Towards a Mechanical Model for anisotropic Glioma Spread using Darcy's law

The growth of a tumor within a finite domain (skull) generates mechanical forces that alter the physical interactions among cells. The relationship between these forces and the tumor architecture remains an open problem subjected to extensive research. Recently, it has been determined that those regions of high mechanical compression can accelerate and intensify the invasive capacity of the malignant cells, forming an irregular tumor whose full extent and edges are difficult to identify. In the present paper, we propose a one-dimensional mathematical model that describes the process of proliferation and diffusion of glioma cells taking into account the mechanical compression generated during its expansion. Supported on the mixture theory, we model the brain-tumor system as a multiphase mixture of cancer cells, healthy cells, biological fluids and extracellular matrix whose densities determine the mechanical loads generated during the volumetric growth. Our model provides a detailed understanding of the pressure distribution on the interface boundary between healthy and cancer cells. It validates the hypothesis that the conferred ability of cancer cells to proliferate depends strongly on the mechanical pressure sensed. Through the analysis of the mechanical pressure, we determine that the anisotropic loads promote cancer cells to grow preferentially in the directions of low mechanical compression.