Mechanical model of the left ventricle of the heart approximated by axisymmetric geometry

Abstract

An axisymmetric model is suggested to simulate mechanical performance of the left ventricle of the heart. Cardiac muscle is treated as incompressible anisotropic material with active tension directed along muscle fibres. This tension depends on kinetic variables that characterize interaction of contractile proteins and regulation of muscle contraction by calcium ions. For numerical simulation of heartbeats the finite element method was implemented. The model reproduces well changes in ventricle geometry between systole and diastole, ejection fraction, pulse wave of ventricular and arterial pressure typical for normal human heart. The model also reproduces well the dependence of the stroke volume on end-diastolic and arterial pressures (the Frank–Starling law of the heart and Anrep effect). The results demonstrate that our model of cardiac muscle can be successfully applied to multiscale 3D simulation of the heart.

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

“…The LV model presented here is an expansion of our previous model . The LV shape was approximated by an axisymmetric body.…”

“…The titin tension F tit was described by an equation of worm‐like chain model commonly used for the description of mechanics of long protein chains; l s and l s0 are the deformed and unstrained sarcomere lengths. Muscle fibres were oriented along spirals with the spiral angle changing linearly through the LV wall from +80° in the endocardium to −55° in the epicardium …”

“…In order to describe the region of the left ventricle where the valves are located, we include circumferential anisotropic stress of very stiff collagen fibres forming the fibrous ring. For this purpose, an elastic term proportional to tensor C (that is a dyadic product of the strained unit vector aligned with circumferential direction) was added to the right hand side of Equation ; it was in details described in our previous work . The collagen density was defined to increase continuously upon approaching the LV base.…”

“…In order to describe stress at the apex, where the fibre orientation is rather complex, we added a term describing isotropic elastic stress depending on n . Corresponding expressions are also given in Syomin and Tsaturyan …”

“…Besides, it reproduced some mechanical features of cardiac muscles such as length‐dependent Ca 2+ activation, which underlies the Starling's law of the heart, the load‐dependent relaxation, tension development and redevelopment upon step increase in Ca 2+ concentration, and fast shortening. We also have developed a simplified model in which the shape of LV was approximated by an axisymmetric body . The model was based on an earlier version of our model of the cardiac muscle .…”