Abstract
ORNL in collaboration with the Vascular Research Lab at the University of Tennessee Graduate School of Medicine (UTGSM) in Knoxville is developing a mathematical model of the vascular disease process intimal hyperplasia (IH). IH may occur in a stenosed artery that has been treated with balloon angioplasty or has been injured in other ways. During the IH process, vascular smooth muscle cells migrate from the middle to the inner layer of the artery wall in response to biochemical gradients of various chemicals such as platelet derived growth factor (PDGF). The IH process may be initiated or enhanced by biochemicals released from invading inflammatory cells. Biochemical processes initiated by the denudation of endothelial cells lining the inner artery wall may also affect the IH process. The long term primary goal of the project is to predict a priory which patients will develop IH after balloon angioplasty. The secondary goal is to understand the conditions under which estrogen and hormone replacement therapy have beneficial and/or detrimental influence on the IH process. A mathematical model of the Boyden Chamber experiment for chemoattractant diffusion was developed using the C++ programming language. The model consists of the classic partial differential equation describing diffusion of a biochemical gradient and was solved using the finite difference method for various experimental conditions in order to obtain parameter estimates for the diffusion parameter. It will be applied to experimental results from Boyden Chamber experiments for the response of vascular smooth muscle cells to platelet derived growth factor. Experimental results are obtained from literature and from experiments conducted by the Vascular Research Lab at the UTGSM in Knoxville.