forces (118; 138) and activation patterns have been found to vary significantly across tasks and individuals (139).  Once validated, simpler models are often sufficient in providing important clinical information.  To validate biomechanical models, in vivo and in vitro intradiscal pressures (80; 140; 141) and internal fixator loads (84; 142) have been measured. 1.3.3 Experimental Models and Measurements 1.3.3.1 Intradiscal Pressure Measurements In 1964, Nachemson measured intervertebral disc pressure using a needle with a pressure-sensitive polyethylene membrane at its tip inserted into the nucleus pulposus of the intervertebral disc of one subject (80).  The pressure measured in the nucleus pulposus of normal or slightly degenerated discs was about 50% higher than the externally applied pressure (applied force per disc cross sectional-area) (143) and followed a linear response to the applied load (141;   Chapter 1: Introduction  28 144; 145).  Therefore, with measurements of the disc’s cross-sectional area, the intradiscal pressure can be converted to intradiscal load. 1.3.3.1.1 In Vivo Studies Nachemson et al. (141) measured the lumbar disc pressure in various body positions and found the mean lumbar disc load increased 50% from neutral standing to standing with a 20° forward tilt, an observation consistent amongst multiple studies (Table 1-2).  Wilke et al. (86) and Takahashi et al. (146) used more advanced needle pressure transducers and found higher loads in standing than sitting (86), opposite to what Nachemson saw, and higher loads during forward bending (146), but otherwise pressures correlated well between studies.  In the only known study measuring thoracic disc pressure, Polga et al. (85) found loading patterns to differ from lumbar levels.  It can therefore be concluded that flexion of the spine does not necessarily cause a constant increase in vertebral loading along the length of the spine and may in fact reduce loading at the thoracic apex, a function of spine curvature, muscle function and moment arms, and other anatomical factors. Sato et al. (144) found that intradiscal pressure was lower in patients with ongoing back problems (disc herniation and spondylosis) compared to healthy individuals, further decreasing with degeneration.  Relating disc load to intradiscal pressure readings may therefore only be viable when measurements are taken from healthy discs.  In fact, Nachemson previously found an average decrease in pressure of 34% in degenerated compared to normal discs in vivo (141).       Chapter 1: Introduction  29 Table 1-2: Results from in vivo intradiscal pressure measurements in healthy subjects in a variety of positions for different disc levels Study Subject mass [kg] Level Measurement Lying (prone) Relaxed Sitting Relaxed Standing Standing with flexion Nachemson, 1966 (141) 70 L3 Intradiscal Load [N] - 1,393 970 1,450 Nachemson, 1981 (124) 70 L3 Intradiscal Load [N] - 700 500 1000 (40°) Schultz, 1982 (82) 66 L3 Intradiscal Pressure [MPa] - 0.3 0.27 1.04 (30°) Theoretical Load [N] - 380 440 1400 (30°) Wilke, 1999 (86)  70 L4 Intradiscal Pressure [MPa] 0.11 0.46 0.50 1.10 Takahashi, 2006 (146) 72 L4 Intradiscal Load [N] - - 645 2305 (30°) Theoretical Load [N] - - 454 1382 (30°) Sato, 1999 (144) 73 L4 Intradiscal Pressure [MPa] 0.09 0.6 0.5 1.3 Intradiscal Load [N] - 900 800 2000 Polga, 2004 (85) 73 T6, T7 Intradiscal Pressure [MPa] 0.29 0.99 1.01 0.94 (30°) T9, T10 Intradiscal Pressure [MPa] 0.20 0.88 0.86 1.09 (30°) 1.3.3.1.2 In Vitro Studies In addition to his in vivo studies, Nachemson also measured lumbar intradiscal pressure of cadaveric specimens during different spinal movements using a compression apparatus (140). Similarly to in vivo findings, pressure increased from a neutral posture compared to a 5° forward tilt, independently of the external load (140).  Rohlmann et al. (147) also measured the intradiscal pressure of a multi-segment cadaveric spine with the application of a pure moment (±3.75 Nm) to determine the effect of an internal fixator on pressure in adjacent regions.  In general, intradiscal pressure increased with an increasing external moment and with the addition   Chapter 1: Introduction  30 of a fixator, mostly in the bridged discs.  However, they found large variation in intradiscal pressure magnitudes across specimens as there was an age range from 16 to 69 years and evidence has shown that intradiscal pressure is highly dependent on disc quality (141; 144). Researchers determined the effect of disc degeneration on intradiscal pressure measurements under an applied compressive force (148).  Compared with normal discs, degenerated discs had a smaller nucleus with a smaller hydrostatic pressure and a wider posterior annulus with higher stress peaks (Figure 1-15); age of the subject correlated significantly with the degree of degeneration.  Similarly, Butterman and Beaubien (145) conducted an investigation of instrumented spines in normal and induced scoliotic curvatures and compared disc pressure profiles in healthy and degenerated discs.  They found healthy discs to exhibit uniform pressure profiles with minimal sensitivity to curvature type while degenerated discs experienced a pressure depression in the nucleus relative to the annulus and asymmetry across the disc with an induced scoliosis.  Figure 1-15: Intradiscal compressive stress profiles (horizontal and vertical) for healthy and degenerated discs, obtained from intradiscal pressure measurements during application of a 2 kN compressive force, as a function of distance across the disc (from posterior to anterior) of (a) a young healthy disc (grade 1) and (b) an old severely degenerated disc (grade 4). Vertical dashed lines indicate the extent of the hydrostatic nucleus which is much larger for the healthy disc. Reproduced and adapted with permission and copyright © of the British Editorial Society of Bone and Joint Surgery (148). (b) (a)   Chapter 1: Introduction  31 To avoid the disparity in intradiscal pressure magnitudes, Cunningham et al. (149) measured the changes in intradiscal pressure at three adjacent disc levels under four conditions of spinal reconstruction (intact, destabilized, laminar hook, and pedicle screw reconstructions), assuming variability in pressure across the disc was constant between conditions.  They found similar results between axial compression and flexion loading; proximal disc pressures increased as much as 45% and operative levels decreased 41-55% after instrumentation, the largest changes seen after pedicle screw reconstruction (149).  This suggests that adjacent segments may be exposed to higher loading after instrumentation, predisposing the proximal junction to failure. However, as this study used a displacement-controlled protocol, the results are largely a function of the experimental design and interpreting them to correlate to the specimen condition may not be accurate (discussed in Section 4.4.2) (150). Alternatively, Rohlmann et al. (151) used a load- controlled protocol to compare the difference in pressures measured during the application of a pure moment of ±7.5 Nm with and without a follower load meant to simulate intersegmental muscles.  With the follower load, there was a 140% and 90% increase in intradiscal pressure at maximum flexion and extension, respectively, but pressure magnitudes still differed from in vivo values (86). In general, since the age is often high and the quality of the disc is often unknown for cadaveric specimens, caution must be practiced when drawing conclusions about spine loading from intradiscal pressure measurements. 1.3.3.2 Strain Gauge Measurements Another method to measure load is to use a voltage producing sensor.  With calibration, this voltage signal can be converted into strain, force, torque, or pressure.  To measure load on a   Chapter 1: Introduction  32 spine-implant construct, electro-resistive sensors (152; 153) and off-the-shelf load cells (62) have been used in the past, while strain gauges are the most common.  Strain gauges are small resistive elements that convert mechanical deformation into an electrical signal by responding proportionally to a change in capacitance, inductance, or resistance caused by small deformations in the material.  They can be affixed to a variety of surfaces and shapes and in biological applications have been placed on a number of bones (154; 155) including vertebrae (156; 157; 158; 159) and facet surfaces (160; 161; 162; 163; 164). They have also been used to measure strain on rods (84; 142; 165; 166; 167), pedicle screws (168; 169; 170), and other implants (171; 172; 173).  These studies have all used foil strain gauges (Appendix A.1), bonded directly to the strained surface, that respond to a change in surface length upon load application.  The corresponding strain is calculated from the electrical resistance of the strain gauge wire which varies linearly with strain (174). 1.3.3.2.1 In Vivo Studies In vivo spinal loads have been inferred by indirect measurement of the load of an internal fixation device, first developed by Rohlmann et al. (83).  A spinal implant (AO-Dick (175)) was modified, similarly to that of the instrumented hip implant previously developed by Bergmann et al. (176), to include six strain gauges.  Two modified fixators were implanted with screws entering left and right pedicles and rods bridging across one vertebra, attached to adjacent vertebrae (84).  Strains were measured during loading and three force and three moment components were determined by the matrix method (177).  In vivo fixator loads of three patients were then measured during standing and flexion (84) and later ten patients in different body positions (142).  Together, these studies reported an average axial compressive force of approximately 80 N and bending moment of 3.3 Nm during standing, while during flexion they   Chapter 1: Introduction  33 were approximately 100 N and 3.2 Nm, respectively.  An interesting finding from these studies was that for a few patients during standing, some fixators experienced small tensile forces and extension moments, opposite loading patterns to those expected, possibly resulting from the variability in indication for surgery, bridged vertebral level, and surgical procedure (142). With the large variation in patient age, health, and general anatomy as well as testing protocol, it is difficult to compare data from different studies.  In vitro studies can reduce some of these difficulties by allowing the development of a stricter protocol with more control over dependent factors. 1.3.3.2.2 In Vitro Studies Rohlmann et al. (84) compared the loads measured by the same instrumented fixation devices implanted in three patients (83) to those mounted on five cadaveric spines.  The cadaveric spines were loaded in pure compression, compression-flexion and compression- extension. The measured axial force was compressive during pure axial compression.  During flexion loading, all measured bending moments were small (maximum of 0.2 Nm) and varied between flexion and extension across specimens. To determine the effect of surgical variables and conditions on implant loads, Oda et al. (168) applied pure compression and a flexion-extension moment to a multi-segment thoracolumbar spine instrumented with rods of varying diameters and type.  Strains at the base of the pedicle screws and on the rods were measured.  They found that a stiffer construct resulted in decreased rod and screw bending strain at the proximal and distal end vertebrae under applied axial compression. Vertebral loading patterns have been approximated by measuring surface strains at the facets and various locations of vertebral bodies during flexibility testing and compressive and shear   Chapter 1: Introduction  34 loading.  Shah et al. (156) first reported the distribution of vertebral body surface strain from strain gauges located at seventeen sites on L4 to which compression, compression-flexion and compression-extension loads were applied. In pure compression, the highest compressive and tensile strains were recorded near the bases of the pedicles and at the posterior vertebral rims, respectively; this finding was corroborated by a later study by Hongo et al. (157) that found similar high strain locations in both thoracic and lumbar vertebrae.  Compression-flexion loading increased the tensile strain and decreased the compressive strain at the bases of the pedicles (156).  However the specimen was embalmed and was constrained in the frontal and transverse planes during loading, decreasing the physiologic nature of the test. Frei et al. (158) used similar loading conditions and measured strains at the anterior, left, and right vertebral rims and the vertebral endplate as well as disc pressure.  In general, the strain was not dependent on vertebral rim location during pure compression but the anterior rim axial strain was compressive, tensile and compressive for pure compression, extension-compression, and flexion-compression, respectively.  There was poor correlation between disc pressure and endplate strain (158).  Linders et al. (159) attempted to correlate vertebral body surface strains with the loads across a lumbar spine segment.  Strain gauges were affixed on the anterior surface of L4 and L5 monkey vertebrae.  During all application modes (pure compression, compression- flexion and compression-extension) smaller strains were seen in L5 compared to L4 but strain magnitudes during pure compression agreed with Frei et al.’s study (582 µs with 400 N applied (159) compared to 840 µs with 500 N applied (158)).  Vertebral strain measurements such as these provide insight on spine loading and can help explain or predict spinal deformities and degeneration.    Chapter 1: Introduction  35 1.3.3.3 Load-Sharing Considerations Although many researchers measured loads on a number of structures, few have drawn conclusions on load distribution across multiple structures.  The lumbar spine model developed by McGill et al. (122) partitioned the supporting structures for a dynamic moment into disc, ligamentous, and muscular components during lifting.  They found the muscles generated approximately 99% of the restorative moment in bending but results were strictly for weight lifting of healthy subjects without spinal implants.  Two groups looked at the load-sharing characteristics of instrumented lumbar spines during flexion-extension loading using pedicle screws (169) and strain-gauged rods (166).  The former study applied ± 8 Nm moments combined with a compressive load and determined differences in pedicle screw loading when two different dynamic stabilization systems were implanted in the spine (169).  They found the stiffer construct resulted in a decreased range of motion and higher pedicle screw moments which infers less loading on the spine, but load-sharing across other structures was not reported. Cripton et al. (166) applied pure moments of ± 8 Nm to lumbar functional spinal units in various conditions and predicted the moments supported by the internal fixator, disc-fixator couple, and the posterior elements using fixator strain and intradiscal pressure measurements and static equilibrium calculations.  They found disc pressure to decrease 46% with the addition of a fixator, suggesting that the instrumentation shielded the disc and subjected other structures to support a larger portion of the load (Figure 1-16).  Fixator forces and moments were dominant in the cranial-caudal direction (ie. shear loads were negligible) and in the plane of the applied moment, respectively (ie. off-axis moments were negligible).  Similar to Rohlmann et al.’s findings (84; 178), moment magnitudes on the fixator were small (approximately 10% of the   Chapter 1: Introduction  36 applied moment) and all measured moments were in the same direction as the applied moment (ie. flexion moments were measured under an applied flexion moment).  Figure 1-16: Moment distribution across spinal structures under an applied pure moment for (a) flexion and (b) extension.  Median values and the associated range are presented for the intact instrumented specimen. Reprinted from Cripton et al., 2000 (166) with permission from Wolters Kluwer Health. 1.4 Study Relevance and Objectives 1.4.1 Clinical Relevance Many predictors of PJK have been suggested and tested in various clinical, in vivo¸ and in vitro investigations, but results remain inconclusive due to a lack of a general biomechanical understanding of the failure.  Patient variability is the largest limitation to predicting surgical outcome. An initial assessment of sagittal balance, highly correlated to surgical failure, is required to characterize the curvature of each patient. Surgeons may then predict loading patterns considering variables in surgical technique and patient anatomy.  A more comprehensive understanding of how the loads supported by spinal structures and implants are affected by these variables can help predict the occurrence of PJK. Forward bending, which naturally occurs in cases of kyphotic deformity and surgical malalignment, increases the susceptibility of vertebral fracture, and thereby PJK occurrence, compared to loading in uniaxial compression (92).  To limit the progression of kyphosis after (a) (b)   Chapter 1: Introduction  37 surgery, clinicians have asked if there is an ideal proximal level up to which a spinal fixation device should be extended (7; 46; 179; 180).  A shorter construct reduces the size of the operation and likelihood of pseudarthrosis but causes concern for gradual kyphosis above the UIV, developing into PJK (181).  It was found that the level of UIV was related to optimal sagittal balance; at ultimate follow-up, 73% and 29% showed suboptimal sagittal balance with lumbar and T9-T10 UIV, respectively (7).  However, outcomes generally vary significantly and the ideal construct length remains controversial.  It has been recognized that an understanding of fundamental biomechanical principles is necessary to use any length construct reliably (46) and an analysis of spine loading as a function of construct length is needed. A possible negative outcome of using a long fixation construct is the amount of musculature that will be damaged intra-operatively. Normally muscles are removed from the spinous processes and laminae to the level of the transverse process (182).  High demands are placed on the extensor muscles to maintain balance in cases of sagittal deformity (19) and as the deformity worsens these demands become higher (183).  The degree of pre-operative deformity, the amount of intra-operative muscle damage, and the post-operative muscle function all provide indications of surgical outcome and the capacity of the patient to maintain the corrected posture. It is known that, compared to chronic low back pain patients, lumbar degenerative kyphosis patients have significantly smaller lumbar musculature and more fat deposits, suggesting decreased strength and increased atrophy, respectively (184).  After lumbar surgery, these characteristics only worsen, evident by clinical studies that recorded decreases in muscle density (185; 186), cross-sectional area (187; 188), muscle strength (186; 189; 190), and muscle thickness (191), and increases in muscle atrophy (184; 185; 191; 192).  After thoracic surgery, there was less muscle activity seen in the thoracic region and higher muscle activity in the   Chapter 1: Introduction  38 lumbar region, suggesting that thoracic muscle atrophy may lead to lumbar muscle hypertrophy and therefore higher stresses in the lumbar spine (193).  A general imbalance has also been reported where patients experienced decreased post-operative trunk extension/flexion strength ratio compared to healthy subjects (190).  Mathematical models have simulated muscle function loss after posterior lumbar surgery and found similar changes in muscle activity (194) and a reduction in maximum extension moment generation capacity of extensor muscles (182).  Often signs of muscle dysfunction extended to areas other than those operated on (182; 185; 188), suggesting it is a result of disuse or inactivity as well as the denervation caused by dissection and retraction (185; 189; 191; 192).  This widespread dysfunction stresses the importance of muscle preservation during surgery, possibly by adoption of less invasive surgical techniques (187; 192; 194) with shorter muscle retraction times (189).  Damaged muscles may never fully regenerate to their pre-operative capacity (189; 191; 193) and resulting thoracolumbar spine loading and load distribution is currently unknown. The effect of other intra-operative events, whether intentional or inadvertent, on loading behaviour at the proximal junction can also provide insight to the cause of failure in this region and how to avoid it in subsequent operations.  For example, the pedicle screw of the uppermost- instrumented vertebra has been reported to breach the supra-adjacent facet joint in up to 30% of patients (195; 196).  Unilateral (197) and bilateral (149; 197) facet violation was simulated in cadaveric thoracolumbar spines and was found to have minimal effect on the adjacent level range of motion (197) or intradiscal pressure (149) during flexion-extension. However, the former study used instrumentation spanning only one segment and gave no measure of loading and the latter study performed the facet violation without any instrumentation, thus an understanding of loading patterns on an instrumented multi-segment spine is of clinical need.   Chapter 1: Introduction  39 Another intra-operative consideration is the protection of spinal ligaments such as the supraspinous and interspinous ligaments and the capsular ligaments at segments adjacent to a posterior construct, considered to be critical in restoring balance in the sagittal plane and in minimizing degeneration of adjacent segments (198).  The contribution of each ligament to spinal stability is known to vary with posture, increasing with increasing flexion or sagittal deformity (199), but the effect of their function on load distribution is unknown. 1.4.2 Study Objectives To address the missing clinical knowledge regarding the occurrence of PJK, a study was conducted that combined a mathematical model and an in vitro experiment to study changes in spine loading patterns resulting from a number of patient variables and relevant surgical conditions.  The specific objectives of the study were to: 1) Develop a two-dimensional statically-determinate equilibrium model of sagittally- imbalanced adult spines to predict: a) pre- and post-operative intervertebral compressive loading behaviour, and b) the effect of osteotomy location and extensor muscle function on the predicted intervertebral compressive loading patterns. 2) Develop an in vitro investigation of a multi-segment thoracolumbar spine to: a) characterize pure moment loading pathways following posterior spinal fixation, and b) determine the effect of relevant surgical conditions on vertebral column loads.  The specific hypotheses related to each objective are: 1a)  intervertebral compressive loading will be higher in more severely deformed spines and after PJK,   Chapter 1: Introduction  40 1b)  different osteotomy locations will not have a significant effect on loading patterns and decreased extensor muscle function will increase spine loading, shifting counterbalancing efforts to surrounding structures, 2a)  the applied load will be distributed between the anterior column and spinal implant, and 2b)  the load on the spinal implant will increase with the progressive destabilization of each spine condition. The following sections are divided into two chapters that discuss the methodology and results of each component of the study separately (objectives 1 and 2) followed by an integrated discussion of the results of both manuscripts. 1.5 Scope The project presented in this thesis is a combined two-dimensional static equilibrium model and in vitro biomechanical study to analyze spine loading in patients with sagittal deformity. The former used sagittal profiles of seven surgically-corrected spines, testing the effect of simulated patient and surgical variables on predicted intervertebral compressive loading.  The latter used six multi-segment thoracolumbar cadaveric spines, simulating the patient and surgical scenario after correction and testing the effect of clinically relevant surgical conditions on implant and spine compressive loading. The model considered the equilibrium response of a grouped extensor muscle to body-weight loads.  With the likely decrease in muscle function that is associated with sagittally deformed spines and fusion surgeries, surrounding structures in the spine are instead required to balance body-weight loads, distribution across which could not be predicted using the model.  This scenario was simulated in vitro where a pure flexion-extension moment represented the   Chapter 1: Introduction  41 kyphosing moment created by body-weight loads in muscle-deficient spines.  Neither model nor experiment considered the contribution of separate local and global spinal muscles. Intervertebral compressive loads were predicted mathematically based on the individual sagittal profiles of patients before and after surgery.  Shear loads were not reported in the current study but may be of interest in future research.  In vitro spine loading was predicted by indirect measurement of vertebral strains at the proximal junction and by rod strains.  Rod strains were converted into loads and moments using theoretical calculations.  The applied moment was meant to simulate that created by body-weight loads, based on predictions from equilibrium model, though its magnitude does not reflect the kyphosing moment in severely deformed spines. Kinematic measurements reported overall range of motion as intersegmental motion of multi- segment spines is not novel and does not directly address the objectives of this study. This study is the first in the area of sagittal deformity and proximal junctional kyphosis for this lab and attempts to address a clinically important topic to which increasing attention has been paid in conferences and amongst surgeons.  Findings from this study alone are not expected to provide justification for changes in spinal implant design or surgical technique but instead to provide insight to the factors and variables that may influence spine loading at the proximal junction and present a basis for further investigation on this topic.  Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  42 Chapter  2: Development of a Two-Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines 2.1 Introduction Adult spinal deformity is of increasing concern in the medical community due to its diversity and the number of people it affects.  The multifaceted nature of spinal disabilities makes it difficult to determine prevalence of individual deformities and the effect each has on dysfunction but the impact of spinal deformity is marked; in 2007, an estimated 1.24 million patients utilized health care resources in the United States for treatment relating to spinal deformity (200). Sagittal imbalance has been linked with the development and progression of spinal deformities (16; 17; 18) and specifically positive sagittal balance was determined as a primary indication of pain and disability (10).  Positive sagittal balance is identified by significant anterior deviation of the C7 plumb line with respect to the sacrum and causes increased loading on the spine.  When debilitation is beyond conservative treatment, spine balance restoration is surgically attempted by means of posterior instrumented spinal fusion with or without corrective osteotomy.  Though patient satisfaction is often initially high with this type of surgery (23; 44), proximal junctional kyphosis (PJK) is developed in up to 46% of surgical cases (4; 5; 6) and any required revision surgeries are reportedly less successful (19; 50). To assess the likelihood of surgical failure based on the individual deformity with which each patient presents requires an appreciation of the loading behaviour of the spine.  Surgeons seek a fundamental biomechanical understanding of how variability in chosen surgical methods and individual patient factors affects spine loading and ultimately surgical outcome. Previous researchers have developed models that quantitatively evaluate and graphically represent the spine for use in surgical planning and deformity progression monitoring (29; 41; 93).  Static equilibrium calculations have been used to determine intervertebral loading for Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  43 individual sagittal profiles (43; 96; 118).  However, these loading predictions have been limited to normal spines and there exists no known evaluation of spinal deformity patients before and after operation. This chapter discusses the development of a two-dimensional equilibrium model of sagittally imbalanced adult spines.  The objectives of this model were to predict: • pre- and post-operative intervertebral compressive loading behaviour, and • the effect of osteotomy location and extensor muscle function on the predicted intervertebral compressive loading patterns. 2.2 Methods 2.2.1 Patient and Radiographic Data Collection Seven adult deformity patients with an average follow-up of eight months (four months to two years) were reviewed retrospectively.  All final operations were performed at a single institution (Vancouver General Hospital).  Patients 4 and 5 had one and two previous operations at the same institution, respectively, Patients 3 and 7 were referred from other institutions after having one previous operation, as was Patient 6 after having two previous operations.  Inclusion criteria consisted of adult deformity treated with instrumented posterior spinal fusion with or without osteotomy, both successful cases and those that required revision.  For the current study, complete radiographic follow-up required adequate pre-operative and early post-operative radiographs of initial and revision surgeries, as well as most recent follow-up.  Full three-foot lateral standing x-rays were required for global assessment of the deformity which was found to be a limiting factor as very few institutions had these available for their deformity patients. Exclusion criteria consisted of severe coronal deformity, severe osteoporosis, and any other Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  44 confounding deformities or diseases that were predicted by the surgeon involved with the study to have an effect on surgical success. Patients were asked to stand upright and 90 degrees laterally to the camera with their knees fully extended, feet together, and arms folded and supported at the elbows.  Lateral x-rays were taken with a radiographic device (Ysio wi-DTM, Siemens, Munich) positioned three metres from the patients, performed by skilled radiologists using a standardized technique.  The average age at the time of the final surgery was 64 years (54 to 73 years), the average body mass was 77.5 kg (65 to 102 kg) and there were five females and two males.  Preoperative diagnosis was degenerative scoliosis in two patients, lumbar flatback in two patients, spondylolisthesis in two patients, and spinal stenosis in one patient; a number of diagnoses were paired with kyphotic deformity.  Patient demographic and surgical data is summarized in Table 2-1.  All patients were sagittally imbalanced, the severity of which varied across deformities.  Surgical correction consisted of a multi-level fusion and various lengths of posterior instrumentation affixed with lamina or pedicle hooks, pedicle screws or a combination thereof.  Radiographs of all patients at various pre- and post-operative stages can be seen in Appendix B.  Patients 3 to 7 underwent initial surgical treatments that were not radiographically analyzed in the current study.  Patients 4, 5, and 6 were referred from other surgeons and Patients 3 and 7 were referred from other institutions, all after failure of initial correction.  Patients 5 and 6 both failed twice previous to profiles analyzed in the current study.  Patient 7 failed by vertebral compression and rod fracture and received a subsequent revision where a metal cage was inserted in place of L3 with no instrumentation changes; this final profile was not analyzed in the current study.    Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  45 Table 2-1: Demographic and surgical data for patients used in this study  Radiographic measurements were taken with a diagnostic image analysis software package (WebDI, Philips iSite PACS, New York) that converted pixel coordinates to absolute measurements in terms of a global horizontal and vertical.  Measurements of interest included the location of the posterior-superior corners of each vertebral body from C1 to S1 (41), the angle between the inferior endplate of each vertebra and the horizontal, and the C7 plumb line from the posterior-superior corner of the C7 vertebra to the posterior-superior corner of the S1 body as a measure of the patient’s sagittal balance.  Vertebral location and angle measurements are represented in Figure 2-1 and were all taken by the same author with an expected accuracy of 0.5 mm (201) and ± 3.3° (202), respectively.  Small variations in choosing the appropriate position of the vertebral body corner were found to not have a large effect on predictive calculations.  An example of the data collected from one radiograph is shown in Appendix C. Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  46 Other information noted for each patient was the location of the uppermost instrumented vertebra (UIV) of all surgeries and information about previous surgeries (diagnosis, instrumentation used, time of failure).  Figure 2-1: Radiographic measurements taken from image analysis program for the current study. The horizontal (anterior-posterior) and vertical (cranial-caudal) distances between the posterior-superior corner of the sacrum (red star) and the posterior-superior corners of all vertebrae (shown on one vertebra with a red circle) was measured (black arrows) to represent global sagittal curvature.  The angle between the inferior endplate of each vertebra and the horizontal (red arrows) was also measured to determine segmental angulation.  These measurements were taken from every x-ray for all patients.  X-ray image courtesy of Dr. John Street with permission from Vancouver General Hospital. 2.2.2 Geometrical Model Development After the location of the posterior-superior aspect of each vertebral body was recorded, a spline function was derived from the data points using a custom software program (Matlab 2009a, The MathWorks, Inc., Natick, MA).  A graphical representation of each patient’s sagittal profile for every x-ray taken was used to demonstrate the severity of the deformity, the correction achieved, and the post-operative progression of the sagittal profile. 2.2.3 Spine Loading Model Development A statically-determinate two-dimensional equilibrium model of the sagittal spine was developed using the vertebral location and angulation data collected.  To compute the loads on Anterior Posterior Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  47 the spine, an imaginary cutting plane in line with the vertebral inferior endplate was created at each vertebral level with assumption that the posterior instrumentation extended up to that level (Figure 2-2a).  The external forces (ie. body-weight loads of the head (FH), trunk (FT), and arms (FA)) imposed on the spine at each level were estimated using previously published data and anthropometric tables.  The magnitudes and lines of action assumed for this study, along with their sources, are summarized in Table 2-2.  To create a statically-determinate model, the muscle forces generated to balance the spine were grouped into one functional unit, representing a counteracting extensor muscle (FM) that was assumed to act in a direction perpendicular to the cutting plane, based on published literature (97). When the spine is cut, there is a net reaction consisting of six components: three net force components and three net moment components.  For simplification, for the sagittal plane this can be reduced to two forces and a moment: compressive force (RC), shear force (RS), and sagittal moment (M) (Figure 2-2b). Static equilibrium calculations were performed using Newton’s Second Law which states that in a state of equilibrium, the following relationships exist: $%&  0                  $%)  0                     $*+  0 (Eq. 2-1) Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  48 (Eq. 2-3)  Figure 2-2: Development of a two-dimensional statically-determinate equilibrium model to predict intervertebral loading.  The coordinate axes are such that y is vertical upwards, z is anterior forwards, x is to the left. (a) The external forces from the head (FH), trunk (FT), and arms (FA) and external muscle force (FM) acting on the spine.  FM is assumed to act in a perpendicular direction to the cutting plane (ie. perpendicular to the vertebral endplate).  The spine is cut at each vertebral level with an imaginary cutting plane (red dotted line), assuming that the instrumentation extends up to that level.  (b) The free-body diagram of the vertebra with reaction forces in compression (RC) and shear (RS) and a reaction moment (M), acting at the vertebral body centre (point O).  The vertebral angulation is shown (θ) along with the moment arms of the external forces: LA, LH, LT, LM represent the distances from point O to the lines of action of the arm, head, trunk, and muscle forces, respectively.  For static equilibrium, the moment about the spine (M) is zero. Due to the angulation of the vertebra, the compressive and shear reactive forces have components in both the z and y directions.  Substituting the known external forces into the above equations yields: ΣF.  %/0123  4	0123  456703  0 ΣF8  %/6703  4	6703  450123  %9  %:  %;!  0 ΣM=  *  %/6703!/  %99  %::  %;;!  0 where Fz and Fy are the forces in the z and y direction, respectively, M is the moment in the sagittal plane, (Eq. 2-2) (Eq. 2-4) Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  49 FH, FA, and FT are the body-weight loads from the head, arm, and trunk, respectively, FM is the muscle force, LH, LA, LT, and LM are the moment arms of the head, arm, trunk, and muscle force, respectively, RC and RS are the reactive compression and shear forces, respectively, and M is the reaction moment on the spine.  M = 0 in equilibrium as the spine’s external forces (body-weight loads) are balanced with the muscle force. The three unknowns, FM, RC, and RS can be solved for using the magnitudes and locations for the external loads FH, FA, FT, and FM (Table 2-2).  The location of all loads were reported with reference to the vertebral centres and since the positions of only the posterior superior vertebral corners were taken from the x-rays, the half vertebral body depth (126; 100) was used to transpose these forces to the vertebral body centre. Table 2-2: Magnitude and location of external forces used in this study External force Magnitude Reference Location Reference Head load (FH) 7.2%BW Clauser, 1969 (109) LH: Centred over T1 Kiefer, 1997 (203) Arm load (FA) 5.42%BW Clauser, 1969 (109) LA: Distributed over T1- T6, 50 mm anterior to T4 Kiefer, 1997 (203) Trunk load (FT) Various %BW taken from CT scans of trunk segments Pearsall, 1996 (110) LT: Difference between trunk centroid and vertebral body centre Kiefer, 1997 (203) Muscle force (FM) Calculated - LM: Approximate distance between centre of disc and tip of spinous process Keller, 1999 (123)  Intervertebral loading could then be predicted along the length of the spine, results of which could be taken to represent the scenario where instrumentation extended up to the vertebral level of interest.  Loading of vertebrae spanned by instrumentation could not be predicted using the statically-determinate model as the unknown load distribution across the spine and implant created indeterminacy.  However, as static equilibrium calculations at any vertebral level had no dependence on the distal structure of the spine, the construct can be assumed to extend up to this level.  Results were compared across the sagittal profile history of Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  50 each patient in its pre- and post-operative states.  This paper will focus on compressive loads only as shear loading was not in the scope of the study. The assumptions made in the development of this model included: • static state and two-dimensional, • vertebral body cannot take a moment, • extensor muscles acted as one force at the given distance from the vertebral centre, • equilibrium occurred between the body-weight loads and extensor muscle force, and • extensor muscle was able to fully counteract body-weight loads in all sagittal profiles. 2.2.4 Patient and Surgical Variables It is of clinical interest to determine how differences in patients and surgical treatments affect the loading on the spine as this may have a direct correlation with surgical outcome.  We were interested in looking at the effect of osteotomy location and extensor muscle function. 2.2.4.1 Osteotomy Location The geometrical and loading models described in the previous sections were combined to predict the change in compressive load at each vertebral level should the patient have had a pedicle subtraction osteotomy (Section 1.2.2.2) at one of the three most common sites: a) L2, b), L3, or c) L4.  To correct the deformed spine in each case, it was assumed that a joint was created at the osteotomy level and the spine proximal to this level was rotated as a rigid body to bring C7 in vertical alignment with S1.  The following steps were conducted to construct the resulting sagittal profiles in each of these three cases (an example of the calculation for one case can be seen in Appendix D): • The pre-operative sagittal profile was developed from radiographic measurements, including horizontal and vertical vertebral locations and angulations from C1 to S1.  These Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  51 measurements were assumed to remain unchanged from S1 up to the level directly inferior to the osteotomy site (ie. up to a) L1, b) L2, or c) L3). • The horizontal position of the C7 vertebra was brought in line with S1.  This represented the correction distance, ie. the pre-operative horizontal position of C7 with respect to S1. • Using trigonometric relationship (42) s, the size of an osteotomy that would be required to achieve this correction was calculated for a given osteotomy location (Figure D-1). • A rotation matrix was used to determine the corresponding location of the vertebrae after correction at each level superior to the osteotomy site, with respect to the osteotomy level. • The final new horizontal and vertical positions of each vertebra superior to the osteotomy site, with respect to the sacrum, were calculated by adding the coordinates found from the rotation matrix to the pre-operative horizontal and vertical positions of the osteotomy level with respect to the sacrum. • The vertical location of each vertebra superior to the osteotomy was further modified to incorporate the vertical drop caused by the osteotomy (Figure 2-3). • The angulations of the corrected vertebrae superior to the osteotomy site were recalculated by adding osteotomy angle to the corresponding pre-operative angulations. • Given these new sagittal profiles, static equilibrium calculations (Section 2.2.3) were performed to predict the compressive loads at each vertebral level. • These steps were iterated for osteotomy locations a), b), and c) for each of the seven patients using a custom software program (Matlab v. R2009b, MathWorks, Natick, MA).   Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  52      Spine geometry was simplified to utilize trigonometric relationships in the process described above so the following assumptions were necessary: • vertebral bodies were rectangular, with superior and inferior endplates running parallel to each other and perpendicular to anterior and posterior edges, • the shift of the spine that ensued after subtraction was rigid, ie. all intervertebral positions remained unchanged and there was only a change of each vertebra with respect to the osteotomy level, • rotation of the spine occurred with the osteotomy site as the point of rotation and could be characterized with a rotation matrix, • the position of the vertebrae inferior to the osteotomy level remained unchanged before and after correction, and • there was no deformation of the spine. 2.2.4.2 Extensor Muscle Function The model was modified to account for variability in extensor muscle function, ranging from 100% muscle function when the extensor muscles were able to fully counteract the body-weight Figure 2-3: Schematic demonstrating the drop in vertical position of vertebrae superior to the osteotomy site, before (left) and after (right) pedicle subtraction osteotomy (green) at a given level.  The osteotomy parameters α, D, and L represent the size, depth, and subtraction distance, respectively.  θ1 and θ2 are the vertebral angulations before and after the subtraction, respectively.  The difference between d1 and d2 is the vertical drop of vertebra following subtraction. L D α θ1 θ2 d1 d2 Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  53 loads to 0% muscle function when they were removed or were otherwise unable to counteract any of the body-weight loads.  At 100% muscle function, the spine is in equilibrium and the muscle force (FM) is calculated by rearranging Eq. 2-4: %/  >??@>AA@>BB!CDEFG With any less than 100% muscle function, to maintain equilibrium the spine moment (M) becomes non-zero.  The magnitude of the spine moment generated in terms of muscle functionality can be calculated by again re-arranging Eq. 2-4, this time in terms of M: *  H%/!/6703  %99  %::  %;;! Where x represents the fraction of muscle functionality, 0 I H I 1. It can be seen that at full functionality (x = 1), M is zero while when x < 1, there is a moment transferred to the spine and M is non-zero.  The resulting spine moment was calculated at each vertebral level in all pre-operative and post-operative sagittal profiles for x = 0, 0.5, and 0.9 for each of the seven patients. Further modifications were made to the model in the case where the muscles have been removed intra-operatively or are otherwise non-functional.  To maintain spine balance, the moment generated from the body-weight loads must instead be transferred to the surrounding structures such as the vertebrae, disc, ligaments, posterior elements, added instrumentation, or a combination thereof.  Two scenarios were analyzed: a) if the vertebral column alone counteracted the body-weight loads or b) if the instrumentation alone counteracted the body- weight loads.  The free-body diagrams describing these two scenarios are shown in Figure 2-4. In both of these cases, the muscle force FM was removed and was replaced with a force generated by either the vertebral column (FV) or an implant (FR), both of which act at a shorter distance from the vertebral body centre (O).  In each of these scenarios, the intervertebral compressive (Eq. 2-5) (Eq. 2-6) Chapter 2: Development of a Two Dimensional Statically  loads were recalculated with Eq.’s 2 was assumed that FV acted at the posterior edge of the vertebra intervertebral disc annulus may resist the body the spinal canal (depth taken from literature vertebral dimensions of each patient. applied a counter-acting force along the longitudinal axis and that internally were minimal.          Figure 2-4: The free-body diagrams of two equilibrium scenarios after muscle loss diagrams in Figure 2-2). To maintain spinal balance, the bodyweight loads the posterior edge of the vertebral column, generating a vertebral column force ( from the vertebral body centre (O), and (b) a posterior rod and pedicle screw construct, generating a rod load (FR) acting a distance (LR) from the vertebral body centre. spine (M) is zero. 2.3 Results This section includes a summary of the results obtained for analysis of seven spinal deformity patients using the developed g plots are shown here for Patient 2 and those of Patients 1 through 7 are included in  (a) RS M y z x O LLV FV -Determinate Equilibrium Model of Sagittally -2 to 2-4, modifying the moment arms where appropriate.  It where ligamentous -weight loads, and that FR acted 1 mm posterior to  (100; 126)), both calculated based on specific   It was also assumed that vertebral and rod structures -generated moments (FM were instead counteracted by (a) FV) acting at a distance (   For static equilibrium, the moment about the eometric and spine loading models.  Representative (b) RRS M O θ FT FA FH RC LA LT LH LR FR -Imbalanced Adult Spines 54 structures and  is removed from LV)  Appendix E. θ FT FA FH C A LT LH Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  55 2.3.1 Geometrical Model The pre-operative curvatures of the seven patients analyzed using the geometric model (Figure 2-5) had an average plumb line (horizontal location of C7 with respect to S1) of +85.3 mm (-50 mm to 197 mm), thoracic kyphosis (T1-T12) of 41.3° (24° to 76°), and lumbar lordosis (L1-S1) of -40° (-70° to 2°), using the modified Cobb technique (28).  These patients presented with various prognoses and severities of sagittal imbalance and were corrected with posterior instrumented fusion at Vancouver General Hospital.  An example of the deformity progression pre-operatively to two years after surgery for Patient 2 is shown in Figure 2-6.  Figure 2-5: Pre-operative sagittal profiles of patients from current study using model.  Each data point represents the location of the posterior-superior corner of each vertebral body from T1 (top) to S1 (bottom), horizontal and vertical distances of which are measured from the location of S1.  A spline function was fit to the data to represent the spine as a smooth curve.  Patients 3 through 7 were referred to VGH for revision surgery after receiving initial operations with other surgeons or at other institutions.  The pre-operative curvatures shown for these patients represent how they presented themselves to Dr. John Street. Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  56  Figure 2-6:  Sagittal profiles of Patient 2 pre-operatively and at three stages after operation, generated with the equilibrium model.  Each data point represents the location of the posterior-superior corner of each vertebral body from T1 (top) to S1 (bottom), horizontal and vertical distances of which are measured from the location of S1.  A spline function was then fit to the data to represent the spine as a smooth curve.  This patient received posterior instrumented fusion surgery from S1 to T9.  He suffered from proximal junctional kyphosis (PJK) two months after correction but was unable to undergo a revision operation due to medical complications.  His follow-up radiographs at 1, 1.5, and 2 years post-operation show significant progression of kyphotic deformity, worst of which occurred from anterior deviation of vertebrae superior to T9. 2.3.2 Spine Loading Model An example of the predicted compressive load as a function of uppermost instrumented vertebral level for Patient 2 is shown in Figure 2-7, calculated using static equilibrium equations described in Section 2.3.2.  The peak muscle force and compressive load predicted for each patient in its pre-operative sagittal profile and peak predicted compressive load for all pre- and post-operative sagittal profiles combined are summarized in Table 2-3.  The uppermost instrumented vertebra at which this maximum occurs is identified and most often is experienced at the patient’s most recent follow-up (Patients 2, 3, 4, and 7) though it occurs at the pre- operative stage for Patients 5 and 6 and immediately after operation for Patient 1.  The sagittal profiles of Patients 5 and 6 are such that they experience a decrease in predicted compressive load after operation (Appendix E). Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  57  Figure 2-7: Predicted intervertebral compressive loads (T1 to S1) of Patient 2, given the sagittal profiles at four stages pre- and post- operation.  The compressive load was calculated using equilibrium calculations under the assumption the spine was corrected using instrumentation extending from the sacrum up to the given vertebral level.  This patient was instrumented from S1 to T9 and had developed proximal junctional kyphosis (PJK) by its one-year post-operative x-ray. Table 2-3: Peak extensor muscle force, and peak predicted compressive loads seen for each patient for pre- operative sagittal profile and for all profiles combined, the percent increase between which is also included. These maximum loads occurred at the uppermost instrumented vertebral level indicated in brackets. Patient Peak  Extensor Muscle Force [N] Peak Compressive Load [N] (UIV) Percent increase in Maximum Compressive Load from Pre-op profile Pre-op profile Pre-op profile Total (all profiles) 1 168 345 (T11) 430 (T12) 25 2 268 520 (T12) 670 (T12) 29 3 248 460 (T12) 495 (T12) 8 4 203 420 (T12) 470 (T12)  12 5 430 730 (T12) 730 (T12) 0 6 293 540 (S1) 540 (S1) 0 7 243 580 (S1) 625 (S1) 8     Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  58 2.3.3 Patient and Surgical Variables 2.3.3.1 Osteotomy Location Example geometric and predicted compressive loading plots for Patient 2 for sagittal profiles at its pre-operative state and after simulated correction by means of an osteotomy at L2, L3, or L4 are shown in Figure 2-8 and Figure 2-9, respectively.  The mean and range of percent differences in predicted intervertebral compressive loads between sagittal profiles resulting from osteotomies at L2, L3, and L4 compared to the pre-operative posture were calculated for all patients (Figure 2-10).  Across all patients, there was an average 6% difference in mean predicted intervertebral compressive loads between osteotomy locations.  Figure 2-8: Sagittal profile of Patient 2 pre-operatively and after simulated correction with an osteotomy at L2, L3, and L4.  Each data point represents the location of the posterior-superior corner of each vertebral body from T1 (top) to S1 (bottom), horizontal and vertical distances of which are measured from the location of S1.  A spline function was then fit to the data to represent the spine as a smooth curve. -250 -200 -150 -100 -50 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  59  Figure 2-9: Predicted intervertebral compressive loads (T1 to S1), given the sagittal profiles of Patient 2 pre- operatively and after simulated correction with an osteotomy at L2, L3, and L4.  The compressive load was calculated using equilibrium calculations under the assumption that the instrumentation extends up to the level analyzed.  The predicted compressive load remains very similar for correction with an osteotomy at all locations.  Figure 2-10: Percent difference in the mean predicted intervertebral compressive load for each patient from its pre-operative profile to those resulting from simulated correction with an osteotomy at (a) L2, (b) L3, and (c) L4.  There is large variation in predicted compressive loads between the pre-operative state and after an osteotomy, the location of which showed minimal effect (less than 7% difference in predictions between three scenarios). 2.3.3.2 Extensor Muscle Function With the extensor muscle functioning at only partial capacity, the proportion of the total moment, generated by the body-weight loads, transferred to the spinal column and surrounding tissues was calculated (Figure 2-11).  This plot is based on the pre-operative posture of Patient 2 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d [N ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy (a) (b) (c) Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  60 for which the peak moment from body-weight loads was 13.5 Nm pre-operatively but this kyphosing moment varies from 10 Nm to 22 Nm across all patients, based on body-weight and sagittal profile.  Figure 2-11:  Predicted moment transferred to the spine when the extensor muscle group is 100%, 90%, 50%, or 0% functional.  The total body-weight moment was calculated based on the individual positions of the head, arm, and torso of Patient 2 in the pre-operative posture.  Static equilibrium assumes that this moment is fully counteracted by the extensor muscle group but if this is not the case, the moment transferred to the spine around surrounding tissues is inversely proportional to the percent functionality of the muscle. Figure 2-12 shows an example of the predicted compressive loads as a function of uppermost instrumented vertebral level for Patient 2, when (a) extensor muscles are fully functional and capable of counteracting the body-weight load, and alternatively when muscles are completely removed and the bodyweight load is transferred to (b) the vertebral body or (c) a rod implant.  The mean percent differences in predicted compressive loads across all sagittal profiles when the body-weight loads are counteracted by only the vertebral body (Figure 2-13a) or a posterior rod (Figure 2-13b) in comparison to when they are counteracted by an extensor muscle group were calculated for each patient.  The maximum difference in predicted intervertebral compressive load between scenarios with full and no muscle function occurred Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  61 mostly in the lumbar spine and reached differences of 525 N (153% increase) and 293 N (49% increase) from when the load was supported by an extensor muscle to when it transferred to a posterior vertebra or rod, respectively (Table 2-4), considering all profiles of each patient. Looking at the pre-operative posture of each patient, the increase in load was calculated when the vertebral column replaced the function of the extensor muscles, representing muscle atrophy often seen in deformity patients.  The sagittal profile immediately after operation was then used to calculate the loading differences across two scenarios: the extensor muscles are still functional enough to maintain sagittal balance, or the posterior rod must immediately balance the body- weight loads.  For the pre-operative and immediate post-operative cases, loading increases were very similar to the overall trends, reaching differences of up to 504 N (152% increase) and 271 N (42% increase), respectively (Table 2-4).      Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  62    Figure 2-13: Percent difference in the mean predicted compressive load from 100% to 0% extensor muscle function where the bodyweight load is instead fully counteracted by (a) the posterior edge of the vertebral body, or (b), a rod implant located 1 mm posterior to the spinal canal at a given vertebral level.  Shown are the mean (circle) and range (vertical lines) of percent differences in predicted compressive load across all sagittal profiles available for Patients (Pt) 1 through 7. T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 1400 1600 Uppermost Instrumented Vertebral level C o m pr e ss iv e  Lo a d (10 0%  m u sc . ) [N ]   Pre-op 1-yr post-op (PJK) 1.5-yr post-op (PJK) 2-yr post-op (PJK) T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 1400 1600 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (0%  m u sc .  -  ve rte br a ) [N ]   Pre-op 1-yr post-op (PJK) 1.5-yr post-op (PJK) 2-yr post-op (PJK) T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 1400 1600 Uppermost Instrumented Vertebral level C o m pr e ss iv e  Lo a d (0%  m u sc .  -  ro d) [N ]   Pre-op 1-yr post-op (PJK) 1.5-yr post-op (PJK) 2-yr post-op (PJK) Figure 2-12: Predicted intervertebral compressive load acting at each vertebral level (T1 to S1) given the sagittal profiles of Patient 2 at four stages pre- and post- operation with (a) 100% muscle function and bodyweight loads counteracted by extensor muscles only, (b) 0% muscle function and body-weight loads counteracted by vertebral body only, and (c) 0% muscle function and bodyweight loads counteracted by a posterior rod only.  Larger compressive loads are seen with smaller moment arms of rod and vertebral body in relation to vertebral body centre.  The compressive load was calculated using equilibrium calculations under the assumption that the instrumentation extends up to the level analyzed. (a) (b) (c) (a) (b) ROD VERTEBRA Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  63 Table 2-4: Maximum difference in predicted intervertebral compressive load magnitudes (and corresponding vertebral level at which this occurred) for each patient between 100% and 0% muscle function, when the body-weight loads are instead counteracted by either the posterior edge of the vertebral body or a posterior rod.  Larger increases are seen in the former due to its smaller moment arm.  Maximum differences are shown for the combination of all profiles as well as for the pre-operative profile (when transferred to the vertebra) and for the immediate post-operative profile (when transferred to a rod). Patient Percent difference corresponding to the maximum increase in predicted intervertebral compressive load (and corresponding vertebral level) Transferred to Vertebra Transferred to Rod All profiles Pre-op profile All profiles Immediate post-op profile 1 122 (L2) 128 (T8) 37 (L2) 37 (L2) 2 149 (L5) 125 (L2) 49 (L3) 39 (L2) 3 130 (T10) 129 (L1) 41 (L2) 38 (L2) 4 153 (S1) 152 (S1) 36 (L2) 29 (L2) 5 148 (L2) 148 (L2) 47 (L3) 42 (L3) 6 144 (L5) 144 (L5) 46 (L3) 30 (L2) 7 97 (S1) 95 (S1) 31 (L2) 26 (L2)  2.4 Discussion Pre-operative and post-operative radiographs of seven patients presenting to Vancouver General Hospital with sagittal imbalance were used to develop a two-dimensional equilibrium model to quantitatively analyze sagittal profiles and to predict resulting spine loading at uppermost instrumented vertebral levels from T1 to S1. The sagittal profiles and alignment parameters of the patients used in this study were compared to those found in other studies with larger subject populations (Table 2-5).  The volunteers were asymptomatic and ranged from 20 to 85 years old across the three studies. Severe positive sagittal balance and less lumbar lordosis exist in the current study’s sagittal deformity patients compared to the asymptomatic volunteers in Gelb et al.’s (12) study, though the age range correlates well.  Similarly, when compared to a younger population (14) the differences seen in these two parameters remain the most marked.  The elderly population studied by Hammerberg et al. (13) presented with positive sagittal balance approaching the current study’s but lumbar lordosis was again higher.  From these comparisons, pain and Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  64 disability severe enough to require surgical intervention may be attributed to positive sagittal balance resulting from a loss of lumbar lordosis.  It is important to study these patients individually and use caution when making surgical decisions based on reported normal spinal parameters as sagittal deformity can cause substantial deviation from these values. Table 2-5: Sagittal angles and displacement measured in current study and in studies of asymptomatic adult volunteers Parameter Current study Jackson & McManus, 1994 (14) Gelb et al., 1995 (12) Hammerberg et al., 2003 (13) Number of cases (M/F ratio) 7 (2/5) 100 (50/50) 100 (46/54) 50 (26/24) Age 64 (54 to 73) 39 (20 to 63) 57 (40 to 82) 76 (70 to 85) Sagittal balance (plumb line) [mm] 85 (-50 to 197) -0.5 (-60 to 65) -32 (-101 to 77) 40 (-37 to 139) Thoracic kyphosis (T1-T12 Cobb angle) [deg] 41 (24 to 76) 42.1 (22 to 68) - 53 (29 to 79) Lumbar lordosis (T12-S1 Cobb angle) [deg] -42 (-77 to -5) -61 (-88 to -31) -64 (-84 to -38) - Lumbar lordosis (L1-S1 Cobb angle) [deg] -40 (-70 to 2) - - -57 (-96 to -30)  Based on these sagittal profiles, the model first assumed equilibrium was maintained between the body-weight loads and an extensor muscle group and in this condition, the peak predicted compressive load increased 8% to 29% from the pre-operative stage to some stage post- operatively in all but two patients.  This increased spine loading after correction may have been a significant contributor to their subsequent failure.  Additionally, the highest predicted compressive loads were seen in Patient 2 who failed at the proximal junction and, without revision, developed positive sagittal balance far beyond that of the pre-operative state.  This suggests that failed corrections may subject the spine to higher loading patterns than the initial deformed sagittal profile.  These correlations could not be validated since the true pre-operative state was not analyzed in the five patients referred from other surgeons or institutions for revision surgeries, two of which conversely experienced decreased peak predicted compressive Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  65 loads after these revisions.  Interestingly however, these patients did not experience subsequent failure which speaks to the efficacy of this model as a predictive tool if applied to surgical planning.  In fact, of the corrections analyzed, only those of Patients 1 and 2 developed PJK causing failure, both of which demonstrated the largest increases in predicted intervertebral compressive loads from corresponding pre-operative state (25% and 29%, respectively).  This suggests PJK increases spine loading but, because of the variability of prognoses and surgical histories of the patients, it was difficult to make conclusions from trends seen.  Further analysis of more patients is required to determine the correlation between spine loading and surgical failures (hypothesis 1a). In all surgical and patient cases analyzed with the model, predicted compressive loading trends were similar, increasing from T1 to T12 with a sharp reduction and then increasing again from L1 to the sacrum.  This peak at the lower thoracic spine is due to a combination of increasing proportion of body-weight load transferred to lower vertebral levels and a sudden increase in extensor muscle moment arm length in the lumbar spine (from 47 mm at T12 to 68 mm at L1 (123)).  With a larger moment arm length, the muscle force required to generate equilibrium with the body-weight loads is reduced, causing a corresponding reduction in the resultant vertebral compressive load.  A similar trend has been previously reported in other studies using two-dimensional models to predict intervertebral spine loading (Figure 2-14) (43; 97), any deviations from which can be attributed to differences in patient anatomy and magnitudes and lines of action chosen for body-weight and muscle forces. Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  66   Harrison et al. (96) also conducted a similar study and, when comparing predicted compressive loading patterns to the current study, it can be seen that a similar trend was followed with consistently lower magnitude loads at each vertebral level (Figure 2-15).  This is likely because the subjects used in their study were young and asymptomatic and the corresponding curvatures were sagittally balanced in a neutral posture, unlike the sagittal imbalance patients analyzed in the current study.  The higher resultant compressive loading seen for spinal deformity patients suggests that loading predictions made with normal spines are not indicative of the loads that will be seen in spines presenting to surgery and may instil overconfidence in anticipated surgical outcome.  To simulate positive sagittal balance, these asymptomatic subjects Figure 2-14: Intervertebral disc (IVD) loading results of two published two-dimensional static equilibrium spine loading models.  (a) IVD compressive load (C-diamond), IVD shear load (S- square), and extensor muscle load (E-triangle) variations from C2 to S1.  The peak predicted compressive load occurs at the T11-T12 disc and is reduced in the lumbar spine Reprinted from Keller et al., 2003 (97) with permission from Wolters Kluwer Health.  (b) Anterior (white) and posterior (black) IVD compressive loads from C2 to S1, showing peaks at or near the T11-T12 disc. Reprinted from Keller et al., 2005 (43) with permission from Elsevier.  (a) (b) Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  67 were then asked to translate the thorax anteriorly.  Although the resulting sagittal profiles were not pathologic, the largest increases in predicted compressive load were similarly from T8 to S1 and agreed well with the pre-operative predicted loads of patients in this study (Appendix E). The results of all of these studies suggest that the thoracolumbar junction should be avoided as the uppermost instrumented level with constructs stopping either below or above this point. Ending at the thoracic apex may also be troublesome as there already exists a large shift of segmental angulation that may predispose the adjacent vertebra to listhesis (204).  Higher loading in these areas, and in sagittally deformed spines in general, may increase the risk of undesired segmental movement, vertebra fracture, and bone-screw interface failure, ultimately jeopardizing long-term correction.  Figure 2-15: Predicted compressive intervertebral loads from current study and literature.  From the current study, predicted compressive intervertebral loads from T1 to S1 are shown for Patient 2 (76.5 kg) at four pre- and post-operative stages.  Also shown are the mean posterior intervertebral disc compressive loads of a study conducted by Harrison et al.  (92) that evaluated intervertebral loading patterns of eighteen young asymptomatic subjects (76.5 ± 16.2 kg) in the neutral posture (black square, dotted line), and in an anteriorly- simulated posture (black diamond, dotted line).  Consistently lower magnitude loads are seen in the neutral posture of this study when compared to all patients from the current study.  In the anterior-deviated posture, loads begin to increase from T8 to S1, approaching values of the pre-operative posture of Patient 2. Asymptomatic subject data modified from Harrison et al., 2005 (92) with permission from SpingerLink. Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  68 To address objective 1b), the model was modified, taking the pre-operative sagittal profiles of each patient and simulating a correction with an osteotomy, and mean predicted compressive loads decreased up to 13% in all but Patient 1 (Figure 2-10).  This patient had negative sagittal balance pre-operatively so a corrective osteotomy actually brought the spine forward causing a 7% increase in predicted intervertebral compressive loads.  The large range in percent differences for Patient 6 may be explained by the severe positive sagittal balance pre-operatively that caused large changes in predicted compressive loads when the spine was realigned.  In general, there were only slight increases in predicted compressive loads for levels T1 to T3 for most patients because the position and magnitude of arm and trunk loads are such that realignment does not have an effect until lower levels.  As the intention of this simulation was to determine if spine loading was affected by the location of the osteotomy, a more important finding was that there was an average difference of only 6% between the mean predicted compressive loads after an osteotomy at each location, confirming the first component of hypothesis 1b) stated in Chapter 1.  This suggests that changing the location of the osteotomy alone is insufficient in increasing the likelihood of surgical success. Up to this point, all results and discussion were under the assumption that extensor muscles were functioning at a sufficient level to maintain equilibrium with the applied body- weight load, a scenario that may not be realistic given that muscle atrophy and intra-operative damage is common among spinal deformity patients.  As the extensor muscles become increasingly less effective, the kyphosing moment generated by body-weight loads is proportionally transferred to the spinal column and surrounding tissues (Figure 2-11).  To maintain balance in this scenario, other structures must compensate to resist kyphosis.  The model was used to simulate this scenario by removing the extensor muscle group force (FM) and Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  69 replacing it with a counteracting force generated by either the vertebral column (FV) or a posterior spinal implant (FR).  As hypothesized, from full muscle function the predicted intervertebral compressive load increased a maximum of 97% to 153% and 31% to 49% in each of these cases, respectively.  Two clinically important questions arise from patients’ pre- operative and immediately post-operative cases: first, how does initial spine loading change in patients with a given pre-operative sagittal profile that have fully-functional muscles to those who have already developed muscle atrophy and loss of strength, and second, after posterior instrumentation, how much additional loading is placed on the spine if muscles are completely damaged intra-operatively.  From the seven patients analyzed, increases of up to 152% and 42% were predicted with a loss of muscle function in these two scenarios, respectively. These compressive loading increases can be explained by the shorter distance from the vertebral body centre at which rod and vertebral forces act when compared to the location of extensor muscles, requiring larger forces to maintain equilibrium and creating more compression on the spine.  The largest differences in predicted loading were most often seen in the lumbar spine because there is a larger proportion of body-weight supported by these levels and the initial extensor moment arm length was larger, causing the decrease to be more pronounced.  The uncertainty in muscle function of presenting sagittal deformity patients is of concern because the intervertebral loading increases that follow muscle atrophy and damage may not be sufficiently considered, leading to unrealistic expectations of surgical outcome.  The magnitude of these increases suggest that when possible, muscles should be conserved intra-operatively and methods aimed to regenerate muscle function after surgery should be further considered, with the hope of improving long-term surgical success. Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  70 Comparing specific muscle force values between studies is difficult since it depends on the magnitude and type of loading applied, the number of muscles considered, and the lines of action and insertion points assumed for each muscle.  This study found an average peak extensor muscle force of 264 N (168 to 427 N) in the pre-operative posture for seven patients.  Reported spinal muscle forces measured from EMG during lifting ranged from 112 N to 1,514 N (122) but the loading was significantly higher (449 Nm compared to at most 21 Nm in the current study). In a combined in vitro and in vivo study, static equilibrium assumptions similar to the current study were used to determine the in vitro muscle forces required to balance the spine such that the external moment was zero (205).  The combination of forces that generated intradiscal pressures and internal fixator loads closest to those measured in vivo were used as muscle force estimates, resulting in estimated erector spinae forces of 100 N for standing, 130 N for 15° extension, and 520 N for 30° flexion (205), results within the range of those from the current study.  The reported increase in muscle force required to balance the spine in flexion agrees with the higher compressive loading trends found in the more severely kyphosed patients of the current study and suggests that extensor muscles are more crucial in flexed postures.  No studies were found that could directly validate the current study’s muscle force predictions and the large range of data and degree of uncertainty surrounding muscle recruitment remains a limitation of all biomechanical and clinical experiments. The equilibrium model developed in this study, though only used retrospectively to date, formed a solid introduction of a predictive tool to be used in surgical planning and deformity progression.  By predicting intervertebral loads on the uppermost instrumented vertebra, surgeons can be given insight to any areas of increased loading to be avoided as the proximal junction.  Collecting radiographs from more subjects diagnosed with positive sagittal imbalance Chapter 2: Development of a Two Dimensional Statically-Determinate Equilibrium Model of Sagittally-Imbalanced Adult Spines  71 will help to validate the model by determining if it can consistently predict higher loading at the proximal junction of those patients who failed.  Beyond this, the model can be used to analyze intervertebral loading on patients’ pre-operative sagittal profiles to plan individual correction methods to maximize the likelihood of surgical success. There are inherent assumptions and limitations of the developed equilibrium model, further discussion of which is included in Chapter 4, including its inability to consider the load distribution across spinal structures at a given vertebral level.  To better understand how the kyphosing moment that results from extensor muscle loss or damage is distributed across an instrumented spine, an in vitro study was developed, described in Chapter 3. Chapter 3: In Vitro Pure Moment Loading Investigation with Instrumented Multi-Segment Adult Spines   72 Chapter  3: In Vitro Pure Moment Loading Investigation with Instrumented Multi-Segment Adult Spines 3.1 Introduction Adult spinal deformity patients have often suffered from severe tissue deformation and adaptation as a result of their age and deformities.  Subsequent surgical correction could exasperate the effect of degeneration and may introduce further damage to tissues surrounding the surgical site with intra-operative tissue displacement and removal.  For example, muscles are normally removed from the spinous processes and laminae to the level of the transverse process along the length of the posterior construct (182).  Any musculature that remains intact during operation may not function at its full capacity after surgery due to an inability to adapt to the spine’s corrected posture or non-reversible muscle atrophy or fatigue (184).  Mathematical models have associated this with a reduction in extension moment generation capacity of extensor muscles (182). An assumption inherent of the intervertebral static equilibrium calculations described in Chapter 2 is that an extensor muscle group maintains equilibrium with anterior body-weight loads of the head, arms, and trunk.  With reduced muscle functionality after surgery, equilibrium maintenance may require the support of the spine and surrounding tissues or a spinal implant. The equilibrium model was used to simulate this scenario and the resulting increase in loading indicates the importance of extensor muscle in minimizing the overall kyphosing moment which may lead to PJK. It is of interest to predict the additional loads transferred to the spine when there is a complete loss of extensor muscle.  Also clinically important is how spine loading is affected by other intra-operative decisions or occurrences beyond those that were considered with the mathematical model (construct length and osteotomy location). Chapter 3: In Vitro Pure Moment Loading Investigation with Instrumented Multi-Segment Adult Spines   73 In vivo studies have predicted spine loading by measuring intradiscal pressure (80; 82; 85; 86; 144) or the load supported by an internal fixator (84) in patients with varying health and during different activities.  However, the large variability in disc health and activity execution between subjects makes it difficult to decipher the portion of load change that is a direct result of the condition or activity of interest. In vitro studies are able to follow stricter protocols with more control over dependent factors and have also been used to measure intradiscal pressure (140; 147)  and internal fixator loads (84).  With the high age of specimens often used in these studies, intradiscal pressure measurements may be unreliable (145; 148) and as such, strain measurements have been taken from vertebral surfaces (156; 157; 158; 159) and rod constructs (165; 166; 167; 142; 84; 168). Most of these studies apply combined loading and many use only functional spinal units.  The flexion mechanics of functional spinal units have been found to significantly differ from those of the same segments within multi-segment specimens so interpretation of the results of pure- moment flexion tests performed on functional spinal units should not be extended to predict loading response of longer segments (206; 207). It is known that the required compensatory activity of posterior spinal musculature increases in flexed (131) and pathological postures (82; 111; 132), a phenomenon that leads to increased vertebral column loads.  With muscle atrophy or damage due to pathological (184) or surgical (182) conditions, respectively, this compensation is lost and it is of interest to determine the resulting additional spine loading.  This scenario was represented with the application of a pure flexion-extension moment, expected to result when extensor muscles are incapable of balancing the spine.  Using measurements described previously, the distribution of this Chapter 3: In Vitro Pure Moment Loading Investigation with Instrumented Multi-Segment Adult Spines   74 kyphosing moment across spinal structures was studied.  This technique has been reported on human functional spinal units (166) but not extended to longer spine segments. The objective of this in vitro study was to better understand how the load is distributed across the spine when extensor muscles are removed intra-operatively.  To simulate this loading scenario, a pure flexion-extension moment was applied to multi-segment thoracolumbar human cadaveric spines.  First, strain measurements from vertebral body surfaces and two posterior rod implants were used to predict the anterior column load under an applied pure moment and second, results were compared across six surgical conditions that had been clinically addressed as possible predictors of PJK (76):  Intact, Intact Instrumented, Medial Bilateral Facetectomy, Complete Bilateral Facetectomy, Posterior Ligament Destabilization, and Anterior Ligament Destabilization, described further in Section 3.2.2.2. 3.2 Methods 3.2.1 Specimens Seven five-segment human cadaveric thoracolumbar spines were used in this study (three T10-L2, one T6-T10, one T8-T12, one T9-L1, and one T11-L3).  Donor ages ranged from 63 to 79 years (median 70 years; two unknown), 49 to 89 kg (median 74.5 kg; three unknown), and there were three males, two females, and two unknown.  Musculature and soft tissue were removed along the length of the specimen while ligaments, joint capsules, and the intervertebral discs were preserved.    Anterior-posterior and lateral x-rays were used to screen for exclusion criteria including fused discs, severe lateral curvature, and poor disc quality.  The most suitable five consecutive segments were chosen for each specimen, however in some cases there were abnormalities that could not be seen in the x-ray and that may have affected the loading behaviour of the specimen (Table 3-1).  Chapter 3: In Vitro Pure Moment Loading Investigation with Instrumented Multi-Segment Adult Spines   75 Table 3-1: Summary of Specimen data Specimen Segments used Sex/Age/Mass Cause of Death Notes 1 T8-T12 M/79 yrs/89 kg Esophogeal cancer All discs fused, discs not mobile 2 T11-L3 F/63 yrs/- Cardiac arrest N/A T10-L2 -/-/- - Osteoporotic bone, *fractured 3 T10-L2 M/64 yrs/64 kg Cancer Bone spur over L1-L2 disc, discs mobile 4 T6-T10 M/77 yrs/85 kg - 5 T10-L2 F/70 yrs/49 kg Respiratory Failure 6 T9-L1 -/-/- - Bone spur over T10-T11 disc - signifies unknown information; *The third specimen (N/A) test was incomplete, not included in results or statistics (the fourth specimen is referred to as Specimen 3 in this document, similarly for subsequent specimens). Specimens will be referred to from 1 to 6 from this point forward. The superior and inferior segments of each specimen were fixated in gypsum potting material (Tru-Stone, Modern Materials Heraeus, South Bend, IN) in custom-made aluminum potting boxes.  Wood screws were inserted into the bone and wrapped with wire to ensure a strong fixation between the vertebral endplate and dental stone throughout testing (Figure 3-1). In cases where the bone quality of the potted vertebrae was questioned, poly(methyl methacrylate) (PMMA) was inserted into the vertebrae to be potted before wood screws were affixed to augment the fixation; care was taken not to allow PMMA to enter the adjacent intervertebral disc.  Figure 3-1: Specimen prepared for potting.  Superior and inferior vertebra were affixed with screws and wire added to secure the fixation. Chapter 3: In Vitro Pure Moment Loading Investigation with Instrumented Multi-Segment Adult Spines   76 The specimen was aligned upright in the potting boxes such that the transverse plane at the midline through the third vertebral body was horizontal.  Six pedicle screws (ø5.5 mm x 35 mm titanium bone screw; Medtronic Inc., Minneapolis, MN) were inserted into under tapped holes in the pedicles of the inferior three vertebrae.  A custom aluminum plate was then attached to each potting box for compatibility with the loading apparatus; the inferior and superior plate was rigidly secured to the base and loading arm of the testing apparatus, respectively. 3.2.2 Testing The specimen was loaded in a pure flexion-extension moment, representing the additional kyphosing moment on the spine when extensor muscles are unable to counteract the body-weight loads.  Each specimen was tested in six sequential states. Each state was surgically created to represent spinal conditions that are commonly seen in a posterior fusion surgery, either intentionally or as a result of surgical error. 3.2.2.1 Loading Apparatus and Testing Software The loading apparatus used for this study was a spine simulator developed to apply unconstrained pure moments to the local axis of the cranial segment of a spine specimen (208). Load-input protocol was used and as such, it was required that the apparatus created three essential conditions during testing: 1) the specimen was able to make completely unconstrained rotations, 2) the applied moment remained a pure moment throughout the duration of the test, and 3) the magnitude and orientation of the moment applied to the cranial segment remained constant (151).  A servo motor (D50R10-0243, Designatronics, New Hyde Park, NY) applied the moment by means of an articulating arm and a universal joint. A ball spline allowed linear translation of the arm while transmitting the moment.  The weight of the articulating arm, upper specimen, and superior potting, potting box and loading plate were balanced by a suspended Chapter 3: In Vitro Pure Moment Loading Investigation with Instrumented Multi-Segment Adult Spines   77 counterweight that translated with specimen motion (Figure 3-2).  The counterweight prevented the mass of the superior potting block and loading arm from applying an initial load on the specimen (208).  More images of the machine can be seen in Appendix F, along with the results of a test that was conducted to verify the pure moment application of the spine simulator and quantify any off-axis moments.        Chapter 3: In Vitro Pure Moment Loading Investigation with Instrumented Multi-Segment Adult Spines   78    Counterweight Pulley Mapplied Inferior plate Superior plate Attached to articulating arm/motor Counterweight Pulley system Loading apparatus base plate Inferior plate Superior plate Latch Motor Universal Joints Ball spline Torque load cell XY table Lateral counterweight Instrumented Specimen Articulating arm (a) (b) Figure 3-2: Schematic and image of spine simulator used to apply pure moment (a) Schematics showing the posterior (left) and lateral (right) views of the specimen in the loading rig.  The specimen was attached to two loading plates; the inferior plate was rigidly secured to the base of the apparatus and the superior plate was rigidly attached to the articulating arm which applied a pure sagittal moment (Mapplied) from a servomotor.  A ball spline allowed linear translation of the arm while two universal joints allowed unconstrained rotation.  A counterweight was attached to the superior loading plate by a pulley system that was hung from an XY translation device (shown in Appendix F), providing unconstrained motion to the specimen. (b) Image of the loading rig with a potted specimen mounted on the base plate and attached to the articulating arm.  Inferior plate Base plate Superior plate Mapplied Chapter 3: In Vitro Pure Moment Loading Investigation with Instrumented Multi-Segment Adult Spines   79 The moment application was controlled by a custom LabVIEW program (LabVIEW 2009 v.8.2.1, National Instruments Co., Austin, TX).  Five cycles of flexion-extension to a peak of ±10 Nm were applied at a rate of two degrees per second to the superior segment attached to the distal end of the articulating arm.  The torque load cell attached to the universal joint measured the moments applied to the specimen, the signal from which was collected at 20 Hz by a personal computer and data acquisition system (LabVIEW 2009 v.8.2.1, National Instruments Co., Austin, TX). 3.2.2.2 Conditions Each specimen was tested in six conditions relevant to posterior fusion surgeries and proximal junction failures.  The description and clinical relevance of these conditions and specimen images and schematics are summarized in Table 3-2 and 3-3, respectively. Table 3-2: Summary of surgical conditions tested for each specimen Condition Description Clinical relevance 1 – Intact Pedicle screws inserted Specimen intact Spine loading prior to surgery 2 – Intact Instrumented Rods attached to pedicle screws Specimen intact Spine loading of initial surgical condition 3 – Medial Bilateral Facetectomy Rods attached to pedicle screws Partial removal of both facets of adjacent vertebra Surgical necessity based on patient anatomy, causing pedicle screw to partially breach adjacent facet 4 – Complete Bilateral Facetectomy Rods attached to pedicle screws Complete removal of both facets of adjacent vertebra Surgical necessity based on patient anatomy, causing pedicle screws to completely breach adjacent facet 5 – Posterior ligament destabilization Rods attached to pedicle screws Interspinous and supraspinous ligaments cut along length of spinous process at all levels Damage of posterior ligaments during surgery and/or lack of ligament function after spine realignment 6 – Anterior ligament destabilization Rods attached to pedicle screws Anterior longitudinal ligament cut at vertebra and discs at all levels Decompression of uppermost instrumented vertebra disc, fracture dislocation, or anterior surgical approaches altering anterior ligaments   Chapter 3: In Vitro Pure Moment Loading Investigation with Instrumented Multi-Segment Adult Spines   80 Table 3-3: Specimen images and schematics of loading during each of the six surgical conditions Condition Specimen Schematic 1 – Intact   2 – Intact Instrumented   3 –Medial bilateral facetectomy  4 – Complete bilateral facetectomy   5 – Posterior ligament destabilization   6 – Anterior ligament destabilization   Vertebra gauges (x4) Pedicle screws Ligaments Mapplied Base plate Superior plate Vertebra gauges (x4) and rod gauges (x12) Pedicle screws Ligaments Rods (x2) Pedicle screws Ligaments Rods (x2) Vertebra gauges (x4) and rod gauges (x12) Bilateral facetectomy Mapplied Base plate Superior plate Pedicle screws Ligaments Rods (x2) Vertebra gauges (x4) and rod gauges (x12) Posterior ligament destabilization Pedicle screws Ligaments Rods (x2) Vertebra gauges (x4) and rod gauges (x12) Anterior ligament destabilization Mapplied Base plate Superior plate Mapplied Base plate Superior plate Mapplied Base plate Superior plate Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  81 Each surgical condition was performed sequentially and was not randomized as each destabilization would affect subsequent conditions and it was desired to study the effect of each in a repeated measures design.  For the Intact Instrumented condition, two rods were attached to the pedicle screws with set screws (details discussed in Section 3.2.3.2) torqued with a digital torque wrench to 9 Nm (± 0.18 Nm). The types of rods and pedicle screws used in this experiment were chosen based on their current clinical utility during spinal fusion surgeries.  The medial and complete bilateral facetectomy at the adjacent vertebra was performed by a spinal surgeon.  For the former, the medial half of each facet was disrupted and bone was removed from both the superior and inferior articular processes using a 2 mm kerrison rongeur.  For the complete bilateral facetectomy, all the bone from the superior and inferior articular processes was removed.  For the final two ligament destabilization conditions the supraspinous and interspinous posterior ligaments were first cut with a scalpel at each vertebral level along the length of the spine, followed by cutting the anterior longitudinal ligament (Figure 1-1). 3.2.3 Measurements 3.2.3.1 Vertebral Body Strain Four 120 Ω nominal resistance uniaxial foil strain gauges (TML FLG-02-23-1L; Tokyo Sokki Kenkyujo Co., Ltd., Shinagawa-ku, Tokyo) were applied to the vertebral body surfaces.  A gauge was placed on both the lateral and anterior vertebral body surface of the uppermost- instrumented vertebra (UIV) and the adjacent vertebra (Figure 3-3).  Each gauge was wired in a quarter-bridge (Appendix A.2) and the four signals were collected at 20 Hz with a personal computer and data acquisition unit (LabVIEW 2010, v.10.0.1, National Instruments Co., Austin, TX) during all tests in every surgical condition. Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  82  Figure 3-3: Vertebra strain gauges on specimen.  Strain gauges were attached to vertebral surfaces of the uppermost instrumented vertebra (UIV) and adjacent vertebra, located on (a) the anterior and (b) the lateral vertebral body surfaces. 3.2.3.1.1 Application of Vertebral Strain Gauges At each gauge site, all tissue was removed, first with a scalpel then with sandpaper (#100), such that approximately 1 cm2 of vertebral bone surface was exposed.  If the exposed bone was poor quality, another nearby gauge site was chosen.  The surface of each gauge site was cleaned and degreased with ethanol. Two layers of polyurethane protective coating (M-coat C Silicone Rubber Coating; Intertechnology Inc., Don Mills, ON) was applied to fill the pores of the vertebra, allowing the coating to completely dry for 20 minutes between applications.  Any excess polyurethane was removed with sandpaper (#400).  A conditioner (M-Prep Conditioner A; Intertechnology Inc., Don Mills, ON) and a neutralizer (M-Prep Neutralizer 5A; Intertechnology Inc., Don Mills, ON) were applied with Q-tips to clean and dry each surface.  A catalyst (200 Catalyst C; Intertechnology Inc., Don Mills, ON) and adhesive (M-Bond 200; Intertechnology Inc., Don Mills, ON) were then applied to the back of the strain gauge and to the bone surface, respectively, allowing the catalyst to completely dry before the gauge was firmly pressed against the vertebra surface and held with a pressing force for at least two minutes. Adjacent UIV (a) (b) Adjacent UIV Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  83 Three layers of polyurethane protective coating were finally applied to the gauges for protection against moisture, tissue contamination, and dirt. 3.2.3.1.2 Calibration To relate the measured strain to a vertebral moment and load, a calibration test was designed. Calibration requires the application of a known applied load to the isolated vertebral column. One fresh-frozen three-segment spine (T12 to L2) was used for this study (Male, 50 years, 122 kg).  All musculature and surrounding tissue was removed and the specimen was potted and prepared for loading as described in Section 3.2.1 with the additional step of removing the posterior elements along the length of the spine.  Three 120 Ω nominal resistance uniaxial foil strain gauges (TML FLG-02-23-1L; Tokyo Sokki Kenkyujo Co., Ltd., Shinagawa-ku, Tokyo) were applied to the vertebral body surfaces using the process described in Section 3.2.3.1.1.  A gauge was placed on the anterior and both lateral vertebral body surfaces of the middle vertebra (L1).  An image of the specimen attached to the loading apparatus can be seen in Figure 3-4.  Figure 3-4: Image of prepared specimen in loading apparatus. Vertebral bodies were isolated, by removing the posterior elements, and strain gauges were placed on the anterior and two lateral sides of the middle vertebral body. Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  84 The specimen was tested in three loading conditions: a pure flexion-extension moment of ± 8 Nm (three cycles), a pure axial compression load of 0 to 300 N (three ramp cycles), and a pure flexion-extension moment of ± 8 Nm (three cycles) in combination with a constant applied axial compression load of 300 N.  For pure moment loading, the load application followed the process described in Section 3.2.2.  The moment applied to the specimen was collected at 20 Hz by a personal computer and data acquisition system (LabVIEW 2009 v.8.2.1, National Instruments Co., Austin, TX).  For axial compression, an Instron actuator (Model A591-4, Instron, Norwood, MA), located directly below the specimen, applied the axial load through a steel cable attached to the superior potting block.  The cables were adjusted such that the lines of action of the loads fell as close as possible to the centre of the disc in the anterior-posterior direction to achieve a neutral compression without visible flexion or extension.  Due to limitations of the testing rig, the neutral axis was slightly offset.  To minimize this effect, a follower load was used; a follower load is a compressive load applied along the path of a wire that follows the curvature of the spine, thus subjecting the whole spine to nearly pure compression (151).  Six metal eyebolts were screwed into the lateral sides of each vertebra at the midpoint of the vertebral height.  A cable was passed from the actuator through each of the bolts and attached to the superior potting block, allowing the load to be applied through the centre of each intervertebral disc (Figure 3-5). This method provided reasonably neutral compression during the application of the axial force alone but the change in the centre of rotation that occurs upon applying a bending moment limited its accuracy.  To improve the system, the position of the follower load should be adjustable in the anterior-posterior direction during bending.   The applied load was measured by the load cell on the actuator and strain signals for the three gauges were collected at 20 Hz with a Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  85 personal computer and data acquisition unit (LabVIEW 2010, v.10.0.1, National Instruments Co., Austin, TX) during all tests.  Figure 3-5: Image specimen in loading apparatus, prepared for calibration test (axial load application).  A follower-load was designed with six eyebolts through which the loading cable passed to maintain central alignment during loading cycles. (a) Posterior view and (b) Lateral view. For the isolated tests (pure moment or pure axial compression), the resulting strains were related to the applied loads with calibration constants.  Coupling effects from the bending and axial loads were accounted for with the matrix method (177), described further in Appendix G. A calibration matrix was constructed from results of both isolated tests and was applied to the strains from the combined moment and axial compression loading test.  The loads and moments predicted using this calibration matrix were then compared to those applied to determine the accuracy of the calculation and the suitability of calculating vertebral forces and moments from measured strain. (a) (b) Eyebolts Attachment to superior plate (slightly offset) Axial Cable Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  86 A linear relationship must exist between the applied load and measured vertebral strain for the calibration matrix to be an accurate tool for predicting vertebral moments and loads during the application of a pure moment.  As shown in Appendix G, the sensitivity of the strain response to changes in applied load was insufficient as the same strain was measured for a large range of applied loads.  This meant that the relationship between measured vertebral strain and applied load was non-linear and therefore the matrix method did not hold.  Without an accurate method of relating measured strains to moments and loads, the raw vertebral strain data are reported in this paper. 3.2.3.2 Rod Strain The posterior fusion rods (ø5.5 mm Titanium) were instrumented with six 120 Ω nominal resistance uniaxial strain gauges (EA-06-031DE-120; Vishay Measurements Group, Inc., Raleigh, NC). Two lengths of rod pairs (85 mm and 91 mm) were used according to specimen anatomy. Specimens 1, 4, and 6 used the long rods and Specimens 2, 3 and 5 used the short rods. Two sets of three strain gauges were affixed to each rod; the long axis of each gauge aligned with that of the rod’s.  Refer to Appendix H for dimensioned drawings of both rod pairs. The gauges were applied 120° apart circumferentially (Figure 3-6) using the process described in the following section. When attached to the specimen, the rods were oriented such that one of the strain gauges (shown as ε2 in Figure 3-6) was facing posteriorly.  With the gauges oriented this way, the measured rod strain could be related to rod moment and load through a theoretical relationship (209) described further in Section 3.2.3.2.2.    Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  87             One pair of rods was used for each specimen test, each of which was affixed to the spine with three multi-axial pedicle screws (ø5.5 mm x 35 mm titanium bone screw; Medtronic Inc., Minneapolis, MN) attached to the rods on either side of the strain gauge sets (Figure 3-7) with set screws (Ti 7540020; Medtronic Inc., Minneapolis, MN) to hold them in place. During conditions 2 through 6, the strain signals from the superior and inferior gauge sets on both rods were simultaneously measured and were collected at 20 Hz by a personal computer and data acquisition system (LabVIEW 2010, v.10.0.1, National Instruments Co., Austin, TX). The location of the rods in relation to the disc centre (parameter a in Figure 3-8) were measured with a mechanical caliper at the level of each pedicle screw and were averaged between the left and right rods. Figure 3-6: Schematic of orientation of strain gauges (ε1, ε2, ε3) on each posterior spinal rod (cross-section shown in blue) in two locations between pedicle screws. Strain gauges are oriented 120° apart to allow the use of a theoretical relationship relating measured strain to rod moment and load (209).  In this configuration, the rod is aligned such that the strain gauge placed at the posterior border is assigned ε2 and that closest to the neutral axis (shown in red) is assigned ε1.  The location of each gauge is measured with respect to the neutral axis (c1, c2, and c3 in orange), about which a pure moment is applied (shown in green), with γ being the angle between ε1 and the neutral axis. +γ POSTERIOR ANTERIOR Mapplied z x y 120° 120° 120° ε1 ε3 ε2 Neutral axis c1 c3 c2 120 - γ 240 - γ Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  88  Figure 3-7: Posterior view of a specimen with two posterior fusion rods, instrumented with strain gauges at the superior and inferior levels, and attached with pedicle screws 3.2.3.2.1 Application of Strain Gauges to Rods Six strain gauges were affixed to each rod by the Electronics Technician in the UBC Department of Mechanical Engineering following the technique described by the strain gauge manufacturer (210).  Sets of three gauges were attached in two locations along the length of each rod (locations are marked A and B as indicated in the mechanical drawings attached in Appendix H).  The titanium rod coating was removed at each of these locations using a lathe and lines were lightly scribed at the gauge mount positions (120 degrees apart) using a mill machine setup to help place accurate lines.  The rods were cleaned in several steps with commercial grade isopropyl alcohol (Rexall 99%) and abrasives (3M) to remove any attached dirt or oils and then the edge of the backing material of each strain gauge was aligned with the longitudinal scribe lines on the rod and was temporarily placed onto the rod, along with its associated bonding pad, using an epoxy adhesive (Micro Measurements MBond 610 adhesive, Vishay Measurements Group, Inc., Raleigh, NC).  Polyimide tape (McMaster Carr) was used to hold the components in Pedicle screws Left Right Superior Inferior Strain gauges Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  89      (Eq. 3-2)      (Eq. 3-3) place temporarily.  After all gauges and bonding pads had been attached, they were pressed against the rod surface with a silicon rubber pad, a curved stainless steel plate and a normal clamping force using a custom designed fixture.  The rods were cured in an oven at 140°C for three hours then the clamps were removed and post curing continued for an additional two hours at 100°C, then the rods were allowed to cool to room temperature overnight.  The polyimide tape was removed and any excess glue was removed by careful light abrasion with 600 Grit wet dry abrasive paper (3M).  The strain gauges were tested for continuity and correct resistance and then electrically wired to the bonding pads using 40 AWG solid copper urethane coated magnet wire. The gauge and the wiring were then coated with a polyurethane solution (MCoat A, Vishay Measurements Group, Inc., Raleigh, NC).  After room temperature curing for one hour, the 32 AWG stranded gauge lead wires were attached to gold plated electrical connectors (Molex, Microfit 3.0 mm) for compatibility with a data acquisition system.  The attachment of strain gauges did not physically alter the rods. 3.2.3.2.2 Calibration The strains measured by three uniaxial strain gauges during loading were related to the moment and load transferred to the rod using a theoretical relationship described by Tuttle (209). The theory behind this relationship is explained in detail in Appendix I.  Briefly, with the configuration shown in Figure 3-6, and ε1 as the intermediate strain value located closest to the neutral axis, the load, P, and moment, M, transferred to each rod, and the orientation of the neutral axis, γ, can be calculated using Eq. 3-1, Eq. 3-2 and Eq. 3-3, respectively: J   :KL M  M  ML! *  NK√LPDEFQ ML  M! R  S2 T √L U1  VWVX!VYVX! Z[      (Eq. 3-1) Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  90 where A is the cross sectional area of the rod [m2] = pir2, E is the modulus of elasticity [Pa], I is the area moment of inertia, [m4] = ¼pir4, r is the radius of rod cross section [m], and γ is the angle between the strain gauge ε1 and the neutral axis [deg] The neutral axis in the above equations is that of the component of load and moment transferred to the rod with the application of a pure moment applied to the specimen.  It is not the neutral axis of the applied pure moment which is located through the anterior column and that varies with each specimen. A test designed to determine the accuracy of the rod moments calculated from measured strain values (Appendix J) found that the percent error was less than 6.0% and 13.7% for the long rods and less than 8.5% and 21.4% for the short rods for the superior and inferior gauge sets, respectively.  A subsequent test was designed to determine the sensitivity of the calculated rod loads and moments to the orientation of the rods (Appendix J).  Both inter-pedicle position of adjacent vertebrae (rod angle) and rod circumferential position had minimal effect on moment calculations (less than 7.8% difference between each rod orientation).  Calculated rod loads could not be compared against a known applied load as only a pure moment was applied.  It was expected that the accuracy of the rod load calculation was similar to rod moment and, given the relationship in Eq. 3-3, load calculation was not sensitive to rod orientation. 3.2.3.2.3 Load-sharing Calculations The applied moment was supported by a combination of both rods, posterior elements, and the anterior column, including vertebral disc and surrounding tissues (166).  The distribution between these structures was calculated assuming static equilibrium at the vertebral level of interest (Figure 3-8) using Eq.’s 3-4 and 3-5, where Fy represents the vertical forces and MO Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  91 represents the moment in the sagittal plane, taken about point O.  The rod force, FR, and moment, MR, were based on direct measurements while the anterior column force, FAC, and moment, MAC, were calculated based on the given relationships.  The rod and anterior column loads form a force couple so by measuring the rod loads, one can infer the load supported by the anterior column (166).  A portion of the applied moment was also supported by the posterior elements, previously found to be 5.0% and 11.3% in flexion and extension, respectively (166).  This percentage of applied moment was subtracted from MAC. ∑%)   0 %]  %:	  0  ∑*+  0 10 *] *:	  %]  0  3.2.3.3 Range of Motion Three-dimensional specimen motion was recorded with a motion capture system (Optotrak Certus, Northern Digital Inc., Waterloo, ON).  Two sets of Optotrak marker carriers were rigidly attached to bone pins which were inserted into the superior and inferior vertebra. On each of the carriers, there were four opto-electric markers which remained in view of the camera to allow motion tracking for the duration of the test (Figure 3-9).  Local coordinate      (Eq. 3-4) (Eq. 3-5) FAC MAC 10 Nm MR FR a y z x Figure 3-8:  Free-body diagram used for published intervertebral loading calculations in Flexion/Extension loading (166).  Subscripts R and AC denote forces (F) or moments (M) supported by the rods and anterior column, respectively.  The distance between the rod and centre of the vertebral column is denoted by a.  The orientation of the vertebra coordinate system is shown, where y, z, and x are positive upwards, forwards, and to the left, respectively.  Schematic was adapted from Cripton et al., 2000 (166) with permission from Wolters Kluwer Health. Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  92 systems were defined on each of the vertebral bodies. The anterior borders of the inferior and superior vertebral endplate of the superior and inferior vertebra, respectively, were digitized with a probe with six markers on its body and one on its tip.  This was used to determine of the location of the superior vertebra coordinate system with respect to that located in the inferior vertebra which was assumed not to move during loading cycles (Figure 3-9).  The kinematic data were collected at 20 Hz on a personal computer using a custom LabVIEW program (LabVIEW 2009 v.8.2.1, National Instruments, Austin, TX).  Figure 3-9: Image of specimen in loading apparatus with optoelectric markers to track the motion of specimen for the duration of the test.  The marker pads are rigidly attached to the superior and inferior vertebra with bone pins. 3.2.4 Data Analysis The vertebral strain, rod strain, and range of motion data were processed with custom software programs (Matlab v. R2009b, MathWorks, Natick, MA).  Data from the fifth loading cycle only was used for subsequent analysis.  The strain measured from each of the gauge sets on both rods was converted into moment and load supported by the implants at the superior and inferior level by summing the moments and loads calculated for the left and right rod at each Optoelectric markers Bone pins y z x y z x Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  93 level.  The conversion from strain to moment and load was done using the theoretical relationships described in Section 3.2.3.2.2.  The load-sharing of the implant was calculated by the process described in Section 3.2.3.2.3 and the moment and load supported by both the rods (superior and inferior levels) and the anterior column at each level are presented in this paper. 3.2.5 Statistics A one-way repeated measures analysis of variance was performed on the vertebral strain, rod moment, rod load, and kinematics results using a statistics software package (Statistica v9, StatSoft Inc., Tulsa, OK).   The independent variable, or factor, was the surgical condition and the dependent variable was the value of strain, moment, load, and position, respectively.  For a significant analysis of variance, a post-hoc Student-Newman-Keuls test was performed to determine between which factors there was a significant difference.   A P-value less than 0.05 was considered significant. Specimen 1 did not have any data available for Condition 5 or position data available for any of the conditions.  For this specimen, the data from Condition 6 were used for Condition 5 and there was no analysis of variance performed for position. 3.3 Results This section includes a summary of the results obtained for analysis of six human thoracolumbar cadaveric spines in pure flexion-extension loading in six relevant surgical conditions. One full set of data for Specimen 4 in the Intact Instrumented condition is included in Appendix K and represents the data taken for each specimen in each condition. 3.3.1 Vertebral Body Strain Vertebral strain data from a specimen tested in the Intact Instrumented condition are shown for the fifth flexion-extension loading cycle in Figure 3-10.  The strain magnitudes Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  94 reached by each gauge at maximum flexion (10 Nm) and maximum extension (-10 Nm) were found for each specimen, the medians of which were calculated in each of the six conditions (Figure 3-11).  Figure 3-10: Vertebral strain time trace and load data for one gauge from Specimen 4 in the Intact Instrumented condition in the fifth loading cycle. Two gauges were affixed to each vertebral body at the proximal junction (UIV and Adjacent vertebra), one each to the anterior (Ant) and lateral (Lat) surfaces. The colours used on the plot correspond to the locations shown in the specimen image at the top.  The applied flexion-extension moment of ± 10 Nm is also plotted (black dotted).  Similar data was collected for each specimen and the strain magnitudes at max flexion and extension (circled in purple) were compared across specimens for each of the six conditions. The one-way repeated measures analysis of variance was significant for specimen condition for all but the UIV Lateral gauge (P< 0.02) and the multiple comparison Student-Newman-Keuls test found the individual vertebral strain magnitudes to be significantly different between the following conditions, and as indicated in Figure 3-11: • Adjacent Lateral- Flexion: conditions 3 and 6 (p<0.05) ; Extension: conditions 1 through 5 and condition 6 (p<0.007). • Adjacent Anterior – Flexion: conditions 1 through 4 and both conditions 5 (p<0.007) and 6 (p<0.03); Extension: conditions 1 through 5 and condition 6 (p<0.03). Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  95 • UIV Anterior – Flexion: conditions 3 and 5 (p<0.05); Extension: condition 1 and conditions 2 through 6 (p<0.03). Despite statistical significance, there were only small differences in strain magnitude between conditions so clinical significance was not met.     Figure 3-11: Median (points) and maximum and minimum (vertical bars) vertebral strain magnitudes across specimens in conditions 1 to 6 at maximum flexion (blue) and maximum extension (red) for (a) the Adjacent Lateral gauge, (b) Adjacent Anterior gauge, (c) Uppermost Instrumented Vertebra gauge, and (d) Uppermost Instrumented Vertebra Anterior gauge.  There is a large range of strain magnitudes across specimens, especially in the anterior gauges.  The results of the repeated measures ANOVA and Student-Newman-Keuls test are shown, where significant differences are indicated with * (p<0.05), ** (p<0.03) and *** (p<0.007).  ADJACENT LATERAL ADJACENT ANTERIOR UIV LATERAL UIV ANTERIOR (a) (b) (c) (d) ** *** ** * * *** ** F1 to F6 = Condition 1 to 6 (Flexion Loading) E1 to E6 = Condition 1 to 6 (Extension Loading)  Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  96 3.3.2 Rod Strain An example of the strain measured from the inferior gauge of the left rod when it was affixed to a specimen during the Intact Instrumented condition during the fifth cycle of flexion- extension loading is shown in Figure 3-12.  These strain data were used with theoretical relationships to predict the combined moments and loads supported by the superior and inferior levels for the left and right rods, an example of which is shown in Figure 3-13. The combined strain magnitudes reached by each level at maximum flexion (10 Nm) and maximum extension (-10 Nm) were found for each specimen, the medians of which were calculated in each of the six conditions (Figure 3-14).  The one-way repeated measures analysis of variance was significant for specimen condition only for the calculated moment of the inferior level (P<0.05) and the multiple comparison Student-Newman-Keuls test found the calculated moment of the inferior level to be significantly different in extension between the conditions 4 and 5 and condition 6, indicated in Figure 3-14..  Figure 3-12: Rod strain time trace for one gauge from Specimen 4 in the Intact Instrumented condition during the fifth cycle of flexion and extension loading (± 10 Nm).  The strain is shown for the three gauges (right, posterior, and left) on the inferior gauge set of a rod implant affixed to the left posterior side of the specimen (identified in schematics on the right).  The posterior gauge (blue) saw compression at maximum flexion and tension at maximum extension, a counterintuitive finding that was typical across specimens.  Max Flexion Max Extension Posterior Left Right 120° 120° 120° Tension Compression Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  97  Figure 3-13: Calculated rod moment and load in flexion loading for Specimen 4 in the Intact Instrumented condition.  The strains measured in the left and right gauge sets were summed for both the superior (blue) and inferior (red) levels and theoretical calculations (Eq.’s 3-1 and 3-2) were used to calculate (a) the total rod moment, with the applied moment shown in black, and (b) the total rod load.  Moment and load magnitudes were taken at points of maximum applied moment (circled).  Based on the strain response shown in Figure 3-12, the calculated rod moments were in the opposite direction as the applied moment (ie. calculated extension moment during applied flexion).          0 2 4 6 8-2 0 2 4 6 8 10 Time [s] M om en t [N m ]   M applied M calc - tot sup M calc - tot inf 0 2 4 6 8 -300 -200 -100 0 100 200 300 Time [s] Lo ad  [N ]   Calc Load - tot sup Calc Load - tot inf MOMENT (FLEXION) LOAD (FLEXION) (a) (b) Flexion Extension Tension Compression Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  98      Figure 3-14: Median (points) and maximum and minimum (vertical bars) calculated rod moments and loads across specimens in conditions 1 to 6 at maximum flexion (blue) and maximum extension (red). Moment and load magnitudes calculated for left and right rod strain gauges were combined for the superior and inferior levels.  The plots represent: (a) calculated moments in the superior level, (b) predicted loads in the superior level, (c) predicted moments in the inferior level, and (d) calculated loads in the inferior level.   The results of the repeated measures ANOVA and Student-Newman-Keuls test are shown, where significant differences are indicated with * (p<0.05). In general, there was a large range in predicted rod moments; both flexion and extension moments were calculated for applied moments in either direction.  This resulted in a large range in the proportion of the applied moment supported by the rods.  All calculated rod moments were * MOMENT (Inferior) LOAD (Inferior) (a) (b) (c) (d) MOMENT (Superior) LOAD (Superior) F1 to F6 = Condition 1 to 6 (Flexion Loading) E1 to E6 = Condition 1 to 6 (Extension Loading)  Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  99 very small magnitude, median moments in all surgical conditions reaching at most -0.9 Nm and 0.8 Nm in flexion and extension, respectively. 3.3.2.1 Load-Sharing Finally, calculated rod moments and loads were used to predict the resultant loads supported by the anterior column under a pure moment.  The load-sharing between the spine and the implant was predicted using equilibrium calculations (Figure 3-8).  Also considered was the moment supported by the posterior elements, found in a previous study to be 5.0% and 11.3% of the applied moment in flexion and extension, respectively (166).  The force couple created between the rod and the anterior column (FR*a) was found to support the majority of the applied moment in all conditions.  The predicted anterior column moments and loads at the superior and inferior levels were calculated at points of maximum flexion and extension for every condition; the medians and range of data across specimens are summarized in Figure 3-15, and in Tables 3- 4 and 3-5.           Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  100     Figure 3-15: Median (points) and maximum and minimum (vertical bars) predicted anterior column moments and loads across specimens in conditions 1 to 6 at maximum flexion (blue) and maximum extension (red). Moment and load magnitudes calculated for left and right rod strain gauges were combined for the superior and inferior levels.  The plots represent: (a) predicted moments at the superior level, (b) predicted loads at the superior level, (c) predicted moments at the inferior level, and (d) predicted loads at the inferior level.      MOMENT (Superior) LOAD (Superior) (a) (b) (c) (d) MOMENT (Inferior) LOAD (Inferior) F1 to F6 = Condition 1 to 6 (Flexion Loading) E1 to E6 = Condition 1 to 6 (Extension Loading)  Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  101 Table 3-4: Median Anterior Column Moments, predicted from distribution of applied moment between rod, anterior column, force couple between rod and anterior column, and posterior elements (based on results from Cripton et al. (166)) Condition Calculated Median (and range) Anterior Column Moment [Nm] Superior Level Inferior Level Flexion Extension Flexion Extension 2 -3.1 (-5.1 to 0.4) 2.6 (-1.3 to 6.9) 1.3 (-4.5 to 7.5) -1.0 (-5.4 to 3.5) 3 -3.1 (-7.2 to 1.8) 4.7 (-2.0 to 6.9) 3.4 (-4.7 to 7.3) 0.4 (-4.4 to 5.1) 4 -2.4 (-7.7 to 3.0) 3.2 (-3.1 to 7.1) 2.2 (-5.6 to 7.6) 2.4 (-2.5 to 5.0) 5 -3.9 (-7.7 to 2.5) 3.9 (-3.3 to 7.4) 2.6 (-2.3 to 7.6) -1.6 (-5.4 to 5.0) 6 -3.1 (-7.7 to 1.0) 2.0 (-8.1 to 7.4) 2.4 (-2.3 to 6.6) 0.7 (-3.5 to 5.0) Table 3-5: Median Anterior Column Loads, predicted from force couple between rod and anterior column. Positive and negative values represent vertebral column tension and compression, respectively. Condition Calculated Median (and range) Anterior Column Load [N] Superior Level Inferior Level Flexion Extension Flexion Extension 2 -146 (-82 to -219) 153 (40 to 199) -269 (-97 to -410) 200 (130 to 358) 3 -144 (-46 to -223) 128 (49 to 214) -314 (-88 to -405) 182 (120 to 336) 4 -158 (-37 to -246) 151 (45 to 234) -278 (-73 to -413) 122 (96 to 272) 5 -150 (-38 to -237) 129 (31 to 240) -298 (-129 to -414) 187 (102 to 360) 6 -156 (-38 to -218) 154 (31 to 345) -292 (-129 to -388) 155 (111 to 270) 3.3.3 Range of Motion In flexion and extension, the dominant motion occurred in the sagittal plane with minimal motion in axial and lateral planes.  An example flexibility curve in the sagittal plane for Specimen 2 in the Intact Instrumented condition during five cycles is shown in Figure 3-16a; range of motion was consistent during the five loading cycles.  The median was taken across Specimens 2 to 6 for the sagittal range of motion at maximum flexion and maximum extension loading of the fifth cycle (Figure 3-16b), reaching peak rotations of 10.2° and -10.4°, respectively both in the Intact condition.  The axial plane motion at maximum flexion and extension was less than 3.9° and -1.8°, respectively.  The lateral plane motion at maximum flexion and extension was less than 2.3° and -3.6°, respectively, except for Specimen 2 which experienced 10.8° and -11.5° of lateral motion at maximum flexion and extension, respectively; Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  102 this was not representative of other specimens.  The range of motion was not measured for Specimen 1.  The one-way repeated measures analysis of variance was significant for specimen condition only in the sagittal plane (P<0.05) and the multiple comparison Student-Newman- Keuls test found the sagittal position to be significantly different between the following conditions, and as  indicated in Figure 3-16: • Flexion: conditions 2 through 4 and both conditions 1 and 6 (p<0.006), conditions 2 and 5 (p<0.05), and conditions 4 and 5 (p<0.05). • Extension: conditions 2 through 5 and both conditions 1 and 6 (p<0.006).    Figure 3-16: Sagittal plane kinematic data during flexion-extension loading. (a) Flexibility curve of Specimen 2 in the Intact Instrumented condition during five cycles of ± 10 Nm flexion-extension loading and (b) median (points) and maximum and minimum (vertical bars) of the sagittal position of Specimens 2 through 5 in conditions 1 to 6 at maximum flexion (blue) and maximum extension (red).  The range of motion was not measured during tests for Specimen 1.  The results of the repeated measures ANOVA and Student-Newman- Keuls test are shown, where significant differences are indicated with * (p<0.05) and ** (p<0.006). 3.4 Discussion Six human cadaveric five-segment spines in six surgical states were tested in pure flexion-extension bending to represent the post-operative kyphosing moment experienced by patients without extensor muscle function.  Vertebral strain at the proximal junction, rod strain, ** ** * * ** ** (a) (b) F1 to F6 = Condition 1 to 6 (Flexion Loading) E1 to E6 = Condition 1 to 6 (Extension Loading)  Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  103 and specimen kinematics were measured and calculated rod moments and loads were used to predict load-sharing between the implant and the anterior column.  The resulting predicted anterior column compressive load represented the additional load to which the spine is subject under an applied moment, beyond that experienced from normal body-weight loads in sagitally- balanced postures.  Upon instrumentation of the specimen, a force couple was created between the anterior column and the implant under an applied flexion-extension moment.  This caused the anterior column to be loaded equally and in the opposite direction as the implant (compare Figure 3-14 and 3-15 b) and d)), reaching  median magnitudes up to 298 N compression and 200 N tension in flexion and extension, respectively.  These magnitudes agree well with the loads Cripton et al. (166) found to be supported by a combination of intervertebral disc and residual structures of the anterior column measured in the intact instrumented condition (150 N and -130 N during flexion and extension, respectively).  In this case, a positive value represented an upwards disc force that resisted applied flexion and vice versa for applied extension.  Cripton et al. applied moments of ± 8 Nm so vertebral column loading can be expected to be smaller than the current study. Measured rod moments were small in magnitude (median moments reaching no more than 0.9 Nm), expected as they only support a portion of the load, shared between the anterior column and posterior spinal structures.  Wilke et al. (205) applied flexion (20°) and extension (-15°) to a lumbar spine, similar to the range of motions that were reached by the thoracolumbar spines in the current study, and consistently measured resultant fixator bending moments of around 1 Nm when no additional external load was applied.  Cripton et al. (166) found the implant to support only 8.7% and 8.2% of the applied moment in flexion and extension, respectively.  In both the latter and current study, static equilibrium calculations were used to Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  104 find the anterior column load and moments based on the applied moment, the force couple seen between the rod and anterior column forces, the measured rod moment, and moment supported by the posterior elements (166). These calculations assumed that together the spine and implant acted as rigid structure with no deformation of any of its components and that there was no slipping at the vertebra- screw and screw-rod interfaces.  Also assumed was that the centre of rotation of the anterior column acted at the vertebral body centre (Figure 3-8).  The location of this centre of rotation affects the moment generated by the force couple between the implant and the anterior column, found to support the majority of the applied moment in both Cripton et al.’s (166) and the current study.  Both studies measured the distance from the vertebral body centre to the fixators (a in Figure 3-8) with a mechanical caliper which introduced uncertainty to its magnitude.  The errors associated with these assumptions and this measurement may have a large effect on predictions about the load distribution across the spine and implant due to the extent of the support provided by the force couple. Cripton et al. (166) did not report any anatomic anomalies or intervertebral disc degeneration that may have affected the loading response of the functional spinal units used in their study and found the internal fixator moments to be in the same direction as the applied moment.  In the current study, however, bone spurs, fusions, or possible disc degeneration may have increased the stiffness of the spine and shifted the centre of rotation from the vertebral body centre.  An increase in spine stiffness would decrease the moment supported by the rods, attesting to the small measured rod moments, and could also substantially affect the loading response of the specimen causing varied directions of rod loading.  In general, the variability in calculated rod moments is likely a result of anatomical differences as sensitivity tests showed Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  105 that the theoretical calculations used to predict rod moments and loads from strain measurements were not affected by rod orientation on the specimen. Larger ranges of calculated rod moments and loads were found for the inferior level than the superior level, affected by the specimen condition at each level.  In a perfect system, the rod surface would have been flush with that of the pedicle screw in each of the three locations and each pedicle screw would have been rigidly attached to the rod with an equal clamping force.  If the specimen rotated purely in the sagittal plane, this would have resulted in uniform loading along the length of the rod.  However, specimen anatomy may have altered the rotation plane and caused adjacent pedicle screws to deviate from vertical alignment, resulting in slight bending of the rod when secured.  The attachment of the middle pedicle screw over-constrained the system and the order the screws were tightened and the force they exerted on the rod would likely change the contact conditions.  This meant that the rod would bend differently between the top two pedicle screws (superior level) and the bottom two pedicle screw (inferior).  The screws were always first tightened from the proximal to the distal end of the rod unless further adjustments had to be made to its rotation. Additionally, the quality of the fixation between the pedicle screws and bone is expected to affect the amount of load transferred through the screws to the rods (134), and it may be more likely to achieve good fixation in larger pedicles.  The five-segment spines used in the current study spanned different vertebral levels and although the UIV was always in the thoracic region, the lowermost instrumented vertebra varied between thoracic and lumbar and thus varied in pedicle size (100; 126).  This may have caused larger variation in fixation quality and contributed to the variation seen at the inferior level.  In general, the screw did not confidently Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  106 achieve a rigid fixation in the vertebra which would cause results to deviate from the expected response of a rod to an applied moment. Despite the anatomical variation that affected the specimen’s loading response, the design of the current study using repeated measures allowed comparison of measurements between surgical conditions.  There were no significant differences found for rod moment or load between conditions, except between conditions 4 and 5 and condition 6 for the inferior rod moment in extension but significance was only moderate.  The modest destabilization from the surgical conditions performed in the current study produced minimal observable changes in the loading response of the specimens between conditions.  Rohlmann et al. (178) found similar results when comparing fixator axial forces and bending moments in three stages of stability. Significant differences in implant loads were found between an intact spine and after destabilization with a corpectomy (removal of adjacent intervertebral discs and intervening vertebral body as far as the posterior longitudinal ligament and pedicles) but no further differences were seen after subsequent sectioning of dorsal ligaments.  During applied flexion, the measured axial force was tensile in the intact spine and compressive in both destabilization conditions, suggesting that the centre of rotation of the loaded spine was initially located anterior to the implant but after destabilization shifted posteriorly.  A corpectomy was therefore a drastic destabilization causing a large shift in load transfer across the spine and thus a large change in implant load was expected.  Similarly, Cripton et al. (166) saw significant differences in implant loading only after performing a discectomy which involved complete removal of intervertebral soft tissues and posterior elements.  Only moderate differences in loading were seen between the intact spine and after removal of only the posterior elements.  Both these studies as well as the current study reported the implant to support a small percentage of the applied load and, Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  107 consequently, it requires significant disruption to the specimen to significantly affect the load distribution across spinal structures. Similarly to rod strains, vertebral strains were variable.  Strain gauges located on the anterior surface of the vertebral bodies showed consistently higher peaks at maximum flexion and extension when compared to those located on the lateral surface.  The anterior gauges were located approximately perpendicular to the neutral axis of the applied moment and as such experienced larger compression and tension in flexion and extension, respectively, whereas lateral gauges were located near parallel to the neutral axis and therefore were strained only a small amount in either direction.  Therefore, only if the specimen experienced substantial lateral movement during flexion-extension would the lateral gauges see comparable strains to anterior gauges.  Since this was not found, specimens were taken to have minimal off-axis bending. The anterior gauge on the uppermost instrumented vertebra saw strains ranging from -584 to -5610 µε and 296  to 5012 µε in flexion and extension, respectively, and the lateral gauge of the same vertebra saw comparable variability in extension (-754 to 3251 µε).  The extent of this range of data can be explained by the differences in the strains measured by Specimen 6 at this vertebral level through all surgical conditions (Figure 3-17).  Due to the small sample size, this specimen could not be labeled as an outlier and was therefore included in the results and statistics of this study, though its anatomy may have caused atypical behaviour.  A bone spur had grown over the disc between the adjacent and uppermost instrumented vertebrae, possibly causing the adjacent level to move with the instrumented segments below it.  However corresponding gauges between the two vertebral levels were not found to measure similar strains. Other factors that affect the strain magnitude are gauge position and the quality of the bond between gauge and bone surfaces.  However, it would be expected that failure to achieve either Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  108 of these would cause lower strains whereas Specimen 6 actually saw increased strain when compared to other specimens.  The centre of rotation of the specimen may have been affected and if it the periphery of the spine supported more of the load, the strain seen on both the anterior and lateral vertebral body surfaces would have increased.  It is therefore expected that general anatomical differences of Specimen 6 culminated in a unique response to loading when compared to the other specimens tested in this study and it is unknown if this response would remain unique with a larger sample size.  Vertebral strain was found to depend on surgical condition for all but the uppermost instrumented vertebra lateral gauge.  In general, the adjacent gauges saw the most significant differences after destabilization of both the posterior and anterior ligaments, possibly correlated Figure 3-17:  Measured Vertebral Strain for each specimen through each condition for (a) the Uppermost Instrumented Vertebra Anterior gauge (UIV-A) in maximum flexion, (b) the Uppermost Instrumented Vertebra Anterior gauge (UIV-A) in maximum extension, and (c) the Uppermost Instrumented Vertebra Lateral gauge (UIV-L) in maximum extension.  Large differences in strain magnitude can be seen for Specimen 6 compared to other specimens which could be a result of specimen anatomical differences or poor bonding or positioning of the Anterior and Lateral gauges on the UIV for this specimen. (a) (b) (c) UIV ANTERIOR (FLEXION) UIV ANTERIOR (EXTENSION) UIV LATERAL (EXTENSION) Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  109 with the significant increase seen in sagittal range of motion in the same condition (Figure 3-16). The increased range of motion of the specimen could translate to increased strain seen at the adjacent vertebra as it is free from instrumentation and is likely to generate the majority of the motion when compared to fixed inferior levels.  At the uppermost instrumented vertebral level, the strains were significantly different in the Intact condition, a finding that was expected for both gauges at this level and for both flexion and extension though it was only found for the anterior gauge in extension.  Upon instrumentation, load-sharing between the vertebra and the rod may decrease vertebral strain at this level.  There was significantly more overall range of motion in the intact condition which would translate to higher strains seen in all vertebral levels. Applying a larger moment would have increased the vertebral strain response and may have better illustrated the effect of condition on strain with marked differences between levels. Most known studies applied pure compression or combined compression-bending so it is not possible to directly compare strain magnitudes with the current study.  Frei et al. (158) applied combined bending-compression of up to 10 Nm to functional spinal units with anterior and lateral vertebral rim strain gauges.  During flexion, they found axial strains of  -230 and -80 µε for anterior and both lateral gauges, respectively and during extension, strains were 300, -50, and 20 µε for anterior, right lateral, and left lateral gauges, respectively.  They found flexion and extension to affect the axial strain of the anterior gauges and the shear strain of the lateral gauges which agrees well with the high anterior and low lateral strains measured axially in the current study.  The small magnitude of strains reported by Frei et al. is likely due to the small degree of motion observed in the functional spinal units as a result of constraint put on the specimen from the compressive component of the applied combined compression-bending (158). Higher vertebral strain magnitudes were expected in the current study due to poor bone quality Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  110 of the specimens as osteoporotic bone would deform more under the same loading, increasing vertebral body surface strains.  Similarly, disc degeneration was seen in many specimens and may have increased the peripheral loading of the vertebrae.  Vertebral strain trends and reported variability in strain response to loading were similar between studies.  The extent of the variation in strain measurements with different loading conditions is evident in Table 3-6, showing a summary of peak vertebral surface strains found by a number of researchers. Frei et al. also reported poor correlation between disc pressure and maximum strain measured on a fourth gauge placed the endplate (158).  Strain measured on vertebral bodies is subject to variations in specimen geometry and material properties that would affect the response to an applied mechanical load.  Conversely, healthy intervertebral discs behave hydrostatically and are therefore insensitive to compressive loading type.  An applied eccentric load to a functional spinal unit will be evenly distributed across a healthy disc while the vertebra will experience asymmetrical loading based on the location of the applied load and transfer through its trabecular structure.  The extent of dependence on specimen properties that are variable in nature and highly influenced by the degenerative state of each structure explains the difficulties found when attempting to calibrate the vertebral strain gauges to predict vertebral loads (Appendix G).       Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  111 Table 3-6:  Peak strains measured at various sites on vertebral body surfaces subject to the corresponding loading condition. Study and gauge site Load application Peak vertebral surface strain Flexion Extension Compression Linders, 2007 (159)– lumbar lateral 5.8 Nm  400 N -50 µε  4.0 Nm 400 N -220 µε Hongo, 1999 (157)– thoracic anterior   490 N -260 µε Shah, 1978 (156)– thoracic anterior   1470 N -400 µε Frei, 2002 (158) – lumbar anterior 8 Nm  400 N -230 µε  8 Nm 400 N -200 µε Current study – thoracic anterior 10 Nm   -1500 µε  10 Nm  2300 µε  To the author’s knowledge, the range of motion of five-segment human spines with and without instrumentation has not been explored.  It is important that quantitative comparisons of specimen kinematics remain strictly between studies using segments of the same length and similar loading patterns.  Two studies found the intersegmental range of motion of the same motion segment to increase from multi-segmental to functional spinal units of sheep and porcine specimens (206; 207).  The number of fused segments spanned by instrumentation also affects the intersegmental range of motion as Untch et al. (211) reported a 15% increase in angular motion of the adjacent segment of a L4-L5 instrumentation to a L4-S1 instrumentation. Conversely, the range of motion decreased at L4-L5 and L5-S1 levels with the longer instrumentation.  Cripton et al. (166) reported decreases of 68% and 59% in flexion and extension, respectively, after the addition of the fixator to functional spinal units while Kuklo et al. (212) reported a decrease of 84% in combined flexion-extension after the addition of instrumentation to a nine-segment thoracic spine.  The current study found the overall range of motion of the superior segment after instrumentation to decrease 40% and 42% in flexion and extension, respectively, and though smaller the difference was still found to be significant between many of the surgical conditions (Figure 3-16).  All but Kuklo et al. (212) reported Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  112 intersegmental rotation only and how this extends to overall specimen range of motion is unknown.  Further, direct comparison of kinematics between the current study’s five-segment thoracolumbar spine and Kuklo et al.’s nine-segment thoracic spine may not be accurate as the loading response may differ across regions of the spine. An additional finding of this study beyond the initial research objectives was noted; in the majority of specimens and conditions, the measured rod strains showed the opposite trend to that expected, ie. the strain gauges on the posterior border of the rods measured compression during applied flexion and tension during applied extension. Rohlmann et al. (84) found similar results when measuring in vitro loads and moments on internal spinal fixation devices subject to flexion-extension loading (6.6 Nm).  Five specimens were used with one vertebra spanned by the fixators and each spine was loaded in both an intact state and after a corpectomy.  When the intact spine was loaded in flexion, the rods experienced tensile forces and bending moments varied between flexion and extension (Figure 3-18).  Similar bending behaviour was found in extension but measured axial forces were compressive.  It wasn’t until a corpectomy was performed that the rods gave the expected loading response with bending moments strictly in the direction of the applied moment.  The small magnitude and direction of these bending moments agree well with the current study and confirms the variable nature of the loading response of cadaveric spines to flexion-extension loading. When Rohlmann’s fixators were placed in patients and loaded in vivo (84), the average measured bending moment magnitudes were higher than the intact in vitro spines (1.3 to 6.4 Nm) but experienced the same variability in terms of sign; some patients’ fixators saw both flexion and extension bending moments during the same flexion activities performed at two different Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  113 visits, for example.  In general, flexion bending moments and axial compression were almost always measured in vivo during both flexion and extension.  The differences seen between in vitro and in vivo results attest to the importance of the contribution of muscle forces and surrounding spinal structures on spine and implant loading, a limitation of both Rohlmann et al.’s and the current study.  Figure 3-18: Published resultant axial force and bending moment in flexion and extension.  Maximum axial force component Fz and maximum bending moment Mb,sag in the sagittal plane measured in the fixators for (a) flexion loading, and (b) extension loading.  The maximum (triangles) and minimum (dots) values are given.  Negative forces = compression, negative bending moments = flexion.  Modified from Rohlmann et al., 1997 (84) with permission from Elsevier. To determine if the rod loading results seen in the current study were caused by the study design and execution or by the specimen itself, a subsequent pure flexion-extension bending test was designed using Specimen 6 in its Anterior Ligament Destabilization condition (Condition 6) with three additional states of destabilization (Figure): State A, where the pedicle screws of the left rod were cemented and otherwise specimen was in Condition 6 (± 5 Nm applied); State B, where the pedicle screws of both the left and right rod were cemented and the posterior elements and facet joints of the UIV were removed (± 5 Nm applied); State C, where the UIV disc and endplate was subsequently removed (± 3 Nm applied).  Details pertaining to these additional Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  114 tests are included in Appendix L.  In State C, the strain gauges on the posterior border of the rods reversed signs and measured tension during applied flexion and compression during applied extension.  This translated to calculated rod moments where only after complete removal of the posterior and anterior structures did the calculated moments coincide with the applied moment. Many compounding factors could have played a role in the resulting loading response of the instrumented specimens used in the current study.  There was an increase in strain response seen after the pedicle screws were cemented that suggested that the strength of the fixation between the pedicle screw and vertebra is important and if there is movement at this interface, the rods may not provide the desired support for the vertebral column during bending.  If there was not a rigid fixation between the screw and vertebra, under an applied bending moment the vertebral column may have rotated independently of the screw, causing a resultant upwards force of the screw on the vertebra.  If this alone had been the cause of the opposite sign of the measured rod moments, it would have been expected that cementing the pedicle screws into the bone would have given the opposite response.  However, since this was not the case, other confounding factors must exist and since cementing is rarely used in a clinical scenario (213), it is advised to only use this approach when necessary, such as for fatigue or other high-cycle tests. The set screws used in this study were designed to have a point at their centre to create a point contact with the rod upon tightening.  Each poly-axial screw could be tightened to the rod at a different angle, possibly resulting in disparity between the location and extent of contact on each rod.  Rod loading is affected by the clamping forces between the screws and the rods (83) and asymmetrical mounting of the rods (214).  The effect of ambiguity at these interfaces on rod strains and off-axis loading requires further investigation with studies that change only the screw-rod contact points while keeping specimen loading and condition constant. Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  115 Consistent rod strains through the removal of posterior elements and facet joints in both flexion and extension suggest minimal contribution of these structures to rod loading while the changes seen after removal of the intervening disc suggest the opposite.  This agrees well with the reported findings of Rohlmann et al. (178) and Cripton et al. (166) discussed previously, where implant loading was affected only after removal of the disc and anterior column structures.  It is known that load is distributed evenly throughout a healthy disc, regardless of the loading mode, while uneven load distribution occurs in degenerated discs (141; 144; 145; 148). Butterman et al. (145) found degenerated discs to have an asymmetrical response to a compressive load when the spine was induced with a scoliotic curve (Figure 3-19).  Extending this to the current study, if the intervertebral discs were degenerated, they may have responded asymmetrically and caused loading out of the plane of bending under an applied flexion- extension moment.  Similarly, if the spine was fused or if bone spurs had grown over one side of the intervertebral disc at any level, spine stiffness would have increased and may have caused increased resistance to bending.  The combination of all of these confounding factors may result in rod bending in directions other than the applied moment.  Supplementary tests that isolate each factor to determine its effect on rod loading, such as comparing loading of known healthy to degenerated discs, are required to determine the basis for the loading results found in the current study. Chapter 3: In vitro pure moment loading investigation with instrumented multi-segment adult spines  116  Figure 3-19: Intradiscal pressure profiles for degenerated discs (L4-L5) in neutral (left) and scoliotic (right) postures.  Highest to lowest pressure profiles are for compressive loads of 1500 N, 1000 N, 500 N, and 0 N, respectively.  Pressure profiles of the healthy disc were symmetric and independent of curvature, demonstrating its hydrostatic nature.  Those of the degenerated disc had lower pressure in the nucleus in the normal curvature and asymmetric loading with induced scoliosis, demonstrating possible structural as opposed to fluid (hydrostatic) load transmission. Reprinted from Butterman et al., 2008 (145) with permission from Wolters Kluwer Health. This in vitro investigation provided insight to spine loading at the proximal junction and at vertebral levels instrumented with a posterior construct for the treatment of sagittal imbalance. The applied pure flexion-extension moment simulated the additional kyphosing moment that occurs in patients with non-functional extensor muscles prior to or after surgical correction and as such, measurements represented the strain and loading to which the spine would be subject in addition to those caused by normal body-weight loads.  Some observations of this study warrant further analyses but even with the limited number of specimens available, insight was provided with respect to the factors of more and lesser importance when predicting the likelihood of failure at the proximal junction.  Chapter 4: Conclusion  117 Chapter  4: Conclusion 4.1 Summary of Thesis Intervertebral compressive loading of sagittally-imbalanced spines was predicted using an equilibrium statically-determinate model and an in vitro investigation, considering clinically relevant patient and surgical variables and surgical conditions.  Seven spinal deformity patients were studied and peak intervertebral compressive loads were consistently found in the lower thoracic spine, regardless of the uppermost instrumented vertebra or the surgical outcome of the patient.  Post-operative loading was not found to depend on the osteotomy level but increased up to 42% after extensor muscle loss when the spine was instead balanced by a posterior implant. As it was not possible to properly account for muscle function loss using the equilibrium model, an in vitro study was designed to simulate the resulting kyphosing moment (pure flexion- extension) and predict the distribution of the additional loads supported by an instrumented spine without extensor muscles.  Six surgical conditions of clinical relevance were performed, reporting changes in implant loads and moments, proximal junction vertebral strains, and overall spine kinematics.  Surgical condition was found to significantly affect vertebral strains at most sites and spine kinematics but rod loads and moments remained relatively constant.  Load- sharing between the implant and the anterior column was predicted with intervertebral static equilibrium and it was found that the force couple created between the anterior column and the implant supported the majority of the applied moment.  The distribution of the applied moment across spinal structures depended on the direction and magnitude of the measured rod bending moment, and varied substantially between specimens.  Good agreement was found between the anterior column loads predicted using the model and in vitro experiment.  Chapter 4: Conclusion  118 4.2 Integration of Mathematical and Experimental Studies The biomechanical equilibrium model was developed as an introduction to pre-operative planning, specialized to each patient’s presenting case.  Resultant intervertebral compressive loads were predicted along the length of the spine and provided information about the construct length that minimized load as well as indicating how these loads changed with corrective osteotomies in three different locations.  These predictions were made assuming an ideal scenario where extensor muscles were able to provide complete counteraction to the body-weight loads that fall anterior to the spine in most sagittal profiles, deviating further from the spine as positive sagittal balance becomes more severe.  The increase in predicted compressive load when the muscle force was removed from the model and replaced with a vertebral column or rod force indicated a need to further study the effect of lost muscle function in a controlled experiment. The in vitro study was first designed to predict the additional loading on the spine and instrumentation when extensor muscle loss generated an unbalanced kyphosing moment, and second to predict the change in loading after controlled and progressive destabilization, two questions that could not be addressed by an equilibrium model. The resulting kyphosing moment created by body-weight loads varied between patients and their respective sagittal profiles, peak moments ranging from 10 Nm to 22 Nm.  Applying the high end of this range to a cadaveric spine was expected to cause damage and, as it was important to maintain specimen integrity between conditions, ±10 Nm was applied.  This means that loading predictions from the in vitro study were underestimates of the loads that may be seen in vivo in some sagittal deformity patients. Using sagittal profiles from radiographs taken immediately after posterior instrumentation, the model predicted up to a 42% increase in peak predicted compressive load Chapter 4: Conclusion  119 from a scenario where an extensor muscle group was still capable of maintaining balance to when muscle loss required equilibrium to be established with the posterior rod.  This translated to a median difference of 140 N between full and no muscle function.  The comparable scenario in the in vitro study was the anterior column loads predicted in the Intact Instrumented condition which reached comparable values to the model based on Figure 3-15, summarized again in Table 4-1.  The maximum loads predicted at both the superior and inferior levels for flexion loading are shown for the experimental study and represent the additional resultant compressive loads on the vertebral column with a loss of muscle function.  For the model, the value in Table 4-1 represents the mean peak difference between the predicted compressive load in the immediate post-operative profile before and after muscle loss.  The corresponding median moment generated by body-weight loads was 8.4 Nm.  In general, these magnitudes agree well but comparison between the results of the equilibrium model and experimental study must remain relatively qualitative as variability in patients and specimens reduces the reliability of the resulting load magnitudes.  Conducting an extended study that analyzed larger in vivo and in vitro populations would allow direct comparisons between the two data sets, providing a stronger means of validation of the model and understanding of loading patterns before and after muscle function loss. Table 4-1: Median (and range) of predicted anterior column compressive loads from both the experiment and the equilibrium model.  Experimental loads represent the intact instrumented condition and the model load is the mean of the peak difference between muscle function and no muscle function in the immediate post- operative sagittal profile across all patients. Experimental Study Equilibrium Model Superior Inferior -146 N (-82 to -219 N) -269 N (-97 to -410 N) -140 N (-107 to -271 N)  Ultimately, it is then of interest to use intervertebral loading predictions to anticipate the likelihood of surgical failure, requiring a further understanding of compressive tolerances of the Chapter 4: Conclusion  120 spine.  Vertebral strength is correlated with many material and geometric factors such as bone mineral density, bone mineral content, vertebral trabecular density, and cross-sectional area (88; 215) and is also affected by loading mode (91) so predicting failure load of sagittal deformity patients who often exhibit atypical values of all of these factors is difficult and could be inaccurate.  The variation in failure load predictions was summarized by Singer et al. (88) who also introduced another confounding factor of loading rate (Figure 4-1). Regardless of the inconsistency in data, it can be seen that vertebral failure loads are on the order of kN.  The current study found compressive loads resulting from body-weight loads and spinal deformity to reach over 700 N (Table 2-3) and the additional loading that results from loss of muscle function to reach over 200 N (Table 4-1), totalling near 1 KN.   Based on these magnitudes and the failures most commonly involved with PJK, ie. vertebral endplate fracture and screw pull-out, the mechanism of failure is likely one of repeated loading occurring at only a fraction of the vertebra’s compressive strength (216; 217).  Additionally,  in circumstances when muscle loss is combined with positive sagittal balance, failure likely results from a combination of compressive and bending so flexural rigidity and bending strength need to also be considered.  When loading vertebral bodies in axial compression and pure bending, Crawford and Keaveny (89) found the vertebral body’s axial rigidity is only moderately predictive of its rigidity in sagittal bending, suggesting that thresholds to both loading modes need to be considered when predicting vertebral strength. A further in vitro study that loads similar multi-segment instrumented spines to failure in compression-bending or fatigue testing would help identify vertebral load thresholds that could be compared to the combined compressive loading predictions from the current study’s model Chapter 4: Conclusion  121 and experiment.  Assessment of failure risk could then be made for each individual’s pre- and post-operative case, advancing the clinical relevance of the current research.  Figure 4-1:  Summary of published segmental trends in vertebral compressive strength for isolated thoracic and lumbar vertebral bodies, showing a general caudal trend for increasing capacity to sustain load despite differences in loading rates.  Data is reported for Messerer , Sonoda, Gozulov, Kazarian, Brassow, Edmonston, and the current study.  Reprinted from Singer et al., 1995 (88) with permission from Elsevier. 4.3 Study Relevance and Applications of Research Findings Biomechanical understanding of spine loading, specifically at the proximal junction, has become of increasing concern in the clinical community.  Due to the consistency of surgically corrected spines failing at the proximal junction, insight into possible predictors is of interest to ultimately guide surgical procedures in the direction of successful outcomes. Patient variability is the ultimate challenge for a surgeon and can be the distinguishing factor between a successful and failed surgery, keeping all techniques and instrumentation consistent. The mathematical model developed in the current study provides means to conduct initial biomechanical assessments of each patient and predict loading that would result from constructs Failure Load [kN] Chapter 4: Conclusion  122 of various lengths, helping to plan surgical approaches based on individual pre-operative sagittal profiles. The importance of osteotomy location and the effect of muscle atrophy or damage when determining a patient’s initial outcome and recovery rate have been questioned clinically. Mathematical simulation addressing both concerns suggested osteotomy location is insignificant to spine loading but confirmed the importance of muscles in maintaining balance and stability and reducing spine loading. Other factors under the surgeon’s control have also been suggested to affect success rate, such as adjacent facet violation and spinal ligament disruption, both of which are common occurrences during an instrumented spinal fusion operation.  The proximity of the pedicle to the supra-adjacent vertebra’s facet is such that the pedicle screw often breaches the facet joint, the extent of which is predetermined by each patient’s anatomy; surgeons are apprehensive of spine instability when injury occurs at the proximal junction and question if this predisposes the patient to PJK.  Medial and full bilateral facetectomies were performed in vitro to simulate this injury in a controlled fashion but neither were found to significantly affect proximal junction vertebral strains, implant loading or specimen range of motion.  It is possible, however, that facet destabilization may have a larger effect on intervertebral shear loading, a question outside of the scope of this study. Ligament disruption, on the other hand, often occurs with correction techniques such as laminectomies or vertebrectomies or when sagittal imbalance is a result of fracture dislocation. In vitro simulation of these scenarios involved destabilizing the supraspinous and intraspinous posterior ligaments followed by the anterior longitudinal ligament, both of which significantly affected vertebral strains and specimen flexibility. Chapter 4: Conclusion  123 The in vitro study was designed to directly address concerns suggested by surgeons as possible contributing factors to PJK.  Results of the study suggest that ligament preservation intra-operatively may be important given the combined muscle damage that is incurred.  Other patient and surgical factors not addressed in the current study may also be accountable for surgical failure such as proximal rod stiffness, quality and type of fixation, and bone quality, requiring further in vitro testing. 4.4 Study Strengths and Limitations 4.4.1 Strengths Both the mathematical model and in vitro portions of this study were developed with direct communication with and frequent feedback from spinal surgeons.  Together, these studies aimed to address the topics most often discussed in the operating room and at clinical conferences worldwide, specifically the occurrence of PJK and its common predictors. To the author’s knowledge, the intervertebral loading patterns of adult deformity patients have not been studied biomechanically.  Numerous researchers have developed geometric (29; 41) and spine loading models (43; 96; 97; 118) based on healthy spines from which intervertebral compressive loading predictions were reportedly lower than those predicted for the deformed spines in the current study.  Even the elderly spines studied by Briggs et al. (98) presented with modest degrees of kyphosis and therefore may not have been representative of spines requiring posterior fusion surgery.  The findings of the current study’s spine loading model provided novel insight to the increased loading of deformity patients and, with clinical collaboration, were further developed to predict loading changes caused by patient and surgical variables understood to have a role in PJK, neither of which having been studied previously. Chapter 4: Conclusion  124 Clinical research has studied correlations between numerous patient and surgical parameters (10; 44; 46; 48; 179; 180; 218; 219) but provide only retrospective information on surgical outcome.  The type, size, and location of corrective osteotomy (42; 69) as well as the patient’s muscle function (182; 184; 187; 188) have been identified as important factors to consider before operation and the current study introduced the first known biomechanical approach to pre-operatively predict their effects on spine loading. The in vitro investigation, designed to give further insight on a loading scenario of patients with decreased muscle function, was novel in its approach to instrument multi-segment thoracolumbar spines leaving a cranial vertebra free to fully represent the proximal junction. This allowed comparison between the vertebral strains of the uppermost instrumented and adjacent vertebrae.  Previous research on the intervertebral loading of human cadaveric spines has used single (166) or short-segment spines (84) or has reported strictly intradiscal pressure (220), a parameter with notable unreliability in cadaver specimens (145; 148).  The current study applied a pure moment to simulate the kyphosing moment created by body-weight loads in a scenario of complete muscle function loss.  The experimental design was such that the ±10 Nm pure bending moment was applied equally to each vertebral level.  Combined compression- bending has been used previously (84; 168) but creates difficulty in interpretation of the intervertebral load response to each loading type.  The current study benefitted by determining loading patterns strictly due to the additional kyphosing moment, augmenting its clinical utility. The design of the current study incorporated a repeated measure of vertebral strain, rod strain, and overall specimen rotation across six specimen conditions.  The repeated testing allowed each specimen to act as its own control, minimizing the effect of specimen variability on Chapter 4: Conclusion  125 the results.  A one-way repeated measures design could then be used in which surgical condition was tested on a single specimen for each parameter measured. 4.4.2 Limitations 4.4.2.1 Equilibrium Model Limitations of the developed equilibrium model reside in areas of patient population, radiographic measurements, and model assumptions.  There was large variability in patient age, diagnosis, surgical history, and pre-operative sagittal profile (Figure 2-5) and four of the patients were referred to VGH from other institutions for a revision operation without radiographs documenting complete surgical history.  Three-foot lateral standing x-rays were required for full- spine analysis which became a limiting factor in the collection of suitable subjects for the model as this was not standard practice at VGH.  Collaboration with other institutions that collect three- foot standing x-rays paired with stricter inclusion and exclusion criteria could help to build a sufficient study population from which spine loading patterns could be reliably analyzed with the developed equilibrium model. Another limitation arises from the use of radiographic digitization to locate vertebral body positions.  Although technicians mandate standard x-ray image collection procedures between patients, such as directives on foot, arm, and shoulder positioning in standing lateral x-rays, it is difficult to control the degree to which each patient follows these instructions.  Angles of the ankles, knees, hips, and arms and segmental movement of the spine to achieve a desired standing position can easily differ between patients, variations that were found to translate the sagittal vertical axis (221; 222).  Out-of-plane curvatures would also change the apparent position of vertebral bodies as seen on two-dimensional radiographs.  These inherent errors in standing lateral radiograph methodology must be considered when deducing spinal balance parameters of Chapter 4: Conclusion  126 sagittal deformity patients.  Enforcing stricter protocols that standardize joint angles before x-ray collection could aid in reducing ambiguity in measurements taken from x-ray images.  However, there is also human error that arises from the measurements themselves as vertebral body borders are often unclear, especially in the thoracic spine where ribs limit visibility.  In this study, the same person made all radiographic measurements which improves the repeatability of the data collection and small differences in vertebral body coordinates were found to have a minimal effect on the predicted spine loads. The accuracy of the spine loading calculations themselves and the degree to which they represent the in vivo situation are limited to the inherent assumptions of the model.  A static two- dimensional simplification, in which equilibrium was found between combined contributions of the head, arms, and trunk and a single grouped extensor muscle, was used to represent a dynamic three-dimensional structure that maintains balance through contributions from a number of surrounding tissues.  Forces generated by these tissues do not act as point loads along straight lines of action, as was assumed in the model.  Also, the individuality of body-weight load magnitudes was not accounted for having used previously reported ratios (110; 123; 203), though they were scaled to total body-weight and posture.  Extensor muscle moment arm was approximated as the distance between the disc centre and the spinous process (123) and was assumed constant through all sagittal profiles, though known to decrease with kyphosis (183) and torso flexion (131).  Many researchers have used two-dimensional spine loading models (96; 98; 118; 123) and have proven to predict comparable compressive loads to three-dimensional models (Table 1-1).  Further, with the intention of providing information about global spine loading patterns, an intricate three-dimensional muscle model was unrealistic and not only outside the Chapter 4: Conclusion  127 scope of this study but also unnecessary considering the macroscopic nature of the study objectives. 4.4.2.2 In Vitro Investigation A major contributor to the variability of the data obtained in this study is the number, variability, and quality of the specimens used.  Different segments were used and the spines varied in size which may have had an effect on fixator loads as they are dependent on instrumented segmental level, distance of the fixator rods to the spinal column, and the bone quality of instrumented segments (205).  Specimen age ranged from 63 to 79 years and of the six specimens that were available, the surgeon performing the surgical conditions noted poor or uncertain disc quality in at least four.  A number of specimens also had natural bony fusions between at least two vertebrae that limited the intervertebral mobility at these levels.  Others had osteoporosis such that it was difficult to ensure rigid fixation of the bone to the potting and pedicle screws. In these cases, PMMA was first inserted into the vertebrae before screws were affixed.  Care was taken to avoid penetration of the PMMA into the adjacent intervertebral disc so its insertion was not expected to affect the loading response of the specimen.  The conditions of specimens likely caused increased stiffness and abnormal loading responses and, although spinal deformity patients are mostly high in age, using younger healthy cadaveric spines would minimize the number and effect of confounding factors in the experiment.  Porcine spines were also considered as they exhibit better disc and bone integrity resulting in more reliable loading measurements.  However, significant differences were reported between porcine and human spines in terms of thoracolumbar anatomy (223; 224; 225) and mechanical loading behaviour (226), ultimately jeopardizing the clinical utility of the study. Chapter 4: Conclusion  128 Other limitations of this study were in the areas of experimental design, implementation, and measurements.  In this study, a pure moment was applied to replicate a kyphosing moment on the spine with no extensor muscle function and no other muscles forces were simulated.  This is a common simplification used in in vitro investigations to simulate physiologic loading.  Wilke et al. (227) evaluated in vitro loads in Rohlmann’s internal fixators (83) during pure moment loading and found comparable loading patterns to in vivo fixator data, partially attributing differences to the fact that muscles were not simulated.  Muscle forces, neglected in many studies, have been shown to have a strong influence on the implant load (228; 229; 230; 231). Wilke et al. (205) simulated the erector spinae and rectus abdominis muscles in an in vitro flexibility investigation.  Intradiscal pressures agreed well between the young specimens and volunteers but anatomical variation at the instrumented level and the lack of intra-abdominal pressure in vitro caused varied fixator loads (205).  Attempting to replicate physiologic muscle forces with multiple insertion points, lines of action, and degree of exertion is difficult and creates its own limitations; it is necessary to simplify in vitro investigations to ensure repeatability and to allow sound conclusions to be drawn. The study design was load-controlled such that the pure moment applied to the superior vertebra was applied equally to all segments of the specimen and remained the same throughout spine rotation.  This Flexibility method is commonly used to obtain spine loading characteristics as they change with clinically relevant surgical or injury conditions (150; 232) but can not evaluate adjacent-level effects.  The magnitude of the pure moment applied along the length of the spine is unaffected by an alteration to the specimen, such as the addition of posterior instrumentation, and therefore the loading response of non-operated spinal levels remains unchanged across specimen tests (233).  To study adjacent-level kinematics and loading, Chapter 4: Conclusion  129 displacement-controlled tests have also been attempted by rotating the spine to a desired displacement while measuring the load (149; 234).  This method introduces difficulties when attempting to define the rotation axis of the specimen and how it changes as the spine deforms, and often results in applying constrained, non-physiological rotation (233).  In both methods, the resulting loading response of the adjacent vertebrae is pre-determined by the test design so deduction of true changes in loading parameters resulting from instrumentation and different surgical conditions is not possible.  Panjabi et al. (233) developed a hybrid test method whereby a pure moment is first applied to the intact specimen and the total range of motion of the spine is measured.  Second, the spine is instrumented and subjected to increasing pure moment until the same range of motion is achieved, measuring changes in parameters between intact and instrumented states.  Though avoiding the limitations associated with load- and displacement- controlled methods, the Hybrid method introduces complexity to the protocol and as adjacent level changes did not directly address the objectives of the current study, the Flexibility method was instead deemed suitable. A follower load, not used in this study, has been reported to render spinal loading with pure moments more physiologic by accounting for the compression on the spine due to body-weight loads (151).  However, the addition of a follower load was found to only increase intradiscal pressure and not significantly change intersegmental rotation in flexion-extension (151).  In the current study, the added response of a follower load would increase the spine load magnitude equally across all conditions and would not provide further insight as this study was concerned with the additional load caused by the applied moment. During the application of a pure flexion-extension moment, only in-plane (sagittal) moments were recorded and only uniaxial strains were measured in both the vertebrae and rods. Chapter 4: Conclusion  130 A separate test was conducted with a six-axis load cell that confirmed that the loading apparatus applied minimal off-axis loading (Appendix F) and as such, off-axis strains were taken to be minimal.  Cripton et al. (166) oriented strain gauges such that they acted as a six-axis load cell to fully describe 3D fixator force and moment and found that in flexion-extension, the dominant measured fixator forces and moments occurred in the cranial-caudal direction and in the sagittal plane, respectively, a similar finding to Rohlmann et al. (178). This justifies the use of uniaxial strain gauges in the current study. The reliability of the strain gauge measurements depended on the quality of the alignment and bond to bone and titanium rod surfaces.  Strict procedures were followed in each case and specific bonding and protective materials were used according to the specific application, provided by Micro-Measurements (Vishay Measurements Group, Inc., Raleigh, NC) and previous studies (235).  However, alignment accuracy was subject to human error and a strain gauge would underestimate bone and rod strain if its neutral axis strayed far from the longitudinal axis.  The orientation of the gauges 120° circumferentially around the rod was of special importance to meet the condition for proper use of Tuttle’s theoretical calculations for loading in a cylinder (209).  An experienced electronics technician affixed all gauges to both pairs of rods to ensure utmost care and attention was paid to gauge alignment. Even with proper alignment and bonding of the strain gauges on the rods, however, the signal remained small during the application of a flexion-extension moment and experienced a considerable amount of noise.  This was expected as the stiffness of titanium would limit its motion during modest bending and the distribution of the load across spinal structures creates variable rod loading when compared to a scenario when only the rod supports the load (compare Figure L-2B and C). Chapter 4: Conclusion  131 Bone strain gauge measurements are also influenced by numerous environmental and anatomical factors such as temperature, surface preparation, water resistance, and bone quality (235), all but the latter of which can be minimized by careful preparation and application techniques.   It is expected that the degree of strain transferred to the vertebral surface remains consistent throughout tests regardless of the specimen’s bone quality and since this study was interested in the change in vertebral strain between conditions, variable bone quality should not largely affect strain gauge data. In the current study, raw vertebral strain measurements were reported and were not used further to predict vertebral forces or moments.  Although this would have been relevant data pertaining to the objectives of the in vitro study, calibration of measured strains was found to give inaccurate and unreliable vertebral load results.  Discussed in Appendix G vertebral bodies did not have a linear strain response to an applied moment, a relationship that is required for use of the matrix method (177).  There have been a number of researchers who have similarly reported vertebral strain when vertebral loading would have provided additional insight to their study objectives pertaining to spinal mechanics (156; 157; 158; 159).  Linders et al. (159) aimed to deduce spinal loading from vertebral body surface strain measurements by correlating measured strain to applied loads.  Although they found this relationship to be linear, only applied loads were used for correlation giving no further indication of the loads supported by the vertebral column only. 4.5 Future Work To be able to draw sound conclusions on the questions asked in both the model and the cadaver experiment, it would be ideal to study patients and specimens, respectively, with stricter inclusion criteria and known histories.  A larger specimen population screened for disc and bone Chapter 4: Conclusion  132 quality would also allow the development of strain and loading patterns and, by minimizing anatomical variability, the deciphering of true outliers. It would also be clinically important to use further in vitro investigations to determine the effect of instrumented spine loading with the application of a shear load, a condition that is expected to be more substantially influenced by injury to the facet joint.  Also, having seen that segmental motion is greater at the free vertebra adjacent to instrumentation, a possible contributing cause to PJK, it would be interesting to study the effect of rods with transition materials, different diameters, or dynamic systems to smooth the transition between the uppermost instrumented vertebra and the adjacent segment, questions previously addressed by other researchers (173; 236; 237). Considering the common failure mechanisms of PJK, including superior endplate fracture or screw pull-out at the uppermost instrumented vertebral level and vertebra fracture or listhesis at the adjacent vertebral level, other contributing factors to failure have been addressed clinically. Pedicle screw loading and movement within the vertebra, vertebral endplate loading, and intersegmental motion at the proximal junction are clear factors that may directly affect failure at the proximal junction, all of which have been addressed to some extent in previous studies but that require further investigation (134; 142; 147; 158; 169; 170; 220; 238). Further research into the spine musculature is being conducted in this lab by means of a three-dimensional finite element model with muscles that will provide insight into the mechanical loading and strength of the spine when subject to a variety of loading scenarios.  Due to the added degree of detail with the inclusion of muscles, the study will first be concerned with localized spine loading of an instrumented functional spinal unit but, once validated, will later extend to global loading along the length of the spine. Chapter 4: Conclusion  133 With reference to the objectives of the current study, it was found that: 1a)  intervertebral compressive loads decreased after surgery in cases where sagittal balance was restored and increased with subsequent progression of the deformity and after proximal junctional kyphosis, 1b)  osteotomy location did not largely affect spine loading but extensor muscle loss significantly increased intervertebral compressive loads at all levels, 2a)  the force couple created between the anterior column and the spinal implant supported the majority of the load in a case where muscle loss was simulated by applying a pure moment, and 2b)  the chosen surgical conditions did not largely affect spine loading; more drastic destabilization or alternative loading is expected to have a more significant effect. The long-term objective of this research is to provide surgeons with a means of biomechanically analyzing each patient before operation to plan an individual correction technique most suited to minimize the likelihood of PJK or related failures.  Attaining a comprehensive understanding of PJK requires continued collaboration of research across scientific and clinical institutes.   134 References 1. Age and Sex. Statistics Canada, 2010. (Accessed December 5, 2011, at http://www12.statcan.gc.ca/census- recensement/2006/rt-td/as-eng.cfm.) 2. Howden, LM and Meyer, JA. Age and Sex Composition: 2010. 2010 Census, 2011. (Accessed December 5, 2011 at http://www.census.gov/prod/cen2010/briefs/c2010br-03.pdf.) 3. Aebi, M, Gunzburg, R and Szpalski, M. The Aging Spine. Berlin : Springer, 2005. ISBN 3-540-24408-5. 4. Lee GA, Betz RR, Clements DH, Huss GK.  Proximal Kyphosis After Posterior Spinal Fusion in Patients with Idiopathic Scoliosis. SPINE  1999;24(8):795-99. 5. Kim,YJ, Bridwell KH, Lenke LG, Kim J, Cho SK. Proximal Junctional Kyphosis in Adolescent Idiopathic Scoliosis Following Segmental Posterio Spinal Instrumentation. SPINE 2005;30(18):2045-50. 6. Glattes RC, Bridwell KH, Lenke LG, Kim YJ, Rinella A, Edwards C. Proximal Junctional Kyphosis in Adult Spinal Deformity Following Long Instrumented Posterior Spinal Fusion. SPINE 2005;30(14):1643- 9. 7. Kim YJ, Bridwell KH, Lenke LG, Rhim S, Cheh G. An Analysis of Sagittal Spinal Alignment Following Long Adult Lumbar Instrumentation and Fusion to L5 or S1: Can We Predict Ideal Lumbar Lordosis? SPINE 2006;31(20):2343-52. 8. Kim J-H, Kim S-S, Suk S-II. Incidence of Proximal Adjacent Failure in Adult Lumbar Deformity Correction Based on Proximal Fusion Level. Asian Spine Journal 2007; 1(1):19-26. 9. Heary, RF and Albert, TJ. Spinal Deformities: the essentials. New York : Thieme Medical Publishers, Inc., 2007. ISBN 1-58890-341-9. 10. Glassman S, Bridwell K, Dimar JR, Horton W, Berven S, Schwab F.  The Impact of Positive Sagittal Balance in Adult Spinal Deformity. SPINE 2005;30(18):2024-9. 11. Bridwell, Keith. Spinal Curves. SpineUniverse, 2011. (Accessed July 2011, at http://www.spineuniverse.com/anatomy/spinal-curves.) 12. Gelb DE, Lenke LG, Bridwell KH, Blanke K, McEnery KW. An Analysis of Sagittal Spinal Alignment in 100 Asymptomatic Middle and Older Aged Volunteers. SPINE 1995;20(12):1351-8. 13. Hammerberg EM, Wood KB. Sagittal Profile of the Elderly. of Spinal Disorders & Techniques 2003;16(1):44-50. 14. Jackson RP, McManus AC. Radiographic analysis of sagittal plane alignment and balance in standing volunteers and patients with low back pain matched for age, sex, and size: A prospective controlled clinical study. SPINE 1994;19(14):1611-8. 15. Fon GT, Pitt MJ, Thies AC Jr. Thoracic Kyphosis: Range in Normal Subjects. American Journal of Roentgenology 1980;134:979-83 16. Bernhardt, M and Bridwell, KH.  Segmental analysis of the sagittal plane alignment of the normal thoracic and lumbar spines and thoracolumbar junction. SPINE 1989;14:717-21. 17. Itoi, E. Roentgenographic analysis of posture in spinal osteoporotics. SPINE, 1991;16:50-6.   135 18. Glassman SD, Berven S, Bridwell, KH. Correlation of radiographic parameters and clinical symptoms in adult scoliosis. SPINE 2005;30:682-8. 19. Farcy JP, Schwab FJ. Management of flatback and related kyphotic decompensation syndromes. SPINE 1997;22:2452-7. 20. Potter BK, Lenke LG, Kuklo TR. Prevention and management of iatrogenic flatback deformity. Journal of Bone and Joint Surgery 2004;86-A:1793-808. 21. Simmons, EH. Kyphotic deformity of the spine in ankylosing spondylitis. Clinical Orthopaedics 1977;128:65-77. 22. Cho KJ, Suk S, Park SR, Kim JH, Kang SB, Kim HS, Oh SJ. Risk Factors of Sagittal Decompensation After Long Posterior Instrumentation and Fusion for Degenerative Lumbar Scoliosis. SPINE 2010;35(17):1595-601. 23. Kostuik, JP, Maurais, GR and Richardson, WJ, Okajima, Y. Combined single stage anterior and posterior osteotomy for correction of iatrogenic lumbar. SPINE 1988;13:257-66. 24. Drake RL, Vogl AW, Mitchell AWM. Gray's Anatomy for Students. 2nd Edition. Philadelphia, PA: Churchill Livingstone Elsevier, 2010. 25. Xray FAQ. Fitch Family Chiropractic, 2011. (Accessed December 5, 2011, at http://fitchfamilychiro.com/custom_content/c_125445_xray_faq.html.) 26. Lowe, TG. Treatment of Kyphosis and Scheuermann's Disease. Spineuniverse, Vertical Health, LLC, 2011. (Accessed December 5, 2011, at http://www.spineuniverse.com/conditions/kyphosis/treatment-kyphosis- scheuermanns-disease.) 27. Hardacker J, Shuford R, Capicotto P, Pryor P. Radiographic standing cervical segmental alignment in adult volunteers without neck symptoms. SPINE 1997;22:1472-80. 28. Briggs A, Wrigley T, Tully E, Adams P, Greig A, Bennel K. Radiographic measure of thoracic kyphosis in osteoporosis: Cobb and vertebral centroid angles. Skeletal Radiology 2007;36:761-7. 29. Singer K, Jones T, Breidahl P. A comparison of radiographic and computer-assisted measurements of thoracic and thoracolumbar sagittal curvature. Skeletal Radiology 1990;19:21-6. 30. Stotts A, Smith J, Santora S, Roach J, D'astous J. Measurement of spinal kyphosis: implications for the management of Scheuermann's kyphosis. SPINE 2002;27:2143-6. 31. Vedantam, R; Lenke, L; Keeney, J; Bridwell, K. Comparison of standing sagittal spinal alignment in asymptomatic adolescents and adults. SPINE 1998;23(2):211-5. 32. Hicks G, George S, Nevitt M, Cauley J, Vogt M. Measuremnt of lumbar lordosis: inter-rater reliability, minimum detectable change and longitudinal variation. Journal of Spinal Disorders 2006;19:501-6. 33. Korovessis P, Stamatakis M, Baikousis A. Reciprocal angulation of vertebral bodies in the sagittal plane in an asymptomatic Greek population. SPINE 1998;23:700-4. 34. Stagnara P, De Mauroy J, Dran G, Gonon G, Costanzo G, Dimnet J, Pasquet A. Reciprocal angulation of vertebral bodies in a sagittal plane: approach to references for the evaluation of kyphosis and lordosis. SPINE 1982;7:335-42.   136 35. Polly D, Kilkelly F, McHale K, Asplund L, Mulligan M, Chang A. Measurement of lumbar lordosis: evaluation of intra-observer, interobserver, and technique variability. SPINE 1996;21:1530-5. 36. Lafage V, Schwab F, Skalli W, Hawkinson N, Gagey PM, Ondra S, Farcy JP. Standing Balance and Sagittal Plane Spinal Deformity. Analysis of Spinopelvic and Gravity Line Parameters. SPINE 2008;33(14):1572-1578. 37. Jackson RP, Hales C. Congruent spinopelvic alignment on standing lateral radiographs of adult volunteers. SPINE 2000; 25:2808-15. 38. During J, Goudfrooij H, Keessen W. Toward standards for posture. Postural characteristics of the lower back system in normal and pathologic conditions. SPINE 1985;10:83-7. 39. Jackson RP, Peterson MD, McManus AC. Compensatory spinopelvic balance over the hip axis and better reliability in measuring lordosis to the pelvic radius on standing lateral radiographs of adult volunteers and patients. SPINE 1998;23:1750-67. 40. Legaye J, Duval-Beaupere G, Hecquet J. Pelvic incidence: a fundamental pelvic parameter for three- dimensional regulation of spinal sagittal cuves. European Spine Journal 1998;7: (1)99-103. 41. Yang BP, Yang CW, Ondra SL. A Novel Mathematical Model of the Sagittal Spine. SPINE 2007;32(4):466-70. 42. Ondra SL, Marzouk S, Koski T, Silva F, Salehi S. Mathematical Calculation of Pedicle Subtraction Osteotomy Size to Allow Precision Correction of Fixed Sagittal Deformity. SPINE  2006;31(25):E973- E979. 43. Keller TS, Colloca CJ, Harrison DE, Harrison DD, Janik TJ. Influence of spine morphology on intervertebral disc loads and stresses in asymptomatic adults: implications for the ideal spine. The Spine Journal 2005;5:297-309. 44. Booth KC, Bridwell KH, Lenke LG, Baldus CR, Blanke KM. Complications and Predictive Factors for the Successful Treatment of Flatback Deformity (Fixed Sagittal Imbalance). SPINE 1999;24(16):1712-20. 45. The Aging Spine: Kyphosis. Scoliosis Research Society, 2011. (Accessed December 5, 2011, at http://www.srs.org/patient_and_family/the_aging_spine/kyposis.htm.) 46. McLain, RF. The Biomechanics of Long Versus Short Fixation for Thoracolumbar Spine Fractures. SPINE 2006;31(11):S70-9. 47. Schlenk, RP, Kowalski, RJ and Benzel, EC. Biomechanics of Spinal Deformity. Neurosurgical Focus 2003. American Association of Neurological Surgeons (February 21, 2003);14(1). 48. Gilad R, Gandhi CD, Arginteanu MS, Moore FM, Steinberger A, Camins M. Uncorrected sagittal plane imbalance predisposes to symptomatic instrumentation failure. The Spine Journal 2008;8:911-7. 49. Kawakami M, Tamaki T, Ando M, Yamada H, Hashizume H, Yoshida M. Lumbar Sagittal Balance Influences the Clinical Outcome After Decompression and Posterolateral Spinal Fusion for Degenerative Lumbar Spondylolisthesis. SPINE 2002;27(1):59-64. 50. LaGrone MO, Bradford DS, Moe JH, Lonstein JE, Winter RB, Ogilvie JW. Treatment of Symptomatic Flatback after Spinal Fusion. The Journal of Bone and Joint Surgery 1988;70(4):569-80.   137 51. Rose PS, Bridwell KH, Lenke LG, Cronen GA, Mulconrey DS, Buchowski JM, Kim YJ. Role of Pelvic Incidence, Thoracic Kyphosis, and Patient Factors on Sagittal Plane Correction Following Pedicle Subtraction Osteotomy. SPINE 2009;34(8):785-91. 52. Nelson MA. A Long-term Review of Posterior Fusion of the Lumbar Spine. Proc. roy. Soc. Med. 1968;61:18-19. 53. Corenman DS. T12-L3 Fixation across L2: Burst Fracture. SpineUniverse, Vertical Health, LLC, 2011. (Accessed December 1, 2001, at http://www.spineuniverse.com/professional/case-studies/corenman/t12-l3- fixation-across-l2-burst-fracture.) 54. Watanabe K, Lenke LG, Bridwell KH, Kim YJ, Koester K, Hensley M. Proximal Junctional Vertebral Fracture in Adults After Spinal Deformity Surgery Using Pedicle Screw Constructs. Analysis of Morphological Features. SPINE 2010;35( ):138-45. 55. Lee SS, Lenke LG, Kuklo TR, Valente L, Bridwell KH, Sides B, Blanke KM. Comparison of Scheuermann Kyphosis Correction by Posterior-Only Thoracic Pedicle Screw Fixation Versus Combined Anterior/Posterior Fusion. SPINE 2006;31(20):2316-21. 56. Kim YJ, Lenke LG, Cho SK, Bridwell KH, Sides B, Blanke K. Comparative Analysis of Pedicle Screw Versus Hook Instrumentation in Posterior Spinal Fusion of Adolescent Idiopathic Scoliosis. SPINE 2004;29(18):2040-8. 57. West JL-III, Bradford DS, Ogilvie JW. Results of spinal arthrodesis with pedicle screw-plate fixation. Journal of Bone and Joint Sugery 1991;73-A:1179-1184. 58. Yuan HA, Garfin SR, Dickman CA, Mardjetko SM. A historical cohort study of pedicle screw fixation in thoracic, lumbar, and sacral spinal fusion. SPINE 1994;19(20):S2279-96. 59. Zdeblikc, TA. A prospective randomized study of lumbar fusion. Preliminary results. SPINE 1993;18:983- 91. 60. Denis F, Sun EC, Winter RB. Incidence and Risk Factors for Proximal and Distal Junctional Kyphosis Following Sugical Treatment for Scheuermann Kyphosis. Minimum Five-Year Follow-up. SPINE 2009, 34(20):E729-E734. 61. Vrtovec T, Pernus F, Likar B. A review of methods for quantitative evaluation of spinal curvature. European Spine Journal 2009;18:593-607. 62. Cheng BC, Burns P, Pirris S, Welch WC. Load sharing and stabilization effects of anterior cervical devices. Journal of Spinal Disorders Tech 2009;22:571-7. 63. Gaines, RW. The Use of Pedicle-Screw Internal Fixation for the Operative Treatment of Spinal Disorders. The Journal of Bone and Joint Surgery 2000;82-A(10):1458-76. 64. Kim KT, Park KJ, Lee JH. Osteotomy of the Spine to Correct the Spinal Deformity. Asian Spine Journal 2009;3(2):113-23. 65. Smith-Petersen MN, Larson CB, Aufranc OE. Osteotomy of the spine for correction of flexion deformity in rheumatoid arthritis. Journal of Bone and Joint Surgery 1945;27:1-11. 66. Bridwell KH. Decision Making Regarding Smith-Petersen vs. Pedicle Subtraction Osteotomy vs. Vertebral Column Resection for Spinal Deformity.SPINE 2006;31(19):S171-8.   138 67. Danisa OA, Turner D, Richardson WJ. Surgical correction of lumbar kyphotic deformity: posterior reduction "eggshell" osteotomy. Journal of Neurosurgery 2000;92:50-6. 68. van Loon PJM, van Stralen G, van Loon CJM, van Susante JLC. A pedicle subtraction osteotomy as an adjunctive tool in the surgical treatment of a rigid thoracolumbar hyperkyphosis; a preliminary report. The Spine Journal 2006;6:195-200. 69. Bridwell KH, Lewis SJ, Lenke LG, Baldus C, Blanke K. Pedicle Subtraction Osteotomy for the Treatment of Fixed Sagittal Imbalance. The Journal of Bone and Joint Surgery 2003;85-A(3):454-63. 70. Kim KT, Suk KS, Cho YJ, Hong GP, Park BJ. Clinical outcome results of pedicle subtraction osteotomy in ankylosing spondylitis with kyphotic deformity. SPINE 2002; 27(6): 612-8. 71. Cho KJ, Bridwell KH, Lenke LG, Berra A. Comparison of Smith-Petersen Versus Pedicle Subtraction Osteotomy for the Correction of Fixed Sagittal Imbalance. SPINE 2005;30(18):2030-7. 72. Chou-kuan HAO, Wei-shi LI, Zhong-qiang C. The height of the osteotomy and the correction of the kyphotic angle in thoracolumbar kyphosis. Chinese Medicle Journal 2008;121(19):1906-10. 73. Van Royen BJ, De Gast A, Smit TH. Deformity planning for sagittal plane corrective osteotomies of the spine in ankylosing spondylitis. European Spine Journal 2000;9(6):492-8. 74. Yang SH, Chen PQ. Proximal Kyphosis After Short Posterior Fusion for Thoracolumbar Scoliosis. Clinical Orthopaedics and Related Research 2003;411:152-8. 75. Yagi M, Akilah KB, Boachie-Adjei O. Incidence, Risk Factors and Classification of Proximal Junctional Kyphosis: Surgical Outcomes Review of Adult Idiopathic Scoliosis. Spine Deformity 2010;36(1):E60-8  76. J. Street (personal communication, June 2, 2011).  77. Cho KJ, Suk S, Park SR, Kim JH, Kim SS, Choi WK, Lee KY, Lee SR. Complications in Posterior Fusion and Instrumentation for Degenerative Lumbar Scoliosis. SPINE 2007;32(20): 2232-7. 78. Kim YJ, Bridwell KH, Lenke L, Rhim S, Cheh G. Sagittal Thoracic Decompensation Following Adult lumbar Spinal Instrumentation and Fusion to L5 or S1: Causes, Prevalence, and Risk Factor Analysis. SPINE 2006;31(2):2359-66. 79. Kim HJ, Yagi M, Nyugen J, Cunningham ME. Combined Anterior-Posterior Surgery is the Most Important Risk Factor for Developing Proximal Junctional Kyphosis in Idiopathic Scoliosis. Clinical Orthop Relat Res 2011. Symposium: Complications of Spine Surgery 80. Nachemson A, Morris JM. In Vivo Measurements of Intradiscal Pressure: Discometry, a method for the determination of pressure in the lower lumbar discs. The Journal of Bone & Joint Surgery 1964,46:1077- 92. 81. Schultz AB, Andersson GJ. Analysis of Loads on the Lumbar Spine. SPINE 1981;6(1):76-82. 82. Schultz AB, Andersson G, Ortengren R, Nachemson, A.  Loads on the lumbar spine. Validation of a biomechanical analysis by measurements of intradiscal pressure and myoelectric signals. The Journal of Bone and Joint Surgery 1982;64:713-20. 83. Rohlmann A, Bergmann G, Graichen F. A Spinal Fixation Device for In Vivo Load Measurement. Journal of Biomechanics 1994;27(7):961-7.   139 84. Rohlmann A, Bergmann G, Graichen F, Weber U. Comparison of loads on internal spinal fixation devices measured in vitro and in vivo. Medical Engineering and Physics Journal 1997;19(6):539-46. 85. Polga DJ, Beaubien BP, Kallemeier PM, Schellhas KP, Lew WD, Buttermann GR, Wood KB. Measurement of In Vivo Intradiscal Pressure in Healthy Thoracic Intervertebral Discs. SPINE 2004;29(12):1320-4. 86. Wilke H-J, Neef P, Caimi M, Hoogland T, Claes LE. New In Vivo Measurements of Pressure in the Intervertebral Disc in Daily Life. SPINE 1999;24(8):755-62. 87. Davis KG, Parnianpour M. Subject-specific compressive tolerance estimates. Technology and Health Care 2003;11:183-93. 88. Singer K, Edmondston S, Day R, Bredahl P, Price R. Prediction of Thoracic and Lumbar Vertebral Body Compressive Strength: Correlations with Bone Mineral Density and Vertebral Region. Bone 1995;17(2):167-74. 89. Crawford RP, Keaveny TM. Relationship Between Axial and Bending Behaviours of the Human Thoracolumbar Vertebra. SPINE 2004;29(20):2248-55. 90. Adams M, Green T, Dolan P. The Strength in Anterior Bending of Lumbar Intervertebral Discs. SPINE 1994;19(19):2197-2203. 91. Osvalder A.-L, Neumann P, Lovsund P, Nordwall A. Ultimate Strength of the Lumbar Spine in Flexion - an in vitro study. Journal of Biomechanics 1990;23(5):453-60. 92. Matsumoto T, Ohnishi I, Bessho M, Imai K, Oashi S, Nakamura K. Prediction of Vertebral Strength Under Loading Conditions Occuring in Activities of Daily Living Using a Computed Tomography-Based Nonlinear Finite Element Method. SPINE 2009;34(14): 1464-9. 93. Harrison DE, Janik TJ, Harrison DD, Cailliet R, Harmon SF. Can the Thoracic Kyphosis Be Modeled With a Simple Geometric Shape? The Results of Circular and Elliptical Modeling in 80 Asymptomatic Patients. Journal of Spinal Disorders & Techniques 2002;3(15):213-20. 94. Harrison DD, Harrison DE, Janik TJ, Cailliet R, Haas J. Do Alterations in Vertebral and Disc Dimensions Affect an Elliptical Model of Thoracic Kyphosis? SPINE 2003;28(5):463-9. 95. Janik TJ, Harrison DD, Cailliet R, Troyanovich SJ, Harrison DE. Can the Sagittal Lumbar Curvature be Closely Approximated by an Ellipse? Journal of Orthopaedic Research 1998;16:766-70. 96. Harrison DE, Colloca CJ, Harrison DD, Janik TJ, Haas JW, Keller TS. Anterior thoracic postures increases thoracolumbar disc loading. European Spine Journal 2005;14:234-42. 97. Keller TS, Harrison DE, Colloca CJ, Harrison DD, Janik TJ. Prediction of Osteoporotic Spinal Deformity. SPINE 2003;28(2):455-62. 98. Briggs AM, van Dieen JH, Wrigley TV, Greig AM, Phillips B, Kai Lo Sing, Bennell KL. Thoracic Kyphosis Affects Spinal Loads and Trunk Muscle Force. Physical Therapy 2007;87(5):595-607. 99. Troyanovich SJ, Cailliet R, Janik TJ, Harrison DD, Harrison DE. Radiographic mensuration characteristics of the sagittal lumbar spine from a normal population with a method to synthesize prior studies of lordosis. Journal of Spinal Disorders 1997;10:280-6. 100. Panjabi MM, Takata K, Goel V, Federico D, Oxland T, Duranceau J, Krag M. Thoracic Human Vertebrae. Quantitative Three-Dimensional Anatomy. SPINE 1991;16(8):888-901.   140 101. Yang  BP, Chen LA, Ondra SL. A novel mathematical model of the sagittal spine: application to pedicle subtraction osteotomy for correction of fixed sagittal deformity. The Spine Journal 2008;8;359-66. 102. Berthonnaud E,Dimnet, J. Analysis of structural features of deformed spines in frontal and sagittal projects. Comput Med Imaging Graph 2007;31:9-16. 103. Kaminsky J, Klinge P, Rodt T, Bokemeyer M, Luderemann W, Samii M. Specially adapted interactive tools for an improved 3D-segmentation of the spine. Comput Med Imaging Graph 2004;28:119-27. 104. Vrtovec T, Likar B, Pernus F. Automated curved planar reformation of 3D spine images. Phys Med Biol 2005;50:4527-40. 105. Vrtovec T, Likar B, Pernus F. Quantitative analysis of spinal curvature in 3D: application to CT images of normal spine. Phys Med Biol 2008;52:2865-78. 106. Peng Z, Zhong JW, Lee JH. Shanghai. Automated vertebra detection and segmentation from the whole spine MR images. 27th annual international conference of the engineering in medicine and biology society (EMBS). IEEE, 2005:2527-30. 107. Vrtovec T, Likar B, Pernus F. Automated generation of curved planar reformations from MR images of the spine. Phys Med Biol 2007;52: 2865-78. 108. Huysmans T, Haex B, Van Audekercke R, Vander Sloten J, Van der Perre G. Three-dimensional mathematical reconstruction of the spinal shape based on active contours. Journal of Biomechanics 2004;37:1793-8. 109. Clauser CE, McConville JT, Young JW. Weight, Volume, and Center of Mass of Segments of the Human Body. Aerospace Medical Research Laboratory, Air Force System Command, 1969. AMRL-TR-69-70. 110. Pearsall DJ, Reid JG, Livingston LA. Segmental Inertial Parameters of the Human Trunk as Determined from Computed Tomography. Annals of Biomedical Engineering 1996;24:198-210. 111. Duval-Beaupere G, Robain G. Visualization on full spine radiographs of the anatomical connections of the centres of the segmental body mass supported by each vertebra and measured in vivo. International Orthopaedics 1987;11:261-9. 112. de Leva P. Adjustments to Zatsiorsky-Seluyanov's Segment Inertia Parameters. Journal of Biomechanics 1996;29(9):1223-30. 113. Winter DA. Biomechanics and Motor Control of Human Movement. 4th Edition. John Wiley & Sons, 2009. 114. Winter DA. Estimations of the horizontal displacement of the total body centre of mass: considerations during standing activities. Gait & Posture 1993;1:141-4. 115. Bazrgari B, Shirazi-Adl A, Larivier C. Trunk response analysis under sudden forward perturbations using a kinematics-driven model. Journal of Biomechanics 2009;42:1193-1200. 116. Arjmand N, Gagnon D, Plamondon A, Shirazi-Adl A, Lariviere C. Comparison of trunk muscle forces and spinal loads estimated by two biomechanical models. Clinical Biomechanics 2009;24:533-41. 117. El-Rich M, Shirazi-Adl A, Arjmand N.  Muscle Activity, Internal Loads, and Stability of the Human Spine in Standing Postures: Combined Model and In Vivo Studies. SPINE 2004;29(23): 2633-42.   141 118. Iyer S, Christiansen BA, Roberts BJ, Valentine MJ, Manoharan RK, Bouxsein MLA. biomechanical model for estimating loads on thoracic and lumbar vertebrae. Clinical Biomechanics 2010;25(9):853-8. 119. Cholewicki J, McGill SM, Norman RW. Comparison of Muscle Forces and Joint Load from an Optimization and EMG Assisted Lumbar Spine Model: Towards Development of a Hybrid Approach. Journal of Biomechanics 1005;28(3):321-31. 120. Brinckmann P, Frobin W, Leivseth G. Musculoskeletal Biomechanics. New York : Thieme, 2003. 121. Dolan P, Earley M, Adams MA. Bending and compressive stresses acting on the lumbar spine during lifting activities. Journal of Biomechanics 1994;27:1237-48. 122. McGill SM, Norman RW. Partioning of the L4-L5 dynamic moment into disc ligamentous and muscular components during lifting. SPINE 1986;11:666-78. 123. Keller TS, Nathan M. Height Change Caused by Creep in Intervertebral Discs: A Sagittal Plane Model. Journal of Spinal Disorders 1999;12(4):313-24. 124. Nachemson A. Disc pressure measurements. SPINE 1981;6:93-7. 125. Nissan M, Gilad I. The cervical and lumbar vertebrae - an anthropometric model. Engineering Medicine 1984;13:111-4. 126. Panjabi MM, Goel V, Oxland T, Takata K, Duranceau J, Krag M, Price M. Human Lumbar Vertebrae. Quantitative Three-Dimensional Anatomy. SPINE 1992;17(3):299-306. 127. Andriacchi T, Schultz A, Belytschko T, Galante J. A model for studies of mechanical interactions between the human spine and rib cage. Journal of Biomechanics 1974;7:497-507. 128. Watkins RT, Watkins III R, William L, Ahlbrand S, Garcia R, Karamanian A, Sharp L, Vo C, Hedman T. Stability provided by the sternum and rib cage in the thoracic spine. SPINE 2005.30(11):1283-6. 129. Cholewicki J, Manohar P, Khachatryan A. Stabilizing Function of Trunk Flexor-Extensor Muscles Around a Neutral Spine Posture. SPINE 1997;22(19): 2207-12. 130. Schultz AB, Warwick DN, Berkson MH, Nachemson A. Mechanical properties o the human lumbar spine motion segments: Part I, Responses to flexion, extension, lateral bending and torsion. ASME Journal of Biomechanical Engineering 1979;101:46-52. 131. Jorgensen MJ, Marras WS, Gupta P, Waters TR. Effect of torso flexion on the lumbar torso extensor muscle sagittal plane moment arms. The Spine Journal 2003;3:363-9. 132. Duval-Beaupere G, Schmidt C, Cosson P. A Barycentremetric sstudy of the sagittal shape of spine and pelvis: The conditions required for an economic standing position. Annual Biomedical Engineering 1992;20:451-62. 133. Arjmand N, Shirazi-Adl A, Bazrgari B. Wrapping of trunk thoracic extensor muscles influences muscle forces and spinal loads in lifting tasks. Clinical Biomechanics 2006; 21:668-75. 134. Chen S-I, Lin R-M, Chang C-H. Biomechanical investigation of pedicle screw-vertebrae complex: a finite element approach using bonded and contact interface conditions. Medical Engineering & Physics 2003.25:275-82. 135. Zander T, Rohlmann A, Calisse J, Bergmann G. Estimation of muscle forces in the lumbar spine during upper-body inclination. Clinical Biomechanics 2001;16(1):S73-S80.   142 136. Calisse J, Rohlmann A, Bergmann G. Estimation of trunk muscle forces using the finite element method and in vivo loads measured by telemeterized internal spinal fixation devices. Journal of Biomechanics 1999;32:727-31. 137. Hato T, Kawahara N, Tomita K, Murakami H, Akamaru T, Tawara D, Sakamoto J, Oda J, Tanaka S. Finite-element analysis on closing-opening correction osteotomy for angular kyphosis of osteoporotic vertebral fractures. Jouranl of Orthopaedic Science 2007;12:354-60. 138. Nussbaum MA, Chaffin DB, Rechtien CJ. Muscle Lines-of-Action Affect Predicted Forces in Optimization-Based Spine Muscle Modeling. Journal of Biomechanics 1995;28(4):401-9. 139. O'Sullivan PB, Grahamslaw KM, Ther MM, Kendell M, Lapenskie SC, Moller NE, Richards KV. The Effect of Different Standing and Sitting Postures on Trunk Muscle Activity in a Pain-Free Population. SPINE 2002;27(11):1238-44. 140. Nachemson A. The Influence of Spinal Movements on the Lumbar Intradiscal Pressure and on the Tensile Stresses in the Annulus Fibrosus. Acto Orthop Scand 1963;33:183-207. 141. Nachemson A. The load on lumbar discs in different positions of the body. Clin Orthop Relat Res 1966;45:107-22. 142. Rohlmann A, Bergmann G, Graichen F. Loads on internal spinal fixators measured in different body positions. European Spine Journal 1999;8:354-9. 143. Nachemson A. Lumbar Intradiscal Pressure. Experimental Studies on Post-Mortem Material. Acta Orthop 1960;43:1-104. 144. Sato K, Kikuchi S, Yonezawa T.  In Vivo Intradiscal Pressure Measurement in Healthy Individuals and in Patients With Ongoing Back Problems. SPINE 1999;24(23):2468-74. 145. Butterman GR, Beaubien BP. In Vitro Disc Pressure Profiles Below Scoliosis Fusion Constructs. SPINE 2008;33(20):2134-42. 146. Takahashi I, Kikuchi S, Sato K, Sato N. Mechanical Load of the Lumbar Spine During Forward Bending Motion of the Trunk - A Biomechanical Study. SPINE 2006;31(1):18-23. 147. Rohlmann A, Neller S, Bergmann G, Graichen F, Claes L, Wilke HJ. Effect of an internal fixator and a bone graft on intersegmental spinal motion and intradiscal pressure in the adjacent regions. European Spine Journal 2001;10:301-8. 148. Adams MA, McNally DS, Dolan P. Stress disstribution inside intervertebral discs: the effects of age and degeneration. Journal of Bone and Joint Surgery 1996;78B:965-72. 149. Cunningham BW, Kotani Y, McNulty P, Cappuccino A, McAfee P. The Effect of Spinal Destabilization and Instrumentation on Lumbar Intradiscal Pressure: An In Vitro Biomechanical Analysis. SPINE 1997;15:2655-63. 150. Panjabi MM. Biomechanical evaluation of spinal fixation devices: I. A conceptual framework. Spine 1988;13:1129-34 151. Rohlmann A, Neller S, Claes L, Bergmann G, Wilke H-J. Influence of a Follower Load on Intradiscal Pressure and Intersegmental Rotation of the Lumbar Spine. SPINE 2001;26(24):E557-61. 152. Niosi CA, Wilson DC, Zhu Q, Keynan O, Wilson DR, Oxland TR. The effect of dynamic posterior stabilization on facet joint contact forces: an in vitro investigation. SPINE 2008;33:19-26.   143 153. Bodke DS, Gollogly S, Bachus KN, Alexander Mohr R, Nguyen BK. Anterior thoracolumbar instrumentation: stiffness and load sharing characteristics of plate and rod systems. SPINE 2003;28:1794- 801. 154. Sample SJ, Behan M, Smith Lesley, Oldenhoff WE, Markel M, Kalscheur VL, Hao Z, Miletic V, Muir P. Functional Adaptation to Loading of Single Bone is Neuronally Regulated and Involves Multiple Bones. Journal of Bone Mineral Research 2008;23(9):1372-81. 155. Muir P, Sample SJ, Barrett JG, McCarthy J, Vanderby R, Markel MD, Porkuski LJ, Kalscheur VL. Effect of fatigue loading and associated matrix microdamage flow and interstitial fluid flow. Bone 2007;40(4):948-56. 156. Shah JS, Hampson WG, Jayson MI. The Distribution of Surface Strain in the Cadaveric Lumbar Spine. The Journal of Bone and Joint Surgery 1978;60-B(2):246-51. 157. Hongo M, Abe E, Shimada Y, Murai H, Ishikawa N, Sato K. Surface Strain Distribution on Thoracic and Lumbar Vertebrae Under Axial Compression: The Role in Burst Fractures. SPINE 1999;24(12):1197-1202. 158. Frei H, Oxland TR, Nolte L-P. Thoracolumbar spine mechanics contrasted under cocmpression and shear loading. Journal of Orthopaedic Research 2002;20:1333-8. 159. Linders DR, Nuckley DJ. Deduction of Spinal Loading from Vertebral Body Surface Strain Measurements. Experimental Mechanics 2007;47:303-10. 160. Buttermann GR, Schendel MJ, Kahmann RD, Lewis JL, Bradford DS. In Vivo Facet Joint Loading of the Canine Lumbar Spine. SPINE 1992;17(1):81-92. 161. Nagata H, Schendel MJ, Transfeldt EE, Lewis JL. The Effects of Immobilization of Long Segments of the Spine on the Adjacent and Distal Facet Force and Lumbosacral Motion. SPINE 1993;18(16):2471-9. 162. Sawa,AG, Crawford NR. The use of surface strain data and a neural networks solution method to determine lumbar facet joint loads during in vitro spine testing. Journal of Biomechanics 2008;41:2647-53. 163. Schendel MJ, Wood KB, Buttermann GR, Lewis JL, Ogilvie JW. Experimental measurement of ligament force, facet force, and segment motion in the human lumbar spine. Journal of Biomechanics 1993;26(4/5):427-83. 164. Wilson DC, Niosi CA, Zhu QA, Oxland TR, Wilson DR. Accuracy and repeatability of a new method for measuring facet loads in the lumbar spine. Journal of Biomechanics 2006;39:348-53. 165. Kettler A, Niemeyer T, Issler L, Merk U, Mahalingam M, Werner K, Claes L, Wilke H.-J. In vitro fixator rod loading after transforaminal compared to anterior lumbar interbody fusion. Clinical Biomechanics 2006;21:435-42. 166. Cripton PA, Jain GM, Wittenberg RH, Nolte LP. Load-Sharing Characteristics of Stabilized Lumbar Spine Segments. SPINE 2000;25(2):170-9. 167. Nolte IP, Jain GM Wittenberg RH, Diaz F. Stiffness and load-sharing of instrumented lumbar fusions in multidirectional loading. Abstract ISSLS 1993;122. 168. Oda I, Cunningham BW, Lee GA, Abumi K, Kaneda K, McAfee PC. Biomechanical Properties of Anterior Thoracolumbar Multisegment Fixation. An Analysis of Construct Stiffness and Screw-Rod Strain. SPINE 2000;18(25):2303-11.   144 169. Meyers K, Tauber M, Sudin Y, Fleischer S, Arnin U, Girardi F, Wright T. Use of instrumented pedicle screws to evaluate load sharing in posterior dynamic stabilization systems. The Spine Journal 2008;8:926- 32. 170. Smith TS, Yerby SA, McLain RJ, McKinley TO. A Device for Measurement of Pedicle Screw Moments. Journal of Biomechanical Engineering 1996;118:423-5. 171. Kim HK, Heo SJ, Koak JY, Kim SK. In vivo comparison of force development with various materials of implant-supported protheses. Journal of Oral Rehabilitation 2009;36(8):616-25. 172. Brunski JB, Hipp JA. In vivo forces on dental implants: Hard-wiring and telemetry methods. Journal of Biomechanics 1984;17(11):855-60. 173. Chang UK, Lim J, Kim DH. Biomechanical study of thoracolumbar junction fixation devices with different diameter dual-rod systems. Journal of Neurosurgical Spine 2006;4:206-12. 174. The Strain Gage. Omega.com. Omega Engineering, 2011. (Accessed November 3, 2011, at http://www.omega.com/literature/transactions/volume3/strain.html.). 175. Dick W, Kluger P, Magerl F, Woersdorfer O, Zach G. A New Device for Internal Fixation of Thoracolumbar and Lumbar Spine Fractures: The 'Fixateur Intern'. Paraplegia 1985;23:225-32. 176. Bergmann G, Graichen F, Siraky J, Jendrzynski H, Rohlmann. A Multi-channel strain gauge telemetry for orthopaedic implants. Journal of Biomechanics 1988;21:169-176. 177. Bergmann JS, Rohlmann A, Kolbel R. Measurement of spatial forces by the 'matrix method'. Proceedings of V/VI of the 9th Wolrd Congress IMECO 1982:395-404. 178. Rohlmann A, Riley LH, Bergmann G, Graichen F. In vitro load measurement using an instrumented spinal fixation device. Med Eng Phys 1996;6(18):485-8. 179. Bridwell KH. Selection of instrumentation and fusion levels for scoliosis: where to start and where to stop. Journal of Neurosurgery: Spine 2004;1:1-8. 180. Kim YJ, Bridwell KH, Lenke LG, Rhim S, Kim YW.  Is the T9, T10, or L1 the more reliable proximal level after adult lumbar or lumbosacral instrumented fusion to L5 or S1? SPINE 27;32(24):2653-61. 181. O’Shaughnessy BA, Bridwell KH, Lenke LG, Cho W, Baldus C, Chang MS, Auerbach JD, Crawford CH. Does a Long Fusion “T3-Sacrum” Portend a Worse Outcome than a Short Fusion “T10-Sacrum” in Primary Surgery for Adult Scoliosis?. SPINE Publish Ahead of Print 2011 182. Gatton ML, Pearcy MJ, Pettet GJ. Computational model of the lumbar spine musculature: Implications of spinal surgery. Clinical Biomechanics 2011;26:116-22. 183. Tveit P, Daggfeldt K, Hetland S, Thorstensson A. Erector Spinae Lever Arm Length Variations with Changes in Spinal Curvature. SPINE 1994;19:199-204. 184. Kang CH, Shin MJ, Kim SM, Lee SH, Lee C-S. MRI of paraspinal muscles in lumbar degenerative kyphosis patients and control patients with chronic low back pain. Clinical Radiology 2007;62:479-86. 185. Airaksinen O, Herno A, Kaukanen E, Saari T, Sihvonen T, Suomalainen O. Density of lumbar muscles 4 years after decompressive spinal surgery. European Spine Journal 1996;5:193-7.   145 186. Mayer TG, Vanharanta H. Gatchel, RJ, Mooney V, Barnes D, Judge L, Smith S, Terry A. Comparison of CT Scan Muscle Measurements and Isokinetic Trunk Strength in Postoperative Patients. SPINE 1989;14(1):33-6. 187. Fan SW, Hu ZJ, Zhoa FD, Zhoa X, Huang Y, Fang X. Multifidus muscle changes and clinical effects of one-level posterior lumbar interbody fusion: minimally invasive procedure versus conventional open approach. European Spine Journal 2010;19:316-24. 188. Gille O, Jolivet E, Dousset V, Degrise C, Obeid, I, Vital JM, Skalli W. Erector Spinae Muscle Changes on Magnetic Resonance Imaging Following Lumbar Surgery Through a Posterior Approach. SPINE 2007;32(11):1236-41. 189. Gejo R, Matsui H, Kawaguchi Y, Ishihara H, Tsuji H. Serial Changes in Trunk Muscle Performance After Posterior Lumbar Surgery. SPINE 1999;10(24):1023-8. 190. Hakkinen A, Ylinen J, Kautiainen H, Airaksinen O, Herno A, Tarvainen U, Kiviranta I. Pain, Trunk Muscle Strength, Spine Mobility and Disability Following Lumbar Disc Surgery. Hakkinen, Journal of Rehabilitation Medicine 2003;35:236-40. 191. Suwa H, Hanakita J, Ohshita N, Gotoh K, Matsuoka N, Morizane A. Postoperative Changes in Paraspinal Muscle Thickness After Various Lumbar Back Surgery Procedures. Neurol Med Chir 2000;40:151-5. 192. Kim DY, Lee SH, Chung SK, Lee HY. Comparison of Multifidus Muscle Atrophy and Trunk Extension Muscle Strength. Percutaneous Versus Open Pedicle Screw Fixation. SPINE 2004;30(1):123-9. 193. Lu WW, Hu Y, Luk KDK, Cheung KMC, Leong JCY. Paraspinal Muscle Activities of Patients with Scoliosis After Spine Fusion. SPINE 2002;27(11):1180-5. 194. Bresnahan L, Fessler RG, Natarajan RN. Evaluation of Change in Muscle Activity as a Result of Posterior Lumbar Spine Surgery Using a Dynamic Modeling System. SPINE 2010;35(16):E761-67. 195. Moshirfar A, Jenis LG, Spector LR, Burker PJ, Losina E, Katz JN, Rand FF, Tromanhauser SG, Banco RJ. Computed tomography evaluation of superior-segment facet-joint violation after pedicle instrumentation of the lumbar spine with a midline surgical approach. SPINE 2006;31(22):2624-9. 196. Shah RR, Mohammed S, Saifuddin A, Taylor BA. Radiologic Evaluation of Adjacent Superior Segment Facet Joint Violation Following Transpedicular Instrumentation of the Lumbar Spine. SPINE 2003;28(3):272-5. 197. Cardoso MJ, Dmitriev AE, Helgeson M, Lehman RA, Kuklo TR, Rosner MK. Does Superior-Segment Facet Violation or Laminectomy Destabilize the Adjacent Level in Lumbar Transpedicular Fixation? An In Vitro Human Cadaveric Assessment. SPINE 2008;33(26):2868-73. 198. Faraj AA, Webb JK. Early complications of spinal pedicle screw. European Spine Journal 1997;6:324-6. 199. Adams MA, Hutton WC, Stott RR. The Resistance to Flexion of the Lumbar Intervertebral Joint. SPINE 1980;5(3):245-53. 200. HCUP Databases.  Healthcare Cost and Utilization Project (HCUP). November 2007.  Agency for Heatlhcare Research and Quality, Rockville, MD. 201. Harrison DE, Cailliet R, Harrison DD, Janik TJ, Holland B. Reliability of Centroid, Cobb, and Harrison Posterior Tangent Methods. Which to Choose for Analysis of Thoracic Kyphosis. SPINE 2001;26(11):E227-34.   146 202. Shea KG, Stevens PM, Nelson M, Smith JT, Masters KS. A Comparison of Manual Versus Computer- Assisted Radiographic MeasurementL Intraobserver Measurement Variability for Cobb Angles. SPINE 1998;23(5):551-5. 203. Kiefer A, Shirazi-Adl A, Parnianpour M. Stability of the human spine in neutral postures. European Spine Journal 1997;6:45-53. 204. Etebar S, Cahill D. Risk factors for adjacent-segment failure following lumbar fixation with rigid instrumentation for degenerative instability. Journal of neurosurgery: Spine 1999;90(2):163-9 205. Wilke H-J, Rohlmann A, Neller S, Graichen F, Claes L, Bergmann GA. Novel Approach to Determine Trunk Muscle Forces During Flexion and Extension. A Comparison of Data From an In Vitro Experiment and In Vivo Measurements. SPINE 2003;28(23_:2585-93. 206. Dickey JP, Kerr DJ. Effect of specimen length: are the mechanics of individual motion segments comparable in functional spinal units and multisegment specimens? Medical Engineering & Physics 2003;25:221-7. 207. Kettler A, Wilke H-J, Haid C, Claes L. Effects of Specimen Length on the Monosegmental Motion Behaviour of the Lumbar Spine. SPINE 2000;25(5):543-50. 208. Goertzen DJ, Lane C, TR Oxland. Neutral zone and range of motion in the spine are greater with stepwise loading than with a continuous loading protocol. An in vitro porcine investigation. Journal of Biomechanics 2004;37:257-61. 209. Tuttle, ME. Load measurement in a cylindrical column or beam using three strain gages. Experimental Techniques 1981;5(4):19-20. 210. Micro-Measurements, Vishay. Surface Preparation for Strain Gage Bonding. Application Note B-129-8. April 14, 2009. 11129. 211. Untch C, Liu Q, Hart R.  Segmental Motion Adjacent to an Instrumented Lumbar Fusion.  The Effect of Extension of Fusion to the Sacrum.  SPINE 2004;29(21):2376-81. 212. Kuklo TR, Dmitriev AE, Cardoso MJ, Lehman RA, Erickson M, Gill NW. Biomechanical Contribution of Transverse Connectors to Segmental Stability Following Segment Instrumentation With Thoracic Pedicle Screws. SPINE 2008;33:E482-7. 213. Aydogan M, Ozturk C, Karatoprak O, Tezer M, Aksu N, Hamzaoglu A. The Pedicle Screw Fixation With Vertebroplasty Augmentation in the Surgical Treatment of the Sever Osteoporotic Spines. Journal of Spinal Disorders and Techniques 2009;22: 444-7. 214. Rohlmann A, Calisse J, Bergmann G, Radvan J, Mayer HM. Clamping stiffness and its influence on load distribution between paired internal spinal fixation devices. Journal of Spinal Disorders 1996;9:234-40. 215. Edmondston SJ, Singer KP, Day RE, Brediahl PD, Price RI. In-vitro relationships between vertebral body density, size, and compressive strength in the elderly thoracolumbar spine. Clinical Biomechanics 1994;9:180-6. 216. Brinckmann P, Johannleweling N, Hilweg D, Biggemann M. Fatigue fracture of human lumbar vertebrae. Clinical Biomechanics 1987;2:94-6. 217. Hansson T, Keller T, Johnson R. Fatigue fracture morphology in human lumbar motion segments. Journal of Spinal Disorders 1988;1(1):33-8.   147 218. Kumar MN, Baklanov A, Chopin D. Correlation between sagittal plane changes and adjacent segment degeneration following lumbar spine fusion. European Spine Journal 2001;10:314-9. 219. Jang J-S, Lee S-H, Min J-H, Maeng D-H. Influence of Lumbar Lordosis Restoration on Thoracic Curve and Sagittal Position in Lumbar Degenerative Kyphosis Patients. SPINE 2009;34(3):280-4. 220. Cunningham BW, Sefter JC, Shono Y, McAfee PC. Static and Cyclical Biomechanical Analysis of Pedicle Screw Spinal Constructs. SPINE 1993;18(12):1677-88. 221. Van Royen BJ, Toussaint HM, Kingma I, Bott SDM, Caspers M, Harlaar J, Wuisman P. Accuracy of the sagittal vertical axis in a standing lateral radiograph as a measurement of balance in spinal deformites. European Spine Journal 1998:7(5):408-12. 222. Vedantam R, Lenke LG, Bridwell KH, Linville DL, Blanke K. The effect of variation in arm position on sagittal spinal alignment. SPINE 2000;25(17):2204-9. 223. Bozkus H, Crawford NR, Chamberlain RH, Valenzuela TD, Espinoza A, Yuksel Z, Dickman CA. Comparitive anatomy of the porcine and human thoracic spines with reference to thoracosopic surgical techniques. Surgical endoscopy 2005;19(12):1652-65. 224. Dath R, Ebinesan AD, Porter KM, Miles AW. Anatomical measurements of porcine lumbar vertebrae. Clinical Biomechanics 2007;22(5):607-13. 225. McLain, RF, Yerby, SA and Moseley, TA. Comparative morphometry of L4 vertebrae: comparison of large animal models for the human lumbar spine. SPINE 2002;27(8):E200-6. 226. Busscher I, van der Veen AJ, van Dieen JH, Kingma I, Verkerke GJ, Veldhuizen AG. In vitro biomechanical characteristis of the spine: a comparison between human and porcine spinal segments. SPINE 2000;35(2):E35-42. 227. Wilke H-J, Rohlmann A, Neller S, Schulteiss M, Bergmann G, Graichen F, Claes LE. Is it Possible to Simulate Physiologic Loading Conditions by Applying Pure Moments? A Comparison of In Vivo and In Vitro Load Components in an Internal Fixator. SPINE 2001;26(6):636-42. 228. Panjabi MM, Abumi K, Duranceau J, Oxland T. Spinal staibilty and intersegmental muscle forces-a biomechanical model. SPINE 1989;14(2):194-200. 229. Wilke H-J, Wolf S, Claes LE, Arand M, Wiesend A. Influence of Varying Muscle Forces on Lumbar Intradiscal Pressure: An In Vitro Study. Journal of Biomechanics 1996;29(4):549-55. 230. Kong WZ, Goel VK, Gilbertson LG, Weinstein JN. Effects of Muscle Dysfunction on Lumbar Spine Mechanics: A Finite Element Study Based on a Two Motion Segments Model. SPINE 1996;21:2197-206. 231. Rohlmann A, Bergmann G, Graichen F, Mayer H-M. Influence of Muscle Forces on Loads in Internal Spinal Fixation Devices. SPINE 1998;23(5):537-42. 232. Wilke HJ, Wenger K, Claes L. Testing criteria for spinal implants: recommendations for the standardization of in vitro stability testing of spinal implant. European Spine Journal 1998;7:148-54. 233. Panjabi MM. Hybrid multidirectional test method to evaluate spinal adjacent-level effects. Clinical Biomechanics 2007;22:257-65.  234. Panjabi MM, Kato Y, Hoffman H, Cholewicki J, Krag M. A study of stiffness protocol as exemplified by testing of a burst fracture model in sagittal plane. SPINE 2000;25:2748-54.   148 235. Viceconti M, Toni A, Giunti, A. Strain gauge analysis of hard tissues: factors influencing measurements. Experimental Mechanics. Technology transfer between high tech engineering and biomechanics. Little E.G. ed. Amsterdam : Elsevier Science Publisher B.V., 1992, pp. 177-84. 236. Schilling C, Kruger S, Grupp TM, Duda GN, Blomer W, Rohlmann A. The effect of design paramaters of dynamic pedicle screw systems on kinematics and load bearing: and in vitro study. European Spine Journal 2011;20:297-307. 237. Tan J-S, Singh S, Zhu Q-A, Dvorak MF, Fisher, CG, Oxland TR. The Effect of Cement Augmentation and Extension of Posterior Instrumentation on Stabilization and Adjacent Level Effects in the Elderly Spine. SPINE 2008;33(25):2728-40. 238. Okuyama K, Abe E, Suzuki T, Tamura Y, Chiba M, Sato K. Can Insertional Torque Predict Screw Loosening and Related Failures? An In Vivo Study of Pedicle Screw Fixation Augmenting Posterior Lumbar Interbody Fusion. SPINE 2000;25(7):858-64. 239. Vishay. The Three-Wire Quarter-Bridge Circuit. Application note: TT-612. Vishay 2005. (Accessed November 25, 2011, at http://www.intertechnology.com/Vishay/TechNotes_TechTips.html. 11092.) 240. Beer, FP, Johnston, ER and DeWolf, JT. Mechanics of Materials. 3rd. New York : McGraw-Hill, 2002. ISBN 0-07-365935-5  Appendix A  149 Appendix A  Strain Gauge Background A.1 Foil Strain Gauge Background Theory A metallic foil strain gauge consists of a grid of wire filament (a resistor) that changes surface length with the movement of the strained surface when a load is applied (Figure A-1). This change in surface length is communicated to the resistor and the corresponding strain is measured in terms of electrical resistance of the foil wire, which varies linearly with strain (174).  Figure A-1: Strain gauge theory: change in wire length (from L to L+∆L) under an applied load.  The cross- sectional area decreases according to the decrease in radius from r1 (blue) to r2 (red). The resistance of a wire can be calculated given a uniform cross section, A, a wire length, L, and a wire resistivity, ρ (Eq. A1). 4   ^  The change in wire length that occurs with an applied load causes a small change in resistance that can be found by taking the derivative of both sides. ∆4  `4  ` ^ : The natural logarithm (ln) of Eq. A2 is: `a24!  `a2^!  `a2!  `a2! Which can be simplified using the relationship d(lnx) = dx/x to get: b] ]  bcc  b  b:: (Eq. A1) P r1 r2 (Eq. A2) (Eq. A3) Appendix A  150 (Eq. A5) The longitudinal and transverse strain, representing the change in wire length and diameter, respectively, are related with Poisson’s Ratio, υ, a material property representing the tendency of the material to contract laterally in response to axial stretching. M  `                            M ;  `d d                            M;  eM Eq. A4 can be simplified further by the knowledge that dA/A = 2dr/r (the differential area of a circle), giving the final equation: `4 4  `^ ^  `   2 `d d `4 4  `^ ^  M  2M; `4 4  `^ ^  M  2eM! b] ]  bcc  1  2e!M Where εL is the longitudinal strain and is written more commonly as ε.  This means the change in resistance of a foil gauge is dependent on the resistivity and the Poisson’s Ratio of the material to which it is bonded.  A commonly reported strain gauge property is the gauge factor (GF) which describes the gauge’s resistivity per unit strain: f%  `4 4⁄M  `^ ^M  1  2e! The gauge factor is often assumed to be constant and varies between 1 ≤ GF  ≤ 2. but in reality, the resistivity of material can change under strain.    (Eq. A4) (Eq. A6) Appendix A  151 A.2 Wheatstone Bridge To measure the small changes in resistance of the wires in the strain gauge as it follows minute dimensional changes on the surface of a specimen (on the order of microstrain), a Wheatstone bridge circuit is used (Figure A-2a).  In its simplest form, it consists of four resistive elements (or bridge arms) connected in a series-parallel arrangement with an excitation voltage source, E.  The connection between the voltage source and pairs of bridge arms act as the input corners while that between the signal (eo) and the pairs of bridge arms act as the output corners (239).  Figure A-2: Wheatstone Bridge circuit in its simplest form.  A quarter-bridge configuration was used in the current study.  The gauge outlined in red is the only active gauge in this setup while the other three are dummy gauges.  Courtesy of Micro-Measurements, a Division of Vishay Precision Group (239). The relationship between the output voltage (signal) and the input voltage can be found using circuit analysis: gh  i  i  j 4L4  4L  4k4  4kl m If each resistor produces an infinitesimal change, ∆R ≈ dR, the change in output voltage can be determined in terms of differentials: `g   j 44L4  4L! n `44  `4L4L o  44k4  4k! n `44  `4k4k ol m When there is no change in resistance, the bridge is balanced and the output voltage is zero.  This occurs when R = R1 = R2 = R3 = R4 which from Eq. A8 yields: (Eq. A7) (Eq. A8) Appendix A  152 `g   U ]Yk]Y b]Y]Y  b]X]X 
  ] Y k]Y b]W]W  b]p]p 
Zm `g   14 j `44  `4L4L  `44  `4k4k l m  f% 4 rM  ML  M  Mksm Given the Gauge Factor relationship defined earlier, GF = (dR/R)/ε. For a quarter-bridge configuration (Figure A-2b), three of the gauges (R1, R3 and R4) are dummy resistances and therefore experience no strain or temperature changes (174).  Therefore the output voltage can be determined in terms of R2 only giving the following relationship: g   f%4 M!m Because there is only one active gauge, temperature fluctuations cannot be separated from strain so the effect of temperature, as well as other extraneous effects such as resistance change in the gauge, acts as an additional strain, limiting the accuracy of the measurements to ±10 microstrain (174).  In this study, the circuit was used in a constant temperature environment and this accuracy was deemed acceptable. In the three-wire quarter-bridge circuit used in this study, R1 is replaced with a strain gauge, RG (Figure A-3).  Leadwire RL1 and RG form one arm of the bridge while RL2 and resistor R4 forms the adjacent arm.  The third leadwire RL3 connects directly to the output voltage and compensates for losses resulting from resistance or temperature changes over the length of the wire.  When using the same leadwire type and length, RL1 and RL2 are initially the same causing the bridge to be symmetrical and balanced.  This is an advantage of the three-wire system as the bridge is less sensitive to temperature changes making it the recommended configuration for quarter-bridge strain gauge circuits for static strain measurement (239). (Eq. A9) (Eq. A10) Appendix A  153  Figure A-3: Three-wire quarter-bridge circuit used in current study.  Courtesy of Micro-Measurements, a Division of Vishay Precision Group (239).  Appendix B  154 Appendix B  Patient Radiographs Table B-1: Pre- and post-operative three-foot standing radiographs for Patients 1 through 7. 1  Pre-op (10/07/09) Post-op (11/25/09) 1-mnth follow-up (PJK@T11) Post- revision op (01/26/10) 1-mnth follow-up (Rod fx) Post- revision op (04/23/10) Appendix B  155 2   No post-op 3-foot standing x-ray was available; no revision surgery due to medical conditions 3  Original surgery (03/15/07) was completed at a different institution where no 3-foot standing x-ray was available.  There was a revision surgery (06/28/10) for a burst fracture at the proximal junction, instrumentation was extended from S1 to T10 (no x-ray available). Pre-op (01/19/07) 1-yr follow- up (PJK@T9) 1.5-yr follow-up (PJK@T9) 2-yr follow- up (PJK@T9) 5-mnth follow-up (L1 wedged) 2-yr,2-mnth follow-up (screw pull-out @L1) 2-yr,4-mnth follow-up (screw loosening @L1) 2-yr,7-mnth follow-up (disc degen. @T11- T12) 2-mnth Post- revision op (08/24/10) Appendix B  156 4  Original surgery was completed at a different institution where no 3-foot x-ray was available. 5  Original surgery was completed at a different institution where no 3-foot x-ray was available. Pre-revision op (08/05/08) Post- revision op (09/22/08) 1-mnth follow-up 3-mnth follow-up 6-mnth follow-up 1-year follow-up 2-year follow-up Pre-revision op (10/23/08) Post- revision op (02/23/09) 4-mnth follow-up Appendix B  157 6  Original surgery was completed at a different institution where no 3-foot x-ray was available, Revision surgery took place 08/14/09 7  Original surgery was completed at a different institution where no 3-foot x-ray was available, Revision surgery took place 05/28/09. Patient underwent a subsequent revision surgery (02/08/10) for vertebral and rod fractures, by means of a partial corpectomy but instrumentation was not extended further (no x-ray available). Pre-revision op (06/05/09) 2-mnth follow-up 1-yr follow-up Pre-revision op (12/16/08) 3-mnth follow-up 5-mnth follow-up 8-mnth follow-up Appendix C 158  Appendix C  Example Radiographic Data Vertebral z (anterior-posterior) and y (cranial-caudal) positions and angulation were measured from radiographs of every patient.  From this data, the plumb line (z position of C7), thoracic kyphosis (angle between T5 and T12), and lumbar lordosis (angle between L1 and S1), among other radiographic parameters could be deduced.  Table C-1 shows the data collected from the pre-operative x-ray for Patient 2.  This patient’s plumb line, thoracic kyphosis, and lumbar lordosis, were 93.2 mm, 24°, and -36°, respectively. Table C-1: Example of measurements collected from patient x-rays.  Data taken from Patient 2’s pre- operative x-ray. Vertebra Z [mm] Y[mm] θ [deg] C1 88.8 538.8 0 C2 90 527.2 -16 C3 85.2 512.4 -16 C4 79.6 489.6 -14 C5 87.6 475.6 -22 C6 86 462.8 -12 C7 93.2 451.6 -3 T1 91.6 434.4 -22 T2 93.2 416 -33 T3 82.4 389.2 -29 T4 75.2 365.6 -23 T5 63.2 344 -19 T6 55.2 322.8 -15 T7 46 296.4 -16 T8 36.8 270.8 -9 T9 30 242 -10 T10 25.6 213.2 -13 T11 19.2 187.2 -2 T12 12.4 160 2 L1 9.6 131.2 4 L2 11.6 101.6 9 L3 22 80.8 7 L4 25.6 55.2 -7 L5 20.8 28 -13 S1 0 0 -32  Plumb line, PL = ZC7 - ZS1 = 93.2 mm Thoracic Kyphosis, TK = θT12 – θT1 = 2 + 22 = 24° Lumbar Lordosis, LL = θS1 – θL1 = -32 – 4 = -36° Appendix D  159  Appendix D  Osteotomy Calculation The corrected sagittal profiles were calculated for each patient after simulating pedicle subtraction osteotomies at L2, L3, and L4, based on initial pre-operative sagittal profiles measured from radiographs.  This section will describe the calculations completed for an osteotomy performed at L3, the geometry of which can be seen in Figure D-1.           Figure D-1: Schematic illustrating geometry used for osteotomy calculation.  (a) Change in sagittal profiles from pre-operative to corrected curvatures (profiles are right lateral).  Here, an osteotomy is performed at L3 (red dot) and the plumb line (PL) from C7 (green dot) is brought back in line with the posterior sacral perpendicular line (PSPL).  All positions of vertebrae below the osteotomy level (red line) remain unchanged between the two profiles.  The positions of vertebrae above the osteotomy are calculated using trigonometric relationships and assumptions listed in Section 2.2.4.1.  (b) Close-up of L3 vertebra where osteotomy is performed.  L is the vertebral depth and D is the height of an osteotomy of size α.  If L3 is at angulation θ in its pre-operative posture, the vertical drop associated with the osteotomy is d (Eq. D7). Correction was achieved by bringing the C7 plumb line (PL) in line with the posterior sacral perpendicular line (PSPL) such that the new horizontal position of C7 relative to S1 would be zero.  To determine the required size of an osteotomy at L3 to achieve this correction, the angles γ1 and γ2 were added, representing the angle necessary to bring C7 in line with a line y z1 z2 γ1 γ2 l l PL PSPL Pre-op Corrected (a) (b) D α L α L D d θ θ Appendix D  160  perpendicular to L3 and the additional angle necessary to bring it in line with the PSPL, respectively.  The following calculations were made, in which the variables used are referencing those in Figure D-1: R  tan &W) 
   tan &tu&vX)tu)vX w  x  a     y      a  zw  x  zw	{  wL!  x	{  xL! R  sin wa 
  sin  wL  w5a 
   R  R  The sagittal profile superior to the osteotomy was then rotated about L3 using the following rotation matrix: Uw} ~€P EF€E€E‚)!x} ~€PEF€E€E‚)!Z  Ucos  sin sin  cos  Z U w} ƒEP EF€E€E‚)!x} ƒEP EF€E€E‚)!Z where zi and yi represent the horizontal and vertical locations, respectively, of the posterior superior corner of each vertebra from C1 down to L2 with respect to L3, before and after the osteotomy.  The vertical locations of the vertebrae were further modified to taken into account the vertical drop that would ensue after subtraction.  The subtraction distance was calculated, with reference to Figure D-1, using:    tan   where L is the vertebral depth and D is the height of an osteotomy of size α.  With L3 initially at an angulation θ, the vertical drop associated with the subtraction is: `   cos 3  The final new horizontal (z) and vertical (y) distances of the posterior-superior corner of each vertebra with respect to S1 after correction were given by:   (Eq. D1) (Eq. D2) (Eq. D3) (Eq. D4) (Eq. D5) (Eq. D6) (Eq. D7) Appendix D  161  wDEPPD€bxDEPPD€b  w}  wL  w5!x}  xL  x5!  `  for C1 to L2 wDEPPD€bxDEPPD€b  w„PE„x„PE„  `             for L3 wDEPPD€bxDEPPD€b  w„PE„x„PE„    for L4 to S1 Finally, the new angulations of all vertebrae superior to L3 were calculated by adding their pre-operative angulations (θ1) to the osteotomy size (α), justification for which is shown in Figure D-2. 3  3         Figure D-2: Schematic of vertebral level above osteotomy before (left) and after (right) subtraction is performed.  If the given osteotomy (green) of size α is brought beside the adjacent vertebra, it can be seen that it forms the same angle α in blue.  The combination of the vertebral angulation θ1 and osteotomy angle α form the angle in blue which, when moved to the schematic on the right can be seen to equal the vertebra’s new angulation (θ2) after the osteotomy is performed.  Therefore the new angulation of all vertebrae superior to the osteotomy can be calculated by adding their pre-operative angulation to the osteotomy angle.  L D α θ1 θ2 α α θ1+ α (Eq. D8) (Eq. D9) Appendix E  162  Appendix E  Equilibrium Model Results (Chapter 2) The following pages include the geometric and compressive loading plots for all osteotomy and muscle function variations for Patients 1 to 7.  Each patient is described by its number, sex, age, mass, deformity type (DS – degenerative scoliosis, KD – kyphotic deformity, LF – lumbar flatback, SP – spondylolisthesis, SS – spinal stenosis), uppermost instrumented vertebra of initial analyzed surgery (UIV), and uppermost instrumented vertebra after extension in subsequent revision surgeries (Ext), when applicable.  For each patient, figures are shown as follows: • A: Geometric plots of sagittal profiles from each available x-ray. • B: Predicted Compressive Loads as a function of uppermost instrumented vertebra for sagittal profiles from each available x-ray, assuming an extensor muscle group fully-counteracts body-weight loads. • C: Geometric plots of pre-operative sagittal profile and those simulated after correction with an osteotomy at L2, L3, and L4. • D: Predicted Compressive Loads as a function of uppermost instrumented vertebra for pre- operative sagittal profile and for those simulated after correction with an osteotomy at L2, L3, and L4. • E: Predicted Compressive Loads as a function of uppermost instrumented vertebra for sagittal profiles from each available x-ray, assuming extensor muscles are removed and a posterior rod fully-counteracts bodyweight loads. • F: Predicted Compressive Loads as a function of uppermost instrumented vertebra for sagittal profiles from each available x-ray, assuming extensor muscles are removed and the vertebral body at the given level fully-counteracts bodyweight loads. Legend entries refer to time before and after surgeries completed at Vancouver General Hospital.  “Pre-op” are those patients who were referred to VGH for corrective surgery, having received initial treatment at another institution.  Appendix E  163     Figure E-1: Model results for Patient 1, plots A to F as described on page 162. (F; 54 yrs; 65 kg; DS; UIV- None (pre-op), T11; Ext – T8 and T4) -200 -100 0 100 200 300 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   Pre-op Immediate post-op 1-mnth post-op (PJK) 2-mnth post-op (Imm. post-rev. op) 3-mnth post-op (Rod fx) 5-mnth post-op (Imm. post-rev2. op) T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 800 900 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (10 0%  m u sc . ) [N ]   Pre-op Immediate post-op 1-mnth post-op (PJK) 2-mnth post-op (Imm. post-rev. op) 3-mnth post-op (Rod fx) 5-mnth post-op (Imm. post-rev2. op) -250 -200 -150 -100 -50 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d [N ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 800 900 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (0%  m u sc .  -  ve rte br a ) [N ]   Pre-op Immediate post-op 1-mnth post-op (PJK) 2-mnth post-op (Imm. post-rev. op) 3-mnth post-op (Rod fx) 5-mnth post-op (Imm. post-rev2. op) T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 800 900 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo ad  (0%  m u sc .  -  ro d) [N ]   Pre-op Immediate post-op 1-mnth post-op (PJK) 2-mnth post-op (Imm. post-rev. op) 3-mnth post-op (Rod fx) 5-mnth post-op (Imm. post-rev2. op) A B C D E F Appendix E  164     Figure E-2: Model results for Patient 2, plots A to F as described on page 162. (M; 73 yrs; 76.5 kg; KD, LF; UIV- none (pre-op), T9; Ext – none) -200 -100 0 100 200 300 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   Pre-op 1-yr post-op (PJK) 1.5-yr post-op (PJK) 2-yr post-op (PJK) T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 1400 1600 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (10 0%  m u sc .) [ N ]   Pre-op 1-yr post-op (PJK) 1.5-yr post-op (PJK) 2-yr post-op (PJK) -250 -200 -150 -100 -50 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d [N ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 1400 1600 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (0%  m u sc .  -  ro d) [N ]   Pre-op 1-yr post-op (PJK) 1.5-yr post-op (PJK) 2-yr post-op (PJK) T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 1400 1600 Uppermost Instrumented Vertebral level Co m pr e ss iv e Lo ad  (0%  m u sc .  -  ve rte br a) [N ]   Pre-op 1-yr post-op (PJK) 1.5-yr post-op (PJK) 2-yr post-op (PJK) A B C D E F Appendix E  165     Figure E-3: Model results for Patient 3, plots A to F as described on page 162. (F; 71 yrs; 67 kg; DS; UIV- L1 (pre-op), T10; Ext – none) -100 0 100 200 300 400 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   4.5-mnth post-op (PJK) 2-yr, 2-mnth post-op 2-yr, 4-mnth post-op 2-yr, 7-mnth post-op 3-yr, 5-mnth post-op (Imm. post-rev.op) T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (10 0%  m u sc . ) [N ]   4.5-mnth post-op (PJK) 2-yr, 2-mnth post-op 2-yr, 4-mnth post-op 2-yr, 7-mnth post-op 3-yr, 5-mnth post-op (Imm. post-rev.op) -250 -200 -150 -100 -50 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d [N ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (0%  m u sc .  -  ro d) [N ]   4.5-mnth post-op (PJK) 2-yr, 2-mnth post-op 2-yr, 4-mnth post-op 2-yr, 7-mnth post-op 3-yr, 5-mnth post-op (Imm. post-rev.op) T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 Uppermost Instrumented Vertebral level C o m pr e ss iv e  Lo a d (0%  m u sc .  -  ve rte br a ) [N ]   4.5-mnth post-op (PJK) 2-yr, 2-mnth post-op 2-yr, 4-mnth post-op 2-yr, 7-mnth post-op 3-yr, 5-mnth post-op (Imm. post-rev.op) A B C D E F Appendix E  166     Figure E-4: Model results for Patient 4, plots A to F as described on page 162. (F; 71 yrs; 71 kg; SP; UIV- L4 (pre-op), L1; Ext – none) -150 -100 -50 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   "Pre-op" Immediate post-op 1-mnth post-op 3-mnth post-op 6-mnth post-op 1-yr, 2-mnth post-op 2-yr post-op T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 800 900 1000 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (10 0%  m u sc . ) [N ]   "Pre-op" Immediate post-op 1-mnth post-op 3-mnth post-op 6-mnth post-op 1-yr, 2-mnth post-op 2-yr post-op -250 -200 -150 -100 -50 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 Uppermost Instrumented Vertebral level C o m pr e ss iv e  Lo a d [N ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 800 900 1000 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (0%  m u sc .  -  ro d) [N ]   "Pre-op" Immediate post-op 1-mnth post-op 3-mnth post-op 6-mnth post-op 1-yr, 2-mnth post-op 2-yr post-op T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 800 900 1000 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (0%  m u sc .  -  ve rte br a ) [N ]   "Pre-op" Immediate post-op 1-mnth post-op 3-mnth post-op 6-mnth post-op 1-yr, 2-mnth post-op 2-yr post-op A B C D E F Appendix E  167     Figure E-5: Model results for Patient 5, plots A to F as described on page 162. (M; 59 yrs; 93 kg; SS, KD; UIV- T11 (pre-op), T10; Ext – none) -150 -100 -50 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   "Pre-op" Immediate post-op 4-mnth post-op T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 1400 1600 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (10 0%  m u sc . ) [N ]   "Pre-op" Immediate post-op 4-mnth post-op -250 -200 -150 -100 -50 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d [N ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 1400 1600 Uppermost Instrumented Vertebral level Co m pr e ss iv e Lo ad  (0%  m u sc .  -  ro d) [N ]   "Pre-op" Immediate post-op 4-mnth post-op T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 1400 1600 Uppermost Instrumented Vertebral level C o m pr e ss iv e  Lo a d (0%  m u sc .  -  ve rte br a ) [N ]   "Pre-op" Immediate post-op 4-mnth post-op A B C D E F Appendix E  168       Figure E-6: Model results for Patient 6, plots A to F as described on page 162. (F; 62 yrs; 68 kg; KD, LF; UIV- T11 (to L5) (pre-op), T11 (to S1); Ext – none) -150 -100 -50 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   "Pre-op" 2-mnth post-op 1-yr post-op T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 Uppermost Instrumented Vertebral level Co m pr es si ve  Lo a d (10 0%  m u sc . ) [N ]   "Pre-op" 2-mnth post-op 1-yr post-op -250 -200 -150 -100 -50 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d [N ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (0%  m u sc .  -  ro d) [N ]   "Pre-op" 2-mnth post-op 1-yr post-op T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (0%  m u sc .  -  ve rte br a ) [N ]   "Pre-op" 2-mnth post-op 1-yr post-op A B C D E F Appendix E  169     Figure E-7: Model results for Patient 7, plots A to F as described on page 162. (F; 58 yrs; 102 kg; SP, KD; UIV- L4 (pre-op), L1; Ext – none) -150 -100 -50 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   "Pre-op" 3-mnth post-op 5-mnth post-op 8-mnth post-op T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 Uppermost Instrumented Vertebral level Co m pr es si ve  Lo a d (10 0%  m u sc . ) [N ]   "Pre-op" 3-mnth post-op 5-mnth post-op 8-mnth post-op -250 -200 -150 -100 -50 0 50 100 150 200 250 0 50 100 150 200 250 300 350 400 450 500 Horizontal distance [mm] Ve rti ca l d is ta n ce  [m m ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 100 200 300 400 500 600 700 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d [N ]   Pre-op L2 osteotomy L3 osteotomy L4 osteotomy T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 Uppermost Instrumented Vertebral level Co m pr e ss iv e  Lo a d (0%  m u sc .  -  ro d) [N ]   "Pre-op" 3-mnth post-op 5-mnth post-op 8-mnth post-op T1 T2 T3 T4 T5 T6 T7 T8 T9 T10T11T12 L1 L2 L3 L4 L5 S1 0 200 400 600 800 1000 1200 Uppermost Instrumented Vertebral level Co m pr es si ve  Lo ad  (0%  m u sc .  -  ve rte br a ) [N ]   "Pre-op" 3-mnth post-op 5-mnth post-op 8-mnth post-op A B C D E F Appendix F 170  Appendix F  - Loading Apparatus and Pure Moment Verification The spine simulator used in this study (208) applied a pure unconstrained flexion- extension moment to the cranial segment of a spine specimen by means of an articulating arm and counterweight pulley system shown in Figures F-1 and F-2.    . Figure F-1: The spine simulator used for this study was constructed out of aluminum extrusions.  It had a counterweight that hung on a pulley attached to an XY translation device to allow it to follow specimen translation. (a) Front view and (b) Left side view. Servomotor Ball spline Universal joint Universal joint Attachment Block Lateral counterweight Torque Load cell Aluminum extrusions Pulley- counterweight system XY translation device Figure F-2: Close-up of articulating arm, consisting of a servomotor, ball spline, two universal joints, a torque load cell, an attachment block to affix the superior loading plate of the specimen, and a lateral counterweight. Appendix F 171  To verify the proper functioning of the loading apparatus and to quantify any off-axis loading errors, the actual applied moments in all three planes were measured during the known application of a sagittal plane moment.  A pair of instrumented rods was attached to plastic blocks each with two pedicle screws and the plastic blocks were then bolted to loading plates. The superior and inferior loading plates were rigidly attached to the spine simulator articulating arm and a six-axis load cell (MC3A, AMTI, Watertown, MA) attached to the base plate, respectively (Figure F-3).  The articulating arm applied a sagittal moment of ±10 Nm for three cycles and the moments and loads in each direction were measured by the load cell.  Based on the coordinate system shown, the measurements in the x, y, and z direction represent a lateral, sagittal, and axial moment, respectively and an anterior-posterior, medial-lateral, and axial load, respectively.  The measured moments and loads for the three loading cycles can be seen in Figure F-4.  Figure F-3: Loading apparatus setup for test with 6-axis load cell, shown from (a) the posterior view and (b) the lateral view.  Instrumented rods were attached to plastic blocks with pedicle screws and affixed to the loading apparatus.  A pure sagittal moment of ± 10 Nm was applied and all moments (Mx, My, Mz) and loads (Fx, Fy, Fz) were measured to determine off-axis loading.  The coordinate system for the load cell is shown.   6 axis Load cell Plastic testing blocks Instrumented rods Articulating arm Counterweight Strain gauges z x y (a) (b Appendix F 172        The applied sagittal moment of ±10 Nm was measured by the six-axis load cell to within 3% and 5% for flexion and extension, respectively.  The off-axis moments were under 6% and 4% for lateral and axial directions, respectively.  The measured loads in the x and y directions and z direction during flexion were under 7 N while during extension, the z direction force was under 17 N.  It was expected that this increase in load magnitude was a result of a drift that was seen in the data throughout the three cycles.  These results verify that the spine simulator applied pure sagittal moments for the current study. Figure F-4: Results from test with 6-axis load cell.  (a) Measured moments in all three planes.  The applied moment (in green) overlays the measured sagittal moment (blue) while lateral and axial moments are small.  (b) Measured loads in all three directions are small.  These results confirm that the loading apparatus is applying pure sagittal moments. (a) (b) Appendix G 173  Appendix G  Preliminary Study: Vertebral Load Calibration using Matrix Method In this study, a pure moment was applied to the specimen and vertebral strains were measured.  It was desired to convert these strains to moment and load transferred to the vertebra to determine how load is distributed between different structures.  A calibration test was therefore designed to convert the strain gauge signals from the vertebral body to load using the matrix method (177).  Three tests were involved: pure moment loading, pure axial compression loading, and combined moment and axial compression loading (Figure G-1).  If strain responses to the applied loads are linear, the following relationship exists: UM/M> Z  j   l U *% Z Where εM and εF are measured strains at two vertebral locations* (anterior and lateral), M and F are known applied moment and axial force, respectively, And Dij are unknown calibration constants.         The applied loads and measured strains were recorded for each of the tests and the four matrix constants were calculated (Eq.’s G2 to G5).  Two of the matrix constants were direct calibration constants (ie. the constants related the applied moment to the vertebral moment prediction or applied axial load to the vertebral axial force prediction) and the other two were    M F     T12 L1 L2 εM εF   Figure G-1: Schematic of loading test (anterior view) where F is axial compression load of 300 N, M is moment of ± 8 Nm, εF is anterior strain gauge (for axial load prediction) and εM is lateral strain gauge (for moment prediction). εM and εF were the measured strains for moment and axial force predictions, respectively. (Eq. G1) Appendix G 174  coupling constants (ie. the constants related the applied moment to the vertebral axial force prediction or applied axial load to the vertebral moment prediction). M//  * 0! yields D11 (direct) M>/  *  0! yields D21 (coupling) M/>  0!  % yields D12 (coupling) M>>  0!  % yields D22 (direct) Theoretically, if the measured strains are multiplied by the inverted calibration matrix (Eq.’s G6 to G9), the moment, M, and force, F, calculated should equal the applied moment and load, respectively.  Any differences found between the known and calculated moments and loads are due to errors in the test design or a result of a non-linear vertebral strain response to loading. UM/M> Z  rs U*% Z rs UM/M> Z  rsrs U*% Z r…s  rs  †‡ˆ ! j    l ‰‚/‹V ‰/‹V  2` rsrs  1 U*% Z  rs U M/M> Z  j … …… …l U M/M> Z The pure moment and pure axial compression loading conditions yielded the following calibration matrix and equation: U*% Z  U5.56H10 L 8.7H10L1.402 1.00 Z U M/M> Z When the strains measured during the combined test were multiplied with this calibration matrix, the predicted moment and force were calculated and compared to known applied loads (Figure G-2).  (Eq. G2) (Eq. G3) (Eq. G4) (Eq. G5) (Eq. G6) (Eq. G7) (Eq. G8) (Eq. G9) (Eq. G10) Appendix G 175    Figure G-2: Comparison between the applied (red) and calculated (blue) (a), (b) moments and (c), (d) loads during flexion loading (left) and extension loading (right) of the third cycle.  Fair agreement was seen between applied and calculated moments but not between the applied and calculated loads. From Figure G-2, it can be deduced that there was relatively good agreement between applied and calculated moments but that there was inadequate agreement between applied and calculated loads on the vertebral bodies.  This can be explained by looking at the raw strain response to both a pure moment and pure axial compressive load, where much better linearity was found with the former.  Figure G-3b shows that the same strain is measured for a large range of applied loads so it is difficult to deduce a load from a measured strain.  Due to this non- 0 50 100 150 200 250-2 0 2 4 6 8 10 0 50 100 150 200 250-10 -8 -6 -4 -2 0 2 0 50 100 150 200 250200 300 400 500 600 0 50 100 150 200 250200 250 300 350 400 M o m en t [ N m ] Lo a d [N ] FLEXION EXTENSION Time [s] Time [s] Time [s] Time [s] (a) (b) (c) (d) Appendix G 176  linearity, the matrix method was an inadequate tool to relate measured strains to moments and loads and therefore only the raw vertebral strain values are reported in this paper.  Figure G-3: Vertebral strain response during the third cycle for the anterior gauge (black) and lateral gauge (red) in response to (a) a pure moment of 0 to 8 Nm and (b) a compressive axial load of 0-300 N.  It can be seen that, especially in the case of the axial load, the same strain response occurs for a large range of loading values, showing a non-linear strain response. -700 -600 -500 -400 -300 -200 -100 0 0 2 4 6 8 S tr a in  [ m ic ro st ra in ] Moment [Nm] -200 -150 -100 -50 0 50 100 0 100 200 300 S tr a in  [ m ic ro st ra in ] Load [N](a) (b) Appendix H  177 Appendix H  Spinal Rod Drawings  Figure H-1: Drawing of the posterior fusion rods used in the current study (short length).  Figure H-2: Drawing of the posterior fusion rods used in the current study (long length). Appendix I  178      (Eq. I2)      (Eq. I4)      (Eq. I5) Appendix I  Rod Loading Theoretical Relationships With the configuration shown in Figure 3-6, the strain gauge numbering convention is determined such that the measured strain value ε1 is the intermediate value (209): M ‘ M ‘ ML or ML ‘ M ‘ M Both requirements to ensure validity of the relationship were met with the rods in our experiment: the rod cross-section was circular, and stresses beyond the yield stress of titanium (140 MPa) were not applied. The strains induced in the cylindrical rod at the cross-section at the gauge site due to and applied load and moment about its neutral axis are given by Eq. I2. M,,L  Jm “ *6,,L”m where A – cross sectional area of the rod [m2] E – modulus of elasticity [Pa] I – area moment of inertia, [m4] = 1/4pir4 r – radius of rod cross section [m] c1, c2, c3 – distances from strain gauges ε1, ε2, ε3, respectively, to neutral axis [m] Since the strain gauges are mounted 120° apart, Eq.’s I1 and I2 imply that ε1 is located nearest the neutral axis.  Any loading configuration can be used as long as it is consistent but, using that shown in Figure 3-6 as an example, Eq. I2 can be solved to give: J   :KL M  M  ML! *  ”m√3d670R ML  M! R  S2 T √L U1  VWVX!VYVX! Z[ P, M, and γ represent the axial load, bending moment, and orientation of the neutral axis of each rod.  If any of the values are found to be negative, the assumed loading conditions were not correct.      (Eq. I1)      (Eq. I3) Appendix J  179 Appendix J  Rod Accuracy and Sensitivity Tests J.1 Accuracy Test To determine the accuracy of the rod loads and moments calculated from measured strain values, a simple bending test was designed to create a loading scenario representative of that in the beam bending theory (240), where the applied moment is transferred through the neutral axis of the rod located at its centroid.  Two polyethylene blocks were attached to both a superior and inferior loading plate and a pedicle screw was inserted into each such that the distance between them imitated that between the pedicles of a vertebra (40 cm).  The superior and inferior pedicle screws were then separated with spacers and clamps by a distance of 52 cm, representing the distance necessary for a rod to span three vertebrae.  The alignment technique and the completed rod-plastic block configuration attached to the loading apparatus can be seen in Figure J-1.  The rods were oriented with one of the strain gauges facing posteriorly and three cycles of a sagittal pure moment of ± 7 Nm was applied (Figure J-2).  This test was repeated for both the long and short rod lengths before and after specimen tests were conducted.  Figure J-1: Rod loading accuracy test. (a) Pedicle screws were inserted into four polyethylene blocks and separated a distance of 52 cm before the rods were attached. Spacers and C-clamps were used to maintain alignment. (b) Two rods attached to polyethylene blocks with pedicle screws, clamped onto the loading apparatus. (a) (b) Appendix J  180  Figure J-2: (a) The rods were aligned so that one of the strain gauges of each set was facing posteriorly. (b) The rod-block system was attached to the loading apparatus and a pure moment, Mapplied, was applied for three cycles. The moment seen by each gauge set was calculated with Eq. I4; the two gauge sets on each rod were expected to measure the same strain and thus have the same calculated moment while the total applied moment was expected to be distributed evenly between the right and left rods.  An example of the raw strain data of the fifth cycle for the left rod superior gauge is shown in Figure J-3a, showing the posterior gauge in tension during flexion and compression during extension, while the other two gauges show similar strain in the opposite direction, as expected. These strains were same for all gauge sets.  The total calculated rod moments for the superior (7.4 Nm) and inferior (8.1 Nm) levels are seen in Figure J-3b and agree well with the applied moment (7.1 Nm).  The accuracy was measured in terms of the percent difference between the magnitude of the applied moment and the total calculated moment at superior and inferior levels at maximum flexion and extension.  An average was taken between the error found at maximum flexion and maximum extension loading of the third cycle (Table J-1) and this error incorporates human error of the strain gauge application as well as experimental error from the system setup and load application.  The moment calculation appears to be more accurate for the superior level Posterior gauges Mapplied (a) (b) Appendix J  181 and for the accuracy test completed before specimen testing.  The differences seen may be a result of the rod slipping within the set screw or of the pedicle screw slipping in the plastic block.  Figure J-3: Results from accuracy study for the short rod before specimen tests. (a) Raw strain data for the superior gauge of the left rod, taken from the third cycle. Similar trends were seen for all gauges. (b) The calculated rod moment during the third flexion loading cycle.  The gauges of the left and right rod were summed together for both the superior (blue) and inferior (red) levels, both of which agree well with the applied moment (black). Table J-1: Percent error between long and short rod moment calculations and applied moment for superior and inferior levels  Long rods Short rods Pre-specimen tests Post-specimen tests Pre-specimen tests Post-specimen tests Average error: Superior level 3.2 6.0 5.6 8.5 Average error: Inferior level 9.5 13.7 17.2 21.4  J.2 Sensitivity Test Two tests of sensitivity of rod orientation on measured strain were conducted.  First was a test of the sensitivity of adjacent pedicle positions and second of the circumferential position of the rods during testing. J.2.1 Adjacent Pedicle Position When inserting pedicle screws into a human spine, adjacent pedicle screws are most often not aligned in the vertical plane because of different vertebral sizes.  To determine the sensitivity (a) (b) Appendix J  182 of the relative position of adjacent pedicle screws on the moments calculated by the rod strain gauges, a test was designed to quantify the difference between measurements made with vertically-aligned rods and angled rods.  Similarly to the aforementioned accuracy test, two plastic blocks were attached to superior and inferior loading plates and were separated by a distance of 52 cm with spacers.  The configuration of the rods for the vertically-aligned case was the same as that of the accuracy test while for the angled case, the inferior pedicle screws were separated instead by a larger distance of 61 cm, shown in Figure J-4.  For both test cases, the block-rod system was attached to the loading apparatus and three cycles of ±5 Nm in flexion- extension was applied.  Figure J-4: Rods were affixed to polyethylene blocks in two orientations: (a) Vertically-aligned (straight) and (b) Angled.  A spacer was used to separate the pedicle screws a distance of 52 cm and C-clamps held the block-rod system in place while set screws were tightened to affix the rods.  These two orientations represent the inter-specimen variation of distances between adjacent pedicles. An example of the total calculated rod moment compared with the applied moment for the short rods during the third flexion loading cycle can be seen in Figure J-5 for the vertically- aligned and angled orientation cases.  Similar trends were found for both rod lengths during flexion and extension loading cycles and there were minimal differences between any of the (a) (b) Appendix J  183 orientations.  Because there was nothing but the rods resisting the motion of the plastic blocks, when a moment was applied at two degrees per second the block-rod system reached 5 Nm very quickly and with fewer data points than with a specimen.  This explains the linear nature of applied and calculated moments.  The offset that can be seen for the calculated rod moments is inherent of the spine simulator and its effect is reduced when there are more data points collected.  Figure J-5: Applied (black) and total calculated superior level (green) and inferior level (red) rod moments for the third flexion loading cycle for rods in two inter-pedicle orientations: (a) Vertically-aligned (straight) and (b) Angled.  The two orientations yield very similar results inferring that the position of the screws in adjacent pedicles will not have a large effect on the calculated rod moments. J.2.2 Rod Circumferential Position During the current study, the rods were aligned such that a strain gauge of each set of three was aligned facing posteriorly.  However, due to human error, there was variability of alignment between tests so it was of interest to determine if the strain measurements were sensitive to the circumferential position of each strain gauge.  Using the short rods in the angled rod orientation discussed previously, two positions were tested for the right rod in the block-rod system: a strain gauge aligned anteriorly, and a strain gauge offset slightly from the desired posterior position (Figure J-6).  The block-rod system was attached to the loading apparatus and three cycles of ±5 Nm in flexion-extension was applied. (a) (b) Appendix J  184          An example of the raw right rod strain data in each orientation is shown in Figure J-7 for each orientation.  It can be seen that from the desired position (a), the right gauge becomes the gauge oriented anteriorly (b), showing large strains in the opposite direction, and that the left gauge becomes very close to the neutral axis (c), showing small strains.  Comparing the calculated rod moments during the third flexion loading cycle for each strain gauge set for the two right rod orientations (Figure J-8), it can be seen that the circumferential position does not have a notable effect.  Figure J-7: Raw rod strains for three configurations: (a) Left rod in desired position (gauge aligned posteriorly), (b) Right rod with gauge aligned anteriorly, and (c) Right rod with posterior gauge slightly offset.  The same strain gauge naming convention has been used for all three orientations for comparison between them.  ‘Posterior’ refers to the gauge aligned posteriorly in the desired position while ‘Right’ and ‘Left’ refer to the gauges the right and left of the posterior gauge, respectively. POSTERIOR ANTERIOR z x y 120° 120° 120° ε1 ε3 ε2 POSTERIOR ANTERIOR 120° 120° 120° ε1 ε3 ε2 POSTERIOR ANTERIOR 120° 120° 120° ε1 ε3 ε2 Neutral axis (a) (b) (c) Figure J-6: Orientation of the strain gauges on the right rod in (a) the desired position (gauge aligned posteriorly), (b) gauge aligned anteriorly and (c) gauge offset slightly from posterior (a) (b) (c) Appendix J  185  Figure J-8: Total calculated rod moments from each strain gauge set for the third flexion loading cycle for two right rod orientations: (a) Gauge aligned anteriorly and (b) Posterior gauge slightly offset.  The two orientations yield very similar results to each other and when comparing them to the left rod moments (for the desired position) inferring that the position of the circumferential position of the rods will not have a large effect on the calculated rod moments. For both sensitivity tests, the difference between the combined calculated moment for both the left and right rod gauge sets at the superior and inferior level and the applied moment determined the accuracy (percent error) of the moment calculation in each case.  An average was taken between the error found at maximum flexion and maximum extension loading of the third cycle.  The sensitivity of rod orientation was then determined by calculating the percent difference between the calculated moments of the vertically-aligned and angled rod cases, and between those of the two circumferential positions.  This difference represents the dependence of rod orientation on the validity of the use of Tuttle’s relationships to calculate rod moment. Given four different rod orientations, the theoretical calculations were able to accurately predict rod moments in all cases (percent error less than 17%) and  calculated  rod moments were not sensitive to orientation (percent difference less than 8%) (Table J-2).      (a) (b) Appendix J  186 Table J-2: Percent error for accuracy and sensitivity between two inter-pedicle orientations  Long rods Short rods Short Angled Straight Angled Straight Angled Anterior gauge Posterior offset Superior Average accuracy 4.0 3.4 4.7 3.3 9.5 2.4 Average sensitivity 7.4 2.8 6.3 Inferior Average accuracy 4.3 7.5 16.9 12.5 11.7 14.4 Average sensitivity 7.8 4.6 3.0 Appendix K  187 Appendix K  Example in vitro Results for Specimen 4 Condition 2 (Chapter 3)  K.1 Vertebral Strain  Figure K-1.1: 5th flexion-extension loading cycle, showing (a) raw vertebral strain, and (b) strain linearity.   Figure K-1.2: Adjacent Vertebra strain magnitudes across conditions for (a) anterior gauge, maximum flexion, (b) anterior gauge, maximum extension, (c) lateral gauge, maximum flexion, and (d) lateral gauge, maximum extension. (a) (b) (a) (b) (c) (d) Appendix K  188   Figure K-1.3: Uppermost Instrumented Vertebra strain magnitudes across conditions for (a) anterior gauge, maximum flexion, (b) anterior gauge, maximum extension, (c) lateral gauge, maximum flexion, and (d) lateral gauge, maximum extension.                  Appendix K  189   K.2 Rod Strain   Figure K-2.1: 5th flexion-extension loading cycle, showing raw rod strain for (a) left rod, superior gauge set, (b) right rod, superior gauge set, (c) left rod, inferior gauge set, and (d) right rod, inferior gauge set.  (a) (b) (c) (d) Appendix K  190   Figure K-2.2: 5th flexion-extension loading cycle, showing strain linearity for (a) left rod, superior gauge set, (b) right rod, superior gauge set, (c) left rod, inferior gauge set, and (d) right rod, inferior gauge set.    (a) (b) (c) (d) Appendix K  191   Figure K-2.3: 5th loading cycle, showing calculated rod bending moments for the left superior (leftsup), left inferior (leftinf), right superior (rightsup), and right inferior (rightinf) gauge levels,  and superior and inferior levels summed (tot sup and tot inf, respectively) for (a), (b) flexion loading, and (c), (d) extension loading.   0 2 4 6 8-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 Flexion Moments (Calculated) Time [s] M om e n t [N m ]   M calc - leftsup M calc - leftinf M calc - rightsup M calc - rightinf 0 2 4 6 8-2 0 2 4 6 8 10 Time [s] M om en t [N m ]   M applied M calc - tot sup M calc - tot inf 0 2 4 6 8 10-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time [s] M om e n t [N m ]   M calc - leftsup M calc - leftinf M calc - rightsup M calc - rightinf 0 2 4 6 8 10-10 -8 -6 -4 -2 0 2 Time [s] M om en t [N m ]   M applied M calc - tot sup M calc - tot inf (a) (b) (c) (d) Appendix K  192   Figure K-2.4: 5th loading cycle, showing calculated rod loads for the left superior (leftsup), left inferior (leftinf), right superior (rightsup), and right inferior (rightinf) gauge levels,  and superior and inferior levels summed (tot sup and tot inf, respectively) for (a), (b) flexion loading, and (c), (d) extension loading.       0 2 4 6 8 -300 -200 -100 0 100 200 300 Time [s] Lo ad  [N ]   leftsup leftinf rightsup rightinf 0 2 4 6 8 -300 -200 -100 0 100 200 300 Time [s] Lo ad  [N ]   Calc Load - tot sup Calc Load - tot inf 0 2 4 6 8 10 -300 -200 -100 0 100 200 300 Time [s] Lo ad  [N ]   leftsup leftinf rightsup rightinf 0 2 4 6 8 10 -300 -200 -100 0 100 200 300 Time [s] Lo a d [N ]   Calc Load - tot sup Calc Load - tot inf (a) (b) (c) (d) Appendix K  193   Figure K-2.5: Calculated rod moment magnitudes across conditions for (a) superior gauge set, maximum flexion, (b) superior gauge set, maximum extension, (c) inferior gauge set, maximum flexion, and (d) inferior gauge set, maximum extension.   Figure K-2.6: Calculated rod load magnitudes across conditions for (a) superior gauge set, maximum flexion, (b) superior gauge set, maximum extension, (c) inferior gauge set, maximum flexion, and (d) inferior gauge set, maximum extension. (a) (b) (c) (d) (a) (b) (c) (d) Appendix K  194 K.3 Anterior Column Loads and Moments   Figure K-3.1: Predicted anterior column moment magnitudes across conditions for (a) superior gauge set, maximum flexion, (b) superior gauge set, maximum extension, (c) inferior gauge set, maximum flexion, and (d) inferior gauge set, maximum extension.    (a) (b) (c) (d) Appendix K  195   Figure K-3.2: Predicted anterior column load magnitudes across conditions for (a) superior gauge set, maximum flexion, (b) superior gauge set, maximum extension, (c) inferior gauge set, maximum flexion, and (d) inferior gauge set, maximum extension. K.4 Range of Motion  Figure K-4.1: Flexibility curve for the 5th loading cycle.  (a) (b) (c) (d) Appendix K  196    Figure K-4.2: Range of motion magnitudes across conditions for (a) sagittal plane, maximum flexion, (b) sagittal plane, maximum extension, (c) transverse plane (axial rotation), maximum flexion, (d) transverse plane (axial), maximum extension, (e) frontal plane (lateral bending), maximum flexion, and (f) frontal plane (lateral bending), maximum extension. 1 1 1 1 1 1 (a) (b) (c) (d) (e) (f) Appendix L  197 Appendix L  Additional Study: Diagnosis of Rod Bending Strain Results To determine if the rod loading results seen in the current study were caused by the study design and execution or by the specimen itself, a subsequent pure flexion-extension bending test was designed using Specimen 6 in its Anterior Ligament Destabilization condition (Condition 6) with three additional states of destabilization (Figure L-1): State A, where the pedicle screws of the left rod were cemented and otherwise specimen was in Condition 6 (± 5 Nm applied); State B, where the pedicle screws of both the left and right rod were cemented and the posterior elements and facet joints of the UIV were removed (± 5 Nm applied); State C, where the UIV disc and endplate was subsequently removed (± 3 Nm applied).  Figure L-1:  Specimen 6 (in the anterior ligament destabilization condition (Condition 6)) prepared for subsequent testing to explain rod strain result.  Left and right rods were affixed to the specimen with the two proximal pedicle screws.  The specimen was re-tested in subsequent states of destabilization. (A) State A: left pedicle screws cemented and right pedicle screws uncemented. Image shows both sides cemented but this was not until State B.  (B) State B: both rods’ pedicle screws cemented and posterior elements and facet joints of the intervening UIV removed. (C) State C: UIV endplate and disc subsequently removed, leaving gap between pedicle screws. Anticipating that the pedicle screw-vertebra interface was the source of the unforeseen rod loading, creating a rigid bond with bone cement was expected to reverse the direction of rod loading.  However, cement was found to increase only the magnitude of rod strain but not its (A) (B) (C) Appendix L  198 loading direction (Figure L-2, A1 and A2).  After posterior element and facet joint removal, rod strains were again comparable to the previous state in both magnitude and sign (Figure L-2B). Anterior column loading was then eliminated by complete removal of the UIV disc and endplate, creating a similar scenario to the plastic block-rod system used for accuracy and sensitivity tests (Appendix J) and to the corpectomy condition created by Rohlmann et al. (84).  Rod loading finally reversed signs and the posterior gauge experienced tension during flexion loading (Figure L-2C).  A clearer signal with higher magnitude strains was seen because spinal structures were no longer supporting any of the applied moment.  This reversal in rod strain signs translated to a similar change in calculated flexion and extension moments between States A and B to State C, where only after complete removal of the posterior and anterior structures did the calculated moments coincide with the applied moment (Figure L-3). Appendix L  199  Figure L-2: Rod strain time traces for each subsequent test.  Strains shown during the third cycle of a ± 5 Nm applied pure moment, measured from the superior level right (black), posterior (blue), and left (red) gauges during three states of destabilization: (A1) State A- only left rod screws cemented; right rod strain shown. (A2) State A- only left rod screws cemented; left rod strain shown. (B) State B- both rods’ screws cemented and posterior elements and facet joints removed; left rod strain shown. (C) State C- UIV disc and endplate subsequentely removed; left rod strain shown (± 3 Nm applied).   (A1) (A2) (B) (C) Appendix L  200  Figure L-3: Calculated moments from rod strains measured during flexion loading for Specimen 6.  Shown are the applied moment (black) and the total rod moment calculated using the sum of strains measured in the left and right gauge sets (M calc in green). (a) Applied 5 Nm in flexion in State B (Posterior elements and facet joints removed, with both rods’ screws cemented).  Calculated rod moments were in the opposite direction as the applied moment for both flexion and extension loading, similarly for State A.  The loading apparatus produced a small jolt in loading seen by the noise at 3 seconds.  (b) Applied 3 Nm in flexion in State C (Posterior elements and facet joints removed, UIV endplate and disc removed, with both rods’ screws cemented).  In this completely destabilized state, calculated rod moments were in the same direction as the applied moment for both flexion and extension loading and were very similar in magnitude.  0 2 4 6-2 -1 0 1 2 3 4 5 Flexion Moments (Calculated) Time [s] M om en t [N m ]   M applied M calc 0 2 4 6-0.5 0 0.5 1 1.5 2 2.5 3 3.5 Flexion Moments (Calculated) Time [s] M o m en t [N m ]   M applied M calc STATE B (FLEXION) STATE C (FLEXION) (a) (b) Flexion Extension Flexion Extension

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