Numerical methods for analysing physiological flows and cardiac electrophysiology

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Numerical simulations are becoming an increasingly important tool in the analysis of physiological systems and pathologies, and the development of biomedical treatment. Techniques and models from continuum mechanics and that were part of traditional engineering are now progressively introduced in medicine, often requiring the development of new simulation methods given the relative complexity of living systems. The current proposal works precisely along this objective of developing models and numerical techniques that apply to two biomedical fields, namely to physiological flows and to cardiac electrophysiology. By physiological flows, we mean blood flows but also flows and aerosol propagation in airways, linking to our previous work in these two areas. A commonality of problems in these fields, i.e. phenomena with several spatial and temporal scales modelled with time-dependent nonlinear partial differential equations, requires a commonality of simulation methods, i.e. adaptative numerical methods with a controlled level of error in space and time. Our research program concentrates on the development of such numerical methods but also includes modelling aspects, in particular for improving our current Eulerian aerosol model. The proposed research program will eventually lead to integrated analysis tools for the process from medical image segmentation => patient-specific geometry => physical model => numerical simulations => visualization.