1st Leibniz MMS Days - Abstract

Caiazzo, Alfonso

Challenges in patient-specific blood flow simulation

This talk presents three current research topics targeting clinically relevant blood flow simulations in patient-specific regimes, i.e. aiming at mathematical models tuned to realistic scenarios. In particular, we will discuss issues related to the stability of the simulations, the efficiency of the computation, and the data assimilation, i.e. the possibility of adjusting the mathematical models according to available measurements. Firstly, we will describe the issue of imposing robust boundary conditions for open (Neumann) boundaries in presence of oscillatory flow regimes, discussing the main mathematical challenges and recently developed methods. Secondly, we will focus on reduced-order modeling, i.e. mathematical methods aiming at reducing the cost of the simulation by using a priori information about the problem. In particular, we will show few examples of reduced models for simulating the blood flow in the pulmonary artery. Finally, the estimation of model parameters starting from experimental measurements (in terms of flow rates and pressures) will be discussed, focusing on one-dimensional models of the cardiovascular system. In alases, we will present recent results and an outlook of possible future developments.