Calculation of effective diffusion coefficient of tracer in tumor tissue with microvasculature using inverse method

In this paper, a numerical algorithm based inverse method is used to estimate effective diffusion coefficient by using experimental tracer distribution. The Algorithm uses factitious experimental data which are produced by adding noise to numerical data obtained from direct problem. A comprehensive model (Diffusion-Convection-Reaction) is used to derive PET tracer distribution in tumor tissue with microvasculature network. This model was used because of considering all transport phenomena in tissue. In this work to achieve accurate distribution of tracer in tumor tissue, convection diffusion reaction equation which is a PDE is implemented. The proposed tracer in this work is Fluorodeoxyglucose (18F). Solution of inverse problem for estimating effective Diffusion Coefficient is based on minimization of least squares norm. In this work Levenberg-Marquardt technique is applied. Solution of parameter estimation problem require calculation of sensitivity matrix which elements are sensitivity coefficients. Sensitivity coefficients shows differentiation of Tracer concentration with respect to Effective Diffusion coefficient variation is calculated using first derivation of concentration equation. The equations of concentration distribution and sensitivity coefficients are solved using Finite volume method. The results show that the numerical algorithm is able to estimate the effective diffusion coefficient in tissue.