Prediction of the Erector Spinae Muscle Lever Arm Distance for Biomechanical Models by Celal G¨ung¨or AdissertationsubmittedtotheGraduateFacultyof Auburn University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Auburn, Alabama May 5, 2013 Keywords: Erector Spinae Muscle Lever Arm, MRI, Musculoskeletal Morphology Copyright 2013 by Celal G¨ung¨or Approved by Richard Sesek, Chair, Assistant Professor of Department of Industrial and Systems Engineering Sean Gallagher, Associate Professor of Department of Industrial and Systems Engineering Jerry Davis, Associate Professor of Department of Industrial and Systems Engineering Robert Thomas, Professor of Department of Industrial and Systems Engineering Abstract Low Back Pain (LBP) remains the U.S.’s most significant and costly injury. Improved biomechanical modeling of the lumbar spine may allow better evaluation of LBP risk. To calculate the forces acting on the spine, accurate biomechanical model inputs are required. However, some biomechanical modelinputs are limited by assumptions. One of the most vital model inputs, the mechanical lever arm of the erector spinae muscle mass, (ESMLA), is typically approximated using a fixed value (5 cm or 2 inches) to simplify biomechanical models. This assumption decreases the sensitivity and applicability of models as well as their credibility. The objective of this study was to develop regression models to estimate the ESMLA distance based solely on (1) easily measured subject variables (gender, age, height, and weight) and (2) some additional anthropometric variables (i.e., lean body mass, sitting height, shoulder width). This will allow currently available biomechanical models to incorporate subject specific parameters and should improve model predictions and risk estimations. In addition to the ESMLA distances at several inter-vertebral disc levels in the lower lumbar region, other morphological parameters of musculoskeletal structure such as the cross-sectional areas (CSA) of the erector spine muscle mass (ESMM) and the inter-vertebral disc (IVD) are investigated. Regression models were also developed for the CSA of the ESMMs at each IVD levels. Magnetic Resonance Images (MRI) were used in this study. They were obtained from (1) a hospital database and (2) a newly conducted study at the Auburn MRI Research Center. The ESMLA distances and the CSA measurements were measured from axial oblique MRI scans by using architectural design software. Measurements were then statistically investigated to determine the relationships between the measurement and subject variables (characteristic and anthropometrics). ii Results indicate that the ESMLA distance and ESMM size can be easily and reliably estimated using subject variables. The results of the present study found that using a fixed ESMLA value could cause errors be as great as 20%. The average error percentage of using the fixed value was 8%. Using an empirically derived average value for a IVD level and gender could cause approximately 5% error in ESMLA distances. On the other hand, using regression models suggested in the present study yielded smaller error percentages. For example, the average error was approximately 4.3% for regression models that had easy to measure anthropometric variables (i.e., height and weight). Regression models that had more predictive variables (i.e., ankle, wrist, and knee indexes), however, can provide much smaller prediction errors. The average absolute residual percentage was 2.15% for the L3/L4 level, 2.39% for the L4/L5 level, and 3.67% for the L5/S1 level. The advantage of using regression equations is that smaller prediction errors in ESMLA distances result in smaller error in spinal loading calculations, especially for extreme subjects. iii Acknowledgments IwouldliketoexpressmyheartfeltgratitudetoDr.RichardSesek,Dr.Robert Thomas, Dr. Sean Gallahger, and Dr. Jerry Davis, who helped me throughout the completion of this dissertation with their support and technical expertise. They have always guided me in the right direction and opened their doors to my questions. I also appreciate Drs. Thomas Denney, Ronald Beyers, and Nouha Salibi from Auburn University MRI Research Center for their tremendous help. I could not conduct this study without their helps. I am thankful to the participants in our study that made this dissertation possible. My love and thanks go to my fiance and my family members, who have all helped get me to where I am today. Their understanding and encouragement supports me as I proceed forward. I would like to express special thanks to the Ministry of National Educational of Republic of Turkey for providing me a scholarship. It would not have been possible without their generous financial support. iv Table of Contents Abstract........................................... ii Acknowledgments...................................... iv ListofFigures ....................................... ix List of Tables . xiii 1 INTRODUCTION .................................. 1 1.1 Low Back Pain (LBP): Epidemiology, Cost, and Risk Factors . 1 1.1.1 Epidemiology of LBP . 1 1.1.2 Cost of LBP . 3 1.1.3 RiskFactorsAssociatedwithLBP . 4 1.2 Erector Spinae Muscle Mass Lever Arm (ESMLA) in Biomechanical Models 5 1.2.1 Definition of the ESMLA . 5 1.2.2 Biomechanical Models . 7 1.2.3 Importance of the ESMLA in Biomechanical Models . 7 1.2.4 Structure of the Dissertation . 10 2 LITERATUREREVIEW .............................. 11 2.1 Biomechanical Models . 11 2.1.1 Biomechanical Model Types (Simple and Complex) . 12 2.1.2 AssumptionsinBiomechanicalModels . 14 2.2 Other Factors in Biomechanical Models . 16 2.2.1 Trunk Internal Spine Loading Structures (Intra-abdominal Pressure, Ligaments,andOtherConnectiveTissues) . 16 2.2.2 Validation of Biomechanical Models . 18 2.3 Erector Spinae Muscle Mass (ESMM) . 19 v 2.3.1 MusclesintheESMM:AnatomyoftheESMM . 20 2.4 ErectorSpinaeMuscleMassLeverArm(ESMLA) . 27 2.4.1 Definition of the ESMLA . 27 2.4.2 HistoryofUsageoftheESMLA . 28 2.4.3 ESMLA Distance Measurement Techniques . 37 2.4.4 Cross-sectional area (CSA) Measurement Techniques . 41 2.4.5 Limitations of Previous Studies . 44 2.4.6 Contribution of This Dissertation . 50 2.4.7 Research Objectives . 52 3 MORPHOLOGICAL INVESTIGATION OF THE LOW BACK STRUCTURE: HISTORICAL DATA POPULATIONS . 54 3.1 Introduction . 54 3.2 Material and Methods . 61 3.2.1 Subjects . 61 3.2.2 Data Collection . 63 3.3 Results . 67 3.3.1 ReproducibilityTests. 67 3.3.2 Descriptive Statistics . 69 3.4 Discussion . 77 3.5 Conclusion . 104 4 PREDICTION OF THE ERECTOR SPINAE MUSCLE MASS LEVER ARM (ESMLA) DISTANCE: REGRESSION MODELS FOR HISTORICAL DATA POPULATIONS ................................... 109 4.1 Introduction . 109 4.2 Material and Methods . 127 4.2.1 Subjects . 127 4.2.2 Data Collection . 128 vi 4.2.3 Statistical Tests . 133 4.2.4 Preliminary Model Investigations for Regression Analyses . 134 4.3 Results . 141 4.3.1 ReproducibilityTests. 141 4.3.2 Descriptive Statistics . 142 4.3.3 RegressionAnalyses . .. 149 4.4 Discussion . 171 4.5 Conclusion . 182 5 MORPHOLOGICAL ANALYSIS OF ERECTOR SPINAE MUSCLE MASS LEVER ARM (ESMLA) DISTANCE: BEST SUBSET REGRESSION MODELS FOR AN ASYMPTOMATIC SUBJECT POPULATION . 187 5.1 Introduction . 187 5.2 Material and Methods . 191 5.2.1 Subjects . 191 5.2.2 Data Collection . 191 5.2.3 Statistical Tests . 199 5.3 Results . 201 5.3.1 Descriptive Statistics . 201 5.3.2 CorrelationandRegressionAnalyses . 215 5.3.3 FurtherStatisticalAnalyses . 233 5.4 Discussion . 239 5.5 Conclusion . 256 6 CONCLUSION.................................... 260 Appendices ......................................... 288 A The University of Utah, Institutional Review Board (IRB) approval letter . 288 B Auburn Univeristy, Institutional Review Board (IRB) approval letter . 290 CIterationsforthetotalESMMsizeregressionmodels...............298 vii D IterationsfortheESMLAdistanceregressionmodels . 301 EDatacollectionform.................................304 FBestsubsetregressionmodelsfortheCSAofthetotalESMM..........306 GBestsubsetregressionmodelsfortheESMLAdistance..............310 viii List of Figures 1.1 Low back pain among adults 18 years of age and over, by selected characteris- tics: United States, selected years 1997-2010 (National Health Interview Survey, NCHS,2012a) .................................... 2 1.2 Erector spinae muscles . 6 1.3 An example to explain the e↵ect of the magnitude of the ESMLA distance . 9 2.1 Mean areas (mm2)ofmuscles(bothsides)atseveralinter-vertebrallevels. 21 2.2 Paraspinal muscles: Erector spinae + multifidus . 25 2.3 Representation of the ESMLA distance . 28 2.4 The ESMLA distance as a function of the torso length (1:8) . 30 2.5 Coronal (medial-lateral) and sagittal (anterior-posterior) ESMLA distances . 38 2.6 Direct measurement from the IVD centroid to the ESMM centroid . 39 2.7 AxialobliquecutsatthreelowerIVDlevels . 51 3.1 AxialobliqueMRIscansatthelowthreeIVDlevels . 65 3.2 MusclesintheESMMattheL3/L4IVDlevel . 66 3.3 MeasurementoftheESMLAdistance. 67 3.4 Gender comparison on the ESMM size . 70 ix 3.5 ESMLAdistancesforeachgenderateachIVDlevel. 76 3.6 Comparison of male ESMLA distances at the L3/L4 IVD level . 94 3.7 Comparison of female ESMLA distances at the L3/L4 IVD level . 95 3.8 Comparison of male ESMLA distances at the L4/L5 IVD level . 96 3.9 Comparison of female ESMLA distances at the L4/L5 IVD level . 97 3.10 Comparison of male ESMLA distances at the L5/S1 IVD level . 98 3.11 Comparison of female ESMLA distances at the L5/S1 IVD level .