Asymptotic Model of Fluid-Tissue Interaction for Mitral Valve Dynamics

The vortex formation process inside the left ventricle is intrinsically connected to the dynamics of the mitral leaflets while they interact with the flow crossing the valve during diastole. The description of the dynamics of a natural mitral valve still represents a challenging issue, especially because its material properties are not measurable in vivo. Medical imaging can provide some indications about the geometry of the valve, but not about its mechanical properties. In this work, we introduce a parametric model of the mitral valve geometry, whose motion is described in the asymptotic limit under the assumption that it moves with the flow, without any additional resistance other than that given by its shape, and without the need to specify its material properties. The mitral valve model is coupled with a simple description of the left ventricle geometry, and their dynamics is solved numerically together with the equations ruling the blood flow. The intra-ventricular flow is analyzed in its relationship with the valvular motion. It is found that the initial valve opening anticipates the peak velocity of the Early filling wave with little influence of the specific geometry; while subsequent closure and re-opening are more dependent on the intraventricular vortex dynamics and thus on the leaflets' geometry itself. The limitations and potential applications of the proposed model are discussed.