This study shows how a probabilistic microstructural model for fibrous connective tissue behavior can be used to objectively describe soft tissue low-load behavior. More specifically, methods to determine tissue reference length and the transition from the strain-stiffening “toe-region” to the more linear region of the stress-strain curve of fibrous connective tissues are presented. According to a microstructural model for uniaxially loaded collagenous tissues, increasingly more fibers are recruited and bear load with increased tissue elongation. Fiber recruitment is represented statistically according to a Weibull probability density function (PDF). The Weibull PDF location parameter in this formulation corresponds to the stretch at which the first fibers begin to bear load and provides a convenient method of determining reference length. The toe-to-linear region transition is defined by utilizing the Weibull cumulative distribution function (CDF) which relates the fraction of loaded fibers to the tissue elongation. These techniques are illustrated using representative tendon and ligament data from the literature, and are shown to be applicable retrospectively to data from specimens that are not heavily preloaded. The reference length resulting from this technique provides an objective datum from which to calculate stretch, strain, and tangent modulus, while the Weibull CDF provides an objective parameter with which to characterize the limits of low-load behavior.
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June 2003
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Application of a Probabilistic Microstructural Model to Determine Reference Length and Toe-to-Linear Region Transition in Fibrous Connective Tissue
Christof Hurschler,
Christof Hurschler
Department of Orthopedics and Rehabilitation and Department of Biomedical Engineering, University of Wisconsin, Madison, WI 53792-7375
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Paolo P. Provenzano,
Paolo P. Provenzano
Department of Orthopedics and Rehabilitation and Department of Biomedical Engineering, University of Wisconsin, Madison, WI 53792-7375
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Ray Vanderby,, Jr.
Ray Vanderby,, Jr.
Department of Orthopedics and Rehabilitation and Department of Biomedical Engineering, University of Wisconsin, Madison, WI 53792-7375
Search for other works by this author on:
Christof Hurschler
Department of Orthopedics and Rehabilitation and Department of Biomedical Engineering, University of Wisconsin, Madison, WI 53792-7375
Paolo P. Provenzano
Department of Orthopedics and Rehabilitation and Department of Biomedical Engineering, University of Wisconsin, Madison, WI 53792-7375
Ray Vanderby,, Jr.
Department of Orthopedics and Rehabilitation and Department of Biomedical Engineering, University of Wisconsin, Madison, WI 53792-7375
Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division December 4, 2001; revised manuscript received November 19, 2002. Associate Editor: M. S. Sacks.
J Biomech Eng. Jun 2003, 125(3): 415-422 (8 pages)
Published Online: June 10, 2003
Article history
Received:
December 4, 2001
Revised:
November 19, 2002
Online:
June 10, 2003
Citation
Hurschler, C., Provenzano , P. P., and Vanderby, , R., Jr. (June 10, 2003). "Application of a Probabilistic Microstructural Model to Determine Reference Length and Toe-to-Linear Region Transition in Fibrous Connective Tissue ." ASME. J Biomech Eng. June 2003; 125(3): 415–422. https://doi.org/10.1115/1.1579046
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