Mathematical Modelling of Glioblastomas Invasion within the Brain: A 3D Multi-Scale Moving-Boundary Approach

Abstract

Brain-related experiments are limited by nature, and so biological insights are often limited or absent. This is particularly problematic in the context of brain cancers, which have very poor survival rates. To generate and test new biological hypotheses, researchers have started using mathematical models that can simulate tumour evolution. However, most of these models focus on single-scale 2D cell dynamics, and cannot capture the complex multi-scale tumour invasion patterns in 3D brains. A particular role in these invasion patterns is likely played by the distribution of micro-fibres. To investigate the explicit role of brain micro-fibres in 3D invading tumours, in this study, we extended a previously introduced 2D multi-scale moving-boundary framework to take into account 3D multi-scale tumour dynamics. T1 weighted and DTI scans are used as initial conditions for our model, and to parametrise the diffusion tensor. Numerical results show that including an anisotropic diffusion term may lead in some cases (for specific micro-fibre distributions) to significant changes in tumour morphology, while in other cases, it has no effect. This may be caused by the underlying brain structure and its microscopic fibre representation, which seems to influence cancer-invasion patterns through the underlying cell-adhesion process that overshadows the diffusion process.