Dynamics and Physics of Cancer: Tumor and Immune Cell Interactions

Abstract

The present work constitutes my PhD thesis, which has been accomplished during the last five years in the research group on Nonlinear Dynamics, Chaos Theory and Complex Systems Group at the Universidad Rey Juan Carlos. It is focused on two core subjects, which are the dynamics of tumor growth in interaction with the cell-mediated immune response, and the application of control techniques to avoid the overgrowth of tumors, both from the point of view of Nonlinear Dynamics and Complex Systems. In order to provide a conceptual framework to this work, I develop a general introduction to complex systems, the biology of cancer, and the immune system function. Then, its main body is comprised by an article on the existence and control of chaos in a cancer model of tumor and immune cell interactions, another in which we validate a mathematical model of tumor growth, two works on the establishment of the mathematical equation that governs the lysis of solid tumors and one last article in which we investigate the transient and asymptotic dynamics of tumor-immune aggregates.