Application-driven model reduction for the simulation of therapeutic infusion processes in multi-component brain tissue

The present article concerns the problem-specific application of suitable model-reduction techniques to obtain an efficient numerical simulation of multi-component brain tissue. For this purpose, a compact summary of the underlying theoretical multi-component brain-tissue model is initially introduced in the framework of the Theory of Porous Media (TPM). Typically, the straight-forward monolithic solution of the arising coupled system of equations yields immense numerical costs. Therefore, the primary aim of this work is to apply the method of proper orthogonal decomposition (POD) for a simplified model and the POD in combination with the discrete-empirical-interpolation method (DEIM) for a general nonlinear model in order to reduce the required computation time significantly. Several numerical simulations are realised and discussed in terms of efficiency, accuracy and parameter variations. In conclusion, the article presents necessary adaptations of the POD(-DEIM) allowing for their application to (nonlinear) strongly coupled and multi-component models.