Flow-driven opening of a valvular leaflet

Abstract

The understanding of valvular opening is a central issue in cardiac flows, whose analysis is often prohibited by the unavailability of (in vivo) data about tissue properties. Asymptotic or approximate representations of fluid-structure interaction are thus sought. The dynamics of an accelerated stream, in a two-dimensional channel initially closed by a rigid inertialess movable leaflet, is studied as a simple model problem aimed at demonstrating the main phenomena contributing to the fluidstructure interaction. The problem is solved by the coupled numerical solution of equations for the flow and solid. The results show that the leaflet initially opens in a no-shedding regime, driven by fluid mass conservation and a predictable dynamics. Then the leaflet motion jumps, after the saturation of a very rapid intermediate vortex-shedding phase, to the asymptotic slower regime with a stable self-similar wake structure. IntroductionThe interaction between a fluid stream and a moving boundary is common in several contexts; numerous examples can be found in the cardiovascular system where flows inside deformable vessels and through cardiac valves are of primary physiological relevance. The original motivation for this work is our interest in the flow through the mitral valve that controls the blood motion from the left atrium to the left ventricle of the heart. More generally, similar phenomena can be found in technological devices when valves are used to control the fluid motion through orifices and possibly to avoid back-flow. Despite the applied background this work is a theoretical one, on the interaction of the flow and a leaflet under ideal conditions. It represents a step towards the understanding of phenomena in a fluid-structure interaction of potentially high applied relevance.When a closed valve is forced to open by a stream, the (typically thin) leaflets rapidly move with the fluid with only a weak resistance to it. A rigorous mathematical model of the flow-structure dynamics should be based on the fluid and solid equations, for the flow and the tissue, respectively, and on the proper coupling relations. Along these lines, a simplified approach, developed for a thin solid without bending stiffness, was introduced by Peskin & McQueen (1989). However, in our experience, the numerical implementation of this mathematically attractive model has several disadvantages, such as the lack of resolution close to the body and unrealistic stress distributions on it. A major difficulty in studying the fluid-solid interaction is the rapidity of the leaflet response to the action of the incoming fluid, and its large movement within the flow domain. A complete numerical solution of the fluid-solid system has been presented for the flow in models of the aortic valve (De Hart et al. 2003; Stijnen et al.

Numerical and experimental investigations of pulsatile blood flow pattern through a dysfunctional mechanical heart valve

“…In previous numerical studies, the flow downstream of a normal BMHV was investigated under steady state flow conditions (Ge et al, 2003) and pulsatile flow conditions with or without Fluid Structure Interaction (FSI) (Grigioni et al, 2005;Pedrizzetti and Domenichini, 2006;Alemu and Bluestein, 2007). It should be noted that in most studies where FSI was considered, the flow through the BMHV was assumed to be laminar (Guivier et al, 2007;Redaelli et al, 2004;Dumont et al, 2007).…”

Role of Mitral Annulus Diastolic Geometry on Intraventricular Filling Dynamics

“…Considering the mitral annulus geometries alone, with the areas kept constant, one would not expect there to be such a difference in vorticity magnitudes, especially since the same piston motion profile was used for both cases. We believe that these differences in vorticity magnitudes are most likely due to the fact that the vortex formed from the D-shaped annulus is a more asymmetric ring, arising due to the interaction between the flat and curved edges, while that formed from O-shaped annulus is more axisymmetric and hence stronger [18,44,45]. This curvature would allow the smoother, more circular, annulus to result in an initially more symmetrical, ringlike vortex, which would be stronger.…”

“…Several types of PHVs for the mitral position are currently available [13][14][15], the most common of which include bileaflet ("three-jet" orifice) and bioprosthetic (circular orifice) designs. Previous studies on PHVs intended for the mitral position have investigated the LV filling fluid mechanics using bileaflet, tilting disk, and monoleaflet designs [11,16,17], as well as using PHVs with asymmetric leaflet lengths as observed in the native MV [18][19][20]. However, most of the studies of LV fluid mechanics employing physical and computational models (excluding in vivo studies) are limited to using a circular mitral annulus as a fundamental assumption.…”

Effect of the curvature of elastic plates on the evolution of pulsatile flow fields

“…there is only one plane of symmetry), (b) the interaction with pulsatile flows is considered, (c) the focus is placed on the evolution of the flow around the plate. In addition, the results of the numerical investigation by Pedrizzetti and Domenichini (2006) concerning the problem of flow-driven opening of rigid leaflet valves are relevant to our study. Some features of the flow field around hinged plates which are impulsively started resemble the ones reported here.…”