Document Type


Date of Degree

Spring 2015

Degree Name

PhD (Doctor of Philosophy)

Degree In

Biomedical Engineering

First Advisor

Lim, Tae-Hong

First Committee Member

Choi, Kyung K

Second Committee Member

Grosland, Nicole M

Third Committee Member

Wilder, David G

Fourth Committee Member

Frey Law, Laura A


Previous in-vivo studies showed that compressive force acting on the spine may exceed 2600 N. However, the ligamentous lumbar spine becomes unstable when subjected to compressive loads less than 100 N. It is generally accepted that the ligamentous spine itself is unstable but can be stabilized by muscle forces (MFs) in vivo. Nevertheless, normal spinal muscle contraction patterns remain unknown.

In recent in vitro studies, when the direction of the applied load was controlled along the spinal curvature so that the internal spinal load became perfect compressive follower loads (CFLs) at all lumbar levels, the ligamentous lumbar spine was found to withstand large compressive load (up to 1200 N) without buckling while maintaining its flexibility in neutral or flexed postures. The results of in-vivo animal studies also have shown that shear stress has a more detrimental effect on the rate of disc degeneration compared to compressive stress. These results suggest CFLs in the lumbar spine would be a normal spinal load whereas the transverse (or shear) load abnormal. An initial test of this postulation would be to investigate whether the spinal muscles can create perfect internal CFLs in the lumbar spine in all 3-D postures. In addition, small intrinsic muscles (SIMs) are crucial for better control of the direction of the internal spinal load along the spinal axis was also proposed.

A finite element (FE) model together with an optimization model were used for this study. Both models consist of the trunk, sacrolumbar spine and 244 spinal muscles. Different from other studies, 54 SIMs were also included in the models. The FE model was validated by comparing the ROM of the spine with the literature data. Minimization of the summation of the spinal loads and moments was used as the cost function for the optimization model. The geometrical data obtained from the FE model was used as the input for the optimization model; it was then used to calculate the MFs required for creating the CFLs at all lumbar spine levels. The MFs determined in the optimization model were then imported back to the FE model as input loads to check the stability of the spine under this loading condition. Five different postures were studied: neutral, flexion 40°, extension 5°, lateral bending 30° and axial rotation 10°.

Many optimization solutions for spinal muscle force combinations creating pure CFLs in the lumbar spine were found available in each posture. However, FE analyses showed that only muscle forces and patterns solved at FLPs along the curve in the vicinity of the baseline curve stabilized the lumbar spine. Stability was determined by small displacement of the trunk (less or equal to 5mm) due to small deformation of the lumbar spine. The magnitudes of joint reaction forces (JRFs) predicted from the optimization model were comparable to those reported in the literature. When the SIMs were removed, optimization solutions were still feasible in all five postures, but JRFs and trunk displacement were increased. This suggests the need of SIM inclusion in future spine biomechanics studies and clinically, damages to the SIMs may have a high risk of future spinal problems, such as spinal instability, early disc degeneration, deformity and/or early failure of spinal fixation devices.

The results from this study supported the hypothesis that the perfect CFLs at all lumbar levels could be the normal physiological load under which the lumbar spinal column could support large load without buckling while allowing flexibility. SIMs played an important role in creating CFLs as by including SIMs in the models, the JRFs at all lumbar spine levels were lowered and the stability of the spine was increased.

Public Abstract

About 80% of adults suffer low back pain (LBP) during their lifetime and this affects the socioeconomic system as billions of dollars are spent on healthcare each year because of it. Although LBP causes such socioeconomic burden to the society, the mechanics of the spine remain unknown. It is unclear what the normal spinal muscle contraction patterns and the normal spinal loads are during daily activities. It is also unclear what mechanics are used for the spine to stay stable and flexible. Without answering these, treatment and prevention of LBP remain challenging.

This research investigated the normal spinal load and normal muscle contraction patterns. It is proposed that the compressive axial forces - forces that are perpendicular to the cross-sectional area of each lumbar spinae, are normal; while shear forces, forces that are parallel to the cross-sectional area of the spinae, are abnormal. Since joint spinal loads are mainly caused by the spinal muscles, mathematical and computational methods were used in this study to check whether it is feasible for the spinal muscles to create only axial forces on the lumbar spine joint during various postures.

It was found that it is feasible for spinal muscles to create only axial force on the lumbar spine, thus it can be concluded that pure axial compressive load can be the normal spinal load. If this is true, the spinal muscle contraction patterns can be predicted and the prevention and treatment of LBP can be significantly improved.


publicabstract, biomechanics, compressive follower load, short intrinsic muscles, spinal muscles, spinal stability, spine


xvii, 128 pages


Includes bibliographical references (pages 124-128).


Copyright 2015 Tianjiao Wang