Parameter estimation using the quasi-linear viscoelastic model proposed by Fung

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Dortmans, L. J. M. G.¹; Sauren, A. A. H. J.¹; Rousseau, E. P. M.¹

Parameter estimation using the quasi-linear viscoelastic model proposed by Fung

J Biomech Eng. August 1984;106(3):198-203

©1984 ASME

Affiliations

¹Eindhoven University of Technology, Department of Mechanical Engineering, Eindhoven, The Netherlands
Abstract

Using the quasi-linear viscoelastic model proposed by Fung for the description of the viscoelastic properties of soft biological tissues, the parameters governing their time-dependent behavior are commonly estimated from relaxation experiments. Exact quantification is possible from the response to a step change in the strain. Since it is physically impossible to realize a true step change in the strain, in practice the response to a steplike strain change is used. In the present study the discrepancies between the exact and the estimated parameter values are investigated using a hypothetical quasi-linear viscoelastic material. The parameter τ₁, governing the fast viscous phenomena, is found to be subject to the largest errors. Methods for obtaining better estimates of τ₁ are outlined in a number of special cases.
Links

DOI: 10.1115/1.3138483

PubMed: 6492764

WoS: A1984TE45200003
History

Received: 1983-08-05

Revised: 1983-12-27

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Cited By (21)

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1995	Arbogast KB, Meaney DF, Thibault LE. Biomechanical characterization of the constitutive relationship for the brainstem. In: Proceedings of the 39th Stapp Car Crash Conference. November 8-10, 1995; San Diego, CA. Warrendale, PA: Society of Automotive Engineers:153-159. SAE 952716.
1995	Myers BS, Van Ee CA, Camacho DLA, Woolley CT, Best TM. On the structural and material properties of mammalian skeletal muscle and its relevance to human cervical impact dynamics. In: Proceedings of the 39th Stapp Car Crash Conference. November 8-10, 1995; San Diego, CA. Warrendale, PA: Society of Automotive Engineers:203-214. SAE 952723.
2001	Weiss JA, Gardiner JC. Computational modeling of ligament mechanics. Crit Rev Biomed Eng. 2001;29(3):303-371.
1987	Nigul I, Nigul U. On algorithms of evaluation of Fung's relaxation function parameters. J Biomech. 1987;20(4):343-352.
1990	Monleón Pradas M, Diaz Calleja R. Nonlinear viscoelastic behaviour of the flexor tendon of the human hand. J Biomech. 1990;23(8):773-781.
1991	Myers BS, McElhaney JH, Doherty BJ. The viscoelastic responses of the human cervical spine in torsion: experimental limitations of quasi-linear theory, and a method for reducing these effects. J Biomech. 1991;24(9):811-817.
1994	Best TM, McElhaney J, Garrett WE, Myers BS. Characterization of the passive responses of live skeletal muscle using the quasi-linear theory of viscoelasticity. J Biomech. April 1994;27(4):413-419.
1997	Iatridis JC, Setton LA, Weidenbaum M, Mow VC. The viscoelastic behavior of the non-degenerate human lumbar nucleus pulposus in shear. J Biomech. October 1997;30(10):1005-1013.
1996	Johnson GA, Livesay GA, Woo SL-Y, Rajagopal KR. A single integral finite strain viscoelastic model of ligaments and tendons. J Biomech Eng. May 1996;118(2):221-226.
2000	Funk JR, Hall GW, Crandall JR, Pilkey WD. Linear and quasi-linear viscoelastic characterization of ankle ligaments. J Biomech Eng. February 2000;122(1):15-22.
2004	Abramowitch SD, Woo SL-Y. An improved method to analyze the stress relaxation of ligaments following a finite ramp time based on the quasi-linear viscoelastic theory. J Biomech Eng. February 2004;126(1):92-97.
1996	Iatridis JC. Biomechanics of the Anulus Fibrosus and Nucleus Pulposus of the Human Lumbar Intervertebral Disc and the Effects of Degeneration [PhD thesis]. Columbia University; 1996.
1993	Best TM. A Biomechanical Study of Skeletal Muscle Strain Injuries [PhD thesis]. Duke University; 1993.
2012	Luck JF. The Biomechanics of the Perinatal, Neonatal and Pediatric Cervical Spine: Investigation of the Tensile, Bending and Viscoelastic Response [PhD thesis]. Durham, NC: Duke University; 2012.
1997	Pioletti DP. Viscoelastic Properties of Soft Tissues Application to Knee Ligaments and Tendons [PhD thesis]. Swiss Federal Institute of Technology Lausanne; 1997.
2004	Abramowitch SD. An Evaluation of the Non-Linear Viscoelastic Properties of the Healing Medial Collateral Ligament [PhD thesis]. University of Pittsburgh; 2004.
2007	Papas NP. Potential of a Bioscaffold to Enhance the Healing of the MCL Following a Mop-End Tear: An Animal Model Study [Master's thesis]. University of Pittsburgh; 2007.
2007	June RK II. Polymer Dynamics as a Mechanism of Cartilage Flow-Independent Viscoelasticity [PhD thesis]. Davis, University of California; December 2007.
2001	Thomopoulos S. Supraspinatus Tendon to Bone Healing: Differences in Biomechanical, Structural, and Compositional Properties Due to a Range of Activity Levels [PhD thesis]. University of Michigan; 2001.
1999	Ledoux WR II. A Biomechanical Model of the Human Foot With Emphasis on the Plantar Soft Tissue [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1999.
1998	Takhounts EG. Experimental Determination of Constitutive Equations for Human and Bovine Brain Tissue [PhD thesis]. Charlottesville, VA: University of Virginia; May 1998.