The diffusion-drift algorithm for modeling the biopotential signals of breast cancer tumors

A two dimensional model is developed to calculate the electric current densities and the biopotentials generated from single and multiple breast cancerous cells at different cell division stages. Three cell division stages are considered: depolarization which occurs at the beginning of the Gap 1 (G1) stage; hyperpolarization which occurs between the G1 and Synthesis (S) stage; and quiescence where the cell neither depolarizes nor hyperpolarizes. The goal is to understand the electrophysiology of the breast cancer cell line termed Michigan Cancer Foundation-7 (MCF-7). The proposed model is based on the semiconductor diffusion--drift analysis. For a single MCF-7 cell, the shorter the duration of the G1/S transition, and the higher the diffusivity and mobility at the cell boundary, the higher the magnitude of the generated electric signals.;The model is extended to include multiple MCF-7 cells. Nonuniform finite-difference discretization is implemented to accommodate the contrast in size between the intercellular spacing and the cell dimension. The results show that the biopotentials increase proportionally with the number of cells, especially when all cells are in the hyperpolarization stage.;In order to increase the number of cells, the diffusion-drift algorithm is parallelized using the Message Passing Interface (MPI) technique. The computational bottleneck of the model involves the solutions of systems of equations, based on the Nernst-Plank, the Poisson and the Continuity equations, to calculate the biopotentials and the ion concentrations. The Portable, Extensible Toolkit for Scientific Computation library is adopted herein. A maximum overall speedup of 15 is achieved using 56 processors on the Star of Arkansas supercomputer.;As known, early stage tumor growth, cancerous cells are prone to forces and interactions which generate highly complex tumor shapes. The generated electric signals of the most common tumor shape patterns, i.e. Papillary, Compact, and Comedo, are investigated in this work. The highest biopotential signal is observed from the compact tumor while the lowest biopotential signal is observed from the papillary pattern. Interestingly, the spatial distribution of the biopotential signals shows a shift in the maximum biopotential amplitude. These observations can have important implications when using the biopotential signals for breast cancer detection.