Talk by Helena Švihlová and Marek Čapek

When, where: Monday October 15, 2018, in K3 from 9:00 till 10:30.

Speaker: Helena Švihlová

Title: Determination of pressure data in aortic valves

Abstract: The problem of ascertaining pressure of the fluid from given velocity field is motivated by the need to obtain the pressure loss during the blood flow in stenotic aortic valves. Because of the narrowing of the valve, stenosis, the heart must pump out more blood and this leads to increase of the pressure at the beginning of the valve. The modern imaging techniques, such 4D magnetic resonance, can give us velocity vectors of fluid particles in some amount of points.
We will present a new model for obtaining the pressure leading to the Stokes problem where the unknowns are the pressure and a correction vector. It brings the more accurate estimation of the pressure loss than the classical pressure Poisson equation. We will also present results concerning the computation of the flow in stenotic valves and the problem of the proper setting of the boundary conditions.

Speaker: Marek Čapek

Title: A non-homogeneous model of blood flow

Abstract: The human blood can be modelled as Newtonian or non-Newtonian fluid. Among its non-Newtonian characteristics count shear-thinning viscosity, viscoelasticity, thixotropy, probably yield stress. The non-Newtonian properties are preferably apparent under rather low-shear rate conditions. Therefore we witness them not only in smaller veins, but also in most interesting locations for current
medicine – in aneurysmas and in stenoses due to atherosclerosis. We will review current non-Newtonian models of blood, pointing at the two categories of models – phenomenologically derived vs microstructure based. We will present the microstructure based model of Owens, which seems to us very promising from the point of capturing the above mentioned non-Newtonian characteristics. We also make a remark about its ability to take into account the Fahraeus effect.