Invited Plenary Talk (Mathematics)

Numerical modelling in hemodynamics

prof. Mária Lukáčová-Medviďová Institute of Mathematics,
Johannes Gutenberg University, Mainz, Germany


Hemodynamics is the study of blood flow or the circulation. In the present talk we will firstly illustrate an importance of studying hemodynamical flows and formulate a mathematical model based on basic conservation laws (conservation of mass and momentum). We will discuss existence of the so-called weak solutions and propose a suitable numerical technique to simulate blood flows in elastic vessels. Finally we will illustrate the behaviour of numerical schemes on a series of numerical experiments. We also show the results for hemodynamic wall parameters; the wall shear stress and the oscillatory shear index that are of special interest for medical doctors.

The present research has been done in cooperation with A. Hundertmark-Zauskova (Mainz) and G. Rusnakova (Kosice / Mainz).