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On the multi-component modelling of human brain tissue to survey clinical interventions

Serious diseases within the brain's tissue often require a medical intervention, such as the treatment of brain tumours. The present contribution aims at predicting the expected impacts of a scheduled clinical procedure via numerical simulations based on a sophisticated constitutive model. The enormous complexity of the tissue's microscopic composition encourages the application of the Theory of Porous Media (TPM), providing a well-suited way to model the brain's tissue aggregate in a compact manner on the macroscale. In particular, a multi-component model is used which is strongly related to the drug-delivery problem within the brain's tissue, cf. [2]. In this model, the solid skeleton is given by the tissue cells (with cell content) and the vascular walls. This solid skeleton is perfused by two mobile but basically separated pore-liquid constituents, the blood and the overall interstitial fluid constituent. To provide the particular description of administered therapeutic agents within the overall interstitial fluid, this real mixture is treated as a chemical solution of two components. These are the liquid solvent and the dissolved therapeutic agent (drug). Numerical examples demonstrate the applicability of the derived model. In particular, infusions of therapeutics into the extra-cellular space (ECS) are simulated under various conditions and complemented by an evaluation of the local numerical sensitivity to survey the influence of certain involved parameters.

A. Wagner & W. Ehlers
On the multi-component modelling of human brain tissue to survey clinical interventions. Proceedings in Applied Mathematics and Mechanics 14 (2014), 125–126.