Mathematical models of the electrical action potential of Purkinje fibre cells

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Identification and characterization of two novel KCNH2 mutations contributing to long QT syndrome

We identified two different inherited mutations in KCNH2 gene, or human ether-a-go-go related gene (hERG), which are linked to Long QT Syndrome. The first mutation was in a 1-day-old infant, whereas the second was in a 14-year-old girl. The two KCNH2 mutations were transiently transfected into either human embryonic kidney (HEK) cells or human induced pluripotent stem-cell derived cardiomyocytes. We performed associated multiscale computer simulations to elucidate the arrhythmogenic potentials of the KCNH2 mutations. Genetic screening of the first and second index patients revealed a heterozygous missense mutation in KCNH2, resulting in an amino acid change (P632L) in the outer loop of the channel and substitution at position 428 from serine to proline (S428P), respectively. Heterologous expression of P632L and S428P into HEK cells produced no hERG current compared to the wild type (WT). Moreover, the co-transfection of WT and P632L yielded no hERG current; however, the co-transfection of WT and S428P yielded partial hERG current. Action potentials were prolonged in a complete or partial blockade of hERG current from computer simulations which was more severe in Purkinje than ventricular myocytes. Three dimensional simulations revealed a higher susceptibility to reentry in the presence of hERG current blockade. Our experimental findings suggest that both P632L and S428P mutations may impair the KCNH2 gene. The Purkinje cells exhibit a more severe phenotype than ventricular myocytes, and the hERG current blockade renders the ventricles an arrhythmogenic substrate from computer modeling.

Combining pharmacokinetic and electrophysiological models for early prediction of drug-induced arrhythmogenicity

BACKGROUND AND OBJECTIVE

In silico methods are gaining attention for predicting drug-induced Torsade de Pointes (TdP) in different stages of drug development. However, many computational models tended not to account for inter-individual response variability due to demographic covariates, such as sex, or physiologic covariates, such as renal function, which may be crucial when predicting TdP. This study aims to compare the effects of drugs in male and female populations with normal and impaired renal function using in silico methods.

METHODS

Pharmacokinetic models considering sex and renal function as covariates were implemented from data published in pharmacokinetic studies. Drug effects were simulated using an electrophysiologically calibrated population of cellular models of 300 males and 300 females. The population of models was built by modifying the endocardial action potential model published by O'Hara et al. (2011) according to the experimentally measured gene expression levels of 12 ion channels.

RESULTS

Fifteen pharmacokinetic models for CiPA drugs were implemented and validated in this study. Eight pharmacokinetic models included the effect of renal function and four the effect of sex. The mean difference in action potential duration (APD) between male and female populations was 24.9 ms (p<0.05). Our simulations indicated that women with impaired renal function were particularly susceptible to drug-induced arrhythmias, whereas healthy men were less prone to TdP. Differences between patient groups were more pronounced for high TdP-risk drugs. The proposed in silico tool also revealed that individuals with impaired renal function, electrophysiologically simulated with hyperkalemia (extracellular potassium concentration [K+]o = 7 mM) exhibited less pronounced APD prolongation than individuals with normal potassium levels. The pharmacokinetic/electrophysiological framework was used to determine the maximum safe dose of dofetilide in different patient groups. As a proof of concept, 3D simulations were also run for dofetilide obtaining QT prolongation in accordance with previously reported clinical values.

CONCLUSIONS

This study presents a novel methodology that combines pharmacokinetic and electrophysiological models to incorporate the effects of sex and renal function into in silico drug simulations and highlights their impact on TdP-risk assessment. Furthermore, it may also help inform maximum dose regimens that ensure TdP-related safety in a specific sub-population of patients.

Prediction of experimental cardiac magnetostimulation thresholds using pig-specific body models

PURPOSE

Modern high-amplitude gradient systems can be limited by the International Electrotechnical Commission 60601-2-33 cardiac stimulation (CS) limit, which was set in a conservative manner based on electrode experiments and E-field simulations in uniform ellipsoidal body models. Here, we show that coupled electromagnetic-electrophysiological modeling in detailed body and heart models can predict CS thresholds, suggesting that such modeling might lead to more detailed threshold estimates in humans. Specifically, we compare measured and predicted CS thresholds in eight pigs.

METHODS

We created individualized porcine body models using MRI (Dixon for the whole body, CINE for the heart) that replicate the anatomy and posture of the animals used in our previous experimental CS study. We model the electric fields induced along cardiac Purkinje and ventricular muscle fibers and predict the electrophysiological response of these fibers, yielding CS threshold predictions in absolute units for each animal. Additionally, we assess the total modeling uncertainty through a variability analysis of the 25 main model parameters.

RESULTS

Predicted and experimental CS thresholds agree within 19% on average (normalized RMS error), which is smaller than the 27% modeling uncertainty. No significant difference was found between the modeling predictions and experiments (p < 0.05, paired t-test).

CONCLUSION

Predicted thresholds matched the experimental data within the modeling uncertainty, supporting the model validity. We believe that our modeling approach can be applied to study CS thresholds in humans for various gradient coils, body shapes/postures, and waveforms, which is difficult to do experimentally.

Enhanced optimization-based method for the generation of patient-specific models of Purkinje networks

Cardiac Purkinje networks are a fundamental part of the conduction system and are known to initiate a variety of cardiac arrhythmias. However, patient-specific modeling of Purkinje networks remains a challenge due to their high morphological complexity. This work presents a novel method based on optimization principles for the generation of Purkinje networks that combines geometric and activation accuracy in branch size, bifurcation angles, and Purkinje-ventricular-junction activation times. Three biventricular meshes with increasing levels of complexity are used to evaluate the performance of our approach. Purkinje-tissue coupled monodomain simulations are executed to evaluate the generated networks in a realistic scenario using the most recent Purkinje/ventricular human cellular models and physiological values for the Purkinje-ventricular-junction characteristic delay. The results demonstrate that the new method can generate patient-specific Purkinje networks with controlled morphological metrics and specified local activation times at the Purkinje-ventricular junctions.

GPU accelerated digital twins of the human heart open new routes for cardiovascular research

The recruitment of patients for rare or complex cardiovascular diseases is a bottleneck for clinical trials and digital twins of the human heart have recently been proposed as a viable alternative. In this paper we present an unprecedented cardiovascular computer model which, relying on the latest GPU-acceleration technologies, replicates the full multi-physics dynamics of the human heart within a few hours per heartbeat. This opens the way to extensive simulation campaigns to study the response of synthetic cohorts of patients to cardiovascular disorders, novel prosthetic devices or surgical procedures. As a proof-of-concept we show the results obtained for left bundle branch block disorder and the subsequent cardiac resynchronization obtained by pacemaker implantation. The in-silico results closely match those obtained in clinical practice, confirming the reliability of the method. This innovative approach makes possible a systematic use of digital twins in cardiovascular research, thus reducing the need of real patients with their economical and ethical implications. This study is a major step towards in-silico clinical trials in the era of digital medicine.

An ECG generative model of myocardial infarction

Background and Objective Computer-aided diagnosis (CAD) of Myocardial Infarction (MI) using machine learning depends on a large amount of clinical Electrocardiogram (ECG) data. Existing infarct ECG databases face the problem of class imbalance. Data augmentation using generative simulation models is a new approach to effectively address this problem. Methods A multiscale ECG generative model was established for ECG data augmentation. In the cellular layer, an ischemic Action Potential (AP) model was established to generate APs in cardiomyocytes with different transmural regions of infraction or different ischemic durations. In the tissue layer, a probability-driven cellular automata excitation propagation model was established to simulate the propagation speed and direction of excitation. An infarct tissue model and a coronary artery model were established to describe the spatiotemporal diversity of MI. A ventricle model, a human torso model, and a computational model of surface ECG based on field source theory were established in the heart-torso layer. Results The model generated pathological 12-lead ECGs of MI with different topography and different extent. When simulating different ventricular wall infarction, the lesions appear in the same leads as the clinical 12-lead ECG. The ST-segment decreases and the T-wave amplitude decreases, similar to the clinical ECG features when simulating subendocardial ischemia. The average fidelity of the 12-lead ECG the model generated is 95.6%, according to the designed DTW-GRA distance algorithm. Conclusions The generative model considers the electrophysiological properties of the natural heart, the pathology of myocardial infarction, and the diversity of clinical ECGs. The model can provide many reliable samples for machine learning of MI.

Ultra-low power deep sustained optogenetic excitation of human ventricular cardiomyocytes with red-shifted opsins: A computational study

KEY POINTS

Formulation of accurate theoretical models of optogenetic control of HVCMs expressed with newly-discovered opsins (ChRmine, bReaChES, and CsChrimson). Under continuous illumination, action potentials in each opsin-expressing HVCMs can only be evoked in a certain range of irradiances. Action potentials in ChRmine-expressing HVCMs can be triggered at ultra-low power (6 μW/mm² at 10 ms pulse or 0.7 μW/mm² at 100 ms pulse at 585 nm), which is 2-3 orders of magnitude lower than reported results. Ongoing APs in ChRmine-expressing HVCMs can be suppressed by continuous illumination of 585 nm light at 2 μW/mm² . ChRmine enables sustained excitation due to its faster recovery from the desensitized state. Optogenetic excitation of deeply situated cardiac cells is possible upto ∼ 7.46 mm and 10.2 mm with ChRmine on illuminating the outer surface of pericardium at safe irradiance at 585 nm and 650 nm, respectively. The study opens up prospects for designing energy-efficient light-induced pacemakers, resynchronization, and termination of ventricular tachycardia.

ABSTRACT

The main challenge in cardiac optogenetics is to have low-power, high-fidelity, and deep excitation of cells with minimal invasiveness and heating. We present a detailed computational study of optogenetic excitation of human ventricular cardiomyocytes (HVCMs) with new ChRmine, bReaChES and CsChrimson red-shifted opsins to overcome the challenge. Action potentials (APs) in ChRmine expressing HVCMs can be triggered at 6 μW/mm² (10 ms pulse) and 0.7 μW/mm2 (100 ms pulse) at 585 nm which are two orders of magnitude lower than ChR2(H134R). This enables safe sustained excitation of deeply situated cardiac cells with ChRmine (7.46 mm) and with bReaChES (6.21 mm) with the light source at the pericardium surface. Deeper excitation upto 10.2 mm can be achieved with ChRmine by illuminating at 650 nm. Photostimulation conditions for minimum charge transfer during AP have been determined, which are important for tissue health under sustained excitation. The action potential duration for all the opsins is constant upto 100 ms pulse-width but increases thereafter. Interestingly, the AP frequency increases with irradiance under continuous illumination, which gets suppressed at higher irradiances. Optimal range of irradiance for each opsin to excite HVCMs has been determined. Under optimal photostimulation conditions, each opsin can precisely excite APs up to 2.5 Hz, while latency and power of light pulse for each AP in a sequence remain most stable and an order lower respectively, in ChRmine-expressing HVCMs. The study highlights the importance of ChRmine and bReaChES for resynchronization, termination of ventricular tachycardia, and designing optogenetic cardiac pacemakers with enhanced battery life. Abstract figure legend Deep optogenetic excitation of opsin-expressing cardiomyocytes by placing the light source (maximum output 5.5 mW/mm² ) at the outer surface of the pericardium. Excitation of cardiomyocytes upto 10.2 mm (at 650 nm) and 7.46 mm (at 585 nm) is possible with ChRmine. This article is protected by copyright. All rights reserved.

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.

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.

An ensemble of parameters from a robust Markov-based model reproduces L-type calcium currents from different human cardiac myocytes

The development of modeling structures at the channel level that can integrate subcellular and cell models and properly reproduce different experimental data is of utmost importance in cardiac electrophysiology. In contrast to gate-based models, Markov Chain models are well suited to promote the integration of the subcellular level of the cardiomyocyte to the whole cell. In this paper, we develop Markov Chain models for the L-type Calcium current that can reproduce the electrophysiology of two established human models for the ventricular and Purkinje cells. In addition, instead of presenting a single set of parameters, we present a collection of set of parameters employing Differential Evolution algorithms that can properly reproduce very different protocol data. We show the importance of using an ensemble of a set of parameter values to obtain proper results when considering a second protocol that suppresses calcium inactivation and mimics a pathological condition. We discuss how model discrepancy, data availability, and parameter identifiability can influence the choice of the size of the collection. In summary, we have modified two cardiac models by proposing new Markov Chain models for the L-type Calcium. We keep the original whole-cell dynamics by reproducing the same characteristic action potential and calcium dynamics, whereas the Markov chain-based description of the L-type Calcium channels allows novel small spatial scale simulations of subcellular processes. Finally, the use of collections of parameters was crucial for addressing model discrepancy, identifiability issues, and avoiding fitting parameters overly precisely, i.e., overfitting.

UT-Heart: A Finite Element Model Designed for the Multiscale and Multiphysics Integration of our Knowledge on the Human Heart

To fully understand the health and pathology of the heart, it is necessary to integrate knowledge accumulated at molecular, cellular, tissue, and organ levels. However, it is difficult to comprehend the complex interactions occurring among the building blocks of biological systems across these scales. Recent advances in computational science supported by innovative high-performance computer hardware make it possible to develop a multiscale multiphysics model simulating the heart, in which the behavior of each cell model is controlled by molecular mechanisms and the cell models themselves are arranged to reproduce elaborate tissue structures. Such a simulator could be used as a tool not only in basic science but also in clinical settings. Here, we describe a multiscale multiphysics heart simulator, UT-Heart, which uses unique technologies to realize the abovementioned features. As examples of its applications, models for cardiac resynchronization therapy and surgery for congenital heart disease will be also shown.

Analysis of vulnerability to reentry in acute myocardial ischemia using a realistic human heart model

Electrophysiological alterations of the myocardium caused by acute ischemia constitute a pro-arrhythmic substrate for the generation of potentially lethal arrhythmias. Experimental evidence has shown that the main components of acute ischemia that induce these electrophysiological alterations are hyperkalemia, hypoxia (or anoxia in complete artery occlusion), and acidosis. However, the influence of each ischemic component on the likelihood of reentry is not completely established. Moreover, the role of the His-Purkinje system (HPS) in the initiation and maintenance of arrhythmias is not completely understood. In the present work, we investigate how the three components of ischemia affect the vulnerable window (VW) for reentry using computational simulations. In addition, we analyze the role of the HPS on arrhythmogenesis. A 3D biventricular/torso human model that includes a realistic geometry of the central and border ischemic zones with one of the most electrophysiologically detailed model of ischemia to date, as well as a realistic cardiac conduction system, were used to assess the VW for reentry. Four scenarios of ischemic severity corresponding to different minutes after coronary artery occlusion were simulated. Our results suggest that ischemic severity plays an important role in the generation of reentries. Indeed, this is the first 3D simulation study to show that ventricular arrhythmias could be generated under moderate ischemic conditions, but not in mild and severe ischemia. Moreover, our results show that anoxia is the ischemic component with the most significant effect on the width of the VW. Thus, a change in the level of anoxia from moderate to severe leads to a greater increment in the VW (40 ms), in comparison with the increment of 20 ms and 35 ms produced by the individual change in the level of hyperkalemia and acidosis, respectively. Finally, the HPS was a necessary element for the generation of approximately 17% of reentries obtained. The retrograde conduction from the myocardium to HPS in the ischemic region, conduction blocks in discrete sections of the HPS, and the degree of ischemia affecting Purkinje cells, are suggested as mechanisms that favor the generation of ventricular arrhythmias.

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.

An in silico hiPSC-Derived Cardiomyocyte Model Built With Genetic Algorithm

The formulation of in silico biophysical models generally requires optimization strategies for reproducing experimentally observed phenomena. In electrophysiological modeling, robust nonlinear regressive methods are often crucial for guaranteeing high fidelity models. Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), though nascent, have proven to be useful in cardiac safety pharmacology, regenerative medicine, and in the implementation of patient-specific test benches for investigating inherited cardiac disorders. This study demonstrates the potency of heuristic techniques at formulating biophysical models, with emphasis on a hiPSC-CM model using a novel genetic algorithm (GA) recipe we proposed. The proposed GA protocol was used to develop a hiPSC-CM biophysical computer model by fitting mathematical formulations to experimental data for five ionic currents recorded in hiPSC-CMs. The maximum conductances of the remaining ionic channels were scaled based on recommendations from literature to accurately reproduce the experimentally observed hiPSC-CM action potential (AP) metrics. Near-optimal parameter fitting was achieved for the GA-fitted ionic currents. The resulting model recapitulated experimental AP parameters such as AP durations (APD₅₀, APD₇₅, and APD₉₀), maximum diastolic potential, and frequency of automaticity. The outcome of this work has implications for validating the biophysics of hiPSC-CMs in their use as viable substitutes for human cardiomyocytes, particularly in cardiac safety pharmacology and in the study of inherited cardiac disorders. This study presents a novel GA protocol useful for formulating robust numerical biophysical models. The proposed protocol is used to develop a hiPSC-CM model with implications for cardiac safety pharmacology.

Chloroquine and hydroxychloroquine provoke arrhythmias at concentrations higher than those clinically used to treat COVID-19: A simulation study

Abstract

The risk of fatal arrhythmias is the major concern for using chloroquine (CQ) or hydroxychloroquine (HCQ) to treat coronavirus disease 2019 (COVID‐19), but the reported number of life‐threatening arrhythmic events or deaths is relatively small. The objective of this study was to assess the arrhythmogenic risk of these two drugs using a multiscale heart simulation, which allows testing even at high concentrations, including those that cause fatal arrhythmias. We measured the inhibitory action of CQ, HCQ, and HCQ with 30 μM azithromycin (AZ) on six ion currents (fast [INa] and late [INa,L] components of the sodium current, L‐type calcium current [ICa,L], rapid [IKr/hERG], and slow [IKs] components of delayed rectifier potassium, and inward rectifier potassium [IK1]) over a wide range of concentrations using the automated patch‐clamp system. Using the concentration–inhibition relationship that was thus obtained, we simulated the drug effects while increasing the concentration until the life‐threatening arrhythmia, torsade de pointes (TdP), was observed. The obtained threshold concentrations for TdP were 12.5, 35, and 22.5 μM for CQ, HCQ, and HCQ with AZ, respectively. Adding therapeutic concentrations of mexiletine or verapamil successfully prevented the occurrence of TdP, and verapamil was more effective. CQ, HCQ, and HCQ with AZ thresholds for TdP were larger than both antiviral concentrations that were reported by in vitro experiments and free plasma concentrations that were attained by the clinically used dosage. The current simulation data provided a safety margin to the currently used clinical dose for CQ and HCQ/AZ.

Precision medicine in human heart modeling : Perspectives, challenges, and opportunities

Precision medicine is a new frontier in healthcare that uses scientific methods to customize medical treatment to the individual genes, anatomy, physiology, and lifestyle of each person. In cardiovascular health, precision medicine has emerged as a promising paradigm to enable cost-effective solutions that improve quality of life and reduce mortality rates. However, the exact role in precision medicine for human heart modeling has not yet been fully explored. Here, we discuss the challenges and opportunities for personalized human heart simulations, from diagnosis to device design, treatment planning, and prognosis. With a view toward personalization, we map out the history of anatomic, physical, and constitutive human heart models throughout the past three decades. We illustrate recent human heart modeling in electrophysiology, cardiac mechanics, and fluid dynamics and highlight clinically relevant applications of these models for drug development, pacing lead failure, heart failure, ventricular assist devices, edge-to-edge repair, and annuloplasty. With a view toward translational medicine, we provide a clinical perspective on virtual imaging trials and a regulatory perspective on medical device innovation. We show that precision medicine in human heart modeling does not necessarily require a fully personalized, high-resolution whole heart model with an entire personalized medical history. Instead, we advocate for creating personalized models out of population-based libraries with geometric, biological, physical, and clinical information by morphing between clinical data and medical histories from cohorts of patients using machine learning. We anticipate that this perspective will shape the path toward introducing human heart simulations into precision medicine with the ultimate goals to facilitate clinical decision making, guide treatment planning, and accelerate device design.

Cardiac transmembrane ion channels and action potentials: cellular physiology and arrhythmogenic behavior

Cardiac arrhythmias are among the leading causes of mortality. They often arise from alterations in the electrophysiological properties of cardiac cells and their underlying ionic mechanisms. It is therefore critical to further unravel the pathophysiology of the ionic basis of human cardiac electrophysiology in health and disease. In the first part of this review, current knowledge on the differences in ion channel expression and properties of the ionic processes that determine the morphology and properties of cardiac action potentials and calcium dynamics from cardiomyocytes in different regions of the heart are described. Then the cellular mechanisms promoting arrhythmias in congenital or acquired conditions of ion channel function (electrical remodeling) are discussed. The focus is on human-relevant findings obtained with clinical, experimental, and computational studies, given that interspecies differences make the extrapolation from animal experiments to human clinical settings difficult. Deepening the understanding of the diverse pathophysiology of human cellular electrophysiology will help in developing novel and effective antiarrhythmic strategies for specific subpopulations and disease conditions.

Genetic Algorithm For Fitting Cardiac Cell Biophysical Model Formulations

Modeling cardiac cell electrophysiology relies on fitting model equations to experimental data obtained under voltage/current clamping conditions. The fitting procedure for these often-nonlinear ionic current equations are mostly executed by trial-and-error by hand or by gradient-based optimization approaches. These methods, though sometimes sufficient at converging at optimal solutions is based on the premise that the characteristic objective function is convex, which often does not apply to cardiac model equations. Meta-heuristic methods, such as evolutionary algorithms and particle swarm algorithms, have proven resilient against early convergence to local optima and saddle-point parameter solutions. This work presents a genetic algorithm-based approach for fitting the adult cardiomyocyte biophysical model formulations to the experimental data obtained in human induced pluripotent stem cell-derived cardiomyocyte (hiPSC-CM). Specifically, whole-cell patch clamp ionic current data of rapid delayed rectifier potassium current, I_Kr, transient outward potassium current, I_to and hyperpolarization-activated current, I_f, was used for fitting. Using a two-point crossover scheme along with initial population and mutation constraints randomly selected from a uniformly distributed constrained parameter space, near-optimal fitting was achieved with R² values (n = 5) of 0.9960±0.0007, 0.9995±0.0002, and 0.9974±0.0014 for I_Kr, I_to and I_f respectively.

Investigating cardiac stimulation limits of MRI gradient coils using electromagnetic and electrophysiological simulations in human and canine body models

Purpose:

Cardiac stimulation (CS) limits to gradient coil switching speed are difficult to measure in humans; instead, current regulatory guidelines (IEC 60601–2-33) are based on animal experiments and electric field–to-dB/dt conversion factors computed for a simple, homogeneous body model. We propose improvement to this methodology by using more detailed CS modeling based on realistic body models and electrophysiological models of excitable cardiac fibers.

Methods:

We compute electric fields induced by a solenoid, coplanar loops, and a commercial gradient coil in two human body models and a canine model. The canine simulations mimic previously published experiments. We generate realistic fiber topologies for the cardiac Purkinje and ventricular muscle fiber networks using rule-based algorithms, and evaluate CS thresholds using validated electrodynamic models of these fibers.

Results:

We were able to reproduce the average measured canine CS thresholds within 5%. In all simulations, the Purkinje fibers were stimulated before the ventricular fibers, and therefore set the effective CS threshold. For the investigated gradient coil, simulated CS thresholds for the x-, y-, and z-axis were at least one order of magnitude greater than the International Electrotechnical Commission limit.

Conclusion:

We demonstrate an approach to simulate gradient-induced CS using a combination of electromagnetic and electrophysiological modeling. Pending additional validation, these simulations could guide the assessment of CS limits to MRI gradient coil switching speed. Such an approach may lead to less conservative, but still safe, operation limits, enabling the use of the maximum gradient amplitude versus slew rate parameter space of recent, powerful gradient systems.

Cardiac computational modelling

Cardiovascular diseases currently have a major social and economic impact, constituting one of the leading causes of mortality and morbidity. Personalized computational models of the heart are demonstrating their usefulness both to help understand the mechanisms underlying cardiac disease, and to optimize their treatment and predict the patient's response. Within this framework, the Spanish Research Network for Cardiac Computational Modelling (VHeart-SN) has been launched. The general objective of the VHeart-SN network is the development of an integrated, modular and multiscale multiphysical computational model of the heart. This general objective is addressed through the following specific objectives: a) to integrate the different numerical methods and models taking into account the specificity of patients; b) to assist in advancing knowledge of the mechanisms associated with cardiac and vascular diseases; and c) to support the application of different personalized therapies. This article presents the current state of cardiac computational modelling and different scientific works conducted by the members of the network to gain greater understanding of the characteristics and usefulness of these models.

Ionic mechanisms of ST segment elevation in electrocardiogram during acute myocardial infarction

ST elevation on an electrocardiogram is a hallmark of acute transmural ischemia. However, the underlying mechanism remains unclear. We hypothesized that high ischemic sensitivities of epicardial adenosine triphosphate-sensitive potassium (IKATP) and sodium (INa) currents play key roles in the genesis of ST elevation. Using a multi-scale heart simulation under moderately ischemic conditions, transmural heterogeneities of IKATP and INa created a transmural gradient, opposite to that observed in subendocardial injury, leading to ST elevation. These heterogeneities also contributed to the genesis of hyper-acute T waves under mildly ischemic conditions. By contrast, under severely ischemic conditions, although action potentials were suppressed transmurally, the potential gradient at the boundary between the ischemic and normal regions caused ST elevation without a contribution from transmural heterogeneity. Thus, transmural heterogeneities of ion channel properties may contribute to the genesis of ST-T changes during mild or moderate transmural ischemia, while ST elevation may be induced without the contribution of heterogeneity under severe ischemic conditions.

In silico models for evaluating proarrhythmic risk of drugs

Safety evaluation of drugs requires examination of the risk of generating Torsade de Pointes (TdP) because it can lead to sudden cardiac death. Until recently, the QT interval in the electrocardiogram (ECG) has been used in the evaluation of TdP risk because the QT interval is known to be associated with the development of TdP. Although TdP risk evaluation based on QT interval has been successful in removing drugs with TdP risk from the market, some safe drugs may have also been affected due to the low specificity of QT interval-based evaluation. For more accurate evaluation of drug safety, the comprehensive in vitro proarrhythmia assay (CiPA) has been proposed by regulatory agencies, industry, and academia. Although the CiPA initiative includes in silico evaluation of cellular action potential as a component, attempts to utilize in silico simulation in drug safety evaluation are expanding, even to simulating human ECG using biophysical three-dimensional models of the heart and torso under the effects of drugs. Here, we review recent developments in the use of in silico models for the evaluation of the proarrhythmic risk of drugs. We review the single cell, one-dimensional, two-dimensional, and three-dimensional models and their applications reported in the literature and discuss the possibility of utilizing ECG simulation in drug safety evaluation.

Human Purkinje in silico model enables mechanistic investigations into automaticity and pro-arrhythmic abnormalities

Cardiac Purkinje cells (PCs) are implicated in lethal arrhythmias caused by cardiac diseases, mutations, and drug action. However, the pro-arrhythmic mechanisms in PCs are not entirely understood, particularly in humans, as most investigations are conducted in animals. The aims of this study are to present a novel human PCs electrophysiology biophysically-detailed computational model, and to disentangle ionic mechanisms of human Purkinje-related electrophysiology, pacemaker activity and arrhythmogenicity. The new Trovato2020 model incorporates detailed Purkinje-specific ionic currents and Ca²⁺ handling, and was developed, calibrated and validated using human experimental data acquired at multiple frequencies, both in control conditions and following drug application. Multiscale investigations were performed in a Purkinje cell, in fibre and using an experimentally-calibrated population of PCs to evaluate biological variability. Simulations demonstrate the human Purkinje Trovato2020 model is the first one to yield: (i) all key AP features consistent with human Purkinje recordings; (ii) Automaticity with funny current up-regulation (iii) EADs at slow pacing and with 85% hERG block; (iv) DADs following fast pacing; (v) conduction velocity of 160 cm/s in a Purkinje fibre, as reported in human. The human in silico PCs population highlights that: (1) EADs are caused by I_CaL reactivation in PCs with large inward currents; (2) DADs and triggered APs occur in PCs experiencing Ca²⁺ accumulation, at fast pacing, caused by large L-type calcium current and small Na⁺/Ca²⁺ exchanger. The novel human Purkinje model unlocks further investigations into the role of cardiac Purkinje in ventricular arrhythmias through computer modeling and multiscale simulations.

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A human in silico AP model was developed to investigate arrhythmia in cardiac Purkinje.

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The new Purkinje model enables multiscale investigations from single cell to tissue.

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Populations of human Purkinje models reproduce and explain experimental variability.

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Ca²⁺-current reactivation triggers EADs in virtual Purkinje cells with weak repolarisation reserve.

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Ca²⁺ accumulation caused by increased Ca²⁺ and NCX currents triggers DADs.

Classifying Drugs by their Arrhythmogenic Risk Using Machine Learning

All medications have adverse effects. Among the most serious of these are cardiac arrhythmias. Current paradigms for drug safety evaluation are costly, lengthy, conservative, and impede efficient drug development. Here, we combine multiscale experiment and simulation, high-performance computing, and machine learning to create a risk estimator to stratify new and existing drugs according to their proarrhythmic potential. We capitalize on recent developments in machine learning and integrate information across 10 orders of magnitude in space and time to provide a holistic picture of the effects of drugs, either individually or in combination with other drugs. We show, both experimentally and computationally, that drug-induced arrhythmias are dominated by the interplay between two currents with opposing effects: the rapid delayed rectifier potassium current and the L-type calcium current. Using Gaussian process classification, we create a classifier that stratifies drugs into safe and arrhythmic domains for any combinations of these two currents. We demonstrate that our classifier correctly identifies the risk categories of 22 common drugs exclusively on the basis of their concentrations at 50% current block. Our new risk assessment tool explains under which conditions blocking the L-type calcium current can delay or even entirely suppress arrhythmogenic events. Using machine learning in drug safety evaluation can provide a more accurate and comprehensive mechanistic assessment of the proarrhythmic potential of new drugs. Our study paves the way toward establishing science-based criteria to accelerate drug development, design safer drugs, and reduce heart rhythm disorders.

Classifying Drugs by their Arrhythmogenic Risk Using Machine Learning

All medications have adverse effects. Among the most serious of these are cardiac arrhythmias. Current paradigms for drug safety evaluation are costly, lengthy, conservative, and impede efficient drug development. Here, we combine multiscale experiment and simulation, high-performance computing, and machine learning to create a risk estimator to stratify new and existing drugs according to their proarrhythmic potential. We capitalize on recent developments in machine learning and integrate information across 10 orders of magnitude in space and time to provide a holistic picture of the effects of drugs, either individually or in combination with other drugs. We show, both experimentally and computationally, that drug-induced arrhythmias are dominated by the interplay between two currents with opposing effects: the rapid delayed rectifier potassium current and the L-type calcium current. Using Gaussian process classification, we create a classifier that stratifies drugs into safe and arrhythmic domains for any combinations of these two currents. We demonstrate that our classifier correctly identifies the risk categories of 22 common drugs exclusively on the basis of their concentrations at 50% current block. Our new risk assessment tool explains under which conditions blocking the L-type calcium current can delay or even entirely suppress arrhythmogenic events. Using machine learning in drug safety evaluation can provide a more accurate and comprehensive mechanistic assessment of the proarrhythmic potential of new drugs. Our study paves the way toward establishing science-based criteria to accelerate drug development, design safer drugs, and reduce heart rhythm disorders.

Pharmacotherapeutic Effects of Quinidine on Short QT Syndrome by Using Purkinje-Ventricle Model: A Simulation Study

AIMS

Short QT syndrome (SQTS) arises due to gene mutations leading to accelerated ventricular repolarization, and increased risk of cardiac arrhythmias and sudden cardiac death (SCD). The SQT1, SQT2 and SQT3 variants of the SQTS result from inherited gain-of-function mutations (e.g. N588K, V307L and D172N, respectively) to potassium channels. However, the effective management of SQTS remains a challenge, and is incompletely understood. In this study, computational modelling was used to investigate pharmacotherapeutic effects of selected class I drug quinidine on SQT1, SQT2 and SQT3 variants.

METHODS AND RESULTS

The biophysically-detailed Stewart et al. model of Purkinje fibre cell action potentials and the ten Tusscher et al. model of ventricular cell action potentials were coupled together into a heterogeneous two-dimensional (2D) tissue model. Previously validated I_Kr, I_Ks and I_K1 channel formulations for SQT1, SQT2 and SQT3 were incorporated in ventricular cell and tissue models. The channel-blocking effects of quinidine on ionic currents were modelled by using Hill coefficient and IC₅₀ values from the literature. At the 10 μM concentration tested in this study, quinidine effectively prolonged the action potential duration (APD) under all the SQT1, SQT2 and SQT3 conditions. In 2D simulations, quinidine prolonged the ventricular repolarization process and prolonged the QT intervals under all SQTS variants conditions.

CONCLUSIONS

Our findings provide a rational basis for the pursuit of pharmacotherapeutic agent quinidine in the treatment of all SQTS variants.

R-From-T as a Common Mechanism of Arrhythmia Initiation in Long QT Syndromes

BACKGROUND

Long QT syndromes (LQTS) arise from many genetic and nongenetic causes with certain characteristic ECG features preceding polymorphic ventricular tachyarrhythmias (PVTs). However, how the many molecular causes result in these characteristic ECG patterns and how these patterns are mechanistically linked to the spontaneous initiation of PVT remain poorly understood.

METHODS

Anatomic human ventricle and simplified tissue models were used to investigate the mechanisms of spontaneous initiation of PVT in LQTS.

RESULTS

Spontaneous initiation of PVT was elicited by gradually ramping up ICa,L to simulate the initial phase of a sympathetic surge or by changing the heart rate, reproducing the different genotype-dependent clinical ECG features. In LQTS type 2 (LQT2) and LQTS type 3 (LQT3), T-wave alternans was observed followed by premature ventricular complexes (PVCs). Compensatory pauses occurred resulting in short-long-short sequences. As ICa,L increased further, PVT episodes occurred, always preceded by a short-long-short sequence. However, in LQTS type 1 (LQT1), once a PVC occurred, it always immediately led to an episode of PVT. Arrhythmias in LQT2 and LQT3 were bradycardia dependent, whereas those in LQT1 were not. In all 3 genotypes, PVCs always originated spontaneously from the steep repolarization gradient region and manifested on ECG as R-on-T. We call this mechanism R-from-T, to distinguish it from the classic explanation of R-on-T arrhythmogenesis in which an exogenous PVC coincidentally encounters a repolarizing region. In R-from-T, the PVC and the T wave are causally related, where steep repolarization gradients combined with enhanced ICa,L lead to PVCs emerging from the T wave. Since enhanced ICa,L was required for R-from-T to occur, suppressing window ICa,L effectively prevented arrhythmias in all 3 genotypes.

CONCLUSIONS

Despite the complex molecular causes, these results suggest that R-from-T is likely a common mechanism for PVT initiation in LQTS. Targeting ICa,L properties, such as suppressing window ICa,L or preventing excessive ICa,L increase, could be an effective unified therapy for arrhythmia prevention in LQTS.

Predicting critical drug concentrations and torsadogenic risk using a multiscale exposure-response simulator

Torsades de pointes is a serious side effect of many drugs that can trigger sudden cardiac death, even in patients with structurally normal hearts. Torsadogenic risk has traditionally been correlated with the blockage of a specific potassium channel and a prolonged recovery period in the electrocardiogram. However, the precise mechanisms by which single channel block translates into heart rhythm disorders remain incompletely understood. Here we establish a multiscale exposure-response simulator that converts block-concentration characteristics from single cell recordings into three-dimensional excitation profiles and electrocardiograms to rapidly assess torsadogenic risk. For the drug dofetilide, we characterize the QT interval and heart rate at different drug concentrations and identify the critical concentration at the onset of torsades de pointes: For dofetilide concentrations of 2x, 3x, and 4x, as multiples of the free plasma concentration Cmax = 2.1 nM, the QT interval increased by +62.0%, +71.2%, and +82.3% compared to baseline, and the heart rate changed by -21.7%, -23.3%, and +88.3%. The last number indicates that, at the critical concentration of 4x, the heart spontaneously developed an episode of a torsades-like arrhythmia. Strikingly, this critical drug concentration is higher than the concentration estimated from early afterdepolarizations in single cells and lower than in one-dimensional cable models. Our results highlight the importance of whole heart modeling and explain, at least in part, why current regulatory paradigms often fail to accurately quantify the pro-arrhythmic potential of a drug. Our exposure-response simulator could provide a more mechanistic assessment of pro-arrhythmic risk and help establish science-based guidelines to reduce rhythm disorders, design safer drugs, and accelerate drug development.

Cardiac optogenetics: a novel approach to cardiovascular disease therapy

Optogenetics is a cell-type specific and high spatial-temporal resolution method that combines genetic encoding of light-sensitive proteins and optical manipulation techniques. Optogenetics technology provides a novel approach for research on cardiac arrhythmia treatment, including pacing, recovering the conduction system, and achieving cardiac resynchronization with precise and low-energy optical control. Photosensitive proteins, which usually act as ion channels, pumps, or receptors, are delivered to target cells, where they respond to light pulses of specific wavelengths, evoke transient flows of transmembrane ion currents, and induce signal transmission. With the development of gene technology, the in vivo efficiency of optogenetics in cardiology has been trialed, and in vitro experiments have been performed to test its potential in cardiac electrophysiology. Challenges for applying optogenetics in large animals and humans include the effectiveness, safety, and long-term expression of photosensitive proteins, unscattered and unattenuated exogenous light stimulation, and the need for implantable miniature light stimulators. Photosensitive proteins, genetic engineering technology, and light equipment are essential for experiments in cardiac optogenetics. Optogenetics may provide an alternative method for evaluating the mechanism of cardiac arrhythmias, testing hypotheses, and treating cardiovascular diseases.

Machine learning in drug development: Characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification

Prolonged QT intervals are a major risk factor for ventricular arrhythmias and a leading cause of sudden cardiac death. Various drugs are known to trigger QT interval prolongation and increase the proarrhythmic potential. Yet, how precisely the action of drugs on the cellular level translates into QT interval prolongation on the whole organ level remains insufficiently understood. Here we use machine learning techniques to systematically characterize the effect of 30 common drugs on the QT interval. We combine information from high fidelity three-dimensional human heart simulations with low fidelity one-dimensional cable simulations to build a surrogate model for the QT interval using multi-fidelity Gaussian process regression. Once trained and cross-validated, we apply our surrogate model to perform sensitivity analysis and uncertainty quantification. Our sensitivity analysis suggests that compounds that block the rapid delayed rectifier potassium current I Kr have the greatest prolonging effect of the QT interval, and that blocking the L-type calcium current I CaL and late sodium current I NaL shortens the QT interval. Our uncertainty quantification allows us to propagate the experimental variability from individual block-concentration measurements into the QT interval and reveals that QT interval uncertainty is mainly driven by the variability in I Kr block. In a final validation study, we demonstrate an excellent agreement between our predicted QT interval changes and the changes observed in a randomized clinical trial for the drugs dofetilide, quinidine, ranolazine, and verapamil. We anticipate that both the machine learning methods and the results of this study will have great potential in the efficient development of safer drugs.

Optimization of Lead Placement in the Right Ventricle During Cardiac Resynchronization Therapy. A Simulation Study

Patients suffering from heart failure and left bundle branch block show electrical ventricular dyssynchrony causing an abnormal blood pumping. Cardiac resynchronization therapy (CRT) is recommended for these patients. Patients with positive therapy response normally present QRS shortening and an increased left ventricle (LV) ejection fraction. However, around one third do not respond favorably. Therefore, optimal location of pacing leads, timing delays between leads and/or choosing related biomarkers is crucial to achieve the best possible degree of ventricular synchrony during CRT application. In this study, computational modeling is used to predict the optimal location and delay of pacing leads to improve CRT response. We use a 3D electrophysiological computational model of the heart and torso to get insight into the changes in the activation patterns obtained when the heart is paced from different regions and for different atrioventricular and interventricular delays. The model represents a heart with left bundle branch block and heart failure, and allows a detailed and accurate analysis of the electrical changes observed simultaneously in the myocardium and in the QRS complex computed in the precordial leads. Computational simulations were performed using a modified version of the O'Hara et al. action potential model, the most recent mathematical model developed for human ventricular electrophysiology. The optimal location for the pacing leads was determined by QRS maximal reduction. Additionally, the influence of Purkinje system on CRT response was assessed and correlation analysis between several parameters of the QRS was made. Simulation results showed that the right ventricle (RV) upper septum near the outflow tract is an alternative location to the RV apical lead. Furthermore, LV endocardial pacing provided better results as compared to epicardial stimulation. Finally, the time to reach the 90% of the QRS area was a good predictor of the instant at which 90% of the ventricular tissue was activated. Thus, the time to reach the 90% of the QRS area is suggested as an additional index to assess CRT effectiveness to improve biventricular synchrony.

Arrhythmic hazard map for a 3D whole-ventricle model under multiple ion channel block

Background and Purpose

To date, proposed in silico models for preclinical cardiac safety testing are limited in their predictability and usability. We previously reported a multi‐scale heart simulation that accurately predicts arrhythmogenic risk for benchmark drugs.

Experimental Approach

We created a comprehensive hazard map of drug‐induced arrhythmia based on the electrocardiogram (ECG) waveforms simulated under wide range of drug effects using the multi‐scale heart simulator described here, implemented with cell models of human cardiac electrophysiology.

Key Results

A total of 9075 electrocardiograms constitute the five‐dimensional hazard map, with coordinates representing the extent of the block of each of the five ionic currents (rapid delayed rectifier potassium current (I_Kr), fast (I_Na) and late (I_Na,L) components of the sodium current, L‐type calcium current (I_Ca,L) and slow delayed rectifier current (I_Ks)), involved in arrhythmogenesis. Results of the evaluation of arrhythmogenic risk based on this hazard map agreed well with the risk assessments reported in the literature. ECG databases also suggested that the interval between the J‐point and the T‐wave peak is a superior index of arrhythmogenicity when compared to the QT interval due to its ability to characterize the multi‐channel effects compared with QT interval.

Conclusion and Implications

Because concentration‐dependent effects on electrocardiograms of any drug can be traced on this map based on in vitro current assay data, its arrhythmogenic risk can be evaluated without performing costly and potentially risky human electrophysiological assays. Hence, the map serves as a novel tool for use in pharmaceutical research and development.

Predicting drug-induced arrhythmias by multiscale modeling

Drugs often have undesired side effects. In the heart, they can induce lethal arrhythmias such as torsades de pointes. The risk evaluation of a new compound is costly and can take a long time, which often hinders the development of new drugs. Here, we establish a high-resolution, multiscale computational model to quickly assess the cardiac toxicity of new and existing drugs. The input of the model is the drug-specific current block from single cell electrophysiology; the output is the spatio-temporal activation profile and the associated electrocardiogram. We demonstrate the potential of our model for a low-risk drug, ranolazine, and a high-risk drug, quinidine: For ranolazine, our model predicts a prolonged QT interval of 19.4% compared with baseline and a regular sinus rhythm at 60.15 beats per minute. For quinidine, our model predicts a prolonged QT interval of 78.4% and a spontaneous development of torsades de pointes both in the activation profile and in the electrocardiogram. Our model reveals the mechanisms by which electrophysiological abnormalities propagate across the spatio-temporal scales, from specific channel blockage, via altered single cell action potentials and prolonged QT intervals, to the spontaneous emergence of ventricular tachycardia in the form of torsades de pointes. Our model could have important implications for researchers, regulatory agencies, and pharmaceutical companies on rationalizing safe drug development and reducing the time-to-market of new drugs.

Predicting the cardiac toxicity of drugs using a novel multiscale exposure-response simulator

A common but serious side effect of many drugs is torsades de pointes, a rhythm disorder that can have fatal consequences. Torsadogenic risk has traditionally been associated with blockage of a specific potassium channel and an increased recovery period in the electrocardiogram. However, the mechanisms that trigger torsades de pointes remain incompletely understood. Here we establish a computational model to explore how drug-induced effects propagate from the single channel, via the single cell, to the whole heart level. Our mechanistic exposure-response simulator translates block-concentration characteristics for arbitrary drugs into three-dimensional excitation profiles and electrocardiogram recordings to rapidly assess torsadogenic risk. For the drug of dofetilide, we show that this risk is highly dose-dependent: at a concentration of 1x, QT prolongation is 55% but the heart maintains its regular sinus rhythm; at 5.7x, QT prolongation is 102% and the heart spontaneously transitions into torsades de points; at 30x, QT prolongation is 132% and the heart adapts a quasi-depolarized state with numerous rapidly flickering local excitations. Our simulations suggest that neither potassium channel blockage nor QT interval prolongation alone trigger torsades de pointes. The underlying mechanism predicted by our model is early afterdepolarization, which translates into pronounced U waves in the electrocardiogram, a signature that is correctly predicted by our model. Beyond the risk assessment of existing drugs, our exposure-response simulator can become a powerful tool to optimize the co-administration of drugs and, ultimately, guide the design of new drugs toward reducing life threatening drug-induced rhythm disorders in the heart.

Isopimaric acid - a multi-targeting ion channel modulator reducing excitability and arrhythmicity in a spontaneously beating mouse atrial cell line

AIM

Atrial fibrillation is the most common persistent cardiac arrhythmia, and it is not well controlled by present drugs. Because some resin acids open voltage-gated potassium channels and reduce neuronal excitability, we explored the effects of the resin acid isopimaric acid (IPA) on action potentials and ion currents in cardiomyocytes.

METHODS

Spontaneously beating mouse atrial HL-1 cells were investigated with the whole-cell patch-clamp technique.

RESULTS

1-25 μmol L^-1 IPA reduced the action potential frequency by up to 50%. The effect of IPA on six different voltage-gated ion channels was investigated; most voltage-dependent parameters of ion channel gating were shifted in the negative direction along the voltage axis, consistent with a hypothesis that a lipophilic and negatively charged compound binds to the lipid membrane close to the positively charged voltage sensor of the ion channels. The major finding was that IPA inactivated sodium channels and L- and T-type calcium channels and activated the rapidly activating potassium channel and the transient outward potassium channel. Computer simulations of IPA effects on all of the ion currents were consistent with a reduced excitability, and they also showed that effects on the Na channel played the largest role to reduce the action potential frequency. Finally, induced arrhythmia in the HL-1 cells was reversed by IPA.

CONCLUSION

Low concentrations of IPA reduced the action potential frequency and restored regular firing by altering the voltage dependencies of several voltage-gated ion channels. These findings can form the basis for a new pharmacological strategy to treat atrial fibrillation.

Interaction between pancreatic β cell and electromagnetic fields: A systematic study toward finding the natural frequency spectrum of β cell system

Interaction between biological systems and environmental electric or magnetic fields has gained attention during the past few decades. Although there are a lot of studies that have been conducted for investigating such interaction, the reported results are considerably inconsistent. Besides the complexity of biological systems, the important reason for such inconsistent results may arise due to different excitation protocols that have been applied in different experiments. In order to investigate carefully the way that external electric or magnetic fields interact with a biological system, the parameters of excitation, such as intensity or frequency, should be selected purposefully due to the influence of these parameters on the system response. In this study, pancreatic β cell, the main player of blood glucose regulating system, is considered and the study is focused on finding the natural frequency spectrum of the system using modeling approach. Natural frequencies of a system are important characteristics of the system when external excitation is applied. The result of this study can help researchers to select proper frequency parameter for electrical excitation of β cell system. The results show that there are two distinct frequency ranges for natural frequency of β cell system, which consist of extremely low (or near zero) and 100-750 kHz frequency ranges. There are experimental works on β cell exposure to electromagnetic fields that support such finding.

Efficient computation of electrograms and ECGs in human whole heart simulations using a reaction-eikonal model

Anatomically accurate and biophysically detailed bidomain models of the human heart have proven a powerful tool for gaining quantitative insight into the links between electrical sources in the myocardium and the concomitant current flow in the surrounding medium as they represent their relationship mechanistically based on first principles. Such models are increasingly considered as a clinical research tool with the perspective of being used, ultimately, as a complementary diagnostic modality. An important prerequisite in many clinical modeling applications is the ability of models to faithfully replicate potential maps and electrograms recorded from a given patient. However, while the personalization of electrophysiology models based on the gold standard bidomain formulation is in principle feasible, the associated computational expenses are significant, rendering their use incompatible with clinical time frames. In this study we report on the development of a novel computationally efficient reaction-eikonal (R-E) model for modeling extracellular potential maps and electrograms. Using a biventricular human electrophysiology model, which incorporates a topologically realistic His-Purkinje system (HPS), we demonstrate by comparing against a high-resolution reaction-diffusion (R-D) bidomain model that the R-E model predicts extracellular potential fields, electrograms as well as ECGs at the body surface with high fidelity and offers vast computational savings greater than three orders of magnitude. Due to their efficiency R-E models are ideally suitable for forward simulations in clinical modeling studies which attempt to personalize electrophysiological model features.

An atlas- and data-driven approach to initializing reaction-diffusion systems in computer cardiac electrophysiology

The cardiac electrophysiology (EP) problem is governed by a nonlinear anisotropic reaction-diffusion system with a very rapidly varying reaction term associated with the transmembrane cell current. The nonlinearity associated with the cell models requires a stabilization process before any simulation is performed. More importantly, when used in a 3-dimensional (3D) anatomy, it is not sufficient to perform this stabilization on the basis of isolated cells only, since the coupling of the different cells through the tissue greatly modulates the dynamics of the system. Therefore, stabilization of the system must be performed on the entire 3D model. This work develops a novel procedure for the initialization of reaction-diffusion systems for numerical simulations of cardiac EP from steady-state conditions. We exploit surface point correspondence to establish volumetric point correspondence. Upon introduction of a new 3D anatomy with surface point correspondence, a prediction of the cell model steady states is derived from the set of earlier biophysical simulations. We show that the prediction error is typically less than 10% for all model variables, with most variables showing even greater accuracy. When initializing simulations with the predicted model states, it is demonstrated that simulation times can be cut by at least two-thirds and potentially more, which saves hours or days of high-performance computing. Overall, these results increase the clinical applicability of detailed computational EP studies on personalized anatomies.

Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks

Cardiac Purkinje fibers provide an important pathway to the coordinated contraction of the heart. We present a numerical algorithm for the solution of electrophysiology problems across the Purkinje network that is efficient enough to be used in in silico studies on realistic Purkinje networks with physiologically detailed models of ion exchange at the cell membrane. The algorithm is on the basis of operator splitting and is provided with 3 different implementations: pure CPU, hybrid CPU/GPU, and pure GPU. Compared to our previous work, we modify the explicit gap junction term at network bifurcations to improve its mathematical consistency. Due to this improved consistency of the model, we are able to perform an empirical convergence study against analytical solutions. The study verified that all 3 implementations produce equivalent convergence rates, and shows that the algorithm produces equivalent result across different hardware platforms. Finally, we compare the efficiency of all 3 implementations on Purkinje networks of increasing spatial resolution using membrane models of increasing complexity. Both hybrid and pure GPU implementations outperform the pure CPU implementation, but their relative performance difference depends on the size of the Purkinje network and the complexity of the membrane model used.

Calcium dynamics in cardiac excitatory and non-excitatory cells and the role of gap junction

Calcium ions aid in the generation of action potential in myocytes and are responsible for the excitation-contraction coupling of heart. The heart muscle has specialized patches of cells, called excitatory cells (EC) such as the Sino-atrial node cells capable of auto-generation of action potential and cells which receive signals from the excitatory cells, called non-excitatory cells (NEC) such as cells of the ventricular and auricular walls. In order to understand cardiac calcium homeostasis, it is, therefore, important to study the calcium dynamics taking into account both types of cardiac cells. Here we have developed a model to capture the calcium dynamics in excitatory and non-excitatory cells taking into consideration the gap junction mediated calcium ion transfer from excitatory cell to non-excitatory cell. Our study revealed that the gap junctional coupling between excitatory and non-excitatory cells plays important role in the calcium dynamics. It is observed that any reduction in the functioning of gap junction may result in abnormal calcium oscillations in NEC, even when the calcium dynamics is normal in EC cell. Sensitivity of gap junction is observed to be independent of the pacing rate and hence a careful monitoring is required to maintain normal cardiomyocyte condition. It also highlights that sarcoplasmic reticulum may not be always able to control the amount of cytoplasmic calcium under the condition of calcium overload.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers

We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-duration-restitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network.

Inter-individual variability and modeling of electrical activity: a possible new approach to explore cardiac safety?

Safety pharmacology aims to predict rare side effects of new drugs. We explored whether rare pro-arrhythmic effects could be linked to the variability of the effects of these drugs on ion currents and whether taking into consideration this variability in computational models could help to better detect and predict cardiac side effects. For this purpose, we evaluated how intra- and inter-individual variability influences the effect of hERG inhibition on both the action potential duration and the occurrence of arrhythmias. Using two computer simulation models of human action potentials (endocardial and Purkinje cells), we analyzed the contribution of two biological parameters on the pro-arrhythmic effects of several hERG channel blockers: (i) spermine concentration, which varies with metabolic status, and (ii) L-type calcium conductance, which varies due to single nucleotide polymorphisms or mutations. By varying these parameters, we were able to induce arrhythmias in 1 out of 16 simulations although conventional modeling methods to detect pro-arrhythmic molecules failed. On the basis of our results, taking into consideration only 2 parameters subjected to intra- and inter-individual variability, we propose that in silico computer modeling may help to better define the risks of new drug candidates at early stages of pre-clinical development.

In Silico Evaluation of the Potential Antiarrhythmic Effect of Epigallocatechin-3-Gallate on Cardiac Channelopathies

Ion channels are transmembrane proteins that allow the passage of ions according to the direction of their electrochemical gradients. Mutations in more than 30 genes encoding ion channels have been associated with an increasingly wide range of inherited cardiac arrhythmias. In this line, ion channels become one of the most important molecular targets for several classes of drugs, including antiarrhythmics. Nevertheless, antiarrhythmic drugs are usually accompanied by some serious side effects. Thus, developing new approaches could offer added values to prevent and treat the episodes of arrhythmia. In this sense, green tea catechins seem to be a promising alternative because of the significant effect of Epigallocatechin-3-Gallate (E3G) on the electrocardiographic wave forms of guinea pig hearts. Thus, the aim of this study was to evaluate the benefits-risks balance of E3G consumption in the setting of ion channel mutations linked with aberrant cardiac excitability phenotypes. Two gain-of-function mutations, Na_v1.5-p.R222Q and Na_v1.5-p.I141V, which are linked with cardiac hyperexcitability phenotypes were studied. Computer simulations of action potentials (APs) show that 30 μM E3G reduces and suppresses AP abnormalities characteristics of these phenotypes. These results suggest that E3G may have a beneficial effect in the setting of cardiac sodium channelopathies displaying a hyperexcitability phenotype.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Modeling Electrophysiological Coupling and Fusion between Human Mesenchymal Stem Cells and Cardiomyocytes

Human mesenchymal stem cell (hMSC) delivery has demonstrated promise in preclinical and clinical trials for myocardial infarction therapy; however, broad acceptance is hindered by limited understanding of hMSC-human cardiomyocyte (hCM) interactions. To better understand the electrophysiological consequences of direct heterocellular connections between hMSCs and hCMs, three original mathematical models were developed, representing an experimentally verified triad of hMSC families with distinct functional ion channel currents. The arrhythmogenic risk of such direct electrical interactions in the setting of healthy adult myocardium was predicted by coupling and fusing these hMSC models to the published ten Tusscher midcardial hCM model. Substantial variations in action potential waveform—such as decreased action potential duration (APD) and plateau height—were found when hCMs were coupled to the two hMSC models expressing functional delayed rectifier-like human ether à-go-go K⁺ channel 1 (hEAG1); the effects were exacerbated for fused hMSC-hCM hybrid cells. The third family of hMSCs (Type C), absent of hEAG1 activity, led to smaller single-cell action potential alterations during coupling and fusion, translating to longer tissue-level mean action potential wavelength. In a simulated 2-D monolayer of cardiac tissue, re-entry vulnerability with low (5%) hMSC insertion was approximately eight-fold lower with Type C hMSCs compared to hEAG1-functional hMSCs. A 20% decrease in APD dispersion by Type C hMSCs compared to hEAG1-active hMSCs supports the claim of reduced arrhythmogenic potential of this cell type with low hMSC insertion. However, at moderate (15%) and high (25%) hMSC insertion, the vulnerable window increased independent of hMSC type. In summary, this study provides novel electrophysiological models of hMSCs, predicts possible arrhythmogenic effects of hMSCs when directly coupled to healthy hCMs, and proposes that isolating a subset of hMSCs absent of hEAG1 activity may offer increased safety as a cell delivery cardiotherapy at low levels of hMSC-hCM coupling.

Myocardial infarction—better known as a heart attack—strikes on average every 43 seconds in America. An emerging approach to treat myocardial infarction patients involves the delivery of human mesenchymal stem cells (hMSCs) to the damaged heart. While clinical trials of this therapeutic approach have yet to report adverse effects on heart electrical rhythm, such consequences have been implicated in simpler experimental systems and thus remain a concern. In this study, we utilized mathematical modeling to simulate electrical interactions arising from direct coupling between hMSCs and human heart cells to develop insight into the possible adverse effects of this therapeutic approach on human heart electrical activity, and to assess a novel strategy for reducing some potential risks of this therapy. We developed the first mathematical models of electrical activity of three families of hMSCs based on published experimental data, and integrated these with previously established mathematical models of human heart cell electrical activity. Our computer simulations demonstrated that one particular family of hMSCs minimized the disturbances in cardiac electrical activity both at the single-cell and tissue levels, suggesting that isolating this specific sub-population of hMSCs for myocardial delivery could potentially increase the safety of future hMSC-based heart therapies.