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Technical Brief

Application of the Restoring Force Method for Identification of Lumbar Spine Flexion-Extension Motion Under Flexion-Extension Moment

[+] Author and Article Information
Sean L. Borkowski

Biomedical Engineering IDP,
University of California, Los Angeles,
J. Vernon Luck, Sr., M.D. Orthopaedic Research Center,
Orthopaedic Biomechanics and Mechanobiology Lab,
Orthopaedic Institute for Children,
403 W. Adams Boulevard,
Los Angeles, CA 90007
e-mail: sborkowski@ucla.edu

Edward Ebramzadeh

J. Vernon Luck, Sr., M.D. Orthopaedic Research Center,
Orthopaedic Biomechanics and Mechanobiology Lab,
Orthopaedic Institute for Children,
403 W. Adams Boulevard,
Los Angeles, CA 90007
e-mail: edward.ebramzadeh@ucla.edu

Sophia N. Sangiorgio

J. Vernon Luck, Sr., M.D. Orthopaedic Research Center,
Orthopaedic Biomechanics and Mechanobiology Lab,
Orthopaedic Institute for Children,
403 W. Adams Boulevard,
Los Angeles, CA 90007
e-mail: ssangiorgio@mednet.ucla.edu

Sami F. Masri

Fellow ASME
Sonny Astani Dept. of Civil and Environmental Eng.,
Viterbi School of Engineering,
University of Southern California,
3620 S. Vermont Ave, KAP 210, MC 2531,
Los Angeles, CA 90089
e-mail: masri@usc.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received March 8, 2013; final manuscript received February 13, 2014; accepted manuscript posted February 21, 2014; published online March 24, 2014. Assoc. Editor: Brian D. Stemper.

J Biomech Eng 136(4), 044501 (Mar 24, 2014) (8 pages) Paper No: BIO-13-1122; doi: 10.1115/1.4026893 History: Received March 08, 2013; Revised February 13, 2014; Accepted February 21, 2014

The restoring force method (RFM), a nonparametric identification technique established in applied mechanics, was used to maximize the information obtained from moment-rotation hysteresis curves under pure moment flexion-extension testing of human lumbar spines. Data from a previous study in which functional spine units were tested intact, following simulated disk injury, and following implantation with an interspinous process spacer device were used. The RFM was used to estimate a surface map to characterize the dependence of the flexion-extension rotation on applied moment and the resulting axial displacement. This described each spine response as a compact, reduced-order model of the complex underlying nonlinear biomechanical characteristics of the tested specimens. The RFM was applied to two datasets, and successfully estimated the flexion-extension rotation, with error ranging from 3 to 23%. First, one specimen, tested in the intact, injured, and implanted conditions, was analyzed to assess the differences between the three specimen conditions. Second, intact specimens (N = 12) were analyzed to determine the specimen variability under equivalent testing conditions. Due to the complexity and nonlinearity of the hysteretic responses, the mathematical fit of each surface was defined in terms of 16 coefficients, or a bicubic fit, to minimize the identified (estimated) surface fit error. The results of the first analysis indicated large differences in the coefficients for each of the three testing conditions. For example, the coefficient corresponding to the linear stiffness (a01) had varied magnitude among the three conditions. In the second analysis of the 12 intact specimens, there was a large variability in the 12 unique sets of coefficients. Four coefficients, including two interaction terms comprised of both axial displacement and moment, were different from zero (p < 0.05), and provided necessary quantitative information to describe the hysteresis in three dimensions. The results suggest that further work in this area has the potential to supplement typical biomechanical parameters, such as range of motion, stiffness, and neutral zone, and provide a useful tool in diagnostic applications for the reliable detection and quantification of abnormal conditions of the spine.

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Figures

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Fig. 1

Biomechanical results from one representative intact specimen demonstrating the following relationships: (a) axial displacement as a function of time, (b) axial displacement as a function of applied flexion-extension moment, (c) flexion-extension rotation as a function of applied flexion-extension moment, (d) flexion-extension rotation as a function of axial displacement, and (e) flexion-extension rotation as a function of both axial displacement and applied flexion-extension moment

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Fig. 2

Comparison between the measured flexion-extension rotation (solid) and estimated flexion-extension rotation (dashed), expressed in terms of axial displacement and applied flexion-extension moment, for the (a) intact, (b) injured, and (c) implanted conditions

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Fig. 3

Normalized bicubic surface plots for the three experimental conditions: (a) intact, (b) injured, and (c) implanted

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Fig. 4

Flexion-extension hysteresis responses as a function of axial displacement and applied flexion-extension moment for the ensemble of 12 nominally identical intact specimens. Abbreviations: x, axial displacement (mm); y, applied flexion-extension moment (Nm); z, flexion-extension rotation (degrees).

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Fig. 5

Mean-square fit error of the RFM flexion-extension estimation for the 12 intact lumbar functional spine units

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Fig. 6

3D representation of the 16 identified Chebychev (Cij) coefficients for the bicubic fit of flexion-extension rotation as a function of axial displacement and applied flexion-extension moment for the ensemble of 12 nominally identical intact specimens

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