Séance Séminaire

Séminaire ACSIOM

Multiscale models for biofluids and their applications to the study of the coupled eye-cerebral system

Multiscale coupling of nonlinear distributed and lumped fluid flow models is often necessary when modeling complex biological vascular systems. When interested in studying in detail a specific segment of the vasculature, usually, to reduce simulation cost, a distributed PDE model is used to simulate the region of interest, while the rest of the vasculature is approximated using a lumped ODE model. We propose a new splitting approach to numerically solve this multiscale problem in an efficient, accurate and affordable manner. The main novelty of the splitting scheme is that it ensures that the energy of the semi-discrete problem mirrors the behavior of the energy of the fully coupled problem. As a result, unconditional stability with respect to the time step choice is ensured without the need of sub-iterating between PDE and ODE sub-steps. We illustrate the capabilities of this framework by applying it to the development of a multiscale model describing the coupled dynamics of different biofluids in the brain and in the eye.