Improving cardiomyocyte model fidelity and utility via dynamic electrophysiology protocols and optimization algorithms

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.

Creating cell-specific computational models of stem cell-derived cardiomyocytes using optical experiments

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) have gained traction as a powerful model in cardiac disease and therapeutics research, since iPSCs are self-renewing and can be derived from healthy and diseased patients without invasive surgery. However, current iPSC-CM differentiation methods produce cardiomyocytes with immature, fetal-like electrophysiological phenotypes, and the variety of maturation protocols in the literature results in phenotypic differences between labs. Heterogeneity of iPSC donor genetic backgrounds contributes to additional phenotypic variability. Several mathematical models of iPSC-CM electrophysiology have been developed to help understand the ionic underpinnings of, and to simulate, various cell responses, but these models individually do not capture the phenotypic variability observed in iPSC-CMs. Here, we tackle these limitations by developing a computational pipeline to calibrate cell preparation-specific iPSC-CM electrophysiological parameters. We used the genetic algorithm (GA), a heuristic parameter calibration method, to tune ion channel parameters in a mathematical model of iPSC-CM physiology. To systematically optimize an experimental protocol that generates sufficient data for parameter calibration, we created simulated datasets by applying various protocols to a population of in silico cells with known conductance variations, and we fitted to those datasets. We found that calibrating models to voltage and calcium transient data under 3 varied experimental conditions, including electrical pacing combined with ion channel blockade and changing buffer ion concentrations, improved model parameter estimates and model predictions of unseen channel block responses. This observation held regardless of whether the fitted data were normalized, suggesting that normalized fluorescence recordings, which are more accessible and higher throughput than patch clamp recordings, could sufficiently inform conductance parameters. Therefore, this computational pipeline can be applied to different iPSC-CM preparations to determine cell line-specific ion channel properties and understand the mechanisms behind variability in perturbation responses.

Computational Modeling of Cardiac Electrophysiology

Mathematical modeling and simulation are well-established and powerful tools to integrate experimental data of individual components of cardiac electrophysiology, excitation-contraction coupling, and regulatory signaling pathways, to gain quantitative and mechanistic insight into pathophysiological processes and guide therapeutic strategies. Here, we briefly describe the processes governing cardiac myocyte electrophysiology and Ca2+ handling and their regulation, as well as action potential propagation in tissue. We discuss the models and methods used to describe these phenomena, including procedures for model parameterization and validation, in addition to protocols for model interrogation and analysis and techniques that account for phenotypic variability and parameter uncertainty. Our objective is to provide a summary of basic concepts and approaches as a resource for scientists training in this discipline and for all researchers aiming to gain an understanding of cardiac modeling studies.

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.

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.

Gradient-based parameter optimization method to determine membrane ionic current composition in human induced pluripotent stem cell-derived cardiomyocytes

Premature cardiac myocytes derived from human induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), probably due to different expression patterns of membrane ionic currents. We developed a method for determining expression patterns of functional channels in terms of whole-cell ionic conductance (G_x) using individual spontaneous AP configurations. It has been suggested that apparently identical AP configurations can be obtained using different sets of ionic currents in mathematical models of cardiac membrane excitation. If so, the inverse problem of G_x estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For a realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output of AP on each experimental AP recorded by conventional manual adjustment of G_xs of the baseline model. G_xs of 4-6 major ionic currents of the 'cell-specific models' were randomized within a range of ± 5-15% and used as an initial parameter set for the gradient-based automatic G_xs recovery by decreasing the mean square error (MSE) between the target and model output. Plotting all data points of the MSE-G_x relationship during optimization revealed progressive convergence of the randomized population of G_xs to the original value of the cell-specific model with decreasing MSE. The absence of any other local minimum in the global search space was confirmed by mapping the MSE by randomizing G_xs over a range of 0.1-10 times the control. No additional local minimum MSE was obvious in the whole parameter space, in addition to the global minimum of MSE at the default model parameter.

Pro-Arrhythmic Effects of Discontinuous Conduction at the Purkinje Fiber-Ventricle Junction Arising From Heart Failure-Induced Ionic Remodeling - Insights From Computational Modelling

Heart failure is associated with electrical remodeling of the electrical properties and kinetics of the ion channels and transporters that are responsible for cardiac action potentials. However, it is still unclear whether heart failure-induced ionic remodeling can affect the conduction of excitation waves at the Purkinje fiber-ventricle junction contributing to pro-arrhythmic effects of heart failure, as the complexity of the heart impedes a detailed experimental analysis. The aim of this study was to employ computational models to investigate the pro-arrhythmic effects of heart failure-induced ionic remodeling on the cardiac action potentials and excitation wave conduction at the Purkinje fiber-ventricle junction. Single cell models of canine Purkinje fiber and ventricular myocytes were developed for control and heart failure. These single cell models were then incorporated into one-dimensional strand and three-dimensional wedge models to investigate the effects of heart failure-induced remodeling on propagation of action potentials in Purkinje fiber and ventricular tissue and at the Purkinje fiber-ventricle junction. This revealed that heart failure-induced ionic remodeling of Purkinje fiber and ventricular tissue reduced conduction safety and increased tissue vulnerability to the genesis of the unidirectional conduction block. This was marked at the Purkinje fiber-ventricle junction, forming a potential substrate for the genesis of conduction failure that led to re-entry. This study provides new insights into proarrhythmic consequences of heart failure-induced ionic remodeling.

Bayesian Calibration of Electrophysiology Models Using Restitution Curve Emulators

Calibration of cardiac electrophysiology models is a fundamental aspect of model personalization for predicting the outcomes of cardiac therapies, simulation testing of device performance for a range of phenotypes, and for fundamental research into cardiac function. Restitution curves provide information on tissue function and can be measured using clinically feasible measurement protocols. We introduce novel "restitution curve emulators" as probabilistic models for performing model exploration, sensitivity analysis, and Bayesian calibration to noisy data. These emulators are built by decomposing restitution curves using principal component analysis and modeling the resulting coordinates with respect to model parameters using Gaussian processes. Restitution curve emulators can be used to study parameter identifiability via sensitivity analysis of restitution curve components and rapid inference of the posterior distribution of model parameters given noisy measurements. Posterior uncertainty about parameters is critical for making predictions from calibrated models, since many parameter settings can be consistent with measured data and yet produce very different model behaviors under conditions not effectively probed by the measurement protocols. Restitution curve emulators are therefore promising probabilistic tools for calibrating electrophysiology models.

In vitro and In silico Models to Study SARS-CoV-2 Infection: Integrating Experimental and Computational Tools to Mimic "COVID-19 Cardiomyocyte"

The rapid dissemination of SARS-CoV-2 has made COVID-19 a tremendous social, economic, and health burden. Despite the efforts to understand the virus and treat the disease, many questions remain unanswered about COVID-19 mechanisms of infection and progression. Severe Acute Respiratory Syndrome (SARS) infection can affect several organs in the body including the heart, which can result in thromboembolism, myocardial injury, acute coronary syndromes, and arrhythmias. Numerous cardiac adverse events, from cardiomyocyte death to secondary effects caused by exaggerated immunological response against the virus, have been clinically reported. In addition to the disease itself, repurposing of treatments by using "off label" drugs can also contribute to cardiotoxicity. Over the past several decades, animal models and more recently, stem cell-derived cardiomyocytes have been proposed for studying diseases and testing treatments in vitro. In addition, mechanistic in silico models have been widely used for disease and drug studies. In these models, several characteristics such as gender, electrolyte imbalance, and comorbidities can be implemented to study pathophysiology of cardiac diseases and to predict cardiotoxicity of drug treatments. In this Mini Review, we (1) present the state of the art of in vitro and in silico cardiomyocyte modeling currently in use to study COVID-19, (2) review in vitro and in silico models that can be adopted to mimic the effects of SARS-CoV-2 infection on cardiac function, and (3) provide a perspective on how to combine some of these models to mimic "COVID-19 cardiomyocytes environment.".

Restitution and adaptation measurements for the estimate of short-term cardiac action potential memory: comparison of five human ventricular models

AIMS

This computational study refines our recently published pacing protocol to measure short-term memory (STM) of cardiac action potential (AP), and apply it to five numerical models of human ventricular AP.

METHODS AND RESULTS

Several formulations of electrical restitution (ER) have been provided over the years, including standard, beat-to-beat, dynamic, steady-state, which make it difficult to compare results from different studies. We discuss here the notion of dynamic ER (dER) by relating it to its steady-state counterpart, and propose a pacing protocol based on dER to measure STM under periodically varying pacing cycle length (CL). Under high and highly variable-pacing rate, all models develop STM, which can be measured over the entire sequence by means of dER. Short-term memory can also be measured on a beat-to-beat basis by estimating action potential duration (APD) adaptation after clamping CL constant. We visualize STM as a phase shift between action potential (AP) parameters over consecutive cycles of CL oscillations, and show that delay between CL and APD oscillation is nearly constant (around 92 ms) in the five models, despite variability in their intrinsic AP properties.

CONCLUSION

dER, as we define it and together with other approaches described in the study, provides an univocal way to measure STM under extreme cardiac pacing conditions. Given the relevance of AP memory for repolarization dynamics and stability, STM should be considered, among other usual biomarkers, to validate and tune cardiac AP models. The possibility of extending the method to in vivo cellular and whole organ models can also be profitably explored.

Improved Accuracy of Cardiac Tissue-Level Simulations by Considering Membrane Resistance as a Cellular-Level Optimization Objective

Cardiac cellular models are utilized as the building blocks for tissue simulation. One of the imprecisions of conventional cellular modeling, especially when the models are used in tissue-level modeling, stems from the mere consideration of cellular properties (e.g., action potential shape) in parameter tuning of the model. In our previous work, we put forward an accurate framework in which membrane resistance (R_m) reflecting inter-cellular characteristics, i.e., electrotonic effects, was considered alongside cellular features in cellular model fitting. This paper, for the first time, examines the hypothesis that considering R_m as an additional optimization objective improves the accuracy of tissue-level modeling. To study this hypothesis, after cellular-level optimization of a well-known model, source-sink mismatch configurations in a 2-dimensional model are investigated. The results demonstrate that including R_m in the optimization protocol yields a substantial improvement in the relative error of the critical transition border which is defined as the minimum window size between source and sink that wave propagates. Model developers can utilize the proposed concept during parameter tuning to increase the accuracy of models.

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.

Genetic algorithm-based personalized models of human cardiac action potential

We present a novel modification of genetic algorithm (GA) which determines personalized parameters of cardiomyocyte electrophysiology model based on set of experimental human action potential (AP) recorded at different heart rates. In order to find the steady state solution, the optimized algorithm performs simultaneous search in the parametric and slow variables spaces. We demonstrate that several GA modifications are required for effective convergence. Firstly, we used Cauchy mutation along a random direction in the parametric space. Secondly, relatively large number of elite organisms (6-10% of the population passed on to new generation) was required for effective convergence. Test runs with synthetic AP as input data indicate that algorithm error is low for high amplitude ionic currents (1.6±1.6% for IKr, 3.2±3.5% for IK1, 3.9±3.5% for INa, 8.2±6.3% for ICaL). Experimental signal-to-noise ratio above 28 dB was required for high quality GA performance. GA was validated against optical mapping recordings of human ventricular AP and mRNA expression profile of donor hearts. In particular, GA output parameters were rescaled proportionally to mRNA levels ratio between patients. We have demonstrated that mRNA-based models predict the AP waveform dependence on heart rate with high precision. The latter also provides a novel technique of model personalization that makes it possible to map gene expression profile to cardiac function.

Simulation of the Effects of Extracellular Calcium Changes Leads to a Novel Computational Model of Human Ventricular Action Potential With a Revised Calcium Handling

The importance of electrolyte concentrations for cardiac function is well established. Electrolyte variations can lead to arrhythmias onset, due to their important role in the action potential (AP) genesis and in maintaining cell homeostasis. However, most of the human AP computer models available in literature were developed with constant electrolyte concentrations, and fail to simulate physiological changes induced by electrolyte variations. This is especially true for Ca2+, even in the O'Hara-Rudy model (ORd), one of the most widely used models in cardiac electrophysiology. Therefore, the present work develops a new human ventricular model (BPS2020), based on ORd, able to simulate the inverse dependence of AP duration (APD) on extracellular Ca2+ concentration ([Ca2+]o), and APD rate dependence at 4 mM extracellular K+. The main changes needed with respect to ORd are: (i) an increased sensitivity of L-type Ca2+ current inactivation to [Ca2+]o; (ii) a single compartment description of the sarcoplasmic reticulum; iii) the replacement of Ca2+ release. BPS2020 is able to simulate the physiological APD-[Ca2+]o relationship, while also retaining the well-reproduced properties of ORd (APD rate dependence, restitution, accommodation and current block effects). We also used BPS2020 to generate an experimentally-calibrated population of models to investigate: (i) the occurrence of repolarization abnormalities in response to hERG current block; (ii) the rate adaptation variability; (iii) the occurrence of alternans and delayed after-depolarizations at fast pacing. Our results indicate that we successfully developed an improved version of ORd, which can be used to investigate electrophysiological changes and pro-arrhythmic abnormalities induced by electrolyte variations and current block at multiple rates and at the population level.

A robust multi-objective optimization framework to capture both cellular and intercellular properties in cardiac cellular model tuning: Analyzing different regions of membrane resistance profile in parameter fitting

Mathematical models of cardiac cells have been established to broaden understanding of cardiac function. In the process of developing electrophysiological models for cardiac myocytes, precise parameter tuning is a crucial step. The membrane resistance (Rm) is an essential feature obtained from cardiac myocytes. This feature reflects intercellular coupling and affects important phenomena, such as conduction velocity, and early after-depolarizations, but it is often overlooked during the phase of parameter fitting. Thus, the traditional parameter fitting that only includes action potential (AP) waveform may yield incorrect values for Rm. In this paper, a novel multi-objective parameter fitting formulation is proposed and tested that includes different regions of the Rm profile as additional objective functions for optimization. As Rm depends on the transmembrane voltage (Vm) and exhibits singularities for some specific values of Vm, analyses are conducted to carefully select the regions of interest for the proper characterization of Rm. Non-dominated sorting genetic algorithm II is utilized to solve the proposed multi-objective optimization problem. To verify the efficacy of the proposed problem formulation, case studies and comparisons are carried out using multiple models of human cardiac ventricular cells. Results demonstrate Rm is correctly reproduced by the tuned cell models after considering the curve of Rm obtained from the late phase of repolarization and Rm value calculated in the rest phase as additional objectives. However, relative deterioration of the AP fit is observed, demonstrating trade-off among the objectives. This framework can be useful for a wide range of applications, including the parameters fitting phase of the cardiac cell model development and investigation of normal and pathological scenarios in which reproducing both cellular and intercellular properties are of great importance.

A Novel Bi-Level Framework for Fitting the Parameters in Cardiac Cellular Models

Cardiac models constructed from sets of differential equations provide invaluable information about heart mechanism and disorder of both human and animals. As tuning the parameters is a profoundly important step of modeling, this paper presents a novel parametrization technique based on a bilevel framework that benefits from two solution approaches, namely mixed integer genetic algorithm (MIGA) and linear least squares (LLS). In the upper-level optimization step, the action potential (AP) of the model is fitted to the reference AP using MIGA. In the lower-level optimization step, the mismatch between the total current of the model and reference is minimized via a clamp concept-based linearization and LLS solution approach. Notably, the clamp concept can diminish the nonlinearity of the parameter fitting problem. The issue of dependency on initial parameters in the lower-level problem, as well as the sensitivity of model parameters to linearization, are circumvented by MIGA in the upper-level optimization. For evaluation of MIGA-LLS performance, two complex human ventricular models are employed. The results demonstrate that in comparison to the genetic algorithm (GA)-based approach, the proposed framework significantly reduces the average and variation of normalized root-mean-squared error (NRMSE) in terms of the AP and total current in different trials. Variability in the resulting parameter values is considerably decreased as well.

A Mathematical Model of the Human Cardiac Na+ Channel

Sodium ion channel is a membrane protein that plays an important role in excitable cells, as it is responsible for the initiation of action potentials. Understanding the electrical characteristics of sodium channels is essential in predicting their behavior under different physiological conditions. We investigated several Markov models for the human cardiac sodium channel Na_V1.5 to derive a minimal mathematical model that describes the reported experimental data obtained using major voltage clamp protocols. We obtained simulation results for peak current-voltage relationships, the voltage dependence of normalized ion channel conductance, steady-state inactivation, activation and deactivation kinetics, fast and slow inactivation kinetics, and recovery from inactivation kinetics. Good agreement with the experimental data provides us with the mechanisms of the fast and slow inactivation of the human sodium channel and the coupling of its inactivation states to the closed and open states in the activation pathway.

A response surface optimization approach to adjust ionic current conductances of cardiac electrophysiological models. Application to the study of potassium level changes

Cardiac electrophysiological computational models are often developed from previously published models. The new models may incorporate additional features to adapt the model to a different species or may upgrade a specific ionic formulation based on newly available experimental data. A relevant challenge in the development of a new model is the estimation of certain ionic current conductances that cannot be reliably identified from experiments. A common strategy to estimate those conductances is by means of constrained non-linear least-squares optimization. In this work, a novel methodology is proposed for estimation of ionic current conductances of cardiac electrophysiological models by using a response surface approximation-based constrained optimization with trust region management. Polynomial response surfaces of a number of electrophysiological markers were built using statistical sampling methods. These markers included action potential duration (APD), triangulation, diastolic and systolic intracellular calcium concentration, and time constants of APD rate adaptation. The proposed methodology was applied to update the Carro et al. human ventricular action potential model after incorporation of intracellular potassium ([K⁺]_i) dynamics. While the Carro et al. model was well suited for investigation of arrhythmogenesis, it did not allow simulation of [K⁺]_i changes. With the methodology proposed in this study, the updated Carro et al. human ventricular model could be used to simulate [K⁺]_i changes in response to varying extracellular potassium ([K⁺]_o) levels. Additionally, it rendered values of evaluated electrophysiological markers within physiologically plausible ranges. The optimal values of ionic current conductances in the updated model were found in a notably shorter time than with previously proposed methodologies. As a conclusion, the response surface optimization-based approach proposed in this study allows estimating ionic current conductances of cardiac electrophysiological computational models while guaranteeing replication of key electrophysiological features and with an important reduction in computational cost with respect to previously published approaches. The updated Carro et al. model developed in this study is thus suitable for the investigation of arrhythmic risk-related conditions, including those involving large changes in potassium concentration.

The Ca2+ transient as a feedback sensor controlling cardiomyocyte ionic conductances in mouse populations

Conductances of ion channels and transporters controlling cardiac excitation may vary in a population of subjects with different cardiac gene expression patterns. However, the amount of variability and its origin are not quantitatively known. We propose a new conceptual approach to predict this variability that consists of finding combinations of conductances generating a normal intracellular Ca²⁺ transient without any constraint on the action potential. Furthermore, we validate experimentally its predictions using the Hybrid Mouse Diversity Panel, a model system of genetically diverse mouse strains that allows us to quantify inter-subject versus intra-subject variability. The method predicts that conductances of inward Ca²⁺ and outward K⁺ currents compensate each other to generate a normal Ca²⁺ transient in good quantitative agreement with current measurements in ventricular myocytes from hearts of different isogenic strains. Our results suggest that a feedback mechanism sensing the aggregate Ca²⁺ transient of the heart suffices to regulate ionic conductances.

A Heart for Diversity: Simulating Variability in Cardiac Arrhythmia Research

In cardiac electrophysiology, there exist many sources of inter- and intra-personal variability. These include variability in conditions and environment, and genotypic and molecular diversity, including differences in expression and behavior of ion channels and transporters, which lead to phenotypic diversity (e.g., variable integrated responses at the cell, tissue, and organ levels). These variabilities play an important role in progression of heart disease and arrhythmia syndromes and outcomes of therapeutic interventions. Yet, the traditional in silico framework for investigating cardiac arrhythmias is built upon a parameter/property-averaging approach that typically overlooks the physiological diversity. Inspired by work done in genetics and neuroscience, new modeling frameworks of cardiac electrophysiology have been recently developed that take advantage of modern computational capabilities and approaches, and account for the variance in the biological data they are intended to illuminate. In this review, we outline the recent advances in statistical and computational techniques that take into account physiological variability, and move beyond the traditional cardiac model-building scheme that involves averaging over samples from many individuals in the construction of a highly tuned composite model. We discuss how these advanced methods have harnessed the power of big (simulated) data to study the mechanisms of cardiac arrhythmias, with a special emphasis on atrial fibrillation, and improve the assessment of proarrhythmic risk and drug response. The challenges of using in silico approaches with variability are also addressed and future directions are proposed.

Reproducible model development in the cardiac electrophysiology Web Lab

The modelling of the electrophysiology of cardiac cells is one of the most mature areas of systems biology. This extended concentration of research effort brings with it new challenges, foremost among which is that of choosing which of these models is most suitable for addressing a particular scientific question. In a previous paper, we presented our initial work in developing an online resource for the characterisation and comparison of electrophysiological cell models in a wide range of experimental scenarios. In that work, we described how we had developed a novel protocol language that allowed us to separate the details of the mathematical model (the majority of cardiac cell models take the form of ordinary differential equations) from the experimental protocol being simulated. We developed a fully-open online repository (which we termed the Cardiac Electrophysiology Web Lab) which allows users to store and compare the results of applying the same experimental protocol to competing models. In the current paper we describe the most recent and planned extensions of this work, focused on supporting the process of model building from experimental data. We outline the necessary work to develop a machine-readable language to describe the process of inferring parameters from wet lab datasets, and illustrate our approach through a detailed example of fitting a model of the hERG channel using experimental data. We conclude by discussing the future challenges in making further progress in this domain towards our goal of facilitating a fully reproducible approach to the development of cardiac cell models.

Population-based mechanistic modeling allows for quantitative predictions of drug responses across cell types

Quantitative mismatches between human physiology and experimental models can be problematic for the development of effective therapeutics. When the effects of drugs on human adult cardiac electrophysiology are of interest, phenotypic differences with animal cells, and more recently stem cell-derived models, can present serious limitations. We addressed this issue through a combination of mechanistic mathematical modeling and statistical analyses. Physiological metrics were simulated in heterogeneous populations of models describing cardiac myocytes from adult ventricles and those derived from induced pluripotent stem cells (iPSC-CMs). These simulated measures were used to construct a cross-cell type regression model that predicts adult myocyte drug responses from iPSC-CM behaviors. We found that (1) quantitatively accurate predictions of responses to selective or non-selective ion channel blocking drugs could be generated based on iPSC-CM responses under multiple experimental conditions; (2) altering extracellular ion concentrations is an effective experimental perturbation for improving the model’s predictive strength; (3) the method can be extended to predict and contrast drug responses in diseased as well as healthy cells, indicating a broader application of the concept. This cross-cell type model can be of great value in drug development, and the approach, which can be applied to other fields, represents an important strategy for overcoming experimental model limitations.

The quantitative limitations of experimental models, which can impair the development of effective therapeutics, can be overcome through a combination of mechanistic simulations and statistical analysis. A team from Icahn School of Medicine at Mount Sinai led by Eric Sobie devised a computational method to quantitatively translate drug responses across cell types. The method involves mechanism-based simulations of heterogeneous populations combined with a multivariable regression model that translates between cell types. Simulation results presented in the study show that the response to a drug in one cell type can be predicted with quantitative accuracy from physiological recordings made in another cell type, as can differential drug responses observed in diseased compared with healthy cells. This methodology can be used in drug development to better predict clinical responses based on experiments performed in preclinical models.

How to Connect Cardiac Excitation to the Atomic Interactions of Ion Channels

Many have worked to create cardiac action potential models that explicitly represent atomic-level details of ion channel structure. Such models have the potential to define new therapeutic directions and to show how nanoscale perturbations to channel function predispose patients to deadly cardiac arrhythmia. However, there have been significant experimental and theoretical barriers that have limited model usefulness. Recently, many of these barriers have come down, suggesting that considerable progress toward creating these long-sought models may be possible in the near term.

β-adrenergic stimulation augments transmural dispersion of repolarization via modulation of delayed rectifier currents IKs and IKr in the human ventricle

Long QT syndrome (LQTS) is an inherited or drug induced condition associated with delayed repolarization and sudden cardiac death. The cardiac potassium channel, I_Kr, and the adrenergic-sensitive cardiac potassium current, I_Ks, are two primary contributors to cardiac repolarization. This study aimed to elucidate the role of β-adrenergic (β-AR) stimulation in mediating the contributions of I_Kr and I_Ks to repolarizing the human left ventricle (n = 18). Optical mapping was used to measure action potential durations (APDs) in the presence of the I_Ks blocker JNJ-303 and the I_Kr blocker E-4031. We found that JNJ-303 alone did not increase APD. However, under isoprenaline (ISO), both the application of JNJ-303 and additional E-4031 significantly increased APD. With JNJ-303, ISO decreased APD significantly more in the epicardium as compared to the endocardium, with subsequent application E-4031 increasing mid- and endocardial APD80 more significantly than in the epicardium. We found that β-AR stimulation significantly augmented the effect of I_Ks blocker JNJ-303, in contrast to the reduced effect of I_Kr blocker E-4031. We also observed synergistic augmentation of transmural repolarization gradient by the combination of ISO and E-4031. Our results suggest β-AR-mediated increase of transmural dispersion of repolarization, which could pose arrhythmogenic risk in LQTS patients.

Differential roles of two delayed rectifier potassium currents in regulation of ventricular action potential duration and arrhythmia susceptibility

KEY POINTS

Arrhythmias result from disruptions to cardiac electrical activity, although the factors that control cellular action potentials are incompletely understood. We combined mathematical modelling with experiments in heart cells from guinea pigs to determine how cellular electrical activity is regulated. A mismatch between modelling predictions and the experimental results allowed us to construct an improved, more predictive mathematical model. The balance between two particular potassium currents dictates how heart cells respond to perturbations and their susceptibility to arrhythmias.

ABSTRACT

Imbalances of ionic currents can destabilize the cardiac action potential and potentially trigger lethal cardiac arrhythmias. In the present study, we combined mathematical modelling with information-rich dynamic clamp experiments to determine the regulation of action potential morphology in guinea pig ventricular myocytes. Parameter sensitivity analysis was used to predict how changes in ionic currents alter action potential duration, and these were tested experimentally using dynamic clamp, a technique that allows for multiple perturbations to be tested in each cell. Surprisingly, we found that a leading mathematical model, developed with traditional approaches, systematically underestimated experimental responses to dynamic clamp perturbations. We then re-parameterized the model using a genetic algorithm, which allowed us to estimate ionic current levels in each of the cells studied. This unbiased model adjustment consistently predicted an increase in the rapid delayed rectifier K⁺ current and a drastic decrease in the slow delayed rectifier K⁺ current, and this prediction was validated experimentally. Subsequent simulations with the adjusted model generated the clinically relevant prediction that the slow delayed rectifier is better able to stabilize the action potential and suppress pro-arrhythmic events than the rapid delayed rectifier. In summary, iterative coupling of simulations and experiments enabled novel insight into how the balance between cardiac K⁺ currents influences ventricular arrhythmia susceptibility.

Potassium channels in the heart: structure, function and regulation

This paper is the outcome of the fourth UC Davis Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias Symposium, a biannual event that aims to bring together leading experts in subfields of cardiovascular biomedicine to focus on topics of importance to the field. The theme of the 2016 symposium was 'K⁺ Channels and Regulation'. Experts in the field contributed their experimental and mathematical modelling perspectives and discussed emerging questions, controversies and challenges on the topic of cardiac K⁺ channels. This paper summarizes the topics of formal presentations and informal discussions from the symposium on the structural basis of voltage-gated K⁺ channel function, as well as the mechanisms involved in regulation of K⁺ channel gating, expression and membrane localization. Given the critical role for K⁺ channels in determining the rate of cardiac repolarization, it is hardly surprising that essentially every aspect of K⁺ channel function is exquisitely regulated in cardiac myocytes. This regulation is complex and highly interrelated to other aspects of myocardial function. K⁺ channel regulatory mechanisms alter, and are altered by, physiological challenges, pathophysiological conditions, and pharmacological agents. An accompanying paper focuses on the integrative role of K⁺ channels in cardiac electrophysiology, i.e. how K⁺ currents shape the cardiac action potential, and how their dysfunction can lead to arrhythmias, and discusses K⁺ channel-based therapeutics. A fundamental understanding of K⁺ channel regulatory mechanisms and disease processes is fundamental to reveal new targets for human therapy.

Rabbit-specific computational modelling of ventricular cell electrophysiology: Using populations of models to explore variability in the response to ischemia

Computational modelling, combined with experimental investigations, is a powerful method for investigating complex cardiac electrophysiological behaviour. The use of rabbit-specific models, due to the similarities of cardiac electrophysiology in this species with human, is especially prevalent. In this paper, we first briefly review rabbit-specific computational modelling of ventricular cell electrophysiology, multi-cellular simulations including cellular heterogeneity, and acute ischemia. This mini-review is followed by an original computational investigation of variability in the electrophysiological response of two experimentally-calibrated populations of rabbit-specific ventricular myocyte action potential models to acute ischemia. We performed a systematic exploration of the response of the model populations to varying degrees of ischemia and individual ischemic parameters, to investigate their individual and combined effects on action potential duration and refractoriness. This revealed complex interactions between model population variability and ischemic factors, which combined to enhance variability during ischemia. This represents an important step towards an improved understanding of the role that physiological variability may play in electrophysiological alterations during acute ischemia.

Predicting the risk of sudden cardiac death

Sudden cardiac death (SCD) is the result of a change of cardiac activity from normal (typically sinus) rhythm to a rhythm that does not pump adequate blood to the brain. The most common rhythms leading to SCD are ventricular tachycardia (VT) or ventricular fibrillation (VF). These result from an accelerated ventricular pacemaker or ventricular reentrant waves. Despite significant efforts to develop accurate predictors for the risk of SCD, current methods for risk stratification still need to be improved. In this article we briefly review current approaches to risk stratification. Then we discuss the mathematical basis for dynamical transitions (called bifurcations) that may lead to VT and VF. One mechanism for transition to VT or VF involves a perturbation by a premature ventricular complex (PVC) during sinus rhythm. We describe the main mechanisms of PVCs (reentry, independent pacemakers and abnormal depolarizations). An emerging approach to risk stratification for SCD involves the development of individualized dynamical models of a patient based on measured anatomy and physiology. Careful analysis and modelling of dynamics of ventricular arrhythmia on an individual basis will be essential in order to improve risk stratification for SCD and to lay a foundation for personalized (precision) medicine in cardiology.