Biophysical models of tumour growth

Tumour growth is a multifactorial process, which has stimulated in recent decades the development of numerous models trying to figure out the mechanisms controlling solid tumours morphogenesis. While the earliest models were focusing on cell proliferation kinetics, modulated by the availability of supplied nutrients, new modelling approaches emphasize the crucial role of several biophysical processes, including local matrix remodelling, active cell migration and traction, and reshaping of host tissue vasculature. After a brief presentation of this experimental background, this review will outline a number of representative models describing, at different scales, the growth of avascular and vascularized tumours. Special attention will be paid to the formulation of tumour-host tissue interactions that selectively drive changes in tumour size and morphology, and which are notably mediated by the mechanical status and elasticity of the tumour microenvironment. Emergence of invasive behaviour through growth instabilities at the tumour-host interface will be presented considering both reaction-diffusion and mechano-cellular models. In the latter part of the review, patient-oriented implications of tumour growth modelling are outlined in the context of brain tumours. Some conceptual views of the adaptive strategies and selective barriers that govern tumour evolution are presented in conclusion as potential guidelines for the development of future models.