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TECHNICAL BRIEFS

# A Computationally Efficient Optimization Kernel for Material Parameter Estimation Procedures

[+] Author and Article Information
H. Schmid1

Bioengineering Institute, University of Auckland, Private Bag 92019, Auckland, 1001 New Zealandh.schmid@auckland.ac.nz

M. P. Nash, A. A. Young, O. Röhrle, P. J. Hunter

Bioengineering Institute, University of Auckland, Private Bag 92019, Auckland, 1001 New Zealand

1

Corresponding author.

J Biomech Eng 129(2), 279-283 (Sep 21, 2006) (5 pages) doi:10.1115/1.2540860 History: Received September 19, 2005; Revised September 21, 2006

## Abstract

Estimating material parameters is an important part in the study of soft tissue mechanics. Computational time can easily run to days, especially when all available experimental data are taken into account. The material parameter estimation procedure is examplified on a set of homogeneous simple shear experiments to estimate the orthotropic constitutive parameters of myocardium. The modification consists of changing the traditional least-squares approach to a weighted least-squares. This objective function resembles a $L2$-norm type integral which is approximated using Gaussian quadrature. This reduces the computational time of the material parameter estimation by two orders of magnitude.

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## Figures

Figure 1

A sketch of all six possible shear modes for myocardium. The first letter indicates the normal vector of the face that is shifted, and the second letter indicates the direction in which it is shifted. The condensed lines indicate the fibers and the other lines indicate the sheets. With courtesy of American Journal of Physiology, Dokos (see Ref. 8).

Figure 2

Convergence analysis of the objective function ∣ΔΩrelGLS∣ and the difference vector ∣ΔϑrelGLSk∣ plotted against the number of Gauss points G

Figure 3

The figure depicts the experimental (dotted) and fitted force-displacement curves (solid) of the Costa law for all six modes for one experiment. The overall error ΩrelGLS is 1.5%. Note the different scales on each graph. The abscissa shows the displacement in mm, whereas the ordinate shows the top face force in mN.

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