Importance of Nonlinear and Multivariable Flexibility Coefficients in the Prediction of Human Cervical Spine Motion

[+] Author and Article Information
Beth A. Winkelstein, Barry S. Myers

Department of Biomedical Engineering, Division of Orthopaedic Surgery, Duke University, Durham, N.C. 27708

J Biomech Eng 124(5), 504-511 (Sep 30, 2002) (8 pages) doi:10.1115/1.1504098 History: Received January 01, 2002; Revised June 01, 2002; Online September 30, 2002
Copyright © 2002 by ASME
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Schematic showing the local coordinate system of a vertebra, with its origin (O) at the center of the anterior face. Also illustrated are the axes orientations (x,y,z) for the local coordinate system. As shown, the positive X-axis is oriented anteriorly along the anterior-posterior direction.
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Schematic diagram showing the flexibility frame with bending moment applicator. The test frame is equipped with a load cell, moment and force applicators, and stereoimaging cameras for motion tracking. Also shown in this illustration is the orientation of the global coordinate system.
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Shown is a representative nonlinear approximation (filled circles) of the measured (open circles) response curve for a typical specimen, illustrating the use of five piecewise linear functions to characterize the nonlinear response. Also shown in this plot is the closeness of the linear fits to the logarithmic description of the response.
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(a) Shown are the primary (flexion angle) and coupled motion responses for an imposed flexion moment on a neutral specimen. The upper plot shows the rotational components and the lower plot demonstrates the coupled translations. These results illustrate the effects of loading in the sagittal plane, producing small lateral translations (y) and bending and axial torsion rotations. (b) Primary and coupled motion response magnitudes for a posteroanterior (+x) shear force applied to a representative neutral specimen.
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Sagittal plane displacement components for a typical specimen. The sagittal plane experimental validation data, as well as the predicted motions from the three matrix models, are shown. For flexion in particular, the improved performance of the multivariable model is evident over the linear and piecewise models. For simplicity, the sagittal plane components of motion are shown as a function of applied flexion moment.
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Lateral displacement components for a typical specimen (same as in Fig. 5) are shown as a function of the applied lateral bending moment from the validation experiment. These plots indicate the failure of the linear model to predict the motions out of the sagittal plane well.
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RMS errors for the different models in their prediction of angular rotations. Here errors are represented as a percentage of the corresponding range of motion in each direction. The similar improvements for the piecewise and multivariable models over the linear one are observed for each motion component.




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