A Feature-Based Mechano-Electric Finite Element Model of the Left Atrium With Pressure-to-Mitral-Flow Coupling

The modeling of complex biological systems requires many degrees of sophistication. Among them, we can enumerate heterogeneous tissue properties, a complex geometry that can be obtained only through proper imaging techniques and the interaction of the organ of interest with the surrounding structures. In the case of the left atrium, three physical domains govern its behavior: mechanical, electrical and fluidic. Different mechanical conditions, in terms of stresses and consequent strains, affect the electrical activity occurring across the tissue, and jointly, the mechanical and electrical activities regulate the correct and timely contraction of the chamber. A strongly coupled mechano-electrical model of the atrial chamber cannot be accomplished without accounting for the directional heterogeneity of the tissue, because both the electrical and the mechanical properties of the tissue are not isotropic. The fluid entering from the pulmonary veins during the filling phase of the atrium causes the pressure in the atrium to rise until the difference between the pressure in the ventricular and atrial chamber is negative (higher atrial pressure) and the mitral valve opens. After the opening of the valve, two distinct emptying phases ensue, a passive and an active one. During the passive emptying phase the pressure in the ventricle slowly rises, affecting the flow through the valve itself. During the active phase, the contraction of the atrium walls causes the pressure in the atrium to rise. Our laboratory has developed a finite element dynamic mechano-electric model of the left atrium behavior starting from multi-detector computed tomography images. We accounted for the directional heterogeneity of the tissue because both the electrical and the mechanical properties of the tissue are not isotropic. As a first step, we modeled the effect of the blood flow in the atrium (fluidic domain) by assuming a temporally varying pressure across the cardiac cycle. In spite of this assumption, i.e. of a “dry” pressure-driven model, we cannot ignore the contribution to the presence of the left ventricle downstream of the mitral valve. In fact, the ventricular pressure counteracts the volume decrease due to the passive and active emptying on the atrial chamber. Moreover, during the active phase of the atrium cycle, the atrial pressure rises in response to the resistance of the mitral flow to time changes (c wave).