Myokit: A simple interface to cardiac cellular electrophysiology

Digital twins for cardiac electrophysiology: state of the art and future challenges

Cardiac arrhythmias remain a major cause of death and disability. Current antiarrhythmic therapies are effective to only a limited extent, likely in large part due to their mechanism-independent approach. Precision cardiology aims to deliver targeted therapy for an individual patient to maximize efficacy and minimize adverse effects. In-silico digital twins have emerged as a promising strategy to realize the vision of precision cardiology. While there is no uniform definition of a digital twin, it typically employs digital tools, including simulations of mechanistic computer models, based on patient-specific clinical data to understand arrhythmia mechanisms and/or make clinically relevant predictions. Digital twins have become part of routine clinical practice in the setting of interventional cardiology, where commercially available services use digital twins to non-invasively determine the severity of stenosis (computed tomography-based fractional flow reserve). Although routine clinical application has not been achieved for cardiac arrhythmia management, significant progress towards digital twins for cardiac electrophysiology has been made in recent years. At the same time, significant technical and clinical challenges remain. This article provides a short overview of the history of digital twins for cardiac electrophysiology, including recent applications for the prediction of sudden cardiac death risk and the tailoring of rhythm control in atrial fibrillation. The authors highlight the current challenges for routine clinical application and discuss how overcoming these challenges may allow digital twins to enable a significant precision medicine-based advancement in cardiac arrhythmia management.

Single-cell ionic current phenotyping explains stem cell-derived cardiomyocyte action potential morphology

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) are a promising tool to study arrhythmia-related factors, but the variability of action potential (AP) recordings from these cells limits their use as an in vitro model. In this study, we use recently published brief (10 s), dynamic voltage-clamp (VC) data to provide mechanistic insights into the ionic currents contributing to AP heterogeneity; we call this approach rapid ionic current phenotyping (RICP). Features of this VC data were correlated to AP recordings from the same cells, and we used computational models to generate mechanistic insights into cellular heterogeneity. This analysis uncovered several interesting links between AP morphology and ionic current density: both L-type calcium and sodium currents contribute to upstroke velocity, rapid delayed rectifier K+ current is the main determinant of the maximal diastolic potential, and an outward current in the activation range of slow delayed rectifier K+ is the main determinant of AP duration. Our analysis also identified an outward current in several cells at 6 mV that is not reproduced by iPSC-CM mathematical models but contributes to determining AP duration. RICP can be used to explain how cell-to-cell variability in ionic currents gives rise to AP heterogeneity. Because of its brief duration (10 s) and ease of data interpretation, we recommend the use of RICP for single-cell patch-clamp experiments that include the acquisition of APs.NEW & NOTEWORTHY We present rapid ionic current phenotyping (RICP), a current quantification approach based on an optimized voltage-clamp protocol. The method captures a rich snapshot of the ionic current dynamics, providing quantitative information about multiple currents (e.g., ICa,L, IKr) in the same cell. The protocol helped to identify key ionic determinants of cellular action potential heterogeneity in iPSC-CMs. This included unexpected results, such as the critical role of IKr in establishing the maximum diastolic potential.

Neural network emulation of the human ventricular cardiomyocyte action potential for more efficient computations in pharmacological studies

Computer models of the human ventricular cardiomyocyte action potential (AP) have reached a level of detail and maturity that has led to an increasing number of applications in the pharmaceutical sector. However, interfacing the models with experimental data can become a significant computational burden. To mitigate the computational burden, the present study introduces a neural network (NN) that emulates the AP for given maximum conductances of selected ion channels, pumps, and exchangers. Its applicability in pharmacological studies was tested on synthetic and experimental data. The NN emulator potentially enables massive speed-ups compared to regular simulations and the forward problem (find drugged AP for pharmacological parameters defined as scaling factors of control maximum conductances) on synthetic data could be solved with average root-mean-square errors (RMSE) of 0.47 mV in normal APs and of 14.5 mV in abnormal APs exhibiting early afterdepolarizations (72.5% of the emulated APs were alining with the abnormality, and the substantial majority of the remaining APs demonstrated pronounced proximity). This demonstrates not only very fast and mostly very accurate AP emulations but also the capability of accounting for discontinuities, a major advantage over existing emulation strategies. Furthermore, the inverse problem (find pharmacological parameters for control and drugged APs through optimization) on synthetic data could be solved with high accuracy shown by a maximum RMSE of 0.22 in the estimated pharmacological parameters. However, notable mismatches were observed between pharmacological parameters estimated from experimental data and distributions obtained from the Comprehensive in vitro Proarrhythmia Assay initiative. This reveals larger inaccuracies which can be attributed particularly to the fact that small tissue preparations were studied while the emulator was trained on single cardiomyocyte data. Overall, our study highlights the potential of NN emulators as powerful tool for an increased efficiency in future quantitative systems pharmacology studies.

Novel Gain-of-Function Mutation in the Kv11.1 Channel Found in the Patient with Brugada Syndrome and Mild QTc Shortening

Brugada syndrome (BrS) is an inherited disease characterized by right precordial ST-segment elevation in the right precordial leads on electrocardiograms (ECG), and high risk of life-threatening ventricular arrhythmia and sudden cardiac death (SCD). Mutations in the responsible genes have not been fully characterized in the BrS patients, except for the SCN5A gene. We identified a new genetic variant, c.1189C>T (p.R397C), in the KCNH2 gene in the asymptomatic male proband diagnosed with BrS and mild QTc shortening. We hypothesize that this variant could alter IKr-current and may be causative for the rare non-SCN5A-related form of BrS. To assess its pathogenicity, we performed patch-clamp analysis on IKr reconstituted with this KCNH2 mutation in the Chinese hamster ovary cells and compared the phenotype with the wild type. It appeared that the R397C mutation does not affect the IKr density, but facilitates activation, hampers inactivation of the hERG channels, and increases magnitude of the window current suggesting that the p.R397C is a gain-of-function mutation. In silico modeling demonstrated that this missense mutation potentially leads to the shortening of action potential in the heart.

Optimization of a cardiomyocyte model illuminates role of increased INa,L in repolarization reserve

Cardiac ion currents may compensate for each other when one is compromised by a congenital or drug-induced defect. Such redundancy contributes to a robust repolarization reserve that can prevent the development of lethal arrhythmias. Most efforts made to describe this phenomenon have quantified contributions by individual ion currents. However, it is important to understand the interplay between all major ion-channel conductances, as repolarization reserve is dependent on the balance between all ion currents in a cardiomyocyte. Here, a genetic algorithm was designed to derive profiles of nine ion-channel conductances that optimize repolarization reserve in a mathematical cardiomyocyte model. Repolarization reserve was quantified using a previously defined metric, repolarization reserve current, i.e., the minimum constant current to prevent normal action potential repolarization in a cell. The optimization improved repolarization reserve current up to 84% compared to baseline in a human adult ventricular myocyte model and increased resistance to arrhythmogenic insult. The optimized conductance profiles were not only characterized by increased repolarizing current conductances but also uncovered a previously unreported behavior by the late sodium current. Simulations demonstrated that upregulated late sodium increased action potential duration, without compromising repolarization reserve current. The finding was generalized to multiple models. Ultimately, this computational approach, in which multiple currents were studied simultaneously, illuminated mechanistic insights into how the metric's magnitude could be increased and allowed for the unexpected role of late sodium to be elucidated.NEW & NOTEWORTHY Genetic algorithms are typically used to fit models or extract desired parameters from data. Here, we use the tool to produce a ventricular cardiomyocyte model with increased repolarization reserve. Since arrhythmia mitigation is dependent on multiple cardiac ion-channel conductances, study using a comprehensive, unbiased, and systems-level approach is important. The use of this optimization strategy allowed us to find robust profiles that illuminated unexpected mechanistic determinants of key ion-channel conductances in repolarization reserve.

Neural network emulation of the human ventricular cardiomyocyte action potential: a tool for more efficient computation in pharmacological studies

Computer models of the human ventricular cardiomyocyte action potential (AP) have reached a level of detail and maturity that has led to an increasing number of applications in the pharmaceutical sector. However, interfacing the models with experimental data can become a significant computational burden. To mitigate the computational burden, the present study introduces a neural network (NN) that emulates the AP for given maximum conductances of selected ion channels, pumps, and exchangers. Its applicability in pharmacological studies was tested on synthetic and experimental data. The NN emulator potentially enables massive speed-ups compared to regular simulations and the forward problem (find drugged AP for pharmacological parameters defined as scaling factors of control maximum conductances) on synthetic data could be solved with average root-mean-square errors (RMSE) of 0.47mV in normal APs and of 14.5mV in abnormal APs exhibiting early afterdepolarizations (72.5% of the emulated APs were alining with the abnormality, and the substantial majority of the remaining APs demonstrated pronounced proximity). This demonstrates not only very fast and mostly very accurate AP emulations but also the capability of accounting for discontinuities, a major advantage over existing emulation strategies. Furthermore, the inverse problem (find pharmacological parameters for control and drugged APs through optimization) on synthetic data could be solved with high accuracy shown by a maximum RMSE of 0.21 in the estimated pharmacological parameters. However, notable mismatches were observed between pharmacological parameters estimated from experimental data and distributions obtained from the Comprehensive in vitro Proarrhythmia Assay initiative. This reveals larger inaccuracies which can be attributed particularly to the fact that small tissue preparations were studied while the emulator was trained on single cardiomyocyte data. Overall, our study highlights the potential of NN emulators as powerful tool for an increased efficiency in future quantitative systems pharmacology studies.

Non-Invasive Electroanatomical Mapping: A State-Space Approach for Myocardial Current Density Estimation

Electroanatomical mapping is a method for creating a model of the electrophysiology of the human heart. Medical professionals routinely locate and ablate the site of origin of cardiac arrhythmias with invasive catheterization. Non-invasive localization takes the form of electrocardiographic (ECG) or magnetocardiographic (MCG) imaging, where the goal is to reconstruct the electrical activity of the human heart. Non-invasive alternatives to catheter electroanatomical mapping would reduce patients' risks and open new venues for treatment planning and prevention. This work introduces a new system state-based method for estimating the electrical activity of the human heart from MCG measurements. Our model enables arbitrary propagation paths and velocities. A Kalman filter optimally estimates the current densities under the given measurements and model parameters. In an outer optimization loop, these model parameters are then optimized via gradient descent. This paper aims to establish the foundation for future research by providing a detailed mathematical explanation of the algorithm. We demonstrate the feasibility of our method through a simplified one-layer simulation. Our results show that the algorithm can learn the propagation paths from the magnetic measurements. A threshold-based segmentation into healthy and pathological tissue yields a DICE score of 0.84, a recall of 0.77, and a precision of 0.93.

Model-driven optimal experimental design for calibrating cardiac electrophysiology models

BACKGROUND AND OBJECTIVE

Models of the cardiomyocyte action potential have contributed immensely to the understanding of heart function, pathophysiology, and the origin of heart rhythm disturbances. However, action potential models are highly nonlinear, making them difficult to parameterise and limiting to describing 'average cell' dynamics, when cell-specific models would be ideal to uncover inter-cell variability but are too experimentally challenging to be achieved. Here, we focus on automatically designing experimental protocols that allow us to better identify cell-specific maximum conductance values for each major current type.

METHODS AND RESULTS

We developed an approach that applies optimal experimental designs to patch-clamp experiments, including both voltage-clamp and current-clamp experiments. We assessed the models calibrated to these new optimal designs by comparing them to the models calibrated to some of the commonly used designs in the literature. We showed that optimal designs are not only overall shorter in duration but also able to perform better than many of the existing experiment designs in terms of identifying model parameters and hence model predictive power.

CONCLUSIONS

For cardiac cellular electrophysiology, this approach will allow researchers to define their hypothesis of the dynamics of the system and automatically design experimental protocols that will result in theoretically optimal designs.

Rapid ionic current phenotyping (RICP) identifies mechanistic underpinnings of iPSC-CM AP heterogeneity

As a renewable, easily accessible, human-derived in vitro model, human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) are a promising tool for studying arrhythmia-related factors, including cardiotoxicity and congenital proarrhythmia risks. An oft-mentioned limitation of iPSC-CMs is the abundant cell-to-cell variability in recordings of their electrical activity. Here, we develop a new method, rapid ionic current phenotyping (RICP), that utilizes a short (10 s) voltage clamp protocol to quantify cell-to-cell heterogeneity in key ionic currents. We correlate these ionic current dynamics to action potential recordings from the same cells and produce mechanistic insights into cellular heterogeneity. We present evidence that the L-type calcium current is the main determinant of upstroke velocity, rapid delayed rectifier K+ current is the main determinant of the maximal diastolic potential, and an outward current in the excitable range of slow delayed rectifier K+ is the main determinant of action potential duration. We measure an unidentified outward current in several cells at 6 mV that is not recapitulated by iPSC-CM mathematical models but contributes to determining action potential duration. In this way, our study both quantifies cell-to-cell variability in membrane potential and ionic currents, and demonstrates how the ionic current variability gives rise to action potential heterogeneity. Based on these results, we argue that iPSC-CM heterogeneity should not be viewed simply as a problem to be solved but as a model system to understand the mechanistic underpinnings of cellular variability.

In silico analysis of the dynamic regulation of cardiac electrophysiology by Kv 11.1 ion-channel trafficking

Cardiac electrophysiology is regulated by continuous trafficking and internalization of ion channels occurring over minutes to hours. Kv 11.1 (also known as hERG) underlies the rapidly activating delayed-rectifier K+ current (IKr ), which plays a major role in cardiac ventricular repolarization. Experimental characterization of the distinct temporal effects of genetic and acquired modulators on channel trafficking and gating is challenging. Computer models are instrumental in elucidating these effects, but no currently available model incorporates ion-channel trafficking. Here, we present a novel computational model that reproduces the experimentally observed production, forward trafficking, internalization, recycling and degradation of Kv 11.1 channels, as well as their modulation by temperature, pentamidine, dofetilide and extracellular K+ . The acute effects of these modulators on channel gating were also incorporated and integrated with the trafficking model in the O'Hara-Rudy human ventricular cardiomyocyte model. Supraphysiological dofetilide concentrations substantially increased Kv 11.1 membrane levels while also producing a significant channel block. However, clinically relevant concentrations did not affect trafficking. Similarly, severe hypokalaemia reduced Kv 11.1 membrane levels based on long-term culture data, but had limited effect based on short-term data. By contrast, clinically relevant elevations in temperature acutely increased IKr due to faster kinetics, while after 24 h, IKr was decreased due to reduced Kv 11.1 membrane levels. The opposite was true for lower temperatures. Taken together, our model reveals a complex temporal regulation of cardiac electrophysiology by temperature, hypokalaemia, and dofetilide through competing effects on channel gating and trafficking, and provides a framework for future studies assessing the role of impaired trafficking in cardiac arrhythmias. KEY POINTS: Kv 11.1 channels underlying the rapidly activating delayed-rectifier K+ current are important for ventricular repolarization and are continuously shuttled from the cytoplasm to the plasma membrane and back over minutes to hours. Kv 11.1 gating and trafficking are modulated by temperature, drugs and extracellular K+ concentration but experimental characterization of their combined effects is challenging. Computer models may facilitate these analyses, but no currently available model incorporates ion-channel trafficking. We introduce a new two-state ion-channel trafficking model able to reproduce a wide range of experimental data, along with the effects of modulators of Kv 11.1 channel functioning and trafficking. The model reveals complex dynamic regulation of ventricular repolarization by temperature, extracellular K+ concentration and dofetilide through opposing acute (millisecond) effects on Kv 11.1 gating and long-term (hours) modulation of Kv 11.1 trafficking. This in silico trafficking framework provides a tool to investigate the roles of acute and long-term processes on arrhythmia promotion and maintenance.

Filter inference: A scalable nonlinear mixed effects inference approach for snapshot time series data

Variability is an intrinsic property of biological systems and is often at the heart of their complex behaviour. Examples range from cell-to-cell variability in cell signalling pathways to variability in the response to treatment across patients. A popular approach to model and understand this variability is nonlinear mixed effects (NLME) modelling. However, estimating the parameters of NLME models from measurements quickly becomes computationally expensive as the number of measured individuals grows, making NLME inference intractable for datasets with thousands of measured individuals. This shortcoming is particularly limiting for snapshot datasets, common e.g. in cell biology, where high-throughput measurement techniques provide large numbers of single cell measurements. We introduce a novel approach for the estimation of NLME model parameters from snapshot measurements, which we call filter inference. Filter inference uses measurements of simulated individuals to define an approximate likelihood for the model parameters, avoiding the computational limitations of traditional NLME inference approaches and making efficient inferences from snapshot measurements possible. Filter inference also scales well with the number of model parameters, using state-of-the-art gradient-based MCMC algorithms such as the No-U-Turn Sampler (NUTS). We demonstrate the properties of filter inference using examples from early cancer growth modelling and from epidermal growth factor signalling pathway modelling.

Electrophysiological and calcium-handling development during long-term culture of human-induced pluripotent stem cell-derived cardiomyocytes

Human-induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) are increasingly used for personalised medicine and preclinical cardiotoxicity testing. Reports on hiPSC-CM commonly describe heterogenous functional readouts and underdeveloped or immature phenotypical properties. Cost-effective, fully defined monolayer culture is approaching mainstream adoption; however, the optimal age at which to utilise hiPSC-CM is unknown. In this study, we identify, track and model the dynamic developmental behaviour of key ionic currents and Ca2+-handling properties in hiPSC-CM over long-term culture (30-80 days). hiPSC-CMs > 50 days post differentiation show significantly larger ICa,L density along with an increased ICa,L-triggered Ca2+-transient. INa and IK1 densities significantly increase in late-stage cells, contributing to increased upstroke velocity and reduced action potential duration, respectively. Importantly, our in silico model of hiPSC-CM electrophysiological age dependence confirmed IK1 as the key ionic determinant of action potential shortening in older cells. We have made this model available through an open source software interface that easily allows users to simulate hiPSC-CM electrophysiology and Ca2+-handling and select the appropriate age range for their parameter of interest. This tool, together with the insights from our comprehensive experimental characterisation, could be useful in future optimisation of the culture-to-characterisation pipeline in the field of hiPSC-CM research.

Importance of modelling hERG binding in predicting drug-induced action potential prolongations for drug safety assessment

Reduction of the rapid delayed rectifier potassium current (IKr) via drug binding to the human Ether-à-go-go-Related Gene (hERG) channel is a well recognised mechanism that can contribute to an increased risk of Torsades de Pointes. Mathematical models have been created to replicate the effects of channel blockers, such as reducing the ionic conductance of the channel. Here, we study the impact of including state-dependent drug binding in a mathematical model of hERG when translating hERG inhibition to action potential changes. We show that the difference in action potential predictions when modelling drug binding of hERG using a state-dependent model versus a conductance scaling model depends not only on the properties of the drug and whether the experiment achieves steady state, but also on the experimental protocols. Furthermore, through exploring the model parameter space, we demonstrate that the state-dependent model and the conductance scaling model generally predict different action potential prolongations and are not interchangeable, while at high binding and unbinding rates, the conductance scaling model tends to predict shorter action potential prolongations. Finally, we observe that the difference in simulated action potentials between the models is determined by the binding and unbinding rate, rather than the trapping mechanism. This study demonstrates the importance of modelling drug binding and highlights the need for improved understanding of drug trapping which can have implications for the uses in drug safety assessment.

ActionPytential: An open source tool for analyzing and visualizing cardiac action potential data

The action potential forms the basis of cardiac pacemaking, conduction, and contraction. Action potentials can be recorded from numerous preparation types, including ventricular or atrial trabecules, Purkinje fibers, isolated cardiac myocytes. Numerous techniques are also available as well, such as the conventional microelectrode and the single-cell current clamp techniques, optical mapping, or in silico modeling. With such a vast array of electrophysiological methods comes an array of available hardware and software solutions. In this work, we present a software with an intuitive graphical user interface, ActionPytential, that enables the analysis of any type of cardiac action potential, regardless of acquisition method or tissue type. In most available software tools, the analysis of continuous (gap-free) recordings often requires manual user interaction to segment the individual action potentials. We provide an automated solution for this, both for slow-response and for externally paced action potentials. As of now, ActionPytential calculates 34 parameters from each action potential. The most often utilized ones, including amplitude, maximal rate of depolarization, and action potential duration values, were validated on 1200 action potentials from human, dog, rabbit, guinea pig, and rat cardiac preparations. We also provide new parameters that were previously only measurable manually, including the position and the depth of the notch in potentials showing a spike-and-dome morphology. Further notable features include a Butterworth-type low-pass filter, the averaging of multiple potentials, automated corrections for baseline drifting, aided manual analysis, high-quality plots, and batch processing for any number of potentials. ActionPytential is available for all major platforms (Windows, MacOS, GNU + Linux, BSD).

Improving the hERG model fitting using a deep learning-based method

The hERG channel is one of the essential ion channels composing the cardiac action potential and the toxicity assay for new drug. Recently, the comprehensive in vitro proarrhythmia assay (CiPA) was adopted for cardiac toxicity evaluation. One of the hurdles for this protocol is identifying the kinetic effect of the new drug on the hERG channel. This procedure included the model-based parameter identification from the experiments. There are many mathematical methods to infer the parameters; however, there are two main difficulties in fitting parameters. The first is that, depending on the data and model, parametric inference can be highly time-consuming. The second is that the fitting can fail due to local minima problems. The simplest and most effective way to solve these issues is to provide an appropriate initial value. In this study, we propose a deep learning-based method for improving model fitting by providing appropriate initial values, even the right answer. We generated the dataset by changing the model parameters and trained our deep learning-based model. To improve the accuracy, we used the spectrogram with time, frequency, and amplitude. We obtained the experimental dataset from https://github.com/CardiacModelling/hERGRapidCharacterisation. Then, we trained the deep-learning model using the data generated with the hERG model and tested the validity of the deep-learning model with the experimental data. We successfully identified the initial value, significantly improved the fitting speed, and avoided fitting failure. This method is useful when the model is fixed and reflects the real data, and it can be applied to any in silico model for various purposes, such as new drug development, toxicity identification, environmental effect, etc. This method will significantly reduce the time and effort to analyze the data.

Models of the cardiac L-type calcium current: A quantitative review

The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.

The virtual sinoatrial node: What did computational models tell us about cardiac pacemaking?

Since its discovery, the sinoatrial node (SAN) has represented a fascinating and complex matter of research. Despite over a century of discoveries, a full comprehension of pacemaking has still to be achieved. Experiments often produced conflicting evidence that was used either in support or against alternative theories, originating intense debates. In this context, mathematical descriptions of the phenomena underlying the heartbeat have grown in importance in the last decades since they helped in gaining insights where experimental evaluation could not reach. This review presents the most updated SAN computational models and discusses their contribution to our understanding of cardiac pacemaking. Electrophysiological, structural and pathological aspects - as well as the autonomic control over the SAN - are taken into consideration to reach a holistic view of SAN activity.

Grapefruit Flavonoid Naringenin Sex-Dependently Modulates Action Potential in an In Silico Human Ventricular Cardiomyocyte Model

Recent in vitro studies showed that grapefruit (Citrus × paradisi) flavonoid naringenin alters the function of cardiac ion channels. Here, we explored the effect of naringenin on cardiomyocyte action potentials (APs) using a detailed in silico model of ventricular electrophysiology. Concentration-dependent effects of naringenin on seven major cardiac ion channels were incorporated into the Tomek–Rodriguez modification of O’Hara–Rudy (ToR-ORd) human ventricular endocardium model. To investigate the sex-dependent effect of naringenin, previously reported sex-specific ionic modifications were implemented into the model. Next, populations of 1000 models accommodating intercellular variability were generated. The results show, naringenin at various concentrations prolonged AP duration (APD) in male and female cardiomyocytes. Pacing cells at higher frequencies abbreviated APD differently in males versus females; for example, at 3 Hz, 50 μM naringenin induced AP and calcium alternans only in the female cardiomyocyte. Finally, a population modeling approach corroborated that naringenin significantly prolonged APD in a concentration-dependent manner, with a larger effect in females than in males. In conclusion, our study demonstrates that the APD-prolonging effect of naringenin was larger in females, and that pacing at faster rates induces AP alternation earlier in females, suggesting a potentially higher proarrhythmic risk of naringenin in females than in males.

Ion channel model reduction using manifold boundaries

Mathematical models of voltage-gated ion channels are used in basic research, industrial and clinical settings. These models range in complexity, but typically contain numerous variables representing the proportion of channels in a given state, and parameters describing the voltage-dependent rates of transition between states. An open problem is selecting the appropriate degree of complexity and structure for an ion channel model given data availability. Here, we simplify a model of the cardiac human Ether-à-go-go related gene (hERG) potassium ion channel, which carries cardiac I_Kr, using the manifold boundary approximation method (MBAM). The MBAM approximates high-dimensional model-output manifolds by reduced models describing their boundaries, resulting in models with fewer parameters (and often variables). We produced a series of models of reducing complexity starting from an established five-state hERG model with 15 parameters. Models with up to three fewer states and eight fewer parameters were shown to retain much of the predictive capability of the full model and were validated using experimental hERG1a data collected in HEK293 cells at 37°C. The method provides a way to simplify complex models of ion channels that improves parameter identifiability and will aid in future model development.

Disruption of a Conservative Motif in the C-Terminal Loop of the KCNQ1 Channel Causes LQT Syndrome

We identified a single nucleotide variation (SNV) (c.1264A > G) in the KCNQ1 gene in a 5-year-old boy who presented with a prolonged QT interval. His elder brother and mother, but not sister and father, also had this mutation. This missense mutation leads to a p.Lys422Glu (K422E) substitution in the Kv7.1 protein that has never been mentioned before. We inserted this substitution in an expression plasmid containing Kv7.1 cDNA and studied the electrophysiological characteristics of the mutated channel expressed in CHO-K1, using the whole-cell configuration of the patch-clamp technique. Expression of the mutant Kv7.1 channel in both homo- and heterozygous conditions in the presence of auxiliary subunit KCNE1 results in a significant decrease in tail current densities compared to the expression of wild-type (WT) Kv7.1 and KCNE1. This study also indicates that K422E point mutation causes a dominant negative effect. The mutation was not associated with a trafficking defect; the mutant channel protein was confirmed to localize at the cell membrane. This mutation disrupts the poly-Lys strip in the proximal part of the highly conserved cytoplasmic A−B linker of Kv7.1 that was not shown before to be crucial for channel functioning.

cellmlmanip and chaste_codegen: automatic CellML to C++ code generation with fixes for singularities and automatically generated Jacobians

Hundreds of different mathematical models have been proposed for describing electrophysiology of various cell types. These models are quite complex (nonlinear systems of typically tens of ODEs and sometimes hundreds of parameters) and software packages such as the Cancer, Heart and Soft Tissue Environment (Chaste) C++ library have been designed to run simulations with these models in isolation or coupled to form a tissue simulation. The complexity of many of these models makes sharing and translating them to new simulation environments difficult. CellML is an XML format that offers a widely-adopted solution to this problem. This paper specifically describes the capabilities of two new Python tools: the cellmlmanip library for reading and manipulating CellML models; and chaste_codegen, a CellML to C++ converter. These tools provide a Python 3 replacement for a previous Python 2 tool (called PyCML) and they also provide additional new features that this paper describes. Most notably, they can generate analytic Jacobians without the use of proprietary software, and also find singularities occurring in equations and automatically generate and apply linear approximations to prevent numerical problems at these points.

A Parameter Representing Missing Charge Should Be Considered when Calibrating Action Potential Models

Computational models of the electrical potential across a cell membrane are longstanding and vital tools in electrophysiology research and applications. These models describe how ionic currents, internal fluxes, and buffering interact to determine membrane voltage and form action potentials (APs). Although this relationship is usually expressed as a differential equation, previous studies have shown it can be rewritten in an algebraic form, allowing direct calculation of membrane voltage. Rewriting in this form requires the introduction of a new parameter, called Γ₀ in this manuscript, which represents the net concentration of all charges that influence membrane voltage but are not considered in the model. Although several studies have examined the impact of Γ₀ on long-term stability and drift in model predictions, there has been little examination of its effects on model predictions, particularly when a model is refit to new data. In this study, we illustrate how Γ₀ affects important physiological properties such as action potential duration restitution, and examine the effects of (in)correctly specifying Γ₀ during model calibration. We show that, although physiologically plausible, the range of concentrations used in popular models leads to orders of magnitude differences in Γ₀, which can lead to very different model predictions. In model calibration, we find that using an incorrect value of Γ₀ can lead to biased estimates of the inferred parameters, but that the predictive power of these models can be restored by fitting Γ₀ as a separate parameter. These results show the value of making Γ₀ explicit in model formulations, as it forces modellers and experimenters to consider the effects of uncertainty and potential discrepancy in initial concentrations upon model predictions.

Integrative Computational Modeling of Cardiomyocyte Calcium Handling and Cardiac Arrhythmias: Current Status and Future Challenges

Cardiomyocyte calcium-handling is the key mediator of cardiac excitation-contraction coupling. In the healthy heart, calcium controls both electrical impulse propagation and myofilament cross-bridge cycling, providing synchronous and adequate contraction of cardiac muscles. However, calcium-handling abnormalities are increasingly implicated as a cause of cardiac arrhythmias. Due to the complex, dynamic and localized interactions between calcium and other molecules within a cardiomyocyte, it remains experimentally challenging to study the exact contributions of calcium-handling abnormalities to arrhythmogenesis. Therefore, multiscale computational modeling is increasingly being used together with laboratory experiments to unravel the exact mechanisms of calcium-mediated arrhythmogenesis. This article describes various examples of how integrative computational modeling makes it possible to unravel the arrhythmogenic consequences of alterations to cardiac calcium handling at subcellular, cellular and tissue levels, and discusses the future challenges on the integration and interpretation of such computational data.

Individual Contributions of Cardiac Ion Channels on Atrial Repolarization and Reentrant Waves: A Multiscale In-Silico Study

The excitation, contraction, and relaxation of an atrial cardiomyocyte are maintained by the activation and inactivation of numerous cardiac ion channels. Their collaborative efforts cause time-dependent changes of membrane potential, generating an action potential (AP), which is a surrogate marker of atrial arrhythmias. Recently, computational models of atrial electrophysiology emerged as a modality to investigate arrhythmia mechanisms and to predict the outcome of antiarrhythmic therapies. However, the individual contribution of atrial ion channels on atrial action potential and reentrant arrhythmia is not yet fully understood. Thus, in this multiscale in-silico study, perturbations of individual atrial ionic currents (I_Na, I_to, I_CaL, I_Kur, I_Kr, I_Ks, I_K1, I_NCX and I_NaK) in two in-silico models of human atrial cardiomyocyte (i.e., Courtemanche-1998 and Grandi-2011) were performed at both cellular and tissue levels. The results show that the inhibition of I_CaL and I_NCX resulted in AP shortening, while the inhibition of I_Kur, I_Kr, I_Ks, I_K1 and I_NaK prolonged AP duration (APD). Particularly, in-silico perturbations (inhibition and upregulation) of I_Kr and I_Ks only minorly affected atrial repolarization in the Grandi model. In contrast, in the Courtemanche model, the inhibition of I_Kr and I_Ks significantly prolonged APD and vice versa. Additionally, a 50% reduction of I_to density abbreviated APD in the Courtemanche model, while the same perturbation prolonged APD in the Grandi model. Similarly, a strong model dependence was also observed at tissue scale, with an observable I_K1-mediated reentry stabilizing effect in the Courtemanche model but not in the Grandi atrial model. Moreover, the Grandi model was highly sensitive to a change on intracellular Ca²⁺ concentration, promoting a repolarization failure in I_CaL upregulation above 150% and facilitating reentrant spiral waves stabilization by I_CaL inhibition. Finally, by incorporating the previously published atrial fibrillation (AF)-associated ionic remodeling in the Courtemanche atrial model, in-silico modeling revealed the antiarrhythmic effect of I_Kr inhibition in both acute and chronic settings. Overall, our multiscale computational study highlights the strong model-dependent effects of ionic perturbations which could affect the model’s accuracy, interpretability, and prediction. This observation also suggests the need for a careful selection of in-silico models of atrial electrophysiology to achieve specific research aims.

Spatiotemporal approximation of cardiac activation and recovery isochrones

BACKGROUND

The sequence of myocardial activation and recovery can be studied in detail by invasive catheter recordings of cardiac electrograms (EGMs), or noninvasive inverse reconstructions thereof with electrocardiographic imaging (ECGI). Local activation and recovery times are obtained from a unipolar EGM by the moment of maximum downslope of the QRS complex or maximum upslope of the T wave, respectively. However, both invasive and noninvasive recordings of intracardiac EGMs may suffer from noise and fractionation, making reliable detection of these deflections nontrivial.

METHODS

Here, we introduce a novel method that benefits from the spatial coupling of these processes, and incorporate not only the temporal EGM deflection, but also the spatial gradients. We validated this approach in computer simulations, in animal data with ECGI and invasive electrode recordings, and illustrated its use in a clinical case.

RESULTS

In the simulated data, the spatiotemporal approach was able to incorporate spatial information to better select the correct deflection in artificially fractionated EGMs and outperformed the traditional temporal-only method. In experimental data, the accuracy of time estimation from ECGI compared to invasive recordings significantly increased from R = 0.73 (activation) and R = 0.58 (recovery) with the temporal-only method to R = 0.79 (activation) and R = 0.72 (recovery) with the novel approach. Localization of the pacing origin of paced beats improved significantly from 36 mm mean error with the temporal-only approach to 23 mm with the spatiotemporal approach.

CONCLUSION

The spatiotemporal method to compute activation and recovery times from EGMs outperformed the traditional temporal-only approach in which spatial information was not taken into account.

chaste codegen: automatic CellML to C++ code generation with fixes for singularities and automatically generated Jacobians

Hundreds of different mathematical models have been proposed for describing electrophysiology of various cell types. These models are quite complex (nonlinear systems of typically tens of ODEs and sometimes hundreds of parameters) and software packages such as the Cancer, Heart and Soft Tissue Environment (Chaste) C++ library have been designed to run simulations with these models in isolation or coupled to form a tissue simulation. The complexity of many of these models makes sharing and translating them to new simulation environments difficult. CellML is an XML format that offers a solution to this problem and has been widely-adopted. This paper specifically describes the capabilities of chaste_codegen, a Python-based CellML to C++ converter based on the new cellmlmanip Python library for reading and manipulating CellML models. While chaste_codegen is a Python 3 redevelopment of a previous Python 2 tool (called PyCML) it has some additional new features that this paper describes. Most notably, chaste_codegen has the ability to generate analytic Jacobians without the use of proprietary software, and also to find singularities occurring in equations and automatically generate and apply linear approximations to prevent numerical problems at these points.

The openCARP simulation environment for cardiac electrophysiology

BACKGROUND AND OBJECTIVE

Cardiac electrophysiology is a medical specialty with a long and rich tradition of computational modeling. Nevertheless, no community standard for cardiac electrophysiology simulation software has evolved yet. Here, we present the openCARP simulation environment as one solution that could foster the needs of large parts of this community.

METHODS AND RESULTS

openCARP and the Python-based carputils framework allow developing and sharing simulation pipelines which automate in silico experiments including all modeling and simulation steps to increase reproducibility and productivity. The continuously expanding openCARP user community is supported by tailored infrastructure. Documentation and training material facilitate access to this complementary research tool for new users. After a brief historic review, this paper summarizes requirements for a high-usability electrophysiology simulator and describes how openCARP fulfills them. We introduce the openCARP modeling workflow in a multi-scale example of atrial fibrillation simulations on single cell, tissue, organ and body level and finally outline future development potential.

CONCLUSION

As an open simulator, openCARP can advance the computational cardiac electrophysiology field by making state-of-the-art simulations accessible. In combination with the carputils framework, it offers a tailored software solution for the scientific community and contributes towards increasing use, transparency, standardization and reproducibility of in silico experiments.

Real-Time Interactive Simulations of Complex Ionic Cardiac Cell Models in 2D and 3D Heart Structures with GPUs on Personal Computers

AIMS

Cardiac modeling in heart structures for the study of arrhythmia mechanisms requires the use of software that runs on supercomputers. Therefore, computational studies are limited to groups with access to computer clusters and personnel with high-performance computing experience. We present how to use and implement WebGL programs via a custom-written library to run and visualize simulations of the most complex ionic models in 2D and 3D, in real time, interactively using the multi-core GPU of a single computer.

METHODS

We use Abubu.js, a library we developed for solving partial differential equations such as those describing crystal growth and fluid flow, along with a newly implemented visualization algorithm, to simulate complex ionic cell models. By combining this library with JavaScript, we allow direct real-time interactions with simulations. We implemented: 1) modification of any model parameters and equations at any time, with direct access to the code while it runs, 2) electrode stimulation anywhere in the 2D/3D tissue with a mouse click, 3) saving the solution of the system at any time to re-initiate the dynamics from saved initial conditions, and 4) rotation/visualization of 3D structures at any angle.

RESULTS

As examples of this modeling platform, we implemented a phenomenological cell model and the human ventricular OVVR model (41 variables). In 2D we illustrate the dynamics in an annulus, disk, and square tissue; in 2D and 3D porcine ventricles, we show the initiation of functional/anatomical reentry, spiral wave dynamics in different regimes, initiation of early afterdepolarizations (EADs), and the effects of model parameter variations in real time.

CONCLUSIONS

We present the first simulations of complex models in anatomical structures with enhanced visualization and extended interactivity that run on a single PC, without software downloads, and as fast as in real-time even for 3D full ventricles.

Sex Differences in Drug-Induced Arrhythmogenesis

The electrical activity in the heart varies significantly between men and women and results in a sex-specific response to drugs. Recent evidence suggests that women are more than twice as likely as men to develop drug-induced arrhythmia with potentially fatal consequences. Yet, the sex-specific differences in drug-induced arrhythmogenesis remain poorly understood. Here we integrate multiscale modeling and machine learning to gain mechanistic insight into the sex-specific origin of drug-induced cardiac arrhythmia at differing drug concentrations. To quantify critical drug concentrations in male and female hearts, we identify the most important ion channels that trigger male and female arrhythmogenesis, and create and train a sex-specific multi-fidelity arrhythmogenic risk classifier. Our study reveals that sex differences in ion channel activity, tissue conductivity, and heart dimensions trigger longer QT-intervals in women than in men. We quantify the critical drug concentration for dofetilide, a high risk drug, to be seven times lower for women than for men. Our results emphasize the importance of including sex as an independent biological variable in risk assessment during drug development. Acknowledging and understanding sex differences in drug safety evaluation is critical when developing novel therapeutic treatments on a personalized basis. The general trends of this study have significant implications on the development of safe and efficacious new drugs and the prescription of existing drugs in combination with other drugs.

Electrophysiological characterization of the hERG R56Q LQTS variant and targeted rescue by the activator RPR260243

Human Ether-à-go-go (hERG) channels contribute to cardiac repolarization, and inherited variants or drug block are associated with long QT syndrome type 2 (LQTS2) and arrhythmia. Therefore, hERG activator compounds present a therapeutic opportunity for targeted treatment of LQTS. However, a limiting concern is over-activation of hERG resurgent current during the action potential and abbreviated repolarization. Activators that slow deactivation gating (type I), such as RPR260243, may enhance repolarizing hERG current during the refractory period, thus ameliorating arrhythmogenicity with reduced early repolarization risk. Here, we show that, at physiological temperature, RPR260243 enhances hERG channel repolarizing currents conducted in the refractory period in response to premature depolarizations. This occurs with little effect on the resurgent hERG current during the action potential. The effects of RPR260243 were particularly evident in LQTS2-associated R56Q mutant channels, whereby RPR260243 restored WT-like repolarizing drive in the early refractory period and diastolic interval, combating attenuated protective currents. In silico kinetic modeling of channel gating predicted little effect of the R56Q mutation on hERG current conducted during the action potential and a reduced repolarizing protection against afterdepolarizations in the refractory period and diastolic interval, particularly at higher pacing rates. These simulations predicted partial rescue from the arrhythmic effects of R56Q by RPR260243 without risk of early repolarization. Our findings demonstrate that the pathogenicity of some hERG variants may result from reduced repolarizing protection during the refractory period and diastolic interval with limited effect on action potential duration, and that the hERG channel activator RPR260243 may provide targeted antiarrhythmic potential in these cases.

Characteristics of mathematical modeling languages that facilitate model reuse in systems biology: a software engineering perspective

Reuse of mathematical models becomes increasingly important in systems biology as research moves toward large, multi-scale models composed of heterogeneous subcomponents. Currently, many models are not easily reusable due to inflexible or confusing code, inappropriate languages, or insufficient documentation. Best practice suggestions rarely cover such low-level design aspects. This gap could be filled by software engineering, which addresses those same issues for software reuse. We show that languages can facilitate reusability by being modular, human-readable, hybrid (i.e., supporting multiple formalisms), open, declarative, and by supporting the graphical representation of models. Modelers should not only use such a language, but be aware of the features that make it desirable and know how to apply them effectively. For this reason, we compare existing suitable languages in detail and demonstrate their benefits for a modular model of the human cardiac conduction system written in Modelica.

Immediate and Delayed Response of Simulated Human Atrial Myocytes to Clinically-Relevant Hypokalemia

Although plasma electrolyte levels are quickly and precisely regulated in the mammalian cardiovascular system, even small transient changes in K⁺, Na⁺, Ca²⁺, and/or Mg²⁺ can significantly alter physiological responses in the heart, blood vessels, and intrinsic (intracardiac) autonomic nervous system. We have used mathematical models of the human atrial action potential (AP) to explore the electrophysiological mechanisms that underlie changes in resting potential (V_r) and the AP following decreases in plasma K⁺, [K⁺]_o, that were selected to mimic clinical hypokalemia. Such changes may be associated with arrhythmias and are commonly encountered in patients (i) in therapy for hypertension and heart failure; (ii) undergoing renal dialysis; (iii) with any disease with acid-base imbalance; or (iv) post-operatively. Our study emphasizes clinically-relevant hypokalemic conditions, corresponding to [K⁺]_o reductions of approximately 1.5 mM from the normal value of 4 to 4.5 mM. We show how the resulting electrophysiological responses in human atrial myocytes progress within two distinct time frames: (i) Immediately after [K⁺]_o is reduced, the K⁺-sensing mechanism of the background inward rectifier current (I_K1) responds. Specifically, its highly non-linear current-voltage relationship changes significantly as judged by the voltage dependence of its region of outward current. This rapidly alters, and sometimes even depolarizes, V_r and can also markedly prolong the final repolarization phase of the AP, thus modulating excitability and refractoriness. (ii) A second much slower electrophysiological response (developing 5-10 minutes after [K⁺]_o is reduced) results from alterations in the intracellular electrolyte balance. A progressive shift in intracellular [Na⁺]_i causes a change in the outward electrogenic current generated by the Na⁺/K⁺ pump, thereby modifying V_r and AP repolarization and changing the human atrial electrophysiological substrate. In this study, these two effects were investigated quantitatively, using seven published models of the human atrial AP. This highlighted the important role of I_K1 rectification when analyzing both the mechanisms by which [K⁺]_o regulates V_r and how the AP waveform may contribute to "trigger" mechanisms within the proarrhythmic substrate. Our simulations complement and extend previous studies aimed at understanding key factors by which decreases in [K⁺]_o can produce effects that are known to promote atrial arrhythmias in human hearts.

Cellular Mechanisms of the Anti-Arrhythmic Effect of Cardiac PDE2 Overexpression

Background: Phosphodiesterases (PDE) critically regulate myocardial cAMP and cGMP levels. PDE2 is stimulated by cGMP to hydrolyze cAMP, mediating a negative crosstalk between both pathways. PDE2 upregulation in heart failure contributes to desensitization to β-adrenergic overstimulation. After isoprenaline (ISO) injections, PDE2 overexpressing mice (PDE2 OE) were protected against ventricular arrhythmia. Here, we investigate the mechanisms underlying the effects of PDE2 OE on susceptibility to arrhythmias. Methods: Cellular arrhythmia, ion currents, and Ca²⁺-sparks were assessed in ventricular cardiomyocytes from PDE2 OE and WT littermates. Results: Under basal conditions, action potential (AP) morphology were similar in PDE2 OE and WT. ISO stimulation significantly increased the incidence of afterdepolarizations and spontaneous APs in WT, which was markedly reduced in PDE2 OE. The ISO-induced increase in I_CaL seen in WT was prevented in PDE2 OE. Moreover, the ISO-induced, Epac- and CaMKII-dependent increase in I_NaL and Ca²⁺-spark frequency was blunted in PDE2 OE, while the effect of direct Epac activation was similar in both groups. Finally, PDE2 inhibition facilitated arrhythmic events in ex vivo perfused WT hearts after reperfusion injury. Conclusion: Higher PDE2 abundance protects against ISO-induced cardiac arrhythmia by preventing the Epac- and CaMKII-mediated increases of cellular triggers. Thus, activating myocardial PDE2 may represent a novel intracellular anti-arrhythmic therapeutic strategy in HF.

Novel insights into the electrophysiology of murine cardiac macrophages: relevance of voltage-gated potassium channels

AIMS

Macrophages (MΦ), known for immunological roles such as phagocytosis and antigen presentation, have been found to electrotonically couple to cardiomyocytes (CM) of the atrio-ventricular node via Cx43, affecting cardiac conduction in isolated mouse hearts. Here, we characterise passive and active electrophysiological properties of murine cardiac resident MΦ, and model their potential electrophysiological relevance for CM.

METHODS AND RESULTS

We combined classic electrophysiological approaches with 3 D florescence imaging, RNA-sequencing, pharmacological interventions and computer simulations. We used Cx3cr1eYFP/+ mice wherein cardiac MΦ were fluorescently labelled. FACS-purified fluorescent MΦ from mouse hearts were studied by whole-cell patch-clamp. MΦ electrophysiological properties include: membrane resistance 2.2 ± 0.1 GΩ (all data mean±SEM), capacitance 18.3 ± 0.1 pF, resting membrane potential -39.6 ± 0.3 mV, and several voltage-activated, outward or inwardly-rectifying potassium currents. Using ion channel blockers (barium, TEA, 4-AP, margatoxin, XEN-D0103, DIDS), flow cytometry, immuno-staining and RNA-sequencing, we identified Kv1.3, Kv1.5 and Kir2.1 as channels contributing to observed ion currents. MΦ displayed four patterns for outward and two for inward-rectifier potassium currents. Additionally, MΦ showed surface expression of Cx43, a prerequisite for homo- and/or heterotypic electrotonic coupling. Experimental results fed into development of an original computational model to describe cardiac MΦ electrophysiology. Computer simulations to quantitatively assess plausible effects of MΦ on electrotonically coupled CM showed that MΦ can depolarise resting CM, shorten early and prolong late action potential duration, with effects depending on coupling strength and individual MΦ electrophysiological properties, in particular resting membrane potential and presence/absence of Kir2.1.

CONCLUSIONS

Our results provide a first electrophysiological characterisation of cardiac resident MΦ, and a computational model to quantitatively explore their relevance in the heterocellular heart. Future work will be focussed at distinguishing electrophysiological effects of MΦ-CM coupling on both cell types during steady-state and in patho-physiological remodelling, when immune cells change their phenotype, proliferate, and/or invade from external sources.

TRANSLATIONAL PERSPECTIVE

Cardiac tissue contains resident macrophages (MΦ) which, beyond immunological and housekeeping roles, have been found to electrotonically couple via connexins to cardiomyocytes (CM), stabilising atrio-ventricular conduction at high excitation rates. Here, we characterise structure and electrophysiological function of murine cardiac MΦ and provide a computational model to quantitatively probe the potential relevance of MΦ-CM coupling for cardiac electrophysiology. We find that MΦ are unlikely to have major electrophysiological effects in normal tissue, where they would hasten early and slow late CM-repolarisation. Further work will address potential arrhythmogenicity of MΦ in patho-physiologically remodelled tissue containing elevated MΦ-numbers, incl. non-resident recruited cells.

Evolution of mathematical models of cardiomyocyte electrophysiology

Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.

Caveolin3 Stabilizes McT1-Mediated Lactate/Proton Transport in Cardiomyocytes

[Figure: see text].

Beta-Adrenergic Receptor Stimulation Modulates the Cellular Proarrhythmic Effects of Chloroquine and Azithromycin

The antimalarial drug, chloroquine (CQ), and antimicrobial drug, azithromycin (AZM), have received significant attention during the COVID-19 pandemic. Both drugs can alter cardiac electrophysiology and have been associated with drug-induced arrhythmias. Meanwhile, sympathetic activation is commonly observed during systemic inflammation and oxidative stress (e.g., in SARS-CoV-2 infection) and may influence the electrophysiological effects of CQ and AZM. Here, we investigated the effect of beta-adrenergic stimulation on proarrhythmic properties of CQ and AZM using detailed in silico models of ventricular electrophysiology. Concentration-dependent alterations in ion-channel function were incorporated into the Heijman canine and O’Hara-Rudy human ventricular cardiomyocyte models. Single and combined drug effects on action-potential (AP) properties were analyzed using a population of 1,000 models accommodating inter-individual variability. Sympathetic stimulation was simulated by increasing pacing rate and experimentally validated isoproterenol (ISO)-induced changes in ion-channel function. In the canine ventricular model at 1 Hz pacing, therapeutic doses of CQ and AZM (5 and 20 μM, respectively) individually prolonged AP duration (APD) by 33 and 13%. Their combination produced synergistic APD prolongation (+161%) with incidence of proarrhythmic early afterdepolarizations in 53.5% of models. Increasing the pacing frequency to 2 Hz shortened APD and together with 1 μM ISO counteracted the drug-induced APD prolongation. No afterdepolarizations occurred following increased rate and simulated application of ISO. Similarly, CQ and AZM individually prolonged APD by 43 and 29% in the human ventricular cardiomyocyte model, while their combination prolonged APD by 76% without causing early afterdepolarizations. Consistently, 1 μM ISO at 2 Hz pacing counteracted the drug-induced APD prolongation. Increasing the I_Ca,L window current produced afterdepolarizations, which were exacerbated by ISO. In both models, reduced extracellular K⁺ reduced the repolarization reserve and increased drug effects. In conclusion, CQ- and AZM-induced proarrhythmia is promoted by conditions with reduced repolarization reserve. Sympathetic stimulation limits drug-induced APD prolongation, suggesting the potential importance of heart rate and autonomic status monitoring in particular conditions (e.g., COVID-19).

Acute effects of alcohol on cardiac electrophysiology and arrhythmogenesis: Insights from multiscale in silico analyses

Acute excessive ethyl alcohol (ethanol) consumption alters cardiac electrophysiology and can evoke cardiac arrhythmias, e.g., in 'holiday heart syndrome'. Ethanol acutely modulates numerous targets in cardiomyocytes, including ion channels, Ca²⁺-handling proteins and gap junctions. However, the mechanisms underlying ethanol-induced arrhythmogenesis remain incompletely understood and difficult to study experimentally due to the multiple electrophysiological targets involved and their potential interactions with preexisting electrophysiological or structural substrates. Here, we employed cellular- and tissue-level in-silico analyses to characterize the acute effects of ethanol on cardiac electrophysiology and arrhythmogenesis. Acute electrophysiological effects of ethanol were incorporated into human atrial and ventricular cardiomyocyte computer models: reduced I_Na, I_Ca,L, I_to, I_Kr and I_Kur, dual effects on I_K1 and I_K,ACh (inhibition at low and augmentation at high concentrations), and increased I_NCX and SR Ca²⁺ leak. Multiscale simulations in the absence or presence of preexistent atrial fibrillation or heart-failure-related remodeling demonstrated that low ethanol concentrations prolonged atrial action-potential duration (APD) without effects on ventricular APD. Conversely, high ethanol concentrations abbreviated atrial APD and prolonged ventricular APD. High ethanol concentrations promoted reentry in tissue simulations, but the extent of reentry promotion was dependent on the presence of altered intercellular coupling, and the degree, type, and pattern of fibrosis. Taken together, these data provide novel mechanistic insight into the potential proarrhythmic interactions between a preexisting substrate and acute changes in cardiac electrophysiology. In particular, acute ethanol exposure has concentration-dependent electrophysiological effects that differ between atria and ventricles, and between healthy and diseased hearts. Low concentrations of ethanol can have anti-fibrillatory effects in atria, whereas high concentrations promote the inducibility and maintenance of reentrant atrial and ventricular arrhythmias, supporting a role for limiting alcohol intake as part of cardiac arrhythmia management.

Calibration of ionic and cellular cardiac electrophysiology models

Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

Reducing complexity and unidentifiability when modelling human atrial cells

Mathematical models of a cellular action potential (AP) in cardiac modelling have become increasingly complex, particularly in gating kinetics, which control the opening and closing of individual ion channel currents. As cardiac models advance towards use in personalized medicine to inform clinical decision-making, it is critical to understand the uncertainty hidden in parameter estimates from their calibration to experimental data. This study applies approximate Bayesian computation to re-calibrate the gating kinetics of four ion channels in two existing human atrial cell models to their original datasets, providing a measure of uncertainty and indication of potential issues with selecting a single unique value given the available experimental data. Two approaches are investigated to reduce the uncertainty present: re-calibrating the models to a more complete dataset and using a less complex formulation with fewer parameters to constrain. The re-calibrated models are inserted back into the full cell model to study the overall effect on the AP. The use of more complete datasets does not eliminate uncertainty present in parameter estimates. The less complex model, particularly for the fast sodium current, gave a better fit to experimental data alongside lower parameter uncertainty and improved computational speed. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Considering discrepancy when calibrating a mechanistic electrophysiology model

Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions-that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-moving-average models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Accounting for variability in ion current recordings using a mathematical model of artefacts in voltage-clamp experiments

Mathematical models of ion channels, which constitute indispensable components of action potential models, are commonly constructed by fitting to whole-cell patch-clamp data. In a previous study, we fitted cell-specific models to hERG1a (Kv11.1) recordings simultaneously measured using an automated high-throughput system, and studied cell-cell variability by inspecting the resulting model parameters. However, the origin of the observed variability was not identified. Here, we study the source of variability by constructing a model that describes not just ion current dynamics, but the entire voltage-clamp experiment. The experimental artefact components of the model include: series resistance, membrane and pipette capacitance, voltage offsets, imperfect compensations made by the amplifier for these phenomena, and leak current. In this model, variability in the observations can be explained by either cell properties, measurement artefacts, or both. Remarkably, by assuming that variability arises exclusively from measurement artefacts, it is possible to explain a larger amount of the observed variability than when assuming cell-specific ion current kinetics. This assumption also leads to a smaller number of model parameters. This result suggests that most of the observed variability in patch-clamp data measured under the same conditions is caused by experimental artefacts, and hence can be compensated for in post-processing by using our model for the patch-clamp experiment. This study has implications for the question of the extent to which cell-cell variability in ion channel kinetics exists, and opens up routes for better correction of artefacts in patch-clamp data. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Reducing complexity and unidentifiability when modelling human atrial cells

Mathematical models of a cellular action potential (AP) in cardiac modelling have become increasingly complex, particularly in gating kinetics, which control the opening and closing of individual ion channel currents. As cardiac models advance towards use in personalized medicine to inform clinical decision-making, it is critical to understand the uncertainty hidden in parameter estimates from their calibration to experimental data. This study applies approximate Bayesian computation to re-calibrate the gating kinetics of four ion channels in two existing human atrial cell models to their original datasets, providing a measure of uncertainty and indication of potential issues with selecting a single unique value given the available experimental data. Two approaches are investigated to reduce the uncertainty present: re-calibrating the models to a more complete dataset and using a less complex formulation with fewer parameters to constrain. The re-calibrated models are inserted back into the full cell model to study the overall effect on the AP. The use of more complete datasets does not eliminate uncertainty present in parameter estimates. The less complex model, particularly for the fast sodium current, gave a better fit to experimental data alongside lower parameter uncertainty and improved computational speed. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Self-restoration of cardiac excitation rhythm by anti-arrhythmic ion channel gating

Homeostatic regulation protects organisms against hazardous physiological changes. However, such regulation is limited in certain organs and associated biological processes. For example, the heart fails to self-restore its normal electrical activity once disturbed, as with sustained arrhythmias. Here we present proof-of-concept of a biological self-restoring system that allows automatic detection and correction of such abnormal excitation rhythms. For the heart, its realization involves the integration of ion channels with newly designed gating properties into cardiomyocytes. This allows cardiac tissue to i) discriminate between normal rhythm and arrhythmia based on frequency-dependent gating and ii) generate an ionic current for termination of the detected arrhythmia. We show in silico, that for both human atrial and ventricular arrhythmias, activation of these channels leads to rapid and repeated restoration of normal excitation rhythm. Experimental validation is provided by injecting the designed channel current for arrhythmia termination in human atrial myocytes using dynamic clamp.

In-silico analysis of aging mechanisms of action potential remodeling in human atrial cardiomyocites

Electrophysiology of cardiomyocytes changes with aging. Agerelated ionic remodeling in cardiomyocytes may increase the incidence and prevalence of atrial fibrillation (AF) in the elderly and affect the efficiency of antiarrhythmic drugs. There is the deep lack of experimental data on an action potential and transmembrane currents recorded in the healthy human cardiomyocytes of different age. Experimental data in mammals is also incomplete and often contradicting depending on the experimental conditions. In this in-silico study, we used a population of ionic models of human atrial cardiomyocytes to transfer data on the age- related ionic remodeling in atrial cardiomyocytes from canines and mice to predict possible consequences for human cardiomyocyte activity. Based on experimental data, we analyzes two hypotheses on the aging effect on the ionic currents using two age-related sets of varied model parameters and evaluated corresponding changes in action potential morphology with aging. Using the two populations of aging models, we analyzed the agedependent sensitivity of atrial cardiomyocytes to Dofetilide which is one of the antiarrhythmic drugs widely used in patients with atrial fibrillation.

Temporal irregularity quantification and mapping of optical action potentials using wave morphology similarity

Background

Cardiac optical mapping enables direct and high spatio-temporal resolution recording of action potential (AP) morphology. Temporal alterations in AP morphology are both predictive and consequent of arrhythmia. Here we sought to test if methods that quantify regularity of recorded waveforms could be applied to detect and quantify periods of temporal instability in optical mapping datasets in a semi-automated, user-unbiased manner.

Methods and results

We developed, tested and applied algorithms to quantify optical wave similarity (OWS) to study morphological temporal similarity of optically recorded APs. Unlike other measures (e.g. alternans ratio, beat-to-beat variability, arrhythmia scoring), the quantification of OWS is achieved without a restrictive definition of specific signal points/features and is instead derived by analysing the complete morphology from the entire AP waveform.

Using model datasets, we validated the ability of OWS to measure changes in AP morphology, and tested OWS mapping in guinea pig hearts and mouse atria. OWS successfully detected and measured alterations in temporal regularity in response to several proarrhythmic stimuli, including alterations in pacing frequency, premature contractions, alternans and ventricular fibrillation.

Conclusion

OWS mapping provides an effective measure of temporal regularity that can be applied to optical datasets to detect and quantify temporal alterations in action potential morphology. This methodology provides a new metric for arrhythmia inducibility and scoring in optical mapping datasets.

Development, calibration, and validation of a novel human ventricular myocyte model in health, disease, and drug block

Human-based modelling and simulations are becoming ubiquitous in biomedical science due to their ability to augment experimental and clinical investigations. Cardiac electrophysiology is one of the most advanced areas, with cardiac modelling and simulation being considered for virtual testing of pharmacological therapies and medical devices. Current models present inconsistencies with experimental data, which limit further progress. In this study, we present the design, development, calibration and independent validation of a human-based ventricular model (ToR-ORd) for simulations of electrophysiology and excitation-contraction coupling, from ionic to whole-organ dynamics, including the electrocardiogram. Validation based on substantial multiscale simulations supports the credibility of the ToR-ORd model under healthy and key disease conditions, as well as drug blockade. In addition, the process uncovers new theoretical insights into the biophysical properties of the L-type calcium current, which are critical for sodium and calcium dynamics. These insights enable the reformulation of L-type calcium current, as well as replacement of the hERG current model.

Four Ways to Fit an Ion Channel Model

Mathematical models of ionic currents are used to study the electrophysiology of the heart, brain, gut, and several other organs. Increasingly, these models are being used predictively in the clinic, for example, to predict the risks and results of genetic mutations, pharmacological treatments, or surgical procedures. These safety-critical applications depend on accurate characterization of the underlying ionic currents. Four different methods can be found in the literature to fit voltage-sensitive ion channel models to whole-cell current measurements: method 1, fitting model equations directly to time-constant, steady-state, and I-V summary curves; method 2, fitting by comparing simulated versions of these summary curves to their experimental counterparts; method 3, fitting to the current traces themselves from a range of protocols; and method 4, fitting to a single current trace from a short and rapidly fluctuating voltage-clamp protocol. We compare these methods using a set of experiments in which hERG1a current was measured in nine Chinese hamster ovary cells. In each cell, the same sequence of fitting protocols was applied, as well as an independent validation protocol. We show that methods 3 and 4 provide the best predictions on the independent validation set and that short, rapidly fluctuating protocols like that used in method 4 can replace much longer conventional protocols without loss of predictive ability. Although data for method 2 are most readily available from the literature, we find it performs poorly compared to methods 3 and 4 both in accuracy of predictions and computational efficiency. Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in safety-critical applications.

Rapid Characterization of hERG Channel Kinetics II: Temperature Dependence

Ion channel behavior can depend strongly on temperature, with faster kinetics at physiological temperatures leading to considerable changes in currents relative to room temperature. These temperature-dependent changes in voltage-dependent ion channel kinetics (rates of opening, closing, inactivating, and recovery) are commonly represented with Q₁₀ coefficients or an Eyring relationship. In this article, we assess the validity of these representations by characterizing channel kinetics at multiple temperatures. We focus on the human Ether-à-go-go-Related Gene (hERG) channel, which is important in drug safety assessment and commonly screened at room temperature so that results require extrapolation to physiological temperature. In Part I of this study, we established a reliable method for high-throughput characterization of hERG1a (Kv11.1) kinetics, using a 15-second information-rich optimized protocol. In this Part II, we use this protocol to study the temperature dependence of hERG kinetics using Chinese hamster ovary cells overexpressing hERG1a on the Nanion SyncroPatch 384PE, a 384-well automated patch-clamp platform, with temperature control. We characterize the temperature dependence of hERG gating by fitting the parameters of a mathematical model of hERG kinetics to data obtained at five distinct temperatures between 25 and 37°C and validate the models using different protocols. Our models reveal that activation is far more temperature sensitive than inactivation, and we observe that the temperature dependency of the kinetic parameters is not represented well by Q₁₀ coefficients; it broadly follows a generalized, but not the standardly-used, Eyring relationship. We also demonstrate that experimental estimations of Q₁₀ coefficients are protocol dependent. Our results show that a direct fit using our 15-s protocol best represents hERG kinetics at any given temperature and suggests that using the Generalized Eyring theory is preferable if no experimental data are available to derive model parameters at a given temperature.