ИСТИНА

Introduction Multiscale modelling of the heart is a very intriguing problem nowadays. There is a number of complex electromechanical models of the heart or its left ventricle. Such models comprised cell models of contraction and electromechanical coupling, tissue models and models of the blood flow. Recent cell models have very detailed description of ionic currents but often have primitive specification of muscle mechanics. This problem is caused by the computational complexity of the majority of accurate cell models. Existing computationally simple mechanical models of muscle contraction, which are based on kinetic models, reproduce only a limited set of experimental data for uniaxial muscle contraction. Here we present a mechanical model of the left ventricle in which active contraction is described by a simple, yet quite accurate, kinetic model. Model An axisymmetric model of the left ventricle of the heart is presented. The shape of the ventricle was close to the real one. The geometry was set by analytical expressions, while muscle fibres were oriented along helices with helical angle changing linearly by 135° through the ventricle wall. The myocardial tissue was considered to be incompressible transversally isotropic continuous medium. Both passive elastic stress caused by myocardium strain and active stress caused by the actin-myosin interactions were considered. The interaction and its calcium regulation were described by our kinetic model, in which kinetic rates depended only on an ensemble-averaged micro-strain of the actin-myosin cross-bridges. Thus the kinetics in the model was set by a system of ODEs, so the model was quite simple computationally. The activation of the contraction of the left ventricle was set by a periodical time function for calcium influx into a cell. Blood flow was specified by a compartmental Windkessel-type model. Results We have simulated a normal heartbeat. The time courses of ventricular and aortic pressures, as well as ventricular volume were in good agreement with those observed in a normal human heart. The changes in the long and short axes of the ventricle, its twist, and the radial and axial local strains in the various regions of the ventricle during a heartbeat (Fig.1) also fit medical data well. We have simulated the dependence of the ejection volume on preload and afterload and examined changes in ventricular performance at various pathologies of the heart valves, vascular bed and myocardial contractility. Results of the simulations have also matched the results of observations. Discussion Even 2D model of the left ventricle based on our kinetic model of contraction have shown good results for the simulation of a heart-beat in normal and pathological conditions. It seems perspective to improve it for 3D modelling. Acknowledgements RFBR 16-04-00693.