An avascular tumor growth model based on porous media mechanics and evolving natural configurations

Mechanical factors play a major role in tumor development and response to treatment. This is more evident for tumors grown in vivo, where cancer cells interact with the different components in the host tissue. Mathematical models are able to characterize the mechanical response of the tumor and can provide a deeper understanding of these interactions. In this work, we present a model for tumor growth based on porous media mechanics. We consider a biphasic system, where tumor cells and the extracellular matrix constitute a solid scaffold, filled with interstitial fluid. A nutrient is dispersed into the fluid phase, supporting the growth of the tumor. The internal reorganization of the tissue in response to external mechanical and chemical stimuli is described by enforcing the multiplicative decomposition of the deformation gradient tensor. In this way, we are able to distinguish the contributions of growth, rearrangement of cellular bonds, and elastic distortion, which occur during tumor evolution. Results are shown for three cases of biological interest, that is growth of a tumor spheroid in (i) culture medium, (ii) host tissue, and (iii) three- dimensional physiological configuration. We report the tumor growth curves for the three cases mentioned above, supplemented with the evolution of quantities of interest, such as the mechanical stresses and interstitial fluid pressures. We analyze the dependence of the tumor development on the mechanical environment, with a particular focus on cell reorganization and its role in stress relaxation. We also address the computational issues of our mathematical model, and discuss the flexibility of the employed numerical implementation. Finally, we speak of further developments, with the scope of providing a deeper understanding of cancer biophysics.