DEVELOPING A NUMERICAL SIMULATION OF VASCULAR BRAIN TUMOR GROWTH USING 3-DIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS.

Abstract

In this paper a model of vascular brain tumor is developed and solved using Adomian Decomposition Method (ADM). The model is developed as a set of partial differential equations giving the spatial-temporal changes in cell nutrients concentrations based on diffusion dynamics. The model predicts the volume of the tumor within certain time schedules. It is formulated in three dimensions whereby the tumor is assumed to be growing in radial symmetry. Under this algorithm, equation is decomposed into a series of Adomian polynomials. The model predicts the volume of the tumor at any time schedule after vascularization without necessarily imaging. Results obtained from the simulation of growth and dynamics of malignant brain tumor (GBM) compares well with those from medical literature hence, can provide clinical practitioners with valuable information on the potential effects of therapies in their exact schedules.

Keywords; Vascular tumor, volume of the tumor, Adomian Decomposition, and Diffusion dynamics.