Autowaves in a model of invasive tumor growth

Abstract

A mathematical model for invasive tumor growth is proposed, which takes into account cell division, death, and motility. The model includes local cell density and the distribution of nutrient (oxygen) concentration. Cancer cells die in the absence of nutrients; therefore, the distribution of oxygen in tissue substantially affects both the tumor proliferation rate and its structure. The model adequately describes the experimentally measured rate of tumor proliferation. The existence of autowave solutions is demonstrated, and their properties are investigated. The results are compared with the properties of the Kolmogorov-Petrovskii-Piskunov and Fisher equations. It is shown that the nutrient distribution influences the selection of speed and the convergence of the initial conditions to the automodel solution.