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

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 of the host tissue. Mathematical models are able to characterize the mechanical response of the tumor and can provide a better understanding of these interactions. In this work, we present a biphasic model for tumor growth based on the mechanics of fluid-saturated porous media. In our model, the porous medium is identified with the tumor cells and the extracellular matrix, and represents the system's solid phase, whereas the interstitial fluid constitutes the liquid phase. A nutrient is transported by the fluid phase, thereby supporting the growth of the tumor. The internal reorganization of the tissue in response to mechanical and chemical stimuli is described by enforcing the multiplicative decomposition of the deformation gradient tensor associated with the solid phase motion. In this way, we are able to distinguish the contributions of growth, rearrangement of cellular bonds, and elastic distortions which occur during tumor evolution. Results are shown for three cases of biological interest, addressing (i) the growth of a tumor spheroid in the culture medium, and (ii) the evolution of an avascular tumor growing first in a soft host tissue and then (iii) in a three-dimensional heterogeneous region. We analyze the dependence of tumor development on the mechanical environment, with particular focus on cell reorganization and its role in stress relaxation.