Prediction of the Erector Spinae Muscle Lever Arm Distance for Biomechanical Models by Celal ...

330 Pages·2013·10 MB·English

Prediction of the Erector Spinae Muscle Lever Arm Distance for
Biomechanical Models
by
Celal Gu¨ngo¨r
A dissertation submitted to the Graduate Faculty of
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 Gu¨ngo¨r
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.
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Acknowledgments
I would like to express my heartfelt gratitude to Dr. Richard Sesek, 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.
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Table of Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Risk Factors Associated with LBP . . . . . . . . . . . . . . . . . . . 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 LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Biomechanical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.1 Biomechanical Model Types (Simple and Complex) . . . . . . . . . . 12
2.1.2 Assumptions in Biomechanical Models . . . . . . . . . . . . . . . . . 14
2.2 Other Factors in Biomechanical Models . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Trunk Internal Spine Loading Structures (Intra-abdominal Pressure,
Ligaments, and Other Connective Tissues) . . . . . . . . . . . . . . . 16
2.2.2 Validation of Biomechanical Models . . . . . . . . . . . . . . . . . . . 18
2.3 Erector Spinae Muscle Mass (ESMM) . . . . . . . . . . . . . . . . . . . . . . 19
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2.3.1 Muscles in the ESMM: Anatomy of the ESMM . . . . . . . . . . . . 20
2.4 Erector Spinae Muscle Mass Lever Arm (ESMLA) . . . . . . . . . . . . . . . 27
2.4.1 Definition of the ESMLA . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.2 History of Usage of the ESMLA . . . . . . . . . . . . . . . . . . . . . 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 Reproducibility Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 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
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4.2.3 Statistical Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.2.4 Preliminary Model Investigations for Regression Analyses . . . . . . . 134
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.3.1 Reproducibility Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.3.2 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
4.3.3 Regression Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5 MORPHOLOGICALANALYSISOFERECTORSPINAEMUSCLEMASSLEVER
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 Correlation and Regression Analyses . . . . . . . . . . . . . . . . . . 215
5.3.3 Further Statistical Analyses . . . . . . . . . . . . . . . . . . . . . . . 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
C Iterations for the total ESMM size regression models . . . . . . . . . . . . . . . 298
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D Iterations for the ESMLA distance regression models . . . . . . . . . . . . . . . 301
E Data collection form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
F Best subset regression models for the CSA of the total ESMM . . . . . . . . . . 306
G Best subset regression models for the ESMLA distance . . . . . . . . . . . . . . 310
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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) of muscles (both sides) at several inter-vertebral levels . . . . 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 Axial oblique cuts at three lower IVD levels . . . . . . . . . . . . . . . . . . . . 51
3.1 Axial oblique MRI scans at the low three IVD levels . . . . . . . . . . . . . . . 65
3.2 Muscles in the ESMM at the L3/L4 IVD level . . . . . . . . . . . . . . . . . . . 66
3.3 Measurement of the ESMLA distance . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4 Gender comparison on the ESMM size . . . . . . . . . . . . . . . . . . . . . . . 70
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3.5 ESMLA distances for each gender at each IVD level . . . . . . . . . . . . . . . . 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 . . . . . . . . . 99
3.12 Comparisons of using a fixed ESMLA distance (5 cm) with average ESMLA
distances for each gender and each IVD level . . . . . . . . . . . . . . . . . . . . 103
3.13 Figure representation of the female results of the present study . . . . . . . . . 106
3.14 Figure representation of the male results of the present study . . . . . . . . . . 107
4.1 The correlation between the CSA of the ESMM and subject weight . . . . . . . 113
4.2 Oblique scans at the L3/L4, L4/L5, L5/S1 IVD levels . . . . . . . . . . . . . . . 130
4.3 Muscles in the ESMM at the L3/L4 IVD level . . . . . . . . . . . . . . . . . . . 131
4.4 Image selection in OsiriXR software . . . . . . . . . . . . . . . . . . . . . . . . 132
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4.5 The ESMLA distance measurement . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.6 Normal quantile-quantile (Q-Q) plots . . . . . . . . . . . . . . . . . . . . . . . 139
4.7 Gender comparisons on the CSAs of ESMMs (a: Right ESMM, b: Left ESMM,
and c: Total ESMM) and IVDs (d) . . . . . . . . . . . . . . . . . . . . . . . . . 145
x