Multi-component modelling of human brain tissue: a contribution to the constitutive and computational description of deformation, flow and diffusion processes with application to the invasive drug-delivery problem

Human brain tissue is complex and multi-component in nature. It consists of an anisotropic hyperelastic solid material composed of tissue cells and blood vessel walls. Brain tissue is permeated by two viscous pore liquids, the interstitial fluid and the blood. Both liquids are mobile within the tissue and exhibit a significant anisotropic perfusion behaviour. To model this complex aggregate, the well-founded Theory of Porous Media, a continuum-mechanical approach for the description of multi-component aggregates, is used. To include microscopic information, the model is enhanced by tissue characteristics obtained from medical imaging techniques. Moreover, the model is applied to invasive drug-delivery strategies, i.e. the direct extra-vascular infusion of therapeutic agents. For this purpose, the overall interstitial fluid is treated as a real two-component mixture of a liquid solvent and a dissolved therapeutic solute. Finally, the continuum-mechanical model results in a set of strongly coupled partial differential equations which are spatially discretised using mixed finite elements and solved in a monolithic manner with an implicit Euler time-integration scheme. Numerical examples demonstrate the applicability of the presented model.