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

Differential effects of mechano-electric feedback mechanisms on whole-heart activation, repolarization, and tension

The human heart is subject to highly variable amounts of strain during day-to-day activities and needs to adapt to a wide range of physiological demands. This adaptation is driven by an autoregulatory loop that includes both electrical and the mechanical components. In particular, mechanical forces are known to feed back into the cardiac electrophysiology system, which can result in pro- and anti-arrhythmic effects. Despite the widespread use of computational modelling and simulation for cardiac electrophysiology research, the majority of in silico experiments ignore this mechano-electric feedback entirely due to the high computational cost associated with solving cardiac mechanics. In this study, we therefore use an electromechanically coupled whole-heart model to investigate the differential and combined effects of electromechanical feedback mechanisms with a focus on their physiological relevance during sinus rhythm. In particular, we consider troponin-bound calcium, the effect of deformation on the tissue diffusion tensor, and stretch-activated channels. We found that activation of the myocardium was only significantly affected when including deformation into the diffusion term of the monodomain equation. Repolarization, on the other hand, was influenced by both troponin-bound calcium and stretch-activated channels and resulted in steeper repolarization gradients in the atria. The latter also caused afterdepolarizations in the atria. Due to its central role for tension development, calcium bound to troponin affected stroke volume and pressure. In conclusion, we found that mechano-electric feedback changes activation and repolarization patterns throughout the heart during sinus rhythm and lead to a markedly more heterogeneous electrophysiological substrate. KEY POINTS: The electrophysiological and mechanical function of the heart are tightly interrelated by excitation-contraction coupling (ECC) in the forward direction and mechano-electric feedback (MEF) in the reverse direction. While ECC is considered in many state-of-the-art computational models of cardiac electromechanics, less is known about the effect of different MEF mechanisms. Accounting for calcium bound to troponin increases stroke volume and delays repolarization. Geometry-mediated MEF leads to more heterogeneous activation and repolarization with steeper gradients. Both effects combine in an additive way. Non-selective stretch-activated channels as an additional MEF mechanism lead to heterogeneous diastolic transmembrane voltage, higher developed tension and delayed repolarization or afterdepolarizations in highly stretched parts of the atria. The differential and combined effects of these three MEF mechanisms during sinus rhythm activation in a human four-chamber heart model may have implications for arrhythmogenesis, both in terms of substrate (repolarization gradients) and triggers (ectopy).

Unsupervised deep network for image texture transformation: Improving the quality of cross-correlation analysis and mechanical vortex visualisation during cardiac fibrillation

Visualisation of cardiac fibrillation plays a very considerable role in cardiophysiological study and clinical applications. One of the ways to obtain the image of these phenomena is the registration of mechanical displacement fields reflecting the track from electrical activity. In this work, we read these fields using cross-correlation analysis from the video of open pig's epicardium at the start of fibrillation recorded with electrocardiogram. However, the quality of obtained displacement fields remains low due to the weak pixels heterogeneity of the frames. It disables to see more clearly such interesting phenomena as mechanical vortexes that underline the mechanical dysfunction of fibrillation. The applying of chemical or mechanical markers to solve this problem can affect the course of natural processes and falsify the results. Therefore, we developed a novel scheme of an unsupervised deep neural network that is based on the state-of-art positional coding technology for a multilayer perceptron. This network enables to generate a couple of frames with a more heterogeneous pixel texture, that is more suitable for cross-correlation analysis methods, from two consecutive frames. The novel network scheme was tested on synthetic pairs of images with different texture heterogeneity and frequency of displacement fields and also it was compared with different filters on our cardiac tissue image dataset. The testing showed that the displacement fields obtained with our method are closer to the ground truth than those which were computed only with the cross-correlation analysis in low contrast images case where filtering is impossible. Moreover, our model showed the best results comparing with the one of the popular filter CLAHE on our dataset. As a result, using our approach, it was possible to register more clearly a mechanical vortex on the epicardium at the start of fibrillation continuously for several milliseconds for the first time.

Mathematical modeling of active contraction of the human cardiac myocyte: A review

Background and objective

In this present research paper, a mathematical model has been developed to study myocyte contraction in the human cardiac muscle, using the Land model. Different parts of the human heart with a focus on the composition of the myocyte cells have been explored numerically to enabling us to determine the interaction of various parameters in the heart muscle. The main objective of the work is to direct the study of the Land model, which has been exploited to simulate the contraction of real human myocytes.

Methods

Mathematical models has been developed based on the Hill model and Huxley model. Myocyte contraction for different scenarios, such as in isometric tension and isotonic tension have been studied.

Results

It is found that increase in stretch, the peak active tension increases, in line with well-established length-dependent tension generation. Five parameters are selected: [Ca2+]T50, Tref, TRPN50, β0, and β1, which have been varied in between the range of -50%-100%, to examine the isometric effects of each parameter on the behavior of the tension developed in the intact myocyte cells, with the most sensitive parameter being [Ca2+]T50.

Conclusion

In conclusion, it is found that the Land model provides a good platform for the analysis of the active contraction of the human cardiac myocyte.

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.

Computational modeling of electromechanical coupling in human cardiomyocyte applied to study hypertrophic cardiomyopathy and its drug response

BACKGROUND AND OBJECTIVE

Knowledge of electromechanical coupling in cardiomyocyte and how it is influenced by various pathophysiological factors is fundamental to understanding the pathogenesis of myocardial disease and its response to medication, which is however hard to be thoroughly addressed by clinical/experimental studies due to technical limitations. At this point, computational modeling offers an alternative approach. The main objective of the study was to develop a computational model capable of simulating the process of electromechanical coupling and quantifying the roles of various factors in play in the human left ventricular cardiomyocyte.

METHODS

A new electrophysiological model was firstly built by combining several existing electrophysiological models and incorporating the mechanism of electrophysiological homeostasis, which was subsequently coupled to models representing the cross-bridge dynamics and active force generation during excitation-contraction coupling and the passive mechanical properties of cardiomyocyte to yield an integrative electromechanical model. Model parameters were calibrated or optimized based on a large amount of experimental data. The resulting model was applied to delineate the characteristics of electromechanical coupling and explore underlying determinant factors in hypertrophic cardiomyopathy (HCM) cardiomyocyte, as well as quantify their changes in response to different medications.

RESULTS

Model predictions captured the major electromechanical characteristics of cardiomyocyte under both normal physiological and HCM conditions. In comparison with normal cardiomyocyte, HCM cardiomyocyte suffered from systemic changes in both electrophysiological and mechanical variables. Numerical simulations of drug response revealed that Mavacamten and Metoprolol could both reduce the active contractility and alleviate calcium overload but had marked differential influences on many other electromechanical variables, which theoretically explained why the two drugs have differential therapeutic effects. In addition, our numerical experiments demonstrated the important role of compensatory ion transport in maintaining electrophysiological homeostasis and regulating cytoplasmic volume.

CONCLUSIONS

A sophisticated computational model has the advantage of providing quantitative and integrative insights for understanding the pathogenesis and drug responses of HCM or other myocardial diseases at the level of cardiomyocyte, and hence may contribute as a useful complement to clinical/experimental studies. The model may also be coupled to tissue- or organ-level models to strengthen the physiological implications of macro-scale numerical simulations.

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.

Work-loop contractions reveal that the afterload-dependent time course of cardiac Ca2+ transients is modulated by preload

Preload and afterload dictate the dynamics of the cyclical work-loop contraction that the heart undergoes in vivo. Cellular Ca²⁺ dynamics drive contraction, but the effects of afterload alone on the Ca²⁺ transient are inconclusive. To our knowledge, no study has investigated whether the putative afterload dependence of the Ca²⁺ transient is preload dependent. This study is designed to provide the first insight into the Ca²⁺ handling of cardiac trabeculae undergoing work-loop contractions, with the aim to examine whether the conflicting afterload dependency of the Ca²⁺ transient can be accounted for by considering preload under isometric and physiological work-loop contractions. Thus, we subjected ex vivo rat right-ventricular trabeculae, loaded with the fluorescent dye Fura-2, to work-loop contractions over a wide range of afterloads at two preloads while measuring stress, length changes, and Ca²⁺ transients. Work-loop control was implemented with a real-time Windkessel model to mimic the contraction patterns of the heart in vivo. We extracted a range of metrics from the measured steady-state twitch stress and Ca²⁺ transients, including the amplitudes, time courses, rates of rise, and integrals. Results show that parameters of stress were afterload and preload dependent. In contrast, the parameters associated with Ca²⁺ transients displayed a mixed dependence on afterload and preload. Most notably, its time course was afterload dependent, an effect augmented at the greater preload. This study reveals that the afterload dependence of cardiac Ca²⁺ transients is modulated by preload, which brings the study of Ca²⁺ transients during isometric contractions into question when aiming to understand physiological Ca²⁺ handling.NEW & NOTEWORTHY This study is the first examination of Ca²⁺ handling in trabeculae undergoing work-loop contractions. These data reveal that reducing preload diminishes the influence of afterload on the decay phase of the cardiac Ca²⁺ transient. This is significant as it reconciles inconsistencies in the literature regarding the influence of external loads on cardiac Ca²⁺ handling. Furthermore, these findings highlight discrepancies between Ca²⁺ handling during isometric and work-loop contractions in cardiac trabeculae operating at their optimal length.

Optogenetic actuation in ChR2-transduced fibroblasts alter excitation-contraction coupling and mechano-electric feedback in coupled cardiomyocytes: a computational modeling study

With the help of the conventional electrical method and the growing optogenetic technology, cardiac fibroblasts (Fbs) have been verified to couple electrically with working myocytes and bring electrophysiological remodeling changes in them. The intrinsic properties of cardiac functional autoregulation represented by excitation-contraction coupling (ECC) and mechano-electric feedback (MEF) have also been extensively studied. However, the roles of optogenetic stimulation on the characteristics of ECC and MEF in cardiomyocytes (CMs) coupled with Fbs have been barely investigated. In this study, we proposed a combined model composed of three modules to explore these influences. Simulation results showed that (1) during ECC, an increased light duration (LD) strengthened the inflow of ChR2 current and prolonged action potential duration (APD), and extended durations of twitch and internal sarcomere deformation through the decreased dissociation of calcium with troponin C (CaTnC) complexes and the prolonged duration of Xb attachment-detachment; (2) during MEF, an increased LD was followed by a longer muscle twitch and deformation, and led to APD prolongation through the inward ChR2 current and its inward rectification kinetics, which far outweighed the effects of the delaying dissociation of CaTnC complexes and the prolonged reverse mode of Na⁺-Ca²⁺ exchange on AP shortening; (3) due to the ChR2 current's rectification feature, enhancing the light irradiance (LI) brought slight variations in peak or valley values of electrophysiological and mechanical parameters while did not change durations of AP and twitch and muscle deformation in both ECC and MEF. In conclusion, the inward ChR2 current and its inward rectification feature were found to affect significantly the durations of AP and twitch in both ECC and MEF. The roles of optogenetic actuation on both ECC and MEF should be considered in future cardiac computational optogenetics at the tissue and organ scale.

Computationally efficient model of myocardial electromechanics for multiscale simulations

A model of myocardial electromechanics is suggested. It combines modified and simplified versions of previously published models of cardiac electrophysiology, excitation-contraction coupling, and mechanics. The mechano-calcium and mechano-electrical feedbacks, including the strain-dependence of the propagation velocity of the action potential, are also accounted for. The model reproduces changes in the twitch amplitude and Ca2+-transients upon changes in muscle strain including the slow response. The model also reproduces the Bowditch effect and changes in the twitch amplitude and duration upon changes in the interstimulus interval, including accelerated relaxation at high stimulation frequency. Special efforts were taken to reduce the stiffness of the differential equations of the model. As a result, the equations can be integrated numerically with a relatively high time step making the model suitable for multiscale simulation of the human heart and allowing one to study the impact of myocardial mechanics on arrhythmias.

Toward the Effective Bioengineering of a Pathological Tissue for Cardiovascular Disease Modeling: Old Strategies and New Frontiers for Prevention, Diagnosis, and Therapy

Cardiovascular diseases (CVDs) still represent the primary cause of mortality worldwide. Preclinical modeling by recapitulating human pathophysiology is fundamental to advance the comprehension of these diseases and propose effective strategies for their prevention, diagnosis, and treatment. In silico, in vivo, and in vitro models have been applied to dissect many cardiovascular pathologies. Computational and bioinformatic simulations allow developing algorithmic disease models considering all known variables and severity degrees of disease. In vivo studies based on small or large animals have a long tradition and largely contribute to the current treatment and management of CVDs. In vitro investigation with two-dimensional cell culture demonstrates its suitability to analyze the behavior of single, diseased cellular types. The introduction of induced pluripotent stem cell technology and the application of bioengineering principles raised the bar toward in vitro three-dimensional modeling by enabling the development of pathological tissue equivalents. This review article intends to describe the advantages and disadvantages of past and present modeling approaches applied to provide insights on some of the most relevant congenital and acquired CVDs, such as rhythm disturbances, bicuspid aortic valve, cardiac infections and autoimmunity, cardiovascular fibrosis, atherosclerosis, and calcific aortic valve stenosis.

The use of Ca-transient to evaluate Ca2+ utilization by myofilaments in living cardiac muscle

The kinetics of Ca2+ interaction with myofilaments is an important determinant of the preload-dependent effects on myocardial contractility (the Frank-Starling Mechanism). However, the direct evaluation of this interaction in intact tissue is limited. To overcome this issue, the method of difference curve was proposed, which implements the subtraction of the referent Ca-transient (measured in non-stretched muscle) from the Ca-transients measured at different preloads. This method was tested on the cardiac trabeculae of healthy (CONT) and monocrotaline-treated rats (MCT), subjected to force-length protocol with simultaneous measurement of isometric twitch and Ca-transient. The difference curve had two components, C2 and C3, which are distinct in their directions and, as hypothesized, may reflect mainly the kinetics of Ca2+ utilization by and release from myofilaments, respectively. Both the components were quantitatively evaluated by their amplitude, integral magnitude and time-to-peak. The C3 component in either CONT or MCT was significantly higher in its amplitude/integral magnitude vs the C2 component, at any preload (P < .05). The time-to-peak value was preload-dependent only for the C3 component. There were tight relationships between the above characteristics of C2/C3 components and the characteristics of isometric tension (peak value, time-to-peak and the maximal rates of rise/decline) in CONT and MCT muscles. The C3 component was highly consistent with tension relaxation (Ca2+ release from myofilaments), but the C2 component was partially consistent with tension development (Ca2+ utilization by myofilaments). The novel method of the analysis of Ca-transients can be utilized for indirect evaluation of Ca2+ interaction with myofilaments in healthy and diseased myocardium.

Mitogen-activated protein kinase p38 modulates pacemaker ion channels differentiation in P19-derived pluripotent cells

Signal regulators during early cardiogenetic differentiation for the cellular automaticity are largely unknown. Our investigations were designed to clarify the role of transcription factors and their modulators in P19-derived cardiomyocytes to the expression of cardiac pacemaker ion channels. Transcription factors Csx/Nkx2.5 and GATA4 but not MEF2C were markedly inhibited by p38 MAP kinase inhibition in a distinct manner; expression but not phosphorylation of GATA4 was reduced by inhibition of p38 MAP kinase actions. In the presence of an ERK1/2,5 inhibitor PD98059 or a JNK MAP kinase inhibitor SP600125, P19 cells successfully differentiated into cardiomyocytes displaying spontaneous beatings with expression of three types of pacemaker ion channels. We demonstrate that acquisition of cellular automaticity and the expression of pacemaker ion channels are regulated by the transcription factors, Csx/Nkx2.5 and GATA4, through intracellular signals including p38 MAP kinase in the process of P19-derived pluripotent cells differentiation into cardiomyocytes.

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.

In-silico human electro-mechanical ventricular modelling and simulation for drug-induced pro-arrhythmia and inotropic risk assessment

Human-based computational modelling and simulation are powerful tools to accelerate the mechanistic understanding of cardiac patho-physiology, and to develop and evaluate therapeutic interventions. The aim of this study is to calibrate and evaluate human ventricular electro-mechanical models for investigations on the effect of the electro-mechanical coupling and pharmacological action on human ventricular electrophysiology, calcium dynamics, and active contraction. The most recent models of human ventricular electrophysiology, excitation-contraction coupling, and active contraction were integrated, and the coupled models were calibrated using human experimental data. Simulations were then conducted using the coupled models to quantify the effects of electro-mechanical coupling and drug exposure on electrophysiology and force generation in virtual human ventricular cardiomyocytes and tissue. The resulting calibrated human electro-mechanical models yielded active tension, action potential, and calcium transient metrics that are in agreement with experiments for endocardial, epicardial, and mid-myocardial human samples. Simulation results correctly predicted the inotropic response of different multichannel action reference compounds and demonstrated that the electro-mechanical coupling improves the robustness of repolarisation under drug exposure compared to electrophysiology-only models. They also generated additional evidence to explain the partial mismatch between in-silico and in-vitro experiments on drug-induced electrophysiology changes. The human calibrated and evaluated modelling and simulation framework constructed in this study opens new avenues for future investigations into the complex interplay between the electrical and mechanical cardiac substrates, its modulation by pharmacological action, and its translation to tissue and organ models of cardiac patho-physiology.

In-silico study of age-related ionic remodeling in human ventricular cardiomyocytes

Ageing is one of the dominant risk factors for cardiovascular diseases. A large number of experimental data is collected on the cellular remodeling in the ageing myocardium from mammals, but very little is known about the human cardiomyocytes. We used a combined electro-mechanical model of human ventricular cardiomyocytes and a population of models approach to investigate the variability in the response of cardiomyocytes to age-related changes in model parameters of the ionic currents.

To generate a control model population, we varied 9 ionic parameters and excluded model samples with biomarkers of cellular action potential (AP) and Ca2+ transient (CT) falling outside the physiological ranges. Using the control population of models, we evaluated the response to age-related reduction in the K+ transient outward current, SERCA pump, and an increase in the Na+Ca2+ exchange current and L-type Ca2+ current. Then, we randomly generated 60 age-related sets of the 4 parameters and applied each set to every model in the control population. We showed an increase in the frequency of repolarization anomalies (RA) and critical AP prolongation in the ageing model populations suggesting arrhythmogenic effects of the ionic remodeling. The population based approach allowed us to assess the pro-arrhythmic contribution of the ionic parameters in ageing cardiomyocytes.