Abstract
Tumor growth strictly depends on the interactions occurring at the cellular scale. In order to obtain the linking between the dynamics described at tissue and cellular scales, asymptotic methods have been employed, consisting in deriving tissue equations by suitable limits of mesoscopic models. In this paper, the evolution at the cellular scale is described by thermostatted kinetic theory that include conservative, nonconservative (proliferation, destruction and mutations), stochastic terms, and the role of external agents. The dynamics at the tissue scale (cell-density evolution) is obtained by performing a low-field scaling and considering the related convergence of the rescaled framework when the scaling parameter goes to zero.
Highlights
Tumor disease has recently attracted the attention of many scientists, including physicists, applied mathematicians and bioinformatics researchers
This section is concerned with the mathematical modeling of the tumor growth at cellular scale by thermostatted kinetic theory that acts as a general paradigm for the derivation of specific models
A mathematical framework at the cellular scale has been proposed for the modeling of tumor-immune system competition
Summary
Tumor disease has recently attracted the attention of many scientists, including physicists, applied mathematicians and bioinformatics researchers. From classical kinetic theory which deals with molecule position and velocity distribution, the thermostatted kinetic theory refers to cells. In this theory, the microscopic state of the cell includes, in addition to classical space and velocity variables, the activity variable which models the ability of a cell to perform specific strategies. This paper deals with the low-field limit of a thermostatted kinetic framework, which includes transitions in the cells strategy, birth/death processes, cell mutations and the role of microscopic external actions, e.g. environment pressure (open systems). The derived macroscopic equation, which refers to the time evolution of the cell density, shows how the different kind of interactions at the cellular scale may affect tumor tissue growth.
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