Estimate of Elastic Properties of Biological Tissues Using a Finite Element Methodology

Abstract

Experimental observations reveal that abnormal biological tissues, such as tumors, found in the breast and prostate, tend to be stiffer than healthy biological tissues. Classical linear elasticity is then used to model the responses of these tissues under small strains. In particular, soft tissues are modeled as linearly elastic, isotropic, and incompressible materials. For a particular class of plane problems, it has been shown that if the shear elastic modulus, $\mu$, is known at four different points in a sample, then it can be uniquely determined from the knowledge of two displacement fields obtained from two distinct experiments performed on the same sample. We use this result to propose a non-iterative numerical procedure to determine $\mu$ in a sample of soft tissue, which is subjected to two quasi-static experiments that are possible to reproduce in laboratory and are simulated numerically using the finite element method. No a priori knowledge of the shear elastic modulus is required, but it is assumed that resultant forces are known on complementary parts of the boundary of the sample. Results for the distribution of $\mu$ in a long cylinder of rectangular cross section containing an eccentric circular inclusion and an inclusion with a complex geometry are presented. The methodology yields numerical results that are both in very good agreement with analytical results and more accurate than numerical results obtained from another methodology presented in the literature. This work is of great interest in the detection of cancerous tumors and in the differential diagnosis of biological tissues.