Numerical Simulation of Blood Flow Through Mechanical Heart Valves Using Meshless Techniques

Heart valve disease is a major contributor to cardiovascular mortality and morbidity. While bioprosthetic valves have satisfactory hemodynamic performance, mechanical heart valves (MHVs) are more durable, so their clinical use is increasing [1]. Unfortunately, current MHVs cause flow abnormalities, thrombosis and hemolysis [2]; they are therefore at a stage far from duplicating the function of natural valves. Recent improvements in computer performance and numerical methods have resulted in significant breakthroughs in MHV design [2]. In particular, computational fluid dynamics has been used to redesign valves to minimize the production of turbulence, regions of high shear stresses, pressure loss and stagnation regions in the vicinity of the leaflets [3]. These studies have, for the most part, used numerical techniques that require domain discretization such as finite element methods (FEM) or finite difference methods (FDM). However, these methods cannot represent the complexity of the moving and deforming boundaries present in an operating valve without extraordinarily high computational costs. That is, methods that use domain discretization require a fine mesh in small gaps between leaflets and near the valve housing. As a result, simplifying assumptions are typically made which introduce error into the results. We have recently implemented two meshless numerical techniques — the boundary element method (BEM) and the radial functions method (RFM) — that compute fluid flow fields without domain discretization and thus can model valve leaflet motions and unsteady flow with reasonable computational costs. The goal of this study was to model blood flow through mechanical heart valves using these techniques. In this paper we present the results of BEM simulations of heart valves in a range of open states. RFM techniques, which can efficiently simulate the nonlinear effects of inertia in the domain, are also described.