The importance of mechanical conditions in the testing of excitation abnormalities in a population of electro-mechanical models of human ventricular cardiomyocytes.

Background: Populations of in silico electrophysiological models of human cardiomyocytes represent natural variability in cell activity and are thoroughly calibrated and validated using experimental data from the human heart. The models have been shown to predict the effects of drugs and their pro-arrhythmic risks. However, excitation and contraction are known to be tightly coupled in the myocardium, with mechanical loads and stretching affecting both mechanics and excitation through mechanisms of mechano-calcium-electrical feedback. However, these couplings are not currently a focus of populations of cell models. Aim: We investigated the role of cardiomyocyte mechanical activity under different mechanical conditions in the generation, calibration, and validation of a population of electro-mechanical models of human cardiomyocytes. Methods: To generate a population, we assumed 11 input parameters of ionic currents and calcium dynamics in our recently developed TP + M model as varying within a wide range. A History matching algorithm was used to generate a non-implausible parameter space by calibrating the action potential and calcium transient biomarkers against experimental data and rejecting models with excitation abnormalities. The population was further calibrated using experimental data on human myocardial force characteristics and mechanical tests involving variations in preload and afterload. Models that passed the mechanical tests were validated with additional experimental data, including the effects of drugs with high or low pro-arrhythmic risk. Results: More than 10% of the models calibrated on electrophysiological data failed mechanical tests and were rejected from the population due to excitation abnormalities at reduced preload or afterload for cell contraction. The final population of accepted models yielded action potential, calcium transient, and force/shortening outputs consistent with experimental data. In agreement with experimental and clinical data, the models demonstrated a high frequency of excitation abnormalities in simulations of Dofetilide action on the ionic currents, in contrast to Verapamil. However, Verapamil showed a high frequency of failed contractions at high concentrations. Conclusion: Our results highlight the importance of considering mechanoelectric coupling in silico cardiomyocyte models. Mechanical tests allow a more thorough assessment of the effects of interventions on cardiac function, including drug testing.

In silico analysis of the contribution of cardiomyocyte-fibroblast electromechanical interaction to the arrhythmia.

Although fibroblasts are about 5-10 times smaller than cardiomyocytes, their number in the ventricle is about twice that of cardiomyocytes. The high density of fibroblasts in myocardial tissue leads to a noticeable effect of their electromechanical interaction with cardiomyocytes on the electrical and mechanical functions of the latter. Our work focuses on the analysis of the mechanisms of spontaneous electrical and mechanical activity of the fibroblast-coupled cardiomyocyte during its calcium overload, which occurs in a variety of pathologies, including acute ischemia. For this study, we developed a mathematical model of the electromechanical interaction between cardiomyocyte and fibroblasts and used it to simulate the impact of overloading cardiomyocytes. In contrast to modeling only the electrical interaction between cardiomyocyte and fibroblasts, the following new features emerge in simulations with the model that accounts for both electrical and mechanical coupling and mechano-electrical feedback loops in the interacting cells. First, the activity of mechanosensitive ion channels in the coupled fibroblasts depolarizes their resting potential. Second, this additional depolarization increases the resting potential of the coupled myocyte, thus augmenting its susceptibility to triggered activity. The triggered activity associated with the cardiomyocyte calcium overload manifests itself in the model either as early afterdepolarizations or as extrasystoles, i.e., extra action potentials and extra contractions. Analysis of the model simulations showed that mechanics contribute significantly to the proarrhythmic effects in the cardiomyocyte overloaded with calcium and coupled with fibroblasts, and that mechano-electrical feedback loops in both the cardiomyocyte and fibroblasts play a key role in this phenomenon.

Mathematical modelling of the mechano-electric coupling in the human cardiomyocyte electrically connected with fibroblasts.

Cardiac fibroblasts are interspersed within mammalian cardiac tissue. Fibroblasts are mechanically passive; however, they may communicate electrically with cardiomyocytes via gap junctions and thus affect the electrical and mechanical activity of myocytes. Several in-silico studies at both cellular (0D) and ventricular (3D) levels analysed the effects of fibroblasts on the myocardial electrical function. However, none of them addressed possible effects of fibroblast-myocyte electrical coupling to cardiomyocyte mechanical activity. In this paper, we propose a mathematical model for studying both electrical and mechanical responses of the human cardiomyocyte to its electrotonic interaction with cardiac fibroblasts. Our simulations have revealed that electrotonic interaction with fibroblasts affects not only the mechanical activity of the cardiomyocyte, comprising either moderate or significant reduction of contractility, but also the mechano-calcium and mechano-electric feedback loops, and all these effects are enhanced as the number of coupled fibroblasts is increased. Obtained results suggest that moderate values of the myocyte-fibroblast gap junction conductance (less than 1 nS) can be attributed to physiological conditions, contrasting to the higher values (2 nS and higher) proper rather for pathological situations (e.g. for infarct and/or border zones), since all mechanical indexes falls down dramatically in the case of such high conductance.

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.

Mechano-electric feedback in one-dimensional model of myocardium.

We utilized our earlier developed 1D mathematical model of the heart muscle strand to study contribution of the bilateral interactions between excitation and contraction on the cellular and tissue levels to the local and global myocardium function. Numerical experiments on the model showed that an initially uniform strand, formed on the inherently identical cells, became functionally heterogeneous due to the asynchronous excitation via the electrical wave spread. Mechanical interactions between the cells and the mechano-electric feedback beat-to-beat affect the functional characteristics of coupled cardiomyocytes further, adjusting their electrical and mechanical heterogeneity to the activation timing. Model simulations showed that functional heterogeneity increases with an enlarged spatial extension of the myocardial strand (in terms of the longer slack length not a higher stretch of the strand), demonstrating a special role of the heart size in its function. Model analysis suggests that cooperative mechanisms of myofilament calcium activation contribute essentially to the generation of cellular functional heterogeneity in contracting cardiac tissue.