×

An efficient algorithm to estimate material parameters of biphasic mixtures. (English) Zbl 0952.74044

Summary: The paper describes an inverse numerical experimental method to determine material parameters for biological tissues. Measured field quantities are compared to calculated field quantities. The field equations are solved with the finite element method, using an assumed constitutive model and estimations of the material parameters. The parameter estimates are improved iteratively by means of an algorithm that calls the finite element program as a subroutine. The paper is focused on biological materials that can be described as biphasic mixtures. An efficient recursive algorithm is presented. All parameters are determined on the basis of displacements and pressures measured at different positions within the material at subsequent points in time. A pseudo-analytical approach is used to determine the sensitivity matrix. The algorithm has been tested in a simulation of an experiment on a mixture of a solid and a fluid. It appears that for this example an iterative loop to determine the material parameters requires no more than 30 per cent of the CPU-time required for the straightforward analysis of the problem.

MSC:

74L15 Biomechanical solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S05 Finite element methods applied to problems in solid mechanics
74G75 Inverse problems in equilibrium solid mechanics
76S05 Flows in porous media; filtration; seepage
92C10 Biomechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] (eds). Material Identification Using Mixed Numerical Experimental Methods. Dordrecht: Kluwer Science Publishers, 1997.
[2] , , , . A numerical experimental approach for the mechanical characterization of composites. In Proceedings of the 9th International Conference on Exp. Mech., Askegaard Y (ed.). 1990; 552-561.
[3] Oomens, Journal of Biomechanics 26 pp 617– (1993)
[4] Mow, Journal of Biomechanical Engineering 102 pp 73– (1980)
[5] Lai, Biorheology 17 pp 111– (1980)
[6] , . A finite element formulation of the nonlinear biphasic model for articular cartilage and hydrated soft tissues including strain-dependent permeability. In Computational Methods in Bioengineering, (eds). ASME:New York, 1988; 81-92.
[7] Oomens, Journal of Biomechanics 20 pp 877– (1987)
[8] Nonlinear finite element models of the beating left ventricle and the intramyocardial coronary circulation. Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.
[9] Bovendeerd, Journal of Biomechanics 25 pp 1129– (1992)
[10] The tri-phasic mechanics of the intervertebral disc–a theoretical, numerical and experimental analysis. Ph.D. Thesis, University of Limburg, Maastricht, The Netherlands.
[11] Simon, Journal of Biomechanical Engineering 107 pp 327– (1985)
[12] Mak, Journal of Biomechanics 20 pp 703– (1987)
[13] Mow, Journal of Biomechanics 22 pp 863– (1989)
[14] Armstrong, Journal of Biomechanical Engineering 106 pp 165– (1984)
[15] Theory of Mixtures. In Continuum Physics, (ed.). Academic Press: New York.
[16] Almeida, Computational Methods in Biomechanical and Biomedical Engineering 1 pp 25– (1997)
[17] Simon, International Journal for Numerical and Analytical Methods in Geomechanics 10 pp 483– (1986) · Zbl 0597.73109
[18] Hsieh, International Journal for Numerical Methods in Engineering 21 pp 267– (1985) · Zbl 0552.73079
[19] Identification Algorithms for time-dependent Materials. Ph.D. Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1996.
[20] An Introduction to Identification. Academic Press: New York, 1986. · Zbl 0617.93064
[21] , . Design Sensitivity Analysis of Structural Systems. Academic Press: Orlando, 1986. · Zbl 0618.73106
[22] Kulkarni, International Journal for Numerical Methods in Engineering 38 pp 183– (1995) · Zbl 0821.73042
[23] Gelin, Communications in Numerical Methods in Engineering 12 pp 161– (1996) · Zbl 0853.73028
[24] Laible, Journal of Biomechanical Engineering 116 pp 19– (1994)
[25] , , . DIANA–a comprehensive, but flexible finite element system. In Finite Element Systems: A Handbook, (ed.). Springer: Berlin, 1985.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.