Haemodynamic determinants of the mitral valve closure sound: A finite element study

Abstract

Automatic acoustic classification and diagnosis of mitral valve disease remain outstanding biomedical problems. Although considerable attention has been given to the evolution of signal processing techniques, the mechanics of the first heart sound generation has been largely overlooked. In this study, the haemodynamic determinants of the first heart sound were examined in a computational model. Specifically, the relationship of the transvalvular pressure and its maximum derivative to the time-frequency content of the acoustic pressure was examined. To model the transient vibrations of the mitral valve apparatus bathed in a blood medium, a dynamic, non-linear, fluid-coupled finite element model of the mitral valve leaflets and chordae tendinae was constructed. It was found that the root mean squared (RMS) acoustic pressure varied linearly (r2= 0.99) from 0.010 to 0.259 mmHg, following an increase in maximum dP/dt from 415 to 12470 mm Hg s(-1). Over that same range, peak frequency varied non-linearly from 59.6 to 88.1 Hz. An increase in left-ventricular pressure at coaptation from 22.5 to 58.5mm Hg resulted in a linear (r2= 0.91) rise in RMS acoustic pressure from 0.017 to 1.41mm Hg. This rise in transmitral pressure was accompanied by a non-linear rise in peak frequency from 63.5 to 74.1 Hz. The relationship between the transvalvular pressure and its derivative and the time-frequency content of the first heart sound has been examined comprehensively in a computational model for the first time. Results suggest that classification schemes should embed both of these variables for more accurate classification.

Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation

“…Previously, several numerical simulations of the mitral apparatus have been conducted with different types of material models for the leaflets (see, e.g. Kunzelman et al [2], Einstein et al [3], Votta et al [4], Dal Pan et al [5]). Several authors have implemented models for soft biological tissues into finite element codes.…”

On the multiscale modeling of heart valve biomechanics in health and disease

“…Loon et al extended fictitious domain method through coupling a Navier-Stokes (Einstein et al 2004) flow solver in Eulerian description to a Neo-Hookean solid model in Lagrangian description to model valve-leaflet blood interaction (Loon et al 2006). Nicosia et al modeled the aortic valve using an anisotropic elastic material model (Nicosia et al 2003), followed by Weinberg et al modeling the aortic valve with a discrete fiber model (Weinberg and Kaazempur Mofrad 2007) and Einstein modeling the mitral valve with a splayed-fiber model (Einstein et al 2004(Einstein et al , 2005aKunzelman et al 2007). The last two models notably are verified against various experimental measures, and Einstein's model is able to predict heart sounds (Einstein et al 2004); see Fig.…”

“…Nicosia et al modeled the aortic valve using an anisotropic elastic material model (Nicosia et al 2003), followed by Weinberg et al modeling the aortic valve with a discrete fiber model (Weinberg and Kaazempur Mofrad 2007) and Einstein modeling the mitral valve with a splayed-fiber model (Einstein et al 2004(Einstein et al , 2005aKunzelman et al 2007). The last two models notably are verified against various experimental measures, and Einstein's model is able to predict heart sounds (Einstein et al 2004); see Fig. 4b for a representation of the mitral valve model which also includes the chordae tendinae, not depicted.…”

“…Currently, the most widely used models incorporate a splayed-fiber model into a shell. This approach has been used successfully in simulating bioprosthetic valves and mitral valves in healthy and diseased states (Einstein et al 2004(Einstein et al , 2005a. Modeling of valve tissue-scale mechanics has been recently reviewed (Weinberg and Kaazempur Mofrad 2005;Sacks and Yoganathan 2007), and the field continues to progress rapidly.…”

“…The most advanced strain energy functions for valve mechanics include fiber splay as well as fiber direction. Such models have been constructed and fit to experimental data for aortic (Billiar and Sacks 2000a,b) and mitral (Einstein et al 2004) valves. Current research in continuum models for leaflet mechanics aims to create a multi layered model of the tissue with continuum models for each layer.…”