A robust and efficient valve model based on resistive immersed surfaces

Abstract

A procedure for modeling the heart valves is presented. Instead of modeling complete leaflet motion, leaflets are modeled in open and closed configurations. The geometry of each configuration can be defined, for example, from in vivo image data. This method enables significant computational savings compared with complete fluid-structure interaction and contact modeling, while maintaining realistic three-dimensional velocity and pressure distributions near the valve, which is not possible from lumped parameter modeling. Leaflets are modeled as immersed, fixed surfaces over which a resistance to flow is assigned. On the basis of local flow conditions, the resistance values assigned for each configuration are changed to switch the valve between open and closed states. This formulation allows for the pressure to be discontinuous across the valve. To illustrate the versatility of the model, realistic and patient-specific simulations are presented, as well as comparison with complete fluid-structure interaction simulation.