Finite difference solutions for the recovery of Lame parameters of a linear elastic membrane

Poster with text describing research conducted by David Kincaid advised by Mohamed Elgindi and Robert Langer.In this project, we present the mathematical equation that governs the displacement of an isotropic membrane due to a traction force applied to a part of its boundary. This leads to a linear elliptic boundary value problem with two parameters representing the Lame moduli, which measure the elastic properties of the membrane. The Lame parameters are constants for homogeneous material but functions of the position otherwise. Since it is possible to measure interior displacements in human tissue (for example using ultrasound), and since cancerous tumors differ markedly in their elastic properties from healthy tissue, it may be possible to detect and locate tumors by solving the inverse problem for the Lame parameters. The objective of this project is to use the Matlab software to develop a numerical code for estimating the (non-constant) Lame moduli for a given traction force and given measurement of the membrane displacement. The numerical results obtained in this project will be compared to those previously obtained and, if possible, with experimental data.University of Wisconsin--Eau Claire Office of Research and Sponsored Programs