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Technical Briefs

Tendon Fascicles Exhibit a Linear Correlation Between Poisson's Ratio and Force During Uniaxial Stress Relaxation

[+] Author and Article Information
Jeffrey A. Weiss

e-mail: jeff.weiss@utah.edu
Department of Bioengineering,
University of Utah,
Salt Lake City, UT 84112

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received May 16, 2012; final manuscript received November 12, 2012; accepted manuscript posted December 8, 2012; published online February 11, 2013. Editor: Beth Winkelstein.

J Biomech Eng 135(3), 034501 (Feb 11, 2013) (5 pages) Paper No: BIO-12-1195; doi: 10.1115/1.4023134 History: Received May 16, 2012; Revised November 12, 2012; Accepted December 08, 2012

The underlying mechanisms for the viscoelastic behavior of tendon and ligament tissue are poorly understood. It has been suggested that both a flow-dependent and flow-independent mechanism may contribute at different structural levels. We hypothesized that the stress relaxation response of a single tendon fascicle is consistent with the flow-dependent mechanism described by the biphasic theory (Armstrong et al., 1984, “An Analysis of the Unconfined Compression of Articular Cartilage,” ASME J. Biomech. Eng., 106, pp. 165–173). To test this hypothesis, force, lateral strain, and Poisson's ratio were measured as a function of time during stress relaxation testing of six rat tail tendon fascicles from a Sprague Dawley rat. As predicted by biphasic theory, the lateral strain and Poisson's ratio were time dependent, a large estimated volume loss was seen at equilibrium and there was a linear correlation between the force and Poisson's ratio during stress relaxation. These results suggest that the fluid dependent mechanism described by biphasic theory may explain some or all of the apparent viscoelastic behavior of single tendon fascicles.

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Figures

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Fig. 5

The normalized force plotted against the normalized Poisson's ratio for all data points. Note that the data were logarithmically sampled in time to provide an equal distribution of points throughout the entire data range. The data points are the black dots and the best fit is represented by a solid black line. The slope and R2 value are displayed in the upper right hand corner.

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Fig. 4

Poisson's ratio and force versus time. (Top) Poisson's ratio versus time (log scale) for all samples. (Bottom) Force versus time (log scale) for all samples. The solid line is the mean value (averaged over all samples) while the dashed line represents the standard deviation for each time point.

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Fig. 3

Lateral and axial strain versus time. (Top) Transverse strain versus time (log scale) for all samples. (Bottom) Axial strain versus time (log scale) for all samples. A linear fit of the axial tissue strain resulted in a negligible slope, indicating that it was constant during relaxation. In both plots the solid line is the mean value (averaged over all samples) while the dashed line represents the standard deviation for each time point. Note that all strains were measured using the transition strain as the reference position.

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Fig. 2

Computing transition strain. A typical curve of force versus applied clamp stretch during the ramping phase is shown, where black triangles represent the data points, the solid line represents the nonlinear curve fit, and an empty circle represents the transition strain.

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Fig. 1

Sample schematic. A typical image used for calculating axial strain, transverse strains, and Poisson's ratio. The sample, marker beads, and the best fit quadrilateral are indicated.

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