Anisotropic and Inhomogeneous Tensile Behavior of the Human Anulus Fibrosus: Experimental Measurement and Material Model Predictions

[+] Author and Article Information
Dawn M. Elliott

Orthopaedic Research Laboratory, Department of Orthopaedic Surgery, Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104

Lori A. Setton

Department of Biomedical Engineering, Department of Surgery, Division of Orthopaedic Surgery, Duke University, Durham, NC 27708

J Biomech Eng 123(3), 256-263 (Dec 21, 2000) (8 pages) doi:10.1115/1.1374202 History: Received December 27, 1999; Revised December 21, 2000
Copyright © 2001 by ASME
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Schematic of anterior AF showing the orientations of the samples prepared for tensile testing. Samples are shown for outer sites only. The coordinate system is related to the disc directions as follows: 1=circumferential, 2=axial, and 3=radial. For each Group “A”-“B”, “A” corresponds to the length of the sample along the direction of applied load and “B” corresponds to the width of the sample along which the transverse strain is measured.
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Gray-scale, digital image of test sample and reference tab (R) for a representative sample. Box shows the approximate size and location that was imaged at higher magnification for optical strain analysis.
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Schematic showing calculation of the strain tensor using the positions of the centroids of a triad of markers (shown as dots) from reference state, which were measured in the initial reference image, to the deformed state, measured in the subsequent images following uniaxial stretch of the sample.
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Strain plots for a representative sample elongated along the axial direction (Group 2-1). Data points represent mean (SD) values at each applied grip strain for all triads on the sample surface; lines represent linear regressions, with R2 as shown. (TOP) Measured longitudinal and transverse Lagrangian strain. (BOTTOM) Poisson’s ratio for the same sample, calculated from strain measures.
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Stress–strain behavior in three orientations for representative samples from the same anulus fibrosus. Line denotes model fit.
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Predicted moduli as a function of fiber angle, ϕ, using average material properties from the outer sites. E1=circumferential orientation, E2=axial, and E3=radial. Y-bars=one standard deviation in experimental measures, X-bars=range of fiber angles reported by Cassidy et al. 4.
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Fraction of total strain energy (W) at outer sites contributed by each term (Wi) in the quadratic strain energy function for (A) pure dilatation, and for simple tension in the (B) circumferential, (C) axial, (D) and radial directions. W5 and W9 are zero due to the model assumption of isotropy in shear.




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