Computational solution of an acid-mediated tumor-growth radial model under logistic growth regimes for normal and cancer cells

Abstract

Tumor invasion follows a complex mechanism which involves cell migration and proliferation. To study the processes in which primary and secondary metastases invade and damage the normal cells, mathematical models are often extremely useful. In this paper, we present a mathematical model of acid-mediated tumor growth consisting of radially symmetric reaction–diffusion equations. The assumption on the radial symmetry of the solutions is imposed here in view that tumors present spherical symmetry at the microscopic level. Moreover, we consider various empirical mechanisms which describe the propagation of tumors by considering cancer cells, normal cells, and the concentration of H[Formula: see text] ions. Among other assumptions, we suppose that these components follow logistic-type growth rates. Evidently, this is an important difference with respect to various other mathematical models for tumor growth available in the literature. Moreover, we also add competition terms of normal and tumor cells growth. We carry out a balancing study of the equations of the model, and a numerical model is proposed to produce simulations. Various practical remarks derived from our assumptions are provided in the discussion of our simulations.