New Mathematical Model of Electromechanical Coupling in Rat Cardiomyocytes

The rat is one of the most widely used laboratory animal species. Therefore development of mathematical models aimed to analyze electromechanical coupling in the rat myocardium is a matter of top interest. We have developed a novel model of excitation-contraction coupling in the rat cardiomyocyte. This model combines equations from the Pandit electrophysiological model and Hinch model of calcium handling with equations describing myofilament mechanical activity from the 'Ekaterinburg-Oxford' mathematical model. The model reproduces both fast and slow responses to mechanical interventions in rat myocardium. © 2018 Creative Commons Attribution.Russian Foundation for Basic Research, RFBR: 18-01-00059The work is performed in the frameworks of IIP UrB RAS projects (Nos. AAAA-A18-118020590031-8, АААА-А18-118020590134-6), and supported by RFBR (No. 18-01-00059), by Act 211 Government of the Russian Federation, contract No. 02.A03.21.0006

Mechano-calcium and mechano-electric feedbacks in the human cardiomyocyte analyzed in a mathematical model

Experiments on animal hearts (rat, rabbit, guinea pig, etc.) have demonstrated that mechano-calcium feedback (MCF) and mechano-electric feedback (MEF) are very important for myocardial self-regulation because they adjust the cardiomyocyte contractile function to various mechanical loads and to mechanical interactions between heterogeneous myocardial segments in the ventricle walls. In in vitro experiments on these animals, MCF and MEF manifested themselves in several basic classical phenomena (e.g., load dependence, length dependence of isometric twitches, etc.), and in the respective responses of calcium transients and action potentials. However, it is extremely difficult to study simultaneously the electrical, calcium, and mechanical activities of the human heart muscle in vitro. Mathematical modeling is a useful tool for exploring these phenomena. We have developed a novel model to describe electromechanical coupling and mechano-electric feedbacks in the human cardiomyocyte. It combines the 'ten Tusscher-Panfilov' electrophysiological model of the human cardiomyocyte with our module of myocardium mechanical activity taken from the 'Ekaterinburg-Oxford' model and adjusted to human data. Using it, we simulated isometric and afterloaded twitches and effects of MCF and MEF on excitation-contraction coupling. MCF and MEF were found to affect significantly the duration of the calcium transient and action potential in the human cardiomyocyte model in response to both smaller afterloads as compared to bigger ones and various mechanical interventions applied during isometric and afterloaded twitches. © 2020 The Author(s).Russian Foundation for Basic Research, RFBR: 18‑01‑00059The work was carried out within the framework of the IIP UrB RAS themes (Nos. AAAA‑A18‑118020590031‑8, AAAA‑A18‑118020590134‑6) and was supported by RFBR (18‑01‑00059) and by Act 211 Government of the Russian Federation, contract No. 02.A03.21.0006

The Effects of Mechanical Preload on Transmural Differences in Mechano-Calcium-Electric Feedback in Single Cardiomyocytes: Experiments and Mathematical Models

Transmural differences in ventricular myocardium are maintained by electromechanical coupling and mechano-calcium/mechano-electric feedback. In the present study, we experimentally investigated the influence of preload on the force characteristics of subendocardial (Endo) and subepicardial (Epi) single ventricular cardiomyocytes stretched by up to 20% from slack sarcomere length (SL) and analyzed the results with the help of mathematical modeling. Mathematical models of Endo and Epi cells, which accounted for regional heterogeneity in ionic currents, Ca2+ handling, and myofilament contractile mechanisms, showed that a greater slope of the active tension–length relationship observed experimentally in Endo cardiomyocytes could be explained by greater length-dependent Ca2+ activation in Endo cells compared with Epi ones. The models also predicted that greater length dependence of Ca2+ activation in Endo cells compared to Epi ones underlies, via mechano-calcium-electric feedback, the reduction in the transmural gradient in action potential duration (APD) at a higher preload. However, the models were unable to reproduce the experimental data on a decrease of the transmural gradient in the time to peak contraction between Endo and Epi cells at longer end-diastolic SL. We hypothesize that preload-dependent changes in viscosity should be involved alongside the Frank–Starling effects to regulate the transmural gradient in length-dependent changes in the time course of contraction of Endo and Epi cardiomyocytes. Our experimental data and their analysis based on mathematical modeling give reason to believe that mechano-calcium-electric feedback plays a critical role in the modulation of electrophysiological and contractile properties of myocytes across the ventricular wall. © Copyright © 2020 Khokhlova, Konovalov, Iribe, Solovyova and Katsnelson.AAAA-A18-118020590031-8Russian Foundation for Basic Research, RFBR: 18-01-00059Russian Science Foundation, RSF: 18-74-10059Funding. Wet experiments were supported by the Russian Science Foundation (#18-74-10059). The development of mouse ventricular cardiomyocyte model was supported by the Russian Foundation for Basic Research (#18-01-00059), IIF UrB RAS theme (AAAA-A18-118020590031-8), and by RF Government Act #211 of March 16, 2013 (agreement 02.A03.21.0006)

Mathematical modelling of active contraction in isolated cardiomyocytes

We investigate the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A consistent mathematical model is presented considering a hyperelastic description of the passive mechanical properties of the cell, combined with an active-strain framework to explain the active shortening of myocytes and its coupling with cytosolic and sarcoplasmic calcium dynamics. A finite element method based on a Taylor-Hood discretization is employed to approximate the nonlinear elasticity equations, whereas the calcium concentration and mechanical activation variables are discretized by piecewise linear finite elements. Several numerical tests illustrate the ability of the model in predicting key experimentally established characteristics including: (i) calcium propagation patterns and contractility, (ii) the influence of boundary conditions and cell shape on the onset of structural and active anisotropy and (iii) the high localized stress distributions at the focal adhesions. Besides, they also highlight the potential of the method in elucidating some important subcellular mechanisms affecting, e.g. cardiac repolarizatio

Mechano-Electric Feedbacks in a New Model of the Excitation-Contraction Coupling in Human Cardiomyocytes

The study is aimed to develop a new human cardiomyocyte model, which describes electromechanical coupling and mechano-electric feedbacks. The combined electromechanical model (TP+M) links the TP06 electrophysiological model of the human cardiomyocyte with our earlier developed model of the myocardium mechanical activity and its calcium regulation. In the TP+M model, we tried to maintain principal features of calcium transients and action potentials during the twitches typical for the human cardiomyocytes. The developed TP+M model allows simulating several basic classic phenomena such as load-dependent relaxation and length-dependence of isometric twitches and respective changes in action potential duration. We have also simulated some age-dependent changes in the electrical and mechanical activity in the human cardiomyocytes. © 2018 Creative Commons Attribution.The work was carried out within the framework of the IIP UrB RAS themes (Nos. AAAA-A18-118020590031-8, АААА-А18-118020590134-6) and was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0006, and by RFBR (18-01-00059 - single cell modeling; 18-015-00368 – ageing simulation)

Virtual cardiac monolayers for electrical wave propagation

The complex structure of cardiac tissue is considered to be one of the main determinants of an arrhythmogenic substrate. This study is aimed at developing the first mathematical model to describe the formation of cardiac tissue, using a joint in silico-in vitro approach. First, we performed experiments under various conditions to carefully characterise the morphology of cardiac tissue in a culture of neonatal rat ventricular cells. We considered two cell types, namely, cardiomyocytes and fibroblasts. Next, we proposed a mathematical model, based on the Glazier-Graner-Hogeweg model, which is widely used in tissue growth studies. The resultant tissue morphology was coupled to the detailed electrophysiological Korhonen-Majumder model for neonatal rat ventricular cardiomyocytes, in order to study wave propagation. The simulated waves had the same anisotropy ratio and wavefront complexity as those in the experiment. Thus, we conclude that our approach allows us to reproduce the morphological and physiological properties of cardiac tissue

Transmural cellular heterogeneity in myocardial electromechanics

Myocardial heterogeneity is an attribute of the normal heart. We have developed integrative models of cardiomyocytes from the subendocardial (ENDO) and subepicardial (EPI) ventricular regions that take into account experimental data on specific regional features of intracellular electromechanical coupling in the guinea pig heart. The models adequately simulate experimental data on the differences in the action potential and contraction between the ENDO and EPI cells. The modeling results predict that heterogeneity in the parameters of calcium handling and myofilament mechanics in isolated ENDO and EPI cardiomyocytes are essential to produce the differences in Ca2+ transients and contraction profiles via cooperative mechanisms of mechano-calcium-electric feedback and may further slightly modulate transmural differences in the electrical properties between the cells. Simulation results predict that ENDO cells have greater sensitivity to changes in the mechanical load than EPI cells. These data are important for understanding the behavior of cardiomyocytes in the intact heart. © 2017, The Physiological Society of Japan and Springer Japan.Japan Society for the Promotion of Science, JSPS: 16K1287

Interactions of Cardiomyocytes and Myofibroblasts: An Experimental and Theoretical Model Study

Cardiomyocytes and fibroblasts make up the majority of cells in natural myocardium. While cardiomyocytes are primarily responsible for the mechanical contraction, fibroblasts are responsible for maintaining the extracellular matrix and tissue compliance. In response to pathologies such as hypertension or infarction, fibroblasts in the heart can convert to myofibroblasts, a larger and more contractile phenotype between a fibroblast and a smooth muscle cell. Myofibroblasts are essential to wound healing, but can change the compliance and functioning of heart tissue and can produce pathological fibrosis, formation of excess fibrous connective tissue. In developing therapeutic approaches it is essential to understand how myofibroblasts modulate the electromechanical functions of fibrotic heart. In this dissertation, the problem is studied by developing computational and experimental models of heart muscle with randomly distributed varying ratios of myofibroblasts. The experimental model consists of engineered heart tissues assembled from embryonic cardiomyocytes and containing defined fractions of myofibroblasts randomly distributed throughout the tissue. The computational model is formulated at the cellular level taking into account individual cardiomyocytes and myofibroblasts to yield the pattern of impulse spread as modulated by the presence of myofibroblasts acting either as insulators or resistors. The excitatory impulse activates the contraction of individual viscoelastic cells that are mechanically linked to other cells and the extracellular matrix. The results give insight into the mechanical and electrical modulation of engineering heart tissue by myofibroblasts

Electromechanical modelling and in silico analysis of a rat cardiac syncytium

none4noIn this paper we studied the mechanics and physiology occurring during the contraction of a 2D syncytium made of rat cardiomyocytes by carrying out numerical simulations of an electromechanical model for its cell and tissue components. Our model was qualitatively compared with experimental results taken from literature and it gave us optimistic outputs providing a tool for future studies into cardiac mechanisms and contraction even in a 3D environment.openDel Bianco F, Colli Franzone P, Scacchi S, Fassina LDEL BIANCO, Fabrizio; Colli Franzone, P; Scacchi, S; Fassina,