A model of cardiac contraction based on novel measurements of tension development in human cardiomyocytes

Elevating performance and interpretability of in silico classifiers for drug proarrhythmia risk evaluations using multi-biomarker approach with ranking algorithm

BACKGROUND AND OBJECTIVE

Using electrophysiological simulations and machine learning to predict drug proarrhythmia risk has gained popularity due to its effectiveness. The leading in silico drug assessment system mainly uses a single biomarker (qNet) to predict proarrhythmia risk, offering good performance and straightforward interpretation. Other advanced classifiers incorporating additional physiological biomarkers provide better predictive capabilities but are less intuitive. Thus, a method that accommodates multiple biomarkers while maintaining interpretability is needed.

METHODS

We enhance the current best ordinal logistic regression (OLR) model by adding more physiological biomarkers to overcome its limitations. We also introduce a general torsade metric score (TMS) for multi-biomarker approaches to facilitate easier interpretation. Additionally, a novel ranking algorithm based on a simple multi-criteria decision analysis method is employed to evaluate various classifiers against standard proarrhythmia risk criteria efficiently.

RESULTS

Our proposed method demonstrates that using multiple well-known biomarkers yields better performance than using qNet alone. Some accepted multi-biomarker OLR models do not incorporate qNet yet outperform those that do. Moreover, some ill-performing biomarkers when utilized individually can show improved performance in combination with other biomarkers.

CONCLUSION

The proposed approach offers an effective way of utilizing multiple biomarkers, including well-known ones, providing practical alternatives for proarrhythmia risk assessment. The interpretability of the accepted models is straightforward, thanks to the TMS thresholds for multi-biomarker OLR models that allow direct evaluation of the classification prediction of individual drugs.

T-World: A highly general computational model of a human ventricular myocyte

Cardiovascular disease is the leading cause of death, demanding new tools to improve mechanistic understanding and overcome limitations of stem cell and animal-based research. We introduce T-World, a highly general virtual model of human ventricular cardiomyocyte suitable for multiscale studies. T-World shows comprehensive agreement with human physiology, from electrical activation to contraction, and is the first to replicate all key cellular mechanisms driving life-threatening arrhythmias. Extensively validated on unseen data, it demonstrates strong predictivity across applications and scales. Using T-World we revealed a likely sex-specific arrhythmia risk in females related to restitution properties, identified arrhythmia drivers in type 2 diabetes, and describe unexpected pro-arrhythmic role of NaV1.8 in heart failure. T-World demonstrates strong performance in predicting drug-induced arrhythmia risk and opens new opportunities for predicting and explaining drug efficacy, demonstrated by unpicking effects of mexiletine in Long QT syndrome 2. T-World is available as open-source code and an online app.

In silico predictions of drug-induced changes in human cardiac contractility align with experimental recordings

Drug-induced changes in cardiac contractility (inotropy) can lead to cardiotoxicity, a major cause of discontinuation in drug development. Preclinical approaches to assess cardiac inotropy are imperfect, with in vitro assays limited to stem cell-derived or adult human primary cardiomyocytes. Human mechanistic in silico modelling and simulations are already successfully applied for proarrhythmia prediction, contributing to cardiac safety assessment strategies in early drug development. In this study, we investigated their ability to predict drug-induced effects on cardiac inotropy. We considered a validation set of 28 neutral/negative inotropic and 13 positive inotropic reference compounds and simulated their effects on cell contractility via ion channel inhibition and perturbation of nine biomechanical modelling parameters, respectively. For each compound, a wide range of drug concentrations was simulated in an experimentally calibrated control population of 323 human ventricular in silico cells. Simulated biomarkers indicating drug-induced inotropic effects were compared with in vitro preclinical data from the literature. Computer simulations predicted drug-induced inotropic changes observed in vitro for 25 neutral/negative inotropes and 10 positive inotropes. Predictions of negative inotropic changes were quantitatively in agreement for 86% of tested drugs. Active tension peak was identified as the biomarker with highest predictive potential. This study describes the validation and application of an in silico cardiac electromechanical model for drug safety evaluation, combining ion channel inhibition data and information on potential inotropic mechanisms to predict inotropic changes. Furthermore, a route for its integration as part of a preclinical drug safety assessment strategy is outlined.

Modeling the effects of thin filament near-neighbor cooperative interactions in mammalian myocardium

The mechanisms underlying cooperative activation and inactivation of myocardial force extend from local, near-neighbor interactions involving troponin-tropomyosin regulatory units (RU) and crossbridges (XB) to more global interactions across the sarcomere. To better understand these mechanisms in the hearts of small and large mammals, we undertook a simplified mathematical approach to assess the contribution of three types of near-neighbor cooperative interactions, i.e., RU-induced, RU-activation (RU-RU), crossbridge-induced, crossbridge-binding (XB-XB), and XB-induced, RU-activation (XB-RU). We measured the Ca2+ and activation dependence of the rate constant of force redevelopment in murine- and porcine-permeabilized ventricular myocardium. Mathematical modeling of these three near-neighbor interactions yielded nonlinear expressions for the RU-RU and XB-RU rate coefficients (kon and koff) and XB-XB rate coefficients describing the attachment of force-generating crossbridges (f and f'). The derivation of single cooperative coefficient parameters (u = RU-RU, w = XB-RU, and v = XB-XB) permitted an initial assessment of the strength of each near-neighbor interaction. The parameter sets describing the effects of discrete XB-XB or XB-RU interactions failed to adequately fit the in vitro contractility data in either murine or porcine myocardium. However, the Ca2+ dependence of ktr in murine and porcine ventricular myocardium was well fit by parameter sets incorporating the RU-RU cooperative interaction. Our results indicate that a significantly stronger RU-RU interaction is present in porcine ventricular myocardium compared with murine ventricular myocardium and that the relative strength of the near-neighbor RU-RU interaction contributes to species-specific myocardial contractile dynamics in small and large mammals.

A Graph-Based Machine-Learning Approach Combined with Optical Measurements to Understand Beating Dynamics of Cardiomyocytes

The development of computational models for the prediction of cardiac cellular dynamics remains a challenge due to the lack of first-principled mathematical models. We develop a novel machine-learning approach hybridizing physics simulation and graph networks to deliver robust predictions of cardiomyocyte dynamics. Embedded with inductive physical priors, the proposed constraint-based interaction neural projection (CINP) algorithm can uncover hidden physical constraints from sparse image data on a small set of beating cardiac cells and provide robust predictions for heterogenous large-scale cell sets. We also implement an in vitro culture and imaging platform for cellular motion and calcium transient analysis to validate the model. We showcase our model's efficacy by predicting complex organoid cellular behaviors in both in silico and in vitro settings.

Stress relaxation rates of myocardium from failing and non-failing hearts

The heart is a dynamic pump whose function is influenced by its mechanical properties. The viscoelastic properties of the heart, i.e., its ability to exhibit both elastic and viscous characteristics upon deformation, influence cardiac function. Viscoelastic properties change during heart failure (HF), but direct measurements of failing and non-failing myocardial tissue stress relaxation under constant displacement are lacking. Further, how consequences of tissue remodeling, such as fibrosis and fat accumulation, alter the stress relaxation remains unknown. To address this gap, we conducted stress relaxation tests on porcine myocardial tissue to establish baseline properties of cardiac tissue. We found porcine myocardial tissue to be fast relaxing, characterized by stress relaxation tests on both a rheometer and microindenter. We then measured human left ventricle (LV) epicardium and endocardium tissue from non-failing, ischemic HF and non-ischemic HF patients by microindentation. Analyzing by patient groups, we found that ischemic HF samples had slower stress relaxation than non-failing endocardium. Categorizing the data by stress relaxation times, we found that slower stress relaxing tissues were correlated with increased collagen deposition and increased α-smooth muscle actin (α-SMA) stress fibers, a marker of fibrosis and cardiac fibroblast activation, respectively. In the epicardium, analyzing by patient groups, we found that ischemic HF had faster stress relaxation than non-ischemic HF and non-failing. When categorizing by stress relaxation times, we found that faster stress relaxation correlated with Oil Red O staining, a marker for adipose tissue. These data show that changes in stress relaxation vary across the different layers of the heart during ischemic versus non-ischemic HF. These findings reveal how the viscoelasticity of the heart changes, which will lead to better modeling of cardiac mechanics for in vitro and in silico HF models.

Clinical phenotypes in acute and chronic infarction explained through human ventricular electromechanical modelling and simulations

Sudden death after myocardial infarction (MI) is associated with electrophysiological heterogeneities and ionic current remodelling. Low ejection fraction (EF) is used in risk stratification, but its mechanistic links with pro-arrhythmic heterogeneities are unknown. We aim to provide mechanistic explanations of clinical phenotypes in acute and chronic MI, from ionic current remodelling to ECG and EF, using human electromechanical modelling and simulation to augment experimental and clinical investigations. A human ventricular electromechanical modelling and simulation framework is constructed and validated with rich experimental and clinical datasets, incorporating varying degrees of ionic current remodelling as reported in literature. In acute MI, T-wave inversion and Brugada phenocopy were explained by conduction abnormality and local action potential prolongation in the border zone. In chronic MI, upright tall T-waves highlight large repolarisation dispersion between the border and remote zones, which promoted ectopic propagation at fast pacing. Post-MI EF at resting heart rate was not sensitive to the extent of repolarisation heterogeneity and the risk of repolarisation abnormalities at fast pacing. T-wave and QT abnormalities are better indicators of repolarisation heterogeneities than EF in post-MI.

Multiphysics simulations reveal haemodynamic impacts of patient-derived fibrosis-related changes in left atrial tissue mechanics

Stroke is a leading cause of death and disability worldwide. Atrial myopathy, including fibrosis, is associated with an increased risk of ischaemic stroke, but the mechanisms underlying this association are poorly understood. Fibrosis modifies myocardial structure, impairing electrical propagation and tissue biomechanics, and creating stagnant flow regions where clots could form. Fibrosis can be mapped non-invasively using late gadolinium enhancement magnetic resonance imaging (LGE-MRI). However, fibrosis maps are not currently incorporated into stroke risk calculations or computational electro-mechano-fluidic models. We present multiphysics simulations of left atrial (LA) myocardial motion and haemodynamics using patient-specific anatomies and fibrotic maps from LGE-MRI. We modify tissue stiffness and active tension generation in fibrotic regions and investigate how these changes affect LA flow for different fibrotic burdens. We find that fibrotic regions and, to a lesser extent, non-fibrotic regions experience reduced myocardial strain, resulting in decreased LA emptying fraction consistent with clinical observations. Both fibrotic tissue stiffening and hypocontractility independently reduce LA function, but, together, these two alterations cause more pronounced effects than either one alone. Fibrosis significantly alters flow patterns throughout the atrial chamber, and particularly, the filling and emptying jets of the left atrial appendage (LAA). The effects of fibrosis in LA flow are largely captured by the concomitant changes in LA emptying fraction except inside the LAA, where a multifactorial behaviour is observed. This work illustrates how high-fidelity, multiphysics models can be used to study thrombogenesis mechanisms in patient-specific anatomies, shedding light onto the links between atrial fibrosis and ischaemic stroke. KEY POINTS: Left atrial (LA) fibrosis is associated with arrhythmogenesis and increased risk of ischaemic stroke; its extent and pattern can be quantified on a patient-specific basis using late gadolinium enhancement magnetic resonance imaging. Current stroke risk prediction tools have limited personalization, and their accuracy could be improved by incorporating patient-specific information such as fibrotic maps and haemodynamic patterns. We present the first electro-mechano-fluidic multiphysics computational simulations of LA flow, including fibrosis and anatomies from medical imaging. Mechanical changes in fibrotic tissue impair global LA motion, decreasing LA and left atrial appendage (LAA) emptying fractions, especially in subjects with higher fibrosis burdens. Fibrotic-mediated LA motion impairment alters LA and LAA flow near the endocardium and the whole cavity, ultimately leading to more stagnant blood regions in the LAA.

Multi-physics simulations reveal hemodynamic impacts of patient-derived fibrosis-related changes in left atrial tissue mechanics

Stroke is a leading cause of death and disability worldwide. Atrial myopathy, including fibrosis, is associated with an increased risk of ischemic stroke, but the mechanisms underlying this association are poorly understood. Fibrosis modifies myocardial structure, impairing electrical propagation and tissue biomechanics, and creating stagnant flow regions where clots could form. Fibrosis can be mapped non-invasively using late gadolinium enhancement magnetic resonance imaging (LGE-MRI). However, fibrosis maps are not currently incorporated into stroke risk calculations or computational electro-mechano-fluidic models. We present multi-physics simulations of left atrial (LA) myocardial motion and hemodynamics using patient-specific anatomies and fibrotic maps from LGE-MRI. We modify tissue stiffness and active tension generation in fibrotic regions and investigate how these changes affect LA flow for different fibrotic burdens. We find that fibrotic regions and, to a lesser extent, non-fibrotic regions experience reduced myocardial strain, resulting in decreased LA emptying fraction consistent with clinical observations. Both fibrotic tissue stiffening and hypocontractility independently reduce LA function, but together, these two alterations cause more pronounced effects than either one alone. Fibrosis significantly alters flow patterns throughout the atrial chamber, and particularly, the filling and emptying jets of the left atrial appendage (LAA). The effects of fibrosis in LA flow are largely captured by the concomitant changes in LA emptying fraction except inside the LAA, where a multi-factorial behavior is observed. This work illustrates how high-fidelity, multi-physics models can be used to study thrombogenesis mechanisms in patient-specific anatomies, shedding light onto the links between atrial fibrosis and ischemic stroke.

Key points

Left atrial (LA) fibrosis is associated with arrhythmogenesis and increased risk of ischemic stroke; its extent and pattern can be quantified on a patient-specific basis using late gadolinium enhancement magnetic resonance imaging.Current stroke risk prediction tools have limited personalization, and their accuracy could be improved by incorporating patient-specific information like fibrotic maps and hemodynamic patterns.We present the first electro-mechano-fluidic multi-physics computational simulations of LA flow, including fibrosis and anatomies from medical imaging. Mechanical changes in fibrotic tissue impair global LA motion, decreasing LA and left atrial appendage (LAA) emptying fractions, especially in subjects with higher fibrosis burdens. Fibrotic-mediated LA motion impairment alters LA and LAA flow near the endocardium and the whole cavity, ultimately leading to more stagnant blood regions in the LAA.

Cardiac length-dependent activation driven by force-dependent thick-filament dynamics

The length-dependent activation (LDA) of maximum force and calcium sensitivity are established features of cardiac muscle contraction but the dominant underlying mechanisms remain to be fully clarified. Alongside the well-documented regulation of contraction via the thin filaments, experiments have identified an additional force-dependent thick-filament activation, whereby myosin heads parked in a so-called off state become available to generate force. This process produces a feedback effect that may potentially drive LDA. Using biomechanical modeling of a human left-ventricular myocyte, this study investigates the extent to which the off-state dynamics could, by itself, plausibly account for LDA, depending on the specific mathematical formulation of the feedback. We hypothesized four different models of the off-state regulatory feedback based on (A) total force, (B) active force, (C) sarcomere strain, and (D) passive force. We tested if these models could reproduce the isometric steady-state and dynamic LDA features predicted by an earlier published model of a human left-ventricle myocyte featuring purely phenomenological length dependences. The results suggest that only total-force feedback (A) is capable of reproducing the expected behaviors, but that passive tension could provide a length-dependent signal on which to initiate the feedback. Furthermore, by attributing LDA to off-state dynamics, our proposed model also qualitatively reproduces experimentally observed effects of the off-state-stabilizing drug mavacamten. Taken together, these results support off-state dynamics as a plausible primary mechanism underlying LDA.

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).

Lower diastolic tension may be indicative of higher proarrhythmic propensity in failing human cardiomyocytes

Chronic heart failure is one of the most common reasons for hospitalization. Current risk stratification is based on ejection fraction, whereas many arrhythmic events occur in patients with relatively preserved ejection fraction. We aim to investigate the mechanistic link between proarrhythmic abnormalities, reduced contractility and diastolic dysfunction in heart failure, using electromechanical modelling and simulations of human failing cardiomyocytes. We constructed, calibrated and validated populations of human electromechanical models of failing cardiomyocytes, that were able to reproduce the prolonged action potential, reduced contractility and diastolic dysfunction as observed in human data, as well as increased propensity to proarrhythmic incidents such as early afterdepolarization and beat-to-beat alternans. Our simulation data reveal that proarrhythmic incidents tend to occur in failing myocytes with lower diastolic tension, rather than with lower contractility, due to the relative preserved SERCA and sodium calcium exchanger current. These results support the inclusion of end-diastolic volume to be potentially beneficial in the risk stratifications of heart failure patients.

Translating myosin-binding protein C and titin abnormalities to whole-heart function using a novel calcium-contraction coupling model

Mutations in cardiac myosin-binding protein C (cMyBP-C) or titin may respectively lead to hypertrophic (HCM) or dilated (DCM) cardiomyopathies. The mechanisms leading to these phenotypes remain unclear because of the challenge of translating cellular abnormalities to whole-heart and system function. We developed and validated a novel computer model of calcium-contraction coupling incorporating the role of cMyBP-C and titin based on the key assumptions: 1) tension in the thick filament promotes cross-bridge attachment mechanochemically, 2) with increasing titin tension, more myosin heads are unlocked for attachment, and 3) cMyBP-C suppresses cross-bridge attachment. Simulated stationary calcium-tension curves, isotonic and isometric contractions, and quick release agreed with experimental data. The model predicted that a loss of cMyBP-C function decreases the steepness of the calcium-tension curve, and that more compliant titin decreases the level of passive and active tension and its dependency on sarcomere length. Integrating this cellular model in the CircAdapt model of the human heart and circulation showed that a loss of cMyBP-C function resulted in HCM-like hemodynamics with higher left ventricular end-diastolic pressures and smaller volumes. More compliant titin led to higher diastolic pressures and ventricular dilation, suggesting DCM-like hemodynamics. The novel model of calcium-contraction coupling incorporates the role of cMyBP-C and titin. Its coupling to whole-heart mechanics translates changes in cellular calcium-contraction coupling to changes in cardiac pump and circulatory function and identifies potential mechanisms by which cMyBP-C and titin abnormalities may develop into HCM and DCM phenotypes. This modeling platform may help identify distinct mechanisms underlying clinical phenotypes in cardiac diseases.

Proposing a Caputo-Land System for active tension. Capturing variable viscoelasticity

Accurate cell-level active tension modeling for cardiomyocytes is critical to understanding cardiac functionality on a subject-specific basis. However, cell-level models in the literature fail to account for viscoelasticity and inter-subject variations in active tension, which are relevant to disease diagnostics and drug screening, e.g., for cardiotoxicity. Thus, we propose a fractional order system to model cell-level active tension by extending Land's state-of-the-art model of cardiac contraction. Our approach features the (left) Caputo derivative of six state variables that identify the mechanistic origins of viscoelasticity in a myocardial cell in terms of the thin filament, thick filament, and length-dependent interactions. This proposed CLS is the first of its kind for active tension modeling in cells and demonstrates notable subject-specificity, with smaller mean square errors than the reference model relative to cell-level experiments across subjects, promising greater clinical relevance than its counterparts in the literature by highlighting the contribution of different cellular mechanisms to apparent viscoelastic cell behavior, and how it could vary with disease.

Analysis of metabolite and strain effects on cardiac cross-bridge dynamics using model linearisation techniques

Multi-scale models of cardiac energetics are becoming crucial in better understanding the prevalent chronic diseases operating at the intersection of metabolic and cardiovascular dysfunction. Computationally efficient models of cardiac cross-bridge kinetics that are sensitive to changes in metabolite concentrations are necessary to simulate the effects of disease-induced changes in cellular metabolic state on cardiac mechanics across disparate spatial scales. While these models do currently exist, deeper analysis of how the modelling of metabolite effects and the assignment of strain dependence within the cross-bridge cycle affect the properties of the model is required. In this study, model linearisation techniques were used to simulate and interrogate the complex modulus of an ODE-based model of cross-bridge kinetics. Active complex moduli were measured from permeabilised rat cardiac trabeculae under five different metabolite conditions with varying ATP and Pi concentrations. Sensitivity to metabolites was incorporated into an existing three-state cross-bridge model using either a direct dependence or a rapid equilibrium approach. Combining the two metabolite binding methods with all possible locations of strain dependence within the cross-bridge cycle produced 64 permutations of the cross-bridge model. Using linear model analysis, these models were systematically explored to determine the effects of metabolite binding and their interaction with strain dependence on the frequency response of cardiac muscle. The results showed that the experimentally observed effects of ATP and Pi concentrations on the cardiac complex modulus could be attributed to their regulation of cross-bridge detachment rates. Analysis of the cross-bridge models revealed a mechanistic basis for the biochemical schemes which place Pi release following cross-bridge formation and ATP binding prior to cross-bridge detachment. In addition, placing strain dependence on the reverse rate of the cross-bridge power stroke produced the model which most closely matched the experimental data. From these analyses, a well-justified metabolite-sensitive model of rat cardiac cross-bridge kinetics is presented which is suitable for parameterisation with other data sets and integration with multi-scale cardiac models.

Advancing clinical translation of cardiac biomechanics models: a comprehensive review, applications and future pathways

Cardiac mechanics models are developed to represent a high level of detail, including refined anatomies, accurate cell mechanics models, and platforms to link microscale physiology to whole-organ function. However, cardiac biomechanics models still have limited clinical translation. In this review, we provide a picture of cardiac mechanics models, focusing on their clinical translation. We review the main experimental and clinical data used in cardiac models, as well as the steps followed in the literature to generate anatomical meshes ready for simulations. We describe the main models in active and passive mechanics and the different lumped parameter models to represent the circulatory system. Lastly, we provide a summary of the state-of-the-art in terms of ventricular, atrial, and four-chamber cardiac biomechanics models. We discuss the steps that may facilitate clinical translation of the biomechanics models we describe. A well-established software to simulate cardiac biomechanics is lacking, with all available platforms involving different levels of documentation, learning curves, accessibility, and cost. Furthermore, there is no regulatory framework that clearly outlines the verification and validation requirements a model has to satisfy in order to be reliably used in applications. Finally, better integration with increasingly rich clinical and/or experimental datasets as well as machine learning techniques to reduce computational costs might increase model reliability at feasible resources. Cardiac biomechanics models provide excellent opportunities to be integrated into clinical workflows, but more refinement and careful validation against clinical data are needed to improve their credibility. In addition, in each context of use, model complexity must be balanced with the associated high computational cost of running these models.

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.

Measuring and Modelling the Effect of Inorganic Phosphate on Cross-bridge Mechanics in Human Cardiac Muscle

Many common chronic diseases operate at the intersection of metabolic and cardiovascular dysfunction. In order to model the effects of these diseases and investigate underlying causes we are developing a cardiomyocyte model which incorporates both the mechanics and metabolic factors that underlie work done by the heart. In this paper we present the first experimental results from our study measuring mechanical properties in human cardiac trabeculae, including the effect of inorganic phosphate (Pi) on the complex modulus at 37 °C. Extending our previous mathematical model, we have developed a computationally efficient model of cardiac cross-bridge mechanics which is sensitive to changes in cellular Pi. This extended model was parameterised with human cardiac complex modulus data. It captured the changes to cardiac mechanics following an increase in Pi concentration that we measured experimentally, including a reduced elastic modulus and a right-shift in frequency. The human cardiac trabecula we studied had a low sensitivity to Pi compared to what has been previously reported in mammalian cardiac tissue, which suggests that the muscle may have cellular compensatory mechanisms to cope with elevated Pi levels. This study demonstrates the feasibility of our experimental-modelling pipeline for future investigation of mechanical and metabolic effects in the diseased human heart.Clinical Relevance- This study presents the first measurement of the effect of Pi on the stiffness frequency response of human cardiac tissue and extends an experimental-modelling framework appropriate for investigating effects of disease on the human heart.

Cell to whole organ global sensitivity analysis on a four-chamber heart electromechanics model using Gaussian processes emulators

Cardiac pump function arises from a series of highly orchestrated events across multiple scales. Computational electromechanics can encode these events in physics-constrained models. However, the large number of parameters in these models has made the systematic study of the link between cellular, tissue, and organ scale parameters to whole heart physiology challenging. A patient-specific anatomical heart model, or digital twin, was created. Cellular ionic dynamics and contraction were simulated with the Courtemanche-Land and the ToR-ORd-Land models for the atria and the ventricles, respectively. Whole heart contraction was coupled with the circulatory system, simulated with CircAdapt, while accounting for the effect of the pericardium on cardiac motion. The four-chamber electromechanics framework resulted in 117 parameters of interest. The model was broken into five hierarchical sub-models: tissue electrophysiology, ToR-ORd-Land model, Courtemanche-Land model, passive mechanics and CircAdapt. For each sub-model, we trained Gaussian processes emulators (GPEs) that were then used to perform a global sensitivity analysis (GSA) to retain parameters explaining 90% of the total sensitivity for subsequent analysis. We identified 45 out of 117 parameters that were important for whole heart function. We performed a GSA over these 45 parameters and identified the systemic and pulmonary peripheral resistance as being critical parameters for a wide range of volumetric and hemodynamic cardiac indexes across all four chambers. We have shown that GPEs provide a robust method for mapping between cellular properties and clinical measurements. This could be applied to identify parameters that can be calibrated in patient-specific models or digital twins, and to link cellular function to clinical indexes.

Mechanoelectric effects in healthy cardiac function and under Left Bundle Branch Block pathology

Mechanoelectric feedback (MEF) in the heart operates through several mechanisms which serve to regulate cardiac function. Stretch activated channels (SACs) in the myocyte membrane open in response to cell lengthening, while tension generation depends on stretch, shortening velocity, and calcium concentration. How all of these mechanisms interact and their effect on cardiac output is still not fully understood. We sought to gauge the acute importance of the different MEF mechanisms on heart function. An electromechanical computer model of a dog heart was constructed, using a biventricular geometry of 500K tetrahedral elements. To describe cellular behavior, we used a detailed ionic model to which a SAC model and an active tension model, dependent on stretch and shortening velocity and with calcium sensitivity, were added. Ventricular inflow and outflow were connected to the CircAdapt model of cardiovascular circulation. Pressure-volume loops and activation times were used for model validation. Simulations showed that SACs did not affect acute mechanical response, although if their trigger level was decreased sufficiently, they could cause premature excitations. The stretch dependence of tension had a modest effect in reducing the maximum stretch, and stroke volume, while shortening velocity had a much bigger effect on both. MEF served to reduce the heterogeneity in stretch while increasing tension heterogeneity. In the context of left bundle branch block, a decreased SAC trigger level could restore cardiac output by reducing the maximal stretch when compared to cardiac resynchronization therapy. MEF is an important aspect of cardiac function and could potentially mitigate activation problems.

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.

Insights from an electro-mechanical heart failure cell model: Role of SERCA enhancement on arrhythmogenesis and myocyte contraction

BACKGROUND AND OBJECTIVE

Structural and electrical remodeling in heart failure predisposes the heart to ventricular arrhythmias. Computer modeling approaches, used to complement experimental results, can provide a more mechanistic knowledge of the biophysical phenomena underlying cardiac pathologies. Indeed, previous in-silico studies have improved the understanding of the electrical correlates of heart failure involved in arrhythmogenesis; however, information on the crosstalk between electrical activity, intracellular Ca²⁺ and contraction is still incomplete. This study aims to investigate the electro-mechanical behavior of virtual failing human ventricular myocytes to help in the development of therapies, which should ideally target pump failure and arrhythmias at the same time.

METHODS

We implemented characteristic remodeling of heart failure with reduced ejection fraction by including reported changes in ionic conductances, sarcomere function and cell structure (e.g. T-tubules disarray). Model parametrization was based on published experimental data and the outcome of simulations was validated against experimentally observed patterns. We focused on two aspects of myocardial dysfunction central in heart failure: altered force-frequency relationship and susceptibility to arrhythmogenic early afterdepolarizations. Because biological variability is a major problem in the generalization of in-silico findings based on a unique set of model parameters, we generated and evaluated a population of models.

RESULTS

The population-based approach is crucial in robust identification of parameters at the core of abnormalities and in generalizing the outcome of their correction. As compared to non-failing ones, failing myocytes had prolonged repolarization, a higher incidence of early afterdepolarizations, reduced contraction and a shallower force-frequency relationship, all features peculiar of heart failure. Component analysis applied to the model population identified reduced SERCA function as a relevant contributor to most of these derangements, which were largely reverted or diminished by restoration of SERCA function alone.

CONCLUSIONS

These simulated results encourage the development of strategies comprising SERCA stimulation and highlight the need to evaluate both electrical and mechanical outcomes.

A cell-based framework for modeling cardiac mechanics

Cardiomyocytes are the functional building blocks of the heart-yet most models developed to simulate cardiac mechanics do not represent the individual cells and their surrounding matrix. Instead, they work on a homogenized tissue level, assuming that cellular and subcellular structures and processes scale uniformly. Here we present a mathematical and numerical framework for exploring tissue-level cardiac mechanics on a microscale given an explicit three-dimensional geometrical representation of cells embedded in a matrix. We defined a mathematical model over such a geometry and parametrized our model using publicly available data from tissue stretching and shearing experiments. We then used the model to explore mechanical differences between the extracellular and the intracellular space. Through sensitivity analysis, we found the stiffness in the extracellular matrix to be most important for the intracellular stress values under contraction. Strain and stress values were observed to follow a normal-tangential pattern concentrated along the membrane, with substantial spatial variations both under contraction and stretching. We also examined how it scales to larger size simulations, considering multicellular domains. Our work extends existing continuum models, providing a new geometrical-based framework for exploring complex cell-cell and cell-matrix interactions.

Varying thin filament activation in the framework of the Huxley'57 model

Muscle contraction is triggered by the activation of the actin sites of the thin filament by calcium ions. It results that the thin filament activation level varies over time. Moreover, this activation process is also used as a regulation mechanism of the developed force. Our objective is to build a model of varying actin site activation level within the classical Huxley'57 two-state framework. This new model is obtained as an enhancement of a previously proposed formulation of the varying thick filament activation within the same framework. We assume that the state of an actin site depends on whether it is activated and whether it forms a cross-bridge with the associated myosin head, which results in four possible states. The transitions between the actin site states are controlled by the global actin sites activation level and the dynamics of these transitions is coupled with the attachment-detachment process. A preliminary calibration of the model with experimental twitch contraction data obtained at varying sarcomere lengths is performed.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

A Novel In Silico Electromechanical Model of Human Ventricular Cardiomyocyte

Contractility has become one of the main readouts in computational and experimental studies on cardiomyocytes. Following this trend, we propose a novel mathematical model of human ventricular cardiomyocytes electromechanics, BPSLand, by coupling a recent human contractile element to the BPS2020 model of electrophysiology. BPSLand is the result of a hybrid optimization process and it reproduces all the electrophysiology experimental indices captured by its predecessor BPS2020, simultaneously enabling the simulation of realistic human active tension and its potential abnormalities. The transmural heterogeneity in both electrophysiology and contractility departments was simulated consistent with previous computational and in vitro studies. Furthermore, our model could capture delayed afterdepolarizations (DADs), early afterdepolarizations (EADs), and contraction abnormalities in terms of aftercontractions triggered by either drug action or special pacing modes. Finally, we further validated the mechanical results of the model against previous experimental and in silico studies, e.g., the contractility dependence on pacing rate. Adding a new level of applicability to the normative models of human cardiomyocytes, BPSLand represents a robust, fully-human in silico model with promising capabilities for translational cardiology.

Impact of Intraventricular Septal Fiber Orientation on Cardiac Electromechanical Function

Cardiac fiber direction is an important factor determining the propagation of electrical activity, as well as the development of mechanical force. In this article, we imaged the ventricles of several species with special attention to the intraventricular septum to determine the functional consequences of septal fiber organization. First, we identified a dual-layer organization of the fiber orientation in the intraventricular septum of ex vivo sheep hearts using diffusion tensor imaging at high field MRI. To expand the scope of the results, we investigated the presence of a similar fiber organization in five mammalian species (rat, canine, pig, sheep, and human) and highlighted the continuity of the layer with the moderator band in large mammalian species. We implemented the measured septal fiber fields in three-dimensional electromechanical computer models to assess the impact of the fiber orientation. The downward fibers produced a diamond activation pattern superficially in the right ventricle. Electromechanically, there was very little change in pressure volume loops although the stress distribution was altered. In conclusion, we clarified that the right ventricular septum has a downwardly directed superficial layer in larger mammalian species, which can have modest effects on stress distribution.

NEW & NOTEWORTHY A dual-layer organization of the fiber orientation in the intraventricular septum was identified in ex vivo hearts of large mammals. The RV septum has a downwardly directed superficial layer that is continuous with the moderator band. Electrically, it produced a diamond activation pattern. Electromechanically, little change in pressure volume loops were noticed but stress distribution was altered. Fiber distribution derived from diffusion tensor imaging should be considered for an accurate strain and stress analysis.

An Integrated Workflow for Building Digital Twins of Cardiac Electromechanics-A Multi-Fidelity Approach for Personalising Active Mechanics

Personalised computer models of cardiac function, referred to as cardiac digital twins, are envisioned to play an important role in clinical precision therapies of cardiovascular diseases. A major obstacle hampering clinical translation involves the significant computational costs involved in the personalisation of biophysically detailed mechanistic models that require the identification of high-dimensional parameter vectors. An important aspect to identify in electromechanics (EM) models are active mechanics parameters that govern cardiac contraction and relaxation. In this study, we present a novel, fully automated, and efficient approach for personalising biophysically detailed active mechanics models using a two-step multi-fidelity solution. In the first step, active mechanical behaviour in a given 3D EM model is represented by a purely phenomenological, low-fidelity model, which is personalised at the organ scale by calibration to clinical cavity pressure data. Then, in the second step, median traces of nodal cellular active stress, intracellular calcium concentration, and fibre stretch are generated and utilised to personalise the desired high-fidelity model at the cellular scale using a 0D model of cardiac EM. Our novel approach was tested on a cohort of seven human left ventricular (LV) EM models, created from patients treated for aortic coarctation (CoA). Goodness of fit, computational cost, and robustness of the algorithm against uncertainty in the clinical data and variations of initial guesses were evaluated. We demonstrate that our multi-fidelity approach facilitates the personalisation of a biophysically detailed active stress model within only a few (2 to 4) expensive 3D organ-scale simulations-a computational effort compatible with clinical model applications.

Basic Research Approaches to Evaluate Cardiac Arrhythmia in Heart Failure and Beyond

Patients with heart failure often develop cardiac arrhythmias. The mechanisms and interrelations linking heart failure and arrhythmias are not fully understood. Historically, research into arrhythmias has been performed on affected individuals or in vivo (animal) models. The latter however is constrained by interspecies variation, demands to reduce animal experiments and cost. Recent developments in in vitro induced pluripotent stem cell technology and in silico modelling have expanded the number of models available for the evaluation of heart failure and arrhythmia. An agnostic approach, combining the modalities discussed here, has the potential to improve our understanding for appraising the pathology and interactions between heart failure and arrhythmia and can provide robust and validated outcomes in a variety of research settings. This review discusses the state of the art models, methodologies and techniques used in the evaluation of heart failure and arrhythmia and will highlight the benefits of using them in combination. Special consideration is paid to assessing the pivotal role calcium handling has in the development of heart failure and arrhythmia.

Functional and structural differences between skinned and intact muscle preparations

Myofilaments and their associated proteins, which together constitute the sarcomeres, provide the molecular-level basis for contractile function in all muscle types. In intact muscle, sarcomere-level contraction is strongly coupled to other cellular subsystems, in particular the sarcolemmal membrane. Skinned muscle preparations (where the sarcolemma has been removed or permeabilized) are an experimental system designed to probe contractile mechanisms independently of the sarcolemma. Over the last few decades, experiments performed using permeabilized preparations have been invaluable for clarifying the understanding of contractile mechanisms in both skeletal and cardiac muscle. Today, the technique is increasingly harnessed for preclinical and/or pharmacological studies that seek to understand how interventions will impact intact muscle contraction. In this context, intrinsic functional and structural differences between skinned and intact muscle pose a major interpretational challenge. This review first surveys measurements that highlight these differences in terms of the sarcomere structure, passive and active tension generation, and calcium dependence. We then highlight the main practical challenges and caveats faced by experimentalists seeking to emulate the physiological conditions of intact muscle. Gaining an awareness of these complexities is essential for putting experiments in due perspective.

Heart-on-Chip for Combined Cellular Dynamics Measurements and Computational Modeling Towards Clinical Applications

Organ-on-chip or micro-engineered three-dimensional cellular or tissue models are increasingly implemented in the study of cardiovascular pathophysiology as alternatives to traditional in vitro cell culture. Drug induced cardiotoxicity is a key issue in drug development pipelines, but the current in vitro and in vivo studies suffer from inter-species differences, high costs, and lack of reliability and accuracy in predicting cardiotoxicity. Microfluidic heart-on-chip devices can impose a paradigm shift to the current tools. They can not only recapitulate cardiac tissue level functionality and the communication between cells and extracellular matrices but also allow higher throughput studies conducive to drug screening especially with their added functionalities or sensors that extract disease-specific phenotypic, genotypic, and electrophysiological information in real-time. Such electrical and mechanical components can tailor the electrophysiology and mechanobiology of the experiment to better mimic the in vivo condition as well. Recent advancements and challenges are reviewed in the fabrication, functionalization and sensor assisted mechanical and electrophysiological measurements, numerical and computational modeling of cardiomyocytes' behavior, and the clinical applications in drug screening and disease modeling. This review concludes with the current challenges and perspectives on the future of such organ-on-chip platforms.

A guide for assessment of myocardial stiffness in health and disease

Myocardial stiffness is an intrinsic property of the myocardium that influences both diastolic and systolic cardiac function. Myocardial stiffness represents the resistance of this tissue to being deformed and depends on intracellular components of the cardiomyocyte, particularly the cytoskeleton, and on extracellular components, such as collagen fibers. Myocardial disease is associated with changes in myocardial stiffness, and its assessment is a key diagnostic marker of acute or chronic pathological myocardial disease with the potential to guide therapeutic decision-making. In this Review, we appraise the different techniques that can be used to estimate myocardial stiffness, evaluate their advantages and disadvantages, and discuss potential clinical applications.

A mathematical model of hiPSC cardiomyocytes electromechanics

Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) are becoming instrumental in cardiac research, human-based cell level cardiotoxicity tests, and developing patient-specific care. As one of the principal functional readouts is contractility, we propose a novel electromechanical hiPSC-CM computational model named the hiPSC-CM-CE. This model comprises a reparametrized version of contractile element (CE) by Rice et al., 2008, with a new passive force formulation, integrated into a hiPSC-CM electrophysiology formalism by Paci et al. in 2020. Our simulated results were validated against in vitro data reported for hiPSC-CMs at matching conditions from different labs. Specifically, key action potential (AP) and calcium transient (CaT) biomarkers simulated by the hiPSC-CM-CE model were within the experimental ranges. On the mechanical side, simulated cell shortening, contraction-relaxation kinetic indices (RT50 and RT25 ), and the amplitude of tension fell within the experimental intervals. Markedly, as an inter-scale analysis, correct classification of the inotropic effects due to non-cardiomyocytes in hiPSC-CM tissues was predicted on account of the passive force expression introduced to the CE. Finally, the physiological inotropic effects caused by Verapamil and Bay-K 8644 and the aftercontractions due to the early afterdepolarizations (EADs) were simulated and validated against experimental data. In the future, the presented model can be readily expanded to take in pharmacological trials and genetic mutations, such as those involved in hypertrophic cardiomyopathy, and study arrhythmia trigger mechanisms.

Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia

We developed a novel patient-specific computational model for the numerical simulation of ventricular electromechanics in patients with ischemic cardiomyopathy (ICM). This model reproduces the activity both in sinus rhythm (SR) and in ventricular tachycardia (VT). The presence of scars, grey zones and non-remodeled regions of the myocardium is accounted for by the introduction of a spatially heterogeneous coefficient in the 3D electromechanics model. This 3D electromechanics model is firstly coupled with a 2-element Windkessel afterload model to fit the pressure-volume (PV) loop of a patient-specific left ventricle (LV) with ICM in SR. Then, we employ the coupling with a 0D closed-loop circulation model to analyze a VT circuit over multiple heartbeats on the same LV. We highlight similarities and differences on the solutions obtained by the electrophysiology model and those of the electromechanics model, while considering different scenarios for the circulatory system. We observe that very different parametrizations of the circulation model induce the same hemodynamical considerations for the patient at hand. Specifically, we classify this VT as unstable. We conclude by stressing the importance of combining electrophysiological, mechanical and hemodynamical models to provide relevant clinical indicators in how arrhythmias evolve and can potentially lead to sudden cardiac death.

Causes of altered ventricular mechanics in hypertrophic cardiomyopathy: an in-silico study

BACKGROUND

Hypertrophic cardiomyopathy (HCM) is typically caused by mutations in sarcomeric genes leading to cardiomyocyte disarray, replacement fibrosis, impaired contractility, and elevated filling pressures. These varying tissue properties are associated with certain strain patterns that may allow to establish a diagnosis by means of non-invasive imaging without the necessity of harmful myocardial biopsies or contrast agent application. With a numerical study, we aim to answer: how the variability in each of these mechanisms contributes to altered mechanics of the left ventricle (LV) and if the deformation obtained in in-silico experiments is comparable to values reported from clinical measurements.

METHODS

We conducted an in-silico sensitivity study on physiological and pathological mechanisms potentially underlying the clinical HCM phenotype. The deformation of the four-chamber heart models was simulated using a finite-element mechanical solver with a sliding boundary condition to mimic the tissue surrounding the heart. Furthermore, a closed-loop circulatory model delivered the pressure values acting on the endocardium. Deformation measures and mechanical behavior of the heart models were evaluated globally and regionally.

RESULTS

Hypertrophy of the LV affected the course of strain, strain rate, and wall thickening-the root-mean-squared difference of the wall thickening between control (mean thickness 10 mm) and hypertrophic geometries (17 mm) was >10%. A reduction of active force development by 40% led to less overall deformation: maximal radial strain reduced from 26 to 21%. A fivefold increase in tissue stiffness caused a more homogeneous distribution of the strain values among 17 heart segments. Fiber disarray led to minor changes in the circumferential and radial strain. A combination of pathological mechanisms led to reduced and slower deformation of the LV and halved the longitudinal shortening of the LA.

CONCLUSIONS

This study uses a computer model to determine the changes in LV deformation caused by pathological mechanisms that are presumed to underlay HCM. This knowledge can complement imaging-derived information to obtain a more accurate diagnosis of HCM.

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.

CalTrack: High-Throughput Automated Calcium Transient Analysis in Cardiomyocytes

[Figure: see text].

Electro-Mechanical Whole-Heart Digital Twins: A Fully Coupled Multi-Physics Approach

Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a fully coupled multi-scale model of the human heart, including electrophysiology, mechanics, and a closed-loop model of circulation. State-of-the-art models based on human physiology are used to describe membrane kinetics, excitation-contraction coupling and active tension generation in the atria and the ventricles. Furthermore, we highlight ways to adapt this framework to patient specific measurements to build digital twins. The validity of the model is demonstrated through simulations on a personalized whole heart geometry based on magnetic resonance imaging data of a healthy volunteer. Additionally, the fully coupled model was employed to evaluate the effects of a typical atrial ablation scar on the cardiovascular system. With this work, we provide an adaptable multi-scale model that allows a comprehensive personalization from ion channels to the organ level enabling digital twin modeling.

Human biventricular electromechanical simulations on the progression of electrocardiographic and mechanical abnormalities in post-myocardial infarction

AIMS

Develop, calibrate and evaluate with clinical data a human electromechanical modelling and simulation framework for multiscale, mechanistic investigations in healthy and post-myocardial infarction (MI) conditions, from ionic to clinical biomarkers.

METHODS AND RESULTS

Human healthy and post-MI electromechanical simulations were conducted with a novel biventricular model, calibrated and evaluated with experimental and clinical data, including torso/biventricular anatomy from clinical magnetic resonance, state-of-the-art human-based membrane kinetics, excitation-contraction and active tension models, and orthotropic electromechanical coupling. Electromechanical remodelling of the infarct/ischaemic region and the border zone were simulated for ischaemic, acute, and chronic states in a fully transmural anterior infarct and a subendocardial anterior infarct. The results were compared with clinical electrocardiogram and left ventricular ejection fraction (LVEF) data at similar states. Healthy model simulations show LVEF 63%, with 11% peak systolic wall thickening, QRS duration and QT interval of 100 ms and 330 ms. LVEF in ischaemic, acute, and chronic post-MI states were 56%, 51%, and 52%, respectively. In linking the three post-MI simulations, it was apparent that elevated resting potential due to hyperkalaemia in the infarcted region led to ST-segment elevation, while a large repolarization gradient corresponded to T-wave inversion. Mechanically, the chronic stiffening of the infarct region had the benefit of improving systolic function by reducing infarct bulging at the expense of reducing diastolic function by inhibiting inflation.

CONCLUSION

Our human-based multiscale modelling and simulation framework enables mechanistic investigations into patho-physiological electrophysiological and mechanical behaviour and can serve as testbed to guide the optimization of pharmacological and electrical therapies.

Multiscale modeling of twitch contractions in cardiac trabeculae

Understanding the dynamics of a cardiac muscle twitch contraction is complex because it requires a detailed understanding of the kinetic processes of the Ca2+ transient, thin-filament activation, and the myosin-actin cross-bridge chemomechanical cycle. Each of these steps has been well defined individually, but understanding how all three of the processes operate in combination is a far more complex problem. Computational modeling has the potential to provide detailed insight into each of these processes, how the dynamics of each process affect the complexity of contractile behavior, and how perturbations such as mutations in sarcomere proteins affect the complex interactions of all of these processes. The mechanisms involved in relaxation of tension during a cardiac twitch have been particularly difficult to discern due to nonhomogeneous sarcomere lengthening during relaxation. Here we use the multiscale MUSICO platform to model rat trabecular twitches. Validation of computational models is dependent on being able to simulate different experimental datasets, but there has been a paucity of data that can provide all of the required parameters in a single experiment, such as simultaneous measurements of force, intracellular Ca2+ transients, and sarcomere length dynamics. In this study, we used data from different studies collected under similar experimental conditions to provide information for all the required parameters. Our simulations established that twitches either in an isometric sarcomere or in fixed-length, multiple-sarcomere trabeculae replicate the experimental observations if models incorporate a length-tension relationship for the nonlinear series elasticity of muscle preparations and a scheme for thick-filament regulation. The thick-filament regulation assumes an off state in which myosin heads are parked onto the thick-filament backbone and are unable to interact with actin, a state analogous to the super-relaxed state. Including these two mechanisms provided simulations that accurately predict twitch contractions over a range of different conditions.

A survey of pathways for mechano-electric coupling in the atria

Mechano-electric coupling (MEC) in atrial tissue has received sparse investigation to date, despite the well-known association between chronic atrial dilation and atrial fibrillation (AF). Of note, no fewer than six different mechanisms pertaining to stretch-activated channels, cellular capacitance and geometric effects have been identified in the literature as potential players. In this mini review, we briefly survey each of these pathways to MEC. We then perform computational simulations using single cell and tissue models in presence of various stretch regimes and MEC pathways. This allows us to assess the relative significance of each pathway in determining action potential duration, conduction velocity and rotor stability. For chronic atrial stretch, we find that stretch-induced alterations in membrane capacitance decrease conduction velocity and increase action potential duration, in agreement with experimental findings. In the presence of time-dependent passive atrial stretch, stretch-activated channels play the largest role, leading to after-depolarizations and rotor hypermeandering. These findings suggest that physiological atrial stretches, such as passive stretch during the atrial reservoir phase, may play an important part in the mechanisms of atrial arrhythmogenesis.

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Passive strains caused by ventricular contraction need to be considered when incorporating mechano-electro feedback in atrial electrophysiology models.

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In chronic stretch, stretch-induced capacitance changes dominate.

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Chronic stretch leads to an increase in action potential duration and a reduction in conduction velocity, consistent with experimental studies.

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In the presence of passive stretch, stretch-activated channels can induce delayed after-depolarisations and lead to rotor hypermeandering.

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Mechano-electro feedback is thus likely to have implications for the genesis and maintenance of atrial arrhythmias.

Biophysically detailed mathematical models of multiscale cardiac active mechanics

We propose four novel mathematical models, describing the microscopic mechanisms of force generation in the cardiac muscle tissue, which are suitable for multiscale numerical simulations of cardiac electromechanics. Such models are based on a biophysically accurate representation of the regulatory and contractile proteins in the sarcomeres. Our models, unlike most of the sarcomere dynamics models that are available in the literature and that feature a comparable richness of detail, do not require the time-consuming Monte Carlo method for their numerical approximation. Conversely, the models that we propose only require the solution of a system of PDEs and/or ODEs (the most reduced of the four only involving 20 ODEs), thus entailing a significant computational efficiency. By focusing on the two models that feature the best trade-off between detail of description and identifiability of parameters, we propose a pipeline to calibrate such parameters starting from experimental measurements available in literature. Thanks to this pipeline, we calibrate these models for room-temperature rat and for body-temperature human cells. We show, by means of numerical simulations, that the proposed models correctly predict the main features of force generation, including the steady-state force-calcium and force-length relationships, the length-dependent prolongation of twitches and increase of peak force, the force-velocity relationship. Moreover, they correctly reproduce the Frank-Starling effect, when employed in multiscale 3D numerical simulation of cardiac electromechanics.

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.

A publicly available virtual cohort of four-chamber heart meshes for cardiac electro-mechanics simulations

Computational models of the heart are increasingly being used in the development of devices, patient diagnosis and therapy guidance. While software techniques have been developed for simulating single hearts, there remain significant challenges in simulating cohorts of virtual hearts from multiple patients. To facilitate the development of new simulation and model analysis techniques by groups without direct access to medical data, image analysis techniques and meshing tools, we have created the first publicly available virtual cohort of twenty-four four-chamber hearts. Our cohort was built from heart failure patients, age 67±14 years. We segmented four-chamber heart geometries from end-diastolic (ED) CT images and generated linear tetrahedral meshes with an average edge length of 1.1±0.2mm. Ventricular fibres were added in the ventricles with a rule-based method with an orientation of -60° and 80° at the epicardium and endocardium, respectively. We additionally refined the meshes to an average edge length of 0.39±0.10mm to show that all given meshes can be resampled to achieve an arbitrary desired resolution. We ran simulations for ventricular electrical activation and free mechanical contraction on all 1.1mm-resolution meshes to ensure that our meshes are suitable for electro-mechanical simulations. Simulations for electrical activation resulted in a total activation time of 149±16ms. Free mechanical contractions gave an average left ventricular (LV) and right ventricular (RV) ejection fraction (EF) of 35±1% and 30±2%, respectively, and a LV and RV stroke volume (SV) of 95±28mL and 65±11mL, respectively. By making the cohort publicly available, we hope to facilitate large cohort computational studies and to promote the development of cardiac computational electro-mechanics for clinical applications.

Sensitivity analysis of a strongly-coupled human-based electromechanical cardiac model: Effect of mechanical parameters on physiologically relevant biomarkers

The human heart beats as a result of multiscale nonlinear dynamics coupling subcellular to whole organ processes, achieving electrophysiologically-driven mechanical contraction. Computational cardiac modelling and simulation have achieved a great degree of maturity, both in terms of mathematical models of underlying biophysical processes and the development of simulation software. In this study, we present the detailed description of a human-based physiologically-based, and fully-coupled ventricular electromechanical modelling and simulation framework, and a sensitivity analysis focused on its mechanical properties. The biophysical detail of the model, from ionic to whole-organ, is crucial to enable future simulations of disease and drug action. Key novelties include the coupling of state-of-the-art human-based electrophysiology membrane kinetics, excitation-contraction and active contraction models, and the incorporation of a pre-stress model to allow for pre-stressing and pre-loading the ventricles in a dynamical regime. Through high performance computing simulations, we demonstrate that 50% to 200% - 1000% variations in key parameters result in changes in clinically-relevant mechanical biomarkers ranging from diseased to healthy values in clinical studies. Furthermore mechanical biomarkers are primarily affected by only one or two parameters. Specifically, ejection fraction is dominated by the scaling parameter of the active tension model and its scaling parameter in the normal direction ( k ort 2 ); the end systolic pressure is dominated by the pressure at which the ejection phase is triggered ( P ej ) and the compliance of the Windkessel fluid model ( C ); and the longitudinal fractional shortening is dominated by the fibre angle ( ϕ ) and k ort 2 . The wall thickening does not seem to be clearly dominated by any of the considered input parameters. In summary, this study presents in detail the description and implementation of a human-based coupled electromechanical modelling and simulation framework, and a high performance computing study on the sensitivity of mechanical biomarkers to key model parameters. The tools and knowledge generated enable future investigations into disease and drug action on human ventricles.