Journal of Disease and Global Health
 

Journal of Disease and Global Health, ISSN No. : 2454-1842, Vol.: 6, Issue.: 1

Original Research Article

DEVELOPING A NUMERICAL SIMULATION OF VASCULAR BRAIN TUMOR USING 2-DIMENSIONAL PARTIAL DIFFERENTIAL EQUATION

 

P. M. WANJAU1*, F. K. GATHERI2 AND J. K. KOSKE1

1School of Biological and Physical Sciences, Moi University, Box 3900 Eldoret, Kenya.

2School of Mathematics and Actuarial Science, Technical University of Kenya, Box 52428 -00200 Nairobi, Kenya.

Abstracts

In this paper, numerical simulation of vascular brain tumor is developed from a partial differential equation model using Adomian Decomposition method. The model is formulated as a set of partial differential equations describing the spatial-temporal changes in cells’ nutrients concentration based on diffusion dynamics. It predicts the cross section area of the tumor within certain time schedules. It is formulated in two dimensions whereby the tumor is assumed to be growing in radial symmetry. Under this algorithm, equation is decomposed into a series of Adomian polynomials and the given conditions are taken into consideration. The model predicts the cross section area 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 computed analytically from the radius obtained from medical literature, hence they can provide clinical practitioners with valuable information on the potential effects of therapies in their exact schedules.

Keywords :

Vascular tumor; cross section area of tumor; adomian decomposition; diffusion dynamics.