Multiscale simulation of the effects of atrioventricular block and valve diseases on heart performance

Abstract

A new mathematical model of the cardiovascular system is proposed. The left ventricle is described by an axisymmetric multiscale model where myocardium is treated as an incompressible transversely isotropic medium with a realistic distribution of fibre orientation. Active tension and its regulation by Ca2+ ions are described by our recent kinetic model. A lumped parameter model is used for the simulation of blood circulation, in which the left and right atria and the right ventricle are described by a system of ordinary differential equations for active pressure‐volume relationships. The stress and strain of the left ventricle myocardium were calculated by the finite element method implemented by the authors. The changes in the haemodynamics upon changes in preload of a healthy heart, upon physical exercise, and in case of atrioventricular block with different types of arrhythmias were simulated. To simulate the effect of stenosis or regurgitation of the aortic or mitral valves, the hydraulic and inertial flow resistances of the heart valves were set as functions of their orifice areas. The model reproduced a number of phenomena observed in clinical practice, including the classification of the severity of valve disease.

Impact of Concomitant Mitral Regurgitation on the Hemodynamic Indicators of Aortic Stenosis

“…Numerous mathematical models of the cardiovascular system and valvular disease have been described in the literature. Many of these computationally based studies examined the hemodynamics of AS 36 , 37 and or MR 38 , 39 , 40 in isolation. To the best of our knowledge, no computationally based studies have simulated both valve pathologies concomitantly.…”

The multiscale simulation of apical myocardial infarction and shape variation of the left ventricle of the heart

“…Our multiscale model of the LV within CVS described by a lumped parameter model reproduces the time-courses of haemodynamic variables (pressures in the LV, aorta, veins, volume of the LV) for an averaged "healthy" patient, and the effects of some arrhythmias and heart valve diseases [3]. Here we report the result of simulation of the effects of apical MI on the LV performance and geometry during a heartbeat.…”

“…The second expression states how F Act depended on activation function e Act and, in order to reproduce Frank's law of the heart, on the chamber volume. The lumped parameter model was described in our recent paper [3]. The equilibrium equations for the LV were related to the lumped parameter model by the volume of the LV cavity V LV and LV pressure P LV , which was included in boundary conditions for the inner wall of the ventricle.…”

“…The LV contractions were initiated by the periodic simultaneous influx of calcium ions to the cells of the ventricular wall and had been performed until the steady periodical solution had been obtained. The details of the model and its numerical implementation are given in our previous works [3,4].…”

“…In particular, myocardial infarction (MI) is a heart disease of interest for computer simulation [2]. Earlier we had developed a model of the cardiovascular system with a focus on the left ventricle (LV) of the heart [3]. The LV was represented by a multiscale model describing the macroscopic pumping function of the ventricle considering the dependence of stress-strain relationships at the tissue level on the microscopic processes at the cell level [4].…”