An Imaging-Informed Mechanical Framework to Provide a Quantitative Description of Brain Tumour Growth and the Subsequent Deformation of White Matter Tracts

The mathematical description of brain tumours is a challenging problem, that may be fundamental to support medical observations and to build personalised therapeutic treatments for the patients. In this respect, we propose a multiphase model, based on Continuum Mechanics, where both the healthy and the diseased regions are treated as mixtures, comprising a solid and a fluid phase. Moreover, we use patient-specific imaging data to reconstruct the preferential directions for nutrient diffusion, fluid and cell motion inside the brain, since they all follow the orientation of white matter tracts. Then, given the mechanical deformation induced by the tumour onto the healthy tissue, we employ it to properly modify the preferential directions of white matter tracts. Our numerical simulations show that tumour-induced displacements and stresses may have a substantial impact on the tissue surrounding the cancer mass, even in regions distant from the tumour position. Furthermore, the model is able to highlight relevant changes in the preferential directions of nutrient diffusion and cell motion, caused by the spread of the cancer. Finally, the proposed framework may be a useful tool for the mechanical and computational modelling of other kinds of tumours growing in highly anisotropic environments and for estimating the effect of the expanding mass on the surrounding tissue.