An efficient algorithm to estimate material parameters of biphasic mixtures

Abstract

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 more CPU-time than one straightforward analysis of the problem. Copyright © 1999 John Wiley & Sons, Ltd.