Metastasis Models: Thermodynamics and Complexity

The thermodynamic formalism of nonequilibrium systems together with the theory of complex systems and systems biology offer an appropriate theoretical framework to explain the complexity observed at the macroscopic level in physiological phenomena. In turn, they allow the establishment of an appropriate conceptual and operational framework to address the study of phenomena such as the emergence and evolution of cancer.This chapter is organized as follows: In Subheading 1, an integrated vision of these disciplines is offered for the characterization of the emergence and evolution of cancer, seen as a nonlinear dynamic system, temporally and spatially self-organized out of thermodynamic equilibrium. The development of the various mathematical models and different techniques and approaches used in the characterization of cancer metastasis is presented in Subheading 2. Subheading 3 is devoted to the time course of cancer metastasis, with particular emphasis on the epithelial-mesenchymal transition (EMT henceforth) as well as chronotherapeutic treatments. In Subheading 4, models of the spatial evolution of cancer metastasis are presented. Finally, in Subheading 5, some conclusions and remarks are presented.