Asymptotic Model of Fluid–Tissue Interaction for Mitral Valve Dynamics

Abstract

Abstract-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.

Numerical prediction of thrombus risk in an anatomically dilated left ventricle: the effect of inflow cannula designs

“…The implementation of a static approximation of a MV, developed by Domenichini et al [19], was able to recreate general physiological flows. Intraventricular flow profiles were similar to a study by Bermejo et al [28], where echocardiographic data was obtained in nonischemic dilated cardiomyopathy patients.…”

“…The MV surface was approximated using a set of parametric equations, as described by Domenichini et al [19]. The equations are as follows: where θ was 100 linearly separated points from 0 to 2π; s was 40 linearly separated points from 0 to 1; ε  = 0.35 described the symmetry ratio between the anterior and posterior leaflets; k  = 0.6 described the ellipticity of the valvular edge; rads described the MV opening angle; and R = 19.5 mm defined the radius of the MV.…”

Modelling mitral valvular dynamics–current trend and future directions

“…109 The classical immersed boundary (IB) method pioneered by Peskin in the 1970s 107 is the earliest work of the overlapping method for heart valves and has since been widely used to simulate the dynamics of the heart and its valves. 59,[110][111][112][113][114][115][116] In the IB framework, the momentum and incompressibility of the whole coupled system are formulated in the Eulerian frame of reference, and the structural dynamics (motion, forces) are described in the Lagrangian frame of reference.…”

Fluid–structure interaction and structural analyses using a comprehensive mitral valve model with 3D chordal structure

“…Three-dimensional computational mechanics models have been developed over the years to better understand both normal MV function [1][2][3][4][5], dysfunction in the presence of disease [6][7][8][9], or function/dysfunction in surgically repaired states [10][11][12][13] Modeling outcomes are typically quantitative predictions of tissue stress or hemodynamic alterations [3,9,14,15] resulting from disease or surgery. Only in the latter case have researchers attempted to model fluid-structure interactions (FSI), because, clearly, the MV exists as a submerged structure in a highly dynamic fluid environment.…”