Mathematical models for acid-mediated tumor invasion: From deterministic to stochastic approaches

Abstract

A common feature of human cancers is the acidity of the tumor microenvironment, which is essentially influencing the development and spread of the neoplastic tissue, tumor invasion and formation of metastases, degradation of normal tissue, and response to therapies. In this chapter we review some of the continuum mathematical modeling approaches used so far to describe these phenomena, with a focus on the invasive behavior of cancer mediated by acidic pH of the surrounding tissue. We also pay particular attention to the issues of multiscaledness and randomness and compare the qualitative behavior of a class of deterministic models with their stochastic counterparts.