Evaluation of a Mechanically Coupled Reaction–Diffusion Model for Macroscopic Brain Tumor Growth

Abstract

The macroscopic growth of brain tumors has been studied by means of different computational modeling approaches. Glioblastoma multiforme (GBM) is the most common malignant type and is commonly modeled as a reaction–diffusion type system, accounting for its invasive growth pattern. Purely biomechanical models have been proposed to represent the mass effect caused by the growing tumor, but only a few models consider mass effect and tissue invasion effects in a single 3D model. We report first results of a comparative study that evaluates the ability of a simple computational model to reproduce the shape of pathologies found in patients. GBM invasion into brain tissue and the mechanical interaction between tumor and healthy tissue components are simulated using the finite element method (FEM). Cell proliferation and invasion are modeled as a reaction–diffusion process; simulation of the mechanic interaction relies on a linear elastic material model. Both are coupled by relating the local increase in tumor cell concentration to the generation of isotropic strain in the corresponding tissue element. The model accounts for multiple brain regions with values for proliferation, isotropic diffusion, and mechanical properties derived from literature. Tumors were seeded at multiple locations in FEM models derived from publicly available human brain atlases. Simulation results for a given tumor volume were compared to patient images. Simulated tumors showed a more symmetric growth pattern compared to their real counterparts. Resulting levels of tumor invasiveness were in agreement with simulation parameters and tumor-induced pressures of realistic magnitude were found.