In this project we have developed an innovative and versatile multi-physics model to simulate the left heart (LH) functioning. The pulsatile and transitional character of the hemodynamics is obtained by solving directly the incompressible Navier–Stokes equations using a staggered finite differences method. The code is complemented with various immersed boundary (IB) techniques to handle complex moving and deforming geometries. The structural mechanics is based on the Fedosov’s interaction potential method to account for the mechanical properties of the biological tissues, which are anisotropic and nonlinear. The electrophysiology, responsible for the active potential propagation in the cardiac tissue triggering the active muscular tension, is incorporated by means of a bidomain model that can account for the different cellular models of the various portions of the heart. All these models are three-way coupled with each other, thus capturing the fully synergistic physics that allows the heart to function continuously using only 8 W of power. The resulting electro-fluid–structure interaction (FSEI) code is tailored to investigate the pulsatile flow in an animated LH beating at 70 bpm. The LH is composed by realistic geometries of the left ventricle and atrium, whose active muscular contraction triggers a structural deformation of the endocardium that originates the hemodynamics, which, in turn, generates stresses on the surrounding cardiac tissue. The numerical framework also includes the bi-leaflet mitral valve, the three-leaflets aortic valve and the thoracic aorta, which are passive tissues experiencing continuous stretching and bending through the cardiac cycle.
The computational framework is seen to provide realistic cardiovascular simulations both in terms of muscular activation, intraventricular hemodynamics and wall shear stresses. In particular, we have shown the propagation of the transmembrane potential over the myocardium triggered by a localized electrical input in the Bachmann and His bundles. The consequent action potential and heart chambers depolarization yields an active muscular tension and tissue contraction that is oriented according to the local direction of the muscular fibers. Hence, the model reproduces also the vigorous three–dimensional twist of the left ventricle from the apex to the valvular plane observed in-vivo. This electro-mechanical activity of the LH chambers originates a complex hemodynamics and valve dynamics, which is in qualitative and quantitative agreement with in-vivo and ex-vivo measurements. The mitral valve connecting the left atrium and ventricle, opens during diastole and closes when the ventricle contracts, owing to the external hydrodynamics loads exerted on its leaflets. At the same time the mitral valve prevents an undesired back-flow of oxygenated blood during systole, the aortic valve opens and blood is propelled in the thoracic aorta. Furthermore, the numerics well reproduces the Wiggers diagram of a healthy human adult reported in medical atlas. This diagram shows the time variation over a heart beat of the pressure in the left ventricle, atrium and thoracic aorta, with the typical pressure variation of 0–120 mmHg in the ventricle. During a heart beat, the ventricular volume diminishes from the maximum (tele-diastolic) volume, which is given as input through the ventricle geometry, to its minimum (tele-systolic) value, which is not imposed and computed as part of the solution. This volume variation of the ventricle corresponds to an ejection fraction of about 60% and a cardiac output of 5.06 l/min, which are typical physiological values for the heart of a healthy adult.
