Parallel implementation of the diffusion–drift algorithm for modeling the electrophysiological activity of breast tumors

Abstract

The diffusion–drift algorithm for calculating the electric signals of growing breast cancerous cells is parallelized based on the Message Passing Interface technique. The parallelized algorithm is analyzed with emphasis on the existing bottlenecks. The model involves the solution of several systems of equations to calculate the biopotentials and ion concentration gradients generated by MCF-7 cells, the most studied breast cancer cell line. The Portable, Extensible Toolkit for Scientific Computation library is investigated for the parallel solution of these systems of equations. The results show that the optimum solver for the biopotential system of equations is the Enhanced Bi-Conjugate Gradient Stabilized ( L ) solver. Also, it is found that the optimum pre-conditioner is the Additive Schwarz Method coupled with the drop tolerance Incomplete LU factorization. A maximum overall speed up of 15 was achieved using 56 processors with an efficiency of 27%. The electrophysiological activity of a tumor a third of a millimeter in size with just over a thousand cancerous cells is simulated. The numerical values of the biopotential could indicate to breast cancer in very early stages.