Electro-fluid-mechanics of the heart

Abstract

This article presents an overview of the dynamics of the human heart and the main goal is the discussion of its fluid mechanic features. We will see, however, that the flow in the heart can not be fully described without considering its electrophysiology and elastomechanics as well as the interaction with the systemic and pulmonary circulations with which it is strongly connected. Biologically, the human heart is similar to that of all warm-blooded mammals and it satisfies the same allometric laws. Since the Paleolithic Age, however, humans have improved their living conditions, have modified the environment to satisfy their needs and, more recently, have developed advanced medical knowledge which has allowed triple the number of heartbeats with respect to other mammals. In the last century, effective diagnostic tools, reliable surgical procedures and prosthetic devices have been developed and refined leading to substantial progress in cardiology and heart surgery with routine clinical practice which nowadays cures many disorders, once lethal. Pulse duplicators have been built to reproduce the pulsatile flow and ‘blood analogues’, have been realized. Heart phantoms, can attain deformations similar to the real heart although the active contraction and the tissue anisotropy still can not be replicated. Numerical models have also become a viable alternative for cardiovascular research: they do not suffer from limitations of material properties and device technologies, thus making possible the realization of truly digital twins. Unfortunately, a high-fidelity model for the whole heart consists of a system of coupled, nonlinear partial differential equations with a number of degrees of freedom of the order of a billion and computational costs become the bottleneck. An additional challenge comes from the inherent human variability and the uncertainty of the heart parameters whose statistical assessment requires a campaign of simulations rather than a single deterministic calculation; reduced and surrogate models can be employed to alleviate the huge computational burden and all possibilities are currently being pursued. In the era of big data and artificial intelligence, cardiovascular research is also advancing by exploiting the latest technologies: equation-based augmented reality, virtual surgery and computational prediction of disease progression are just a few examples among many that will become standard practice in the forthcoming years.

A comprehensive and biophysically detailed computational model of the whole human heart electromechanics

“…10]). The shape of the pressure-volume loops finds a very good agreement with the medical literature [20,61,67,68,135]. While this is not the first time that an electromechanical model is able to describe the ventricular physiology [26,27,46], to the best of our knowledge the eight-shaped pressure-volume loops of the atria have never been shown so accurately by a computational model.…”

“…We also describe the phases of the cardiac cycle, focusing on the differences of the atrial and ventricular function. For a more in-depth overview of the cardiac anatomy and physiology, we refer to [20,32,[58][59][60][61][62].…”

“…The squared shape of the ventricular diagram is a direct consequence of the state of the valves and of the two isovolumetric phases. To this counterclockwise loop is associated the (positive) ejection work exerted by the tissue on the blood [20], that increases if the maximum difference in pressures (or in volumes) arises. The difference among the ventricular End Diastolic Volume (EDV) and End Systolic Volume (ESV) is called Stroke Volume (SV) and represents the volume of blood pumped out from each ventricle during a heartbeat.…”

“…Finally, once the reference configuration Ω 0 has been recovered, we can set proper values of p i = p i,0 and T a = T a,0 corresponding to the phase of the cardiac cycle at the initial time t = 0 of the unsteady electromechanical model and solve again Eq. (20). In this way, we obtain the initial condition d 0 = d(x 0 , p i,0 , T a,0 ) for the unsteady mechanical problem (M ) of Eq.…”

“…Computational models of the cardiac function are progressively increasing their role in cardiology, revealing diagnostic information, contributing to the development of new therapies and promising patient-specific treatments based on individual pathophysiology [4][5][6]. Successful examples can be found in the context of cardiac electrophysiology [7][8][9][10][11], electromechanics [12][13][14][15][16] and fluid-dynamics [17][18][19][20].…”