Charles University, Czech Republic
Helena Svihlova is a PhD student at Mathematical Institute at Charles University in Prague. Her area of interest is computational fluid mechanics with application in biomechanics, especially flow in diseased valves and arteries.
Stenotic heart valve diseases are among the leading causes of death worldwide. A stenosis in the cardiovascular system is a reduction in cross-sectional area of a structure acrosswhich blood flows. Because of the stenosis in valve, theheartmust pump out more blood and this leads to increaseof the pressure at the beginning of the valve. In order to compute this pressure, we can use the information about velocity field obtained from the modern imaging techniques such as 4D magnetic resonance. The "gold standard" of ascertaining pressure difference is Gorlin formula based on Bernoulli equation improved by empirical constant. There were some attempts to prove the concept using Bernoulli equation. The standard methodology is however based on several unrealistic assumptions. We used two techniques to obtain the pressure directly from the Navier-Stokes equations when the velocity field is considered to be known or at least approximated. The first technique is to derive the gradient of pressure directly from the Navier-Stokes equations. This leads to a Poisson equation and was investigated. The second technique was suggested in and leads to a Stokes problem where the unknowns are the pressure and some correction vector. In both cases, we fix the value of the pressure at the outlet boundary which represents the pressure measured in the aorta. The results confirming that the second technique provides more accurate estimation of the pressure.