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Introduction. One of the risk factors for cardiovascular diseases is the toxic metal pollution of the industrial area and the environment. Lead is the most critical of toxic metals. In industrial conditions, the body’s exposure to harmful substances is often combined with muscular work of varying severity. It has not been studied enough how these combinations influence the development of pathological processes associated with harmful exposure. Materials and methods. The subchronic experiment was carried out on white outbred male rats for six weeks. Intoxication was simulated by repeated intraperitoneal injections of lead acetate three times a week. Running was chosen to model the muscle exercise at a 25 m/min speed for 10 minutes 5 days a week. We performed biochemical and electrocardiographic studies. Blood pressure parameters were recorded. Muscle contractility was studied on isolated multicellular preparations of the right ventricular myocardium in isometric and physiological contraction modes. The ratio of myosin heavy chains was determined by the polyacrylamide gel electrophoresis. The sliding velocity of reconstituted thin filaments on myosin using an in vitro motility assay. Results. Physical exercise under lead intoxication normalized the level of calcium and the angiotensin-converting enzyme activity in the blood serum, the voltage of the isoelectric line and the amplitude of the T wave on the electrocardiogram. The combined action of lead and physical exercise showed an increase in the creatinine kinase-MB level. We found that the effect of exercise under lead intoxication on myocardial contractility was ambiguous. The maximum isotonic shortening velocity in trabeculae was normalized, but the maximum rate of strength development in the isometric mode in the papillary muscles decreased to a greater extent than under lead intoxication. The maximum sliding velocity of reconstituted thin filaments and myosin and the heavy chain ratio was partly normalized. Conclusion. In general, muscle exercise attenuated the lead cardiotoxic effects.

Background: As by-products of copper smelting, lead and cadmium pollute both workplace air at metallurgical plants and adjacent territories. Their increased levels in the human body pose a higher risk of cardiovascular diseases. The objective of our study was evaluate changes in the rat myocardium contractile function following moderate subchronic exposure to soluble lead and/or cadmium salts and its attenuation by means of a complex of bioprotectors. Materials and methods: The subchronic exposure of rats was modelled by intraperitoneal injections of 3-H2O lead acetate and/or 2.5-H2O cadmium chloride in single doses, 6.01 mg of Pb and 0.377 mg of Cd per kg of body weight, respectively, 3 times a week during 6 weeks. The myosin heavy chains isoform ratio was estimated by gel electrophoresis. Biomechanical measurements were performed on isolated multicellular preparations of the myocardium (trabeculae and papillary muscles) from the right ventricle. Results: The subchronic lead exposure slowed down the contraction and relaxation cycle and increased myosin expression towards slowly cycling V3 isomyosins. Cadmium intoxication, on the contrary, shortened the contraction and relaxation cycle and shifted the ratio of isomyosin forms towards rapidly cycling V1. Following the combined exposure to lead and cadmium, some contractile characteristics changed in the direction typical of the effect of lead while others – in that of cadmium. We observed that the metal combination either neutralized or enhanced the isolated damaging effect of each heavy metal. The use of a complex of bioprotectors normalized the myocardial contractility impaired by the exposure to lead and cadmium either partially or completely. Discussion: Despite the changes in myocardial contractility following the subchronic lead and cadmium exposure, the mechanisms of heterometric regulation were maintained. The adverse cardiotoxic effect of the combination of these industrial contaminants may be weakened by administering a complex of bioprotectors.

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.

Exposure to lead is associated with an increased risk of cardiovascular diseases. Outbred white male rats were injected with lead acetate intraperitoneally three times a week and/or were forced to run at a speed of 25 m/min for 10 min 5 days a week. We performed noninvasive recording of arterial pressure, electrocardiogram and breathing parameters, and assessed some biochemical characteristics. Electrophoresis in polyacrylamide gel was used to determine the ratio of myosin heavy chains. An in vitro motility assay was employed to measure the sliding velocity of regulated thin filaments on myosin. Isolated multicellular preparations of the right ventricle myocardium were used to study contractility in isometric and physiological modes of contraction. Exercise under lead intoxication normalized the level of calcium and activity of the angiotensin-converting enzyme in the blood serum, normalized the isoelectric line voltage and T-wave amplitude on the electrocardiogram, increased the level of creatine kinase-MB and reduced the inspiratory rate. Additionally, the maximum sliding velocity and the myosin heavy chain ratio were partly normalized. The effect of exercise under lead intoxication on myocardial contractility was found to be variable. In toto, muscular loading was found to attenuate the effects of lead intoxication, as judged by the indicators of the cardiovascular system.

A moderate subchronic lead intoxication was observed in male rats after repeated intraperitoneal injections of lead acetate. Right ventricular trabeculae and papillary muscles were isolated for in vitro studying of the contraction-relaxation cycle under isotonic and physiological loading. The contractile function of the myocardium was also assessed by measuring the velocity of thin filament movement over myosin. Lead intoxication led in papillary muscles to a decrease in the maximal rate of isotonic shortening for all afterloads and a decrease in the thin filament sliding velocity. Papillary muscles from lead-exposed rats displayed marked changes in most of the main characteristics of afterload contraction-relaxation cycles, but in trabeculae these changes were less pronounced. The reported changes were attenuated to some extent in rats treated with a Ca-containing bioprotector. The amount of work produced by both types of heart muscle preparations was not changed by lead. Only in papillary muscles the load-dependent relaxation index was significantly increased in the lead-treated groups. Thus subchronic lead intoxication affects the peak rate of force development and relaxation properties of cardiac muscle contracting in isotonic/physiological regimes rather than the total amount of mechanical work, which may reflect adaptive changes in the myocardial function under decreased contractility.

Ventricular contraction cycle is characterized by specific scenario of the mechanical loading, which in experiments with the heart muscles/myocytes is mimicked by a work-loop mode of the myocardium twitch. We used recently developed electromechanical model of human ventricular cardiomyocyte to simulate its action potential generation, intracellular calcium dynamics and mechanical activity during work-loop twitches under different afterloads in normal and failing myocardium. The model reproduces well the changes in the force development and shortening observed in experiment with normal and failing human left ventricular wall preparations. The model was also used to predict and explain concomitant changes in action potential generation and calcium transient time course. We also calculated the useful work performed by the virtual muscle in normal and failing myocardium revealing that decrease in sarcoplasmic reticulum calcium content during heart failure may underlie the decrease in myocardial work.

Subchronic intoxication was induced in outbred male rats by repeated intraperitoneal injections with lead oxide (PbO) and/or cadmium oxide (CdO) nanoparticles (NPs) 3 times a week during 6 weeks for the purpose of examining its effects on the contractile characteristics of isolated right ventricle trabeculae and papillary muscles in isometric and afterload contractions. Isolated and combined intoxication with these NPs was observed to reduce the mechanical work produced by both types of myocardial preparation. Using the in vitro motility assay, we showed that the sliding velocity of regulated thin filaments drops under both isolated and combined intoxication with CdO– NP and PbO–NP. These results correlate with a shift in the expression of myosin heavy chain (MHC) isoforms towards slowly cycling β–MHC. The type of CdO–NP + PbO–NP combined cardiotoxicity depends on the effect of the toxic impact, the extent of this effect, the ratio of toxicant doses, and the degree of stretching of cardiomyocytes and muscle type studied. Some indices of combined Pb–NP and CdO–NP cardiotoxicity and general toxicity (genotoxicity included) became fully or partly normalized if intoxication developed against background administration of a bioprotective complex. © 2021 by the authors. Licensee MDPI, Basel, Switzerland. The work was carried out partly within the framework of the IIF UrB RAS themes No AAA?A18?118020590031?8 and AAAA?A18?118020590135?3. This work was performed using the equipment of the Shared Research Center of Scientific Equipment SRC IIP UrB RAS.

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-A18-118020590031-8 Russian Foundation for Basic Research, RFBR: 18-01-00059 Russian Science Foundation, RSF: 18-74-10059 Funding. 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).

Outbred male rats were repeatedly injected IP with sub-lethal doses of lead acetate 3 times a week during 5 weeks. They developed an explicit, even if moderate, lead intoxication characterized by typical hematological and some other features. The next day after the last injection the heart of each animal was excised, and the trabecules and papillary muscles from the right ventricle were used for modeling in vitro isometric (with varying starting length of the preparation) regimes of the contraction-relaxation cycle with different preloads. Several well-established parameters of this model were found changed compared with the preparations taken from the hearts of healthy control rats. Background in vivo calcium treatment attenuated both systemic and cardiotoxic effects of lead to an extent. We show for the first time that subchronic intoxication with lead caused myocardial preparations in a wide range of lengths to respond by a decrease in the time and speed parameters of the isometric contraction while maintaining its amplitude and by a decrease in the passive stiffness of trabecules. The responses of the various heart structures are outlined, and the isomyosin ratio is shown to have shifted towards the slow isoform. Mechanistic and toxicological inferences from the results are discussed.

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: 18‑01‑00059 The 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.

Cardiac fibroblasts are widely represented in mammalian cardiac tissue. These cells are connected with cardiomyocytes by gap junctions and they have own changeable membrane potential, so that fibroblasts can influence cardiomyocyte electrical activity. This effect may be analyzed in mathematical models. Existing mathematical models of fibroblast-cardiomyocyte interaction allow anyone to study only electrical responses of the cardiomyocytes and fibroblasts to their electrical interaction. In our work we have considered the fibroblast influence on the cardiomyocytes mechanics. In numerical experiments we reveal significant changes in the cardiomyocyte action potential duration and force depending on the number of fibroblast connected with the cardiomyocyte.

Mechano-calcium feedbacks that provide fine tuning of electrical and calcium activation of the heart muscle to mechanical conditions of contractions are an important element of electromechanical coupling as a key mechanism of the autoregulation of the contractile activity of the myocardium. A large quantity of experimental and theoretical evidence supports the cooperative dependence of the calcium-troponin complex kinetics on the cross-bridge concentration as a principal mechanism that underlies the mechano-calcium feedback in the intact myocardium. At the same time, experiments performed using skinned myocardial preparations have demonstrated that mechanical conditions significantly affected only the calcium sensitivity of the Ca2+–force relationship rather than its Hill coefficient of cooperativity. These data make some investigators doubt the contribution of cooperativity to the mechano-calcium feedbacks. To overcome these arising discrepancies, we propose an improved conception of cooperativity that reveals the extent of intensity differently in the steady state and in transitional processes. The proposed conception enables us to reproduce and explain both the mechanodependence of calcium activation in the intact myocardium and the results with skinned muscle within the framework of a mathematical model.

A modification of the mathematical model of the shape and fiber direction field of the left cardiac ventricle is presented. The model was developed based on the idea of nested spiral surfaces. The ventricle is composed of surfaces that model myocardial layers. Each layer is filled with curves corresponding to myocardial fibers. The tangents to these curves form the myofiber direction field. A modified spherical coordinate system is linked with the model left ventricle, where the ventricular boundaries are coordinate surfaces. The model is based on echocardiographic, computed-tomography, or magnetic-resonance-imaging data. For this purpose, four-chamber and two-chamber echocardiography views or sections along the long axis of the left ventricle from these tomographic data in several positions are approximated with a model profile. To construct a 3D model, we then interpolate model parameters by periodic cubic splines and the vector field of the tangents to the model fibers is calculated. For verification of the model, we used diffusion-tensor magneticresonance-imaging data of the human heart.

It is known that preferential paths for the propagation of an electrical excitation wave in the human ventricular myocardium are associated with muscle fibers in tissue. The speed of the excitation wave along a fiber is several times higher than that across the direction of the fiber. To estimate the effect of the architecture and anisotropy of the myocardium of the left ventricle on the process of its electrical activation, we have studied the relation between the speed of the electrical excitation wave in a one-dimensional isolated myocardial fiber consisting of sequentially coupled cardiomyocytes and in an identical fiber located in the wall of a threedimensional anatomical model of the left ventricle. It has been shown that the speed of a wavefront along the fiber in the three-dimensional myocardial tissue is much higher than that in the one-dimensional fiber. The acceleration of the signal is due to the rotation of directions of fibers in the wall and to the position of the excitation wavefront with respect to the direction of this fiber. The observed phenomenon is caused by the approach of the excitable tissue with rotational anisotropy in its properties to a pseudoisotropic tissue.

This investigation continues our study of the effects of Pb-Cd poisoning on the heart, extending the enquiry from isometric to auxotonic contractions, thereby examining the effect on the ability of myocardial tissues to perform mechanical work. Different shifts were revealed in myocardial force-velocity relations following subchronic exposure of rats to lead acetate and cadmium chloride acting separately, in combination, or in combination with a bioprotective complex (BPC). The experiments were conducted on isolated preparations of trabecules and papillary muscles of the right ventricle in physiological loading conditions and on isolated heart muscle contractile proteins examined by the in vitro motility assay. The results of the latter correlate with the shifts in the ratio of cardiac myosin isoforms. The amount of work performed by the myocardium was calculated on the basis of the tension-shortening loop area and was found to be similar in the preparations from all experimental groups. This fact presumably reflects adaptive capacity of the myocardial function even when contractility is damaged due to the metallic intoxication of a moderate severity. Some characteristics of rat myocardium altered by the impact of lead-cadmium intoxication became fully or partly normalized if intoxication developed against background administration of a bioprotective complex (BPC). Together with previously reported results obtained in the isometric mode of contractility, all these results strengthen the scientific foundations of risk assessment and risk management projects in the occupational and environmental conditions characterized by human exposure to lead and/or cadmium.

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: 18-01-00059 The 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.

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).

Our new mathematical model of the electromechanical coupling in human ventricular cardiomyocytes combines human-specific O'Hara-Rudy electrophysiological model and a sub-model of myocardium mechanics and its calcium activation adopted from our developed earlier Ekaterinburg-Oxford model.

We developed a three-dimensional computational model for describing electro-mechanical behavior of wedge-shaped preparation extracted from the left ventricular wall including excitation wave propagation, high-resolution geometry and fiber orientation. The cardiac tissue is simulated by an incompressible hyperplastic material. We used non-linear partial differential equations describing the deformation of the cardiac tissue, and a detailed 'Ekaterinburg-Oxford' (EO) cellular model of the electrical and mechanical activity of the cardiomyocytes in the tissue. Electro-mechanical coupling in the model accounts for mechano-electric feedbacks both in the cells and in the tissue. Numerical experiments with the model of the wedge preparation formed of initially identical cardiomyocytes revealed that electrical and mechanical interaction between the cells, as well as intracellular mechanoelectric feedbacks caused pronounced nonuniformity of their behavior. © 2018 Creative Commons Attribution. Russian Foundation for Basic Research, RFBR: 18-31-00416 Russian Academy of Sciences, RAS: АААА-А18- 118020590030-1 This work was carried out within the framework of the IIF UrB RAS themes (Nos. AAAA-A18-118020590031-8) and was supported by RFBR (18-31-00416), the Program of the Presidium RAS #27 (project АААА-А18- 118020590030-1) and Act 211 Government of the Russian Federation, contract № 02.A03.21.0006.

Mechanical properties of cardiomyocytes from different transmural regions are heterogeneous in the left ventricular wall. The cardiomyocyte mechanical environment affects this heterogeneity because of mechano-electric feedback mechanisms. In the present study, we investigated the effects of the mechanical load (preload and afterload) on transmural differences in contraction of subendocardial (ENDO) and subepicardial (EPI) single cells isolated from the murine left ventricle. Various preloads imposed via axial stretch and afterloads (unloaded and heavy loaded conditions) were applied to the cells using carbon fiber techniques for single myocytes. To simulate experimentally obtained results and to predict mechanisms underlying the cellular response to change in load, our mathematical models of the ENDO and EPI cells were used. Our major findings are the following. Our results show that ENDO and EPI cardiomyocytes have different mechanical responses to changes in preload to the cells. Under auxotonic contractions at low preload (unstretched cells), time to peak contraction (Tmax) and the time constant of [Ca2+]i transient decay were significantly longer in ENDO cells than in EPI cells. An increase in preload (stretched cells) prolonged Tmax in both cell types; however, the prolongation was greater in EPI cells, resulting in a decrease in the transmural gradient in Tmax at high preload. Comparing unloaded and heavy loaded (isometric) contractions of the cells we found that transmural gradient in the time course of contraction is independent of the loading conditions. Our mathematical cell models were able to reproduce the experimental results on the distinct cellular responses to changes in the mechanical load when we accounted for an ENDO/EPI difference in the parameters of cooperativity of calcium activation of myofilaments.

Mechanical properties of cardiomyocytes from different transmural regions are heterogeneous in the left ventricular wall. The cardiomyocyte mechanical environment affects this heterogeneity because of mechano-electric feedback mechanisms. In the present study, we investigated the effects of the mechanical load (preload and afterload) on transmural differences in contraction of subendocardial (ENDO) and subepicardial (EPI) single cells isolated from the murine left ventricle. Various preloads imposed via axial stretch and afterloads (unloaded and heavy loaded conditions) were applied to the cells using carbon fiber techniques for single myocytes. To simulate experimentally obtained results and to predict mechanisms underlying the cellular response to change in load, our mathematical models of the ENDO and EPI cells were used. Our major findings are the following. Our results show that ENDO and EPI cardiomyocytes have different mechanical responses to changes in preload to the cells. Under auxotonic contractions at low preload (unstretched cells), time to peak contraction (Tmax) and the time constant of [Ca2+]i transient decay were significantly longer in ENDO cells than in EPI cells. An increase in preload (stretched cells) prolonged Tmax in both cell types; however, the prolongation was greater in EPI cells, resulting in a decrease in the transmural gradient in Tmax at high preload. Comparing unloaded and heavy loaded (isometric) contractions of the cells we found that transmural gradient in the time course of contraction is independent of the loading conditions. Our mathematical cell models were able to reproduce the experimental results on the distinct cellular responses to changes in the mechanical load when we accounted for an ENDO/EPI difference in the parameters of cooperativity of calcium activation of myofilaments.

Based on the experimental evidence, we developed a one-dimensional (1D) model of heterogeneous myocardial tissue consisting of in-series connected cardiomyocytes from distant transmural regions using mathematical models of subendocardial and subepicardial cells. The regional deformation patterns produced by our 1D model are consistent with the transmural regional strain patterns obtained experimentally in the normal heart in vivo. The modelling results suggest that the mechanical load may essentially affect the transmural gradients in the electrical and mechanical properties of interacting myocytes within a tissue, thereby regulating global myocardial output.

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: 16K12878

The heart is structurally and functionally a highly non-homogenous organ, yet its main function as a pump can only be achieved by the co-ordinated contraction of millions of ventricular cells. This apparent contradiction gives rise to the hypothesis that 'well-organised' inhomogeneity may be a pre-requisite for normal cardiac function. Here, we present a set of novel experimental and theoretical tools for the study of this concept. Heterogeneity, in its most condensed form, can be simulated using two individually controlled, mechanically interacting elements (duplex). We have developed and characterised three different types of duplexes: (i) biological duplex, consisting of two individually perfused biological samples (like thin papillary muscles or a trabeculae), (ii) virtual duplex, made-up of two interacting mathematical models of cardiac muscle, and (iii) hybrid duplex, containing a biological sample that interacts in real-time with a virtual muscle. In all three duplex types, in-series or in-parallel mechanical interaction of elements can be studied during externally isotonic, externally isometric, and auxotonic modes of contraction and relaxation. Duplex models, therefore, mimic (patho-)physiological mechano-electric interactions in heterogeneous myocardium at the multicellular level, and in an environment that allows one to control mechanical, electrical and pharmacological parameters. Results obtained using the duplex method show that: (i) contractile elements in heterogeneous myocardium are not 'independent' generators of tension/shortening, as their ino- and lusitropic characteristics change dynamically during mechanical interaction-potentially matching microscopic contractility to macroscopic demand, (ii) mechanical heterogeneity contributes differently to action potential duration (APD) changes, depending on whether mechanical coupling of elements is in-parallel or in-series, which may play a role in mechanical tuning of distant tissue regions, (iii) electro-mechanical activity of mechanically interacting contractile elements is affected by their activation sequence, which may optimise myocardial performance by smoothing intrinsic differences in APD. In conclusion, we present a novel set of tools for the experimental and theoretical investigation of cardiac mechano-electric interactions in healthy and/or diseased heterogeneous myocardium, which allows for the testing of previously inaccessible concepts.

Effects of cardiac mechanical heterogeneity on the electrical function of the heart are difficult to assess experimentally, yet they pose a serious (patho-)physiological challenge. Here, we present an in silico study of the effects of mechanical heterogeneity on action potential duration (APD) in mechanically interacting muscle regions and consequent effects on the dispersion of repolarization, a well-established determinant of cardiac arrhythmogenesis.Using a novel mathematical description of ventricular electromechanical activity (virtual muscle), we first assessed how differences in intrinsic contractile properties affect the electrical behavior of cardiac muscle representations. In spite of identical electrophysiological model descriptions in virtual muscle samples, faster muscle models show shorter APD than their slower counterparts. This is a consequence of Ca2+-mediated feedback from mechanical to electrical activity in the individual muscle models.This mechano-electric feedback (MEF) is, of course, significantly more complex in native cardiac tissue, as the heterogeneous muscle elements interact both mechanically and electrically. Cardiac mechanical heterogeneity, in its most reduced form, can be represented by a duplex consisting of two mechanically interacting muscle segments. Our in silico model of heterogeneous myocardium therefore consists of two individual virtual muscles that are mechanically interconnected in-series to form a virtual heterogeneous duplex. During isometric contraction of the duplex (i.e. at constant external length), internal mechanical interactions affect Ca2+handling and APD of muscle elements, resulting in an increased dispersion of repolarization beyond the intrinsic APD differences.Duplex electromechanical activity is strongly affected by the activation sequence of its elements. Late activation of the faster (subepicardial type) duplex element, postponed by time-lags that correspond to normal transmural activation delays, optimizes duplex contractility and smoothes out intrinsic APD differences, thereby reducing dispersion in repolarization. This smoothing effect is not observed upon delayed activation of the slower (subendocardial type) duplex element. In both settings, changes in repolarization timing follow a nonlinear dependence of APD on activation delay. Furthermore, asynchronous activation of identical elements in a homogeneous duplex causes an impairment of contractile function and increases dispersion of repolarization. This suggests that the normal electrical activation sequence in the heart requires matching mechanical and electrical heterogeneity for optimal cardiac performance.On the subcellular level, our results suggest that mechanical modulation of Ca2+handling is a key mechanism of MEF in heterogeneous myocardium, which contributes to the matching of local mechanical and/or electrical activity to global hemodynamic demand.

Classically, the slow force response (SFR) of myocardium refers to slowly developing changes in cardiac muscle contractility induced by external mechanical stimuli, e.g. sustained stretch. We present evidence for an intra-myocardial SFR (SFRIM), caused by the internal mechanical interactions of muscle segments in heterogeneous myocardium. Here we study isometric contractions of a pair of end-to-end connected functionally heterogeneous cardiac muscles (an in-series muscle duplex). Duplex elements can be either biological muscles (BM), virtual muscles (VM), or a hybrid combination of BM and VM. The VM implements an Ekaterinburg-Oxford mathematical model accounting for the ionic and myofilament mechanisms of excitation-contraction coupling in cardiomyocytes. SFRIM is expressed in gradual changes in the overall duplex force and in the individual contractility of each muscle, induced by cyclic auxotonic deformations of coupled muscles. The muscle that undergoes predominant cyclic shortening shows force enhancement upon return to its isometric state in isolation, whereas average cyclic lengthening may decrease the individual muscle contractility. The mechanical responses are accompanied with slow and opposite changes in the shape and duration of both the action potential and Ca2+ transient in the cardiomyocytes of interacting muscles. Using the mathematical model we found that the contractility changes in interacting muscles follow the alterations in the sarcoplasmic reticulum loading in cardiomyocytes which result from the length-dependent Ca2+ activation of myofilaments and intracellular mechano-electrical feedback. The SFRIM phenomena unravel an important mechanism of cardiac functional auto-regulation applicable to the heart in norm and pathology, especially to hearts with severe electrical and/or mechanical dyssynchrony. © 2012 Elsevier Ltd.

A mathematical model was used for comparative analysis of the contribution to the myocardial mechanical activity of two potentially possible variants of the cooperative influence of myosin cross-bridges on calcium activation of sarcomere actin filaments. One of these variants implies that the cooperative action of the cross-bridge on the affinity of troponin C for calcium is localized within the functional group A7TmTn (seven adjacent globular actin monomers, tropomyosin, and one troponin complex TnC + TnI + TnT) where this bridge is attached. The second variant is based on the assumption that cross-bridges may influence the troponin C affinity for calcium also in neighboring A7TmTn groups (and the closer the group is positioned relative to the bridge, the stronger is the influence on the CaTnC complex affinity in this group). The contribution of each of these two variants to the active mechanical behavior of the cardiac muscle in the contraction-relaxation cycle was assessed. It turned out that adequate simulation of the muscle mechanical activity is provided only by the second variant. Thus, the results of modeling argue in favor of the existence of just this variant of cooperativity.

The dependences of thin filament sliding velocity on the calcium concentration in solution (pCa 5 to 8) for rabbit cardiac myosin isoforms V1 and V3 were determined in a set of experiments using an in vitro motility assay with a reconstructed thin filament. The constructed pCa-versus-velocity curves had a sigmoid shape. It was demonstrated that the sliding velocity of regulated thin filament at the saturating calcium concentration (pCa 5) did not differ from the actin sliding velocity for each isoform. The determined values of Hill’s cooperativity coefficient for isomyosins V1 and V3 were 1.04 and 0.75, respectively. It was demonstrated that isomyosin V3 was more sensitive to calcium as compared with isomyosin V1. Using the same assay, the dependence of thin filament sliding velocity on the concentration of the actin-binding protein α-actinin (analog of a force-velocity dependence) was determined at the saturating calcium concentration for each myosin isoform (V1 and V3). The results suggest that the calcium regulation of V1 and V3 contractile activity follows different mechanisms.

A mathematical model of the cardiomyocyte electromechanical function is used to study contribution of mechanical factors to rhythm disturbances in the case of the cardiomyocyte calcium overload. Particular attention is paid to the overload caused by diminished activity of the sodium-potassium pump. It is shown in the framework of the model, where mechano-calcium feedback is accounted for that myocardium mechanics may significantly enhance arrhythmogenicity of the calcium overload. Specifically, a role of cross-bridge attachment/detachment processes, a role of mechanical conditions of myocardium contractions (length, load), and a role of myocardium viscosity in the case of simulated calcium overload have been revealed. Underlying mechanisms are analyzed. Several approaches are designed in the model and compared to each other for recovery of the valid myocardium electrical and mechanical performance in the case of the partially suppressed sodium-potassium pump.

Possible contribution of the mechanics to the arrhythmogenesis in Ca2+ overloaded cardiomyocytes has been under appreciated. Earlier developed mathematical model of cardiomyocyte electromechanical function predicted a significant role of intra- and extracellular mechanical factors in triggering rhythm abnormalities.

There is a complicated interplay between different factors contributing to the calcium regulation of the heart muscle contraction. Mathematical modeling is an efficient approach to analyze this compound system and recognize the key links. In this work the modeling is applied to the analysis of mechano-calcium feedback mechanisms and their role in the cardiomyocyte calcium activation.

Cardiac arrhythmias and long QT syndrome may be associated with increased sodium currents. Possible effects of enhanced function of sodium channels on the transmural gradient in the electrical and mechanical properties of myocardium have not been sufficiently studied. We used our cellular mathematical models to investigate effects of an increased late sodium current on the electromechanical coupling in single subendocardial and subepicardial cells and in a strand of transmurally heterogeneous myocardium. Modeling results predicted that subepicardial cells are more vulnerable to rhythm disturbances than single subendocardial cells under these pathological conditions. Within the transmurally heterogeneous strand, mechanical and electrical interactions between such abnormal cells affected the patterns of electromechanical disturbances as compared to the single cells. This allowed myocardium to contract even in those conditions where single EPI cells lost contractility.

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.

Mathematical models of the electromechanical function of cardiomyocytes and muscle duplexes, the simplest mechanically inhomogeneous myocardial systems, are developed. Using these models, the contribution of mechanoelectrical feedbacks to the contractive activity of the myocardium in normal and abnormal conditions is studied. In particular, the influence of the mechanical conditions of contraction on the shape and duration of the action potentials is reproduced and interpreted. In this context, different types of mechanical heterogeneity of the myocardium are analyzed. It is established that this heterogeneity can play a positive or negative role depending on the distribution of heterogeneous properties and on the order the elements of the system are activated. Using the same models, the contribution of mechanical factors to arrhythmogenesis under calcium overload of cardiomyocytes due to the weakening of the sodium-potassium pump is studied. Methods for correction of the contractive activity of cardiomyocytes in the case of such abnormalities are outlined.