An Application Of Pde To Predict Brain Tumor Growth Using High Performance Computing System

Abstract

This study is to predict two-dimensional brain tumors growth through parallel algorithm using the High Performance Computing System. The numerical finite-difference method is highlighted as a platform for discretization of twodimensional parabolic equations. The consequence of a type of finite difference approximation namely explicit method will be presented in this paper. The numerical solution is applied in the medical field by solving a mathematical model for the diffusion of brain tumors which is a new technique to predict brain tumor growth. A parabolic mathematical model used to describe and predict the evolution of tumor from the avascular stage to the vascular, through the angiogenic process. The parallel algorithm based on High Performance Computing (HPC) System is used to capture the growth of brain tumors cells in two-dimensional visualization. PVM (Parallel Virtual Machine) software is used as communication platform in the HPC System. The performance of the algorithm evaluated in terms of speedup, efficiency, effectiveness and temporal performance. Keywords: Partial Differential Equation (PDE); parabolic equation; explicit method; Red Black Gauss-Seidel; Parallel Virtual Machine (PVM); High Performance Computing (HPC); Brain Tumor. DOI: http://dx.doi.org/10.3329/diujst.v6i1.9335 DIUJST 2011; 6(1): 60-68