Properties and ionic mechanisms of action potential adaptation, restitution, and accommodation in canine epicardium

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.

Circadian regulation of sinoatrial nodal cell pacemaking function: Dissecting the roles of autonomic control, body temperature, and local circadian rhythmicity

Strong circadian (~24h) rhythms in heart rate (HR) are critical for flexible regulation of cardiac pacemaking function throughout the day. While this circadian flexibility in HR is sustained in diverse conditions, it declines with age, accompanied by reduced maximal HR performance. The intricate regulation of circadian HR involves the orchestration of the autonomic nervous system (ANS), circadian rhythms of body temperature (CRBT), and local circadian rhythmicity (LCR), which has not been fully understood. Here, we developed a mathematical model describing ANS, CRBT, and LCR in sinoatrial nodal cells (SANC) that accurately captures distinct circadian patterns in adult and aged mice. Our model underscores how the alliance among ANS, CRBT, and LCR achieves circadian flexibility to cover a wide range of firing rates in SANC, performance to achieve maximal firing rates, while preserving robustness to generate rhythmic firing patterns irrespective of external conditions. Specifically, while ANS dominates in promoting SANC flexibility and performance, CRBT and LCR act as primary and secondary boosters, respectively, to further enhance SANC flexibility and performance. Disruption of this alliance with age results in impaired SANC flexibility and performance, but not robustness. This unexpected outcome is primarily attributed to the age-related reduction in parasympathetic activities, which maintains SANC robustness while compromising flexibility. Our work sheds light on the critical alliance of ANS, CRBT, and LCR in regulating time-of-day cardiac pacemaking function and dysfunction, offering insights into novel therapeutic targets for the prevention and treatment of cardiac arrhythmias.

Targeted activation of human ether-à-go-go-related gene channels rescues electrical instability induced by the R56Q+/- long QT syndrome variant

AIMS

Long QT syndrome type 2 (LQTS2) is associated with inherited variants in the cardiac human ether-à-go-go-related gene (hERG) K+ channel. However, the pathogenicity of hERG channel gene variants is often uncertain. Using CRISPR-Cas9 gene-edited hiPSC-derived cardiomyocytes (hiPSC-CMs), we investigated the pathogenic mechanism underlying the LQTS-associated hERG R56Q variant and its phenotypic rescue by using the Type 1 hERG activator, RPR260243.

METHODS AND RESULTS

The above approaches enable characterization of the unclear causative mechanism of arrhythmia in the R56Q variant (an N-terminal PAS domain mutation that primarily accelerates channel deactivation) and translational investigation of the potential for targeted pharmacologic manipulation of hERG deactivation. Using perforated patch clamp electrophysiology of single hiPSC-CMs, programmed electrical stimulation showed that the hERG R56Q variant does not significantly alter the mean action potential duration (APD90). However, the R56Q variant increases the beat-to-beat variability in APD90 during pacing at constant cycle lengths, enhances the variance of APD90 during rate transitions, and increases the incidence of 2:1 block. During paired S1-S2 stimulations measuring electrical restitution properties, the R56Q variant was also found to increase the variability in rise time and duration of the response to premature stimulations. Application of the hERG channel activator, RPR260243, reduces the APD variance in hERG R56Q hiPSC-CMs, reduces the variability in responses to premature stimulations, and increases the post-repolarization refractoriness.

CONCLUSION

Based on our findings, we propose that the hERG R56Q variant leads to heterogeneous APD dynamics, which could result in spatial dispersion of repolarization and increased risk for re-entry without significantly affecting the average APD90. Furthermore, our data highlight the antiarrhythmic potential of targeted slowing of hERG deactivation gating, which we demonstrate increases protection against premature action potentials and reduces electrical heterogeneity in hiPSC-CMs.

Multichannel modulation of depolarizing and repolarizing ion currents increases the positive rate-dependent action potential prolongation

Prolongation of the action potential duration (APD) could prevent reentrant arrhythmias if prolongation occurs at the fast excitation rates of tachycardia with minimal prolongation at slow excitation rates (i.e., if prolongation is positive rate-dependent). APD prolongation by current anti-arrhythmic agents is either reverse (larger APD prolongation at slow rates than at fast rates) or neutral (similar APD prolongation at slow and fast rates), which may not result in an effective anti-arrhythmic action. In this report we show that, in computer models of the human ventricular action potential, the combined modulation of both depolarizing and repolarizing ion currents results in a stronger positive rate-dependent APD prolongation than modulation of repolarizing potassium currents. A robust positive rate-dependent APD prolongation correlates with an acceleration of phase 2 repolarization and a deceleration of phase 3 repolarization, which leads to a triangulation of the action potential. A positive rate-dependent APD prolongation decreases the repolarization reserve with respect to control, which can be managed by interventions that prolong APD at fast excitation rates and shorten APD at slow excitation rates. For both computer models of the action potential, I_CaL and I_K1 are the most important ion currents to achieve a positive rate-dependent APD prolongation. In conclusion, multichannel modulation of depolarizing and repolarizing ion currents, with ion channel activators and blockers, results in a robust APD prolongation at fast excitation rates, which should be anti-arrhythmic, while minimizing APD prolongation at slow heart rates, which should reduce pro-arrhythmic risks.

Spatiotemporal patterns of early afterdepolarizations underlying abnormal T-wave morphologies in a tissue model of the Purkinje-ventricular system

Sudden cardiac death (SCD) is a leading cause of death worldwide, and the majority of SCDs are caused by acute ventricular arrhythmias (VAs). Early afterdepolarizations (EADs) are an important trigger of VA under pathological conditions, e.g., inherited or acquired long QT syndrome (LQTS). However, it remains unclear how EAD events at the cellular level are spatially organized at the tissue level to induce and maintain ventricular arrhythmias and whether the spatial-temporal patterns of EADs at the tissue level are associated with abnormal T-wave morphologies that are often observed in LQTS, such as broad-based, notched or bifid; late appearance; and pointed T-waves. Here, a tissue model of the Purkinje-ventricular system (PVS) was developed to quantitatively investigate the complex spatial-temporal dynamics of EADs during T-wave abnormalities. We found that (1) while major inhibition of ICaL can substantially reduce the excitability of the PVS leading to conduction failures, moderate ICaL inhibition can promote occurrences of AP alternans at short cycle lengths (CLs), and EAD events preferentially occur with a major reduction of IKr (>50%) at long CLs; (2) with a minor reduction of ICaL, spatially synchronized steady-state EAD events with inverted and biphasic T-waves can be "weakened" into beat-to-beat concurrences of spatially synchronized EADs and T-wave alternans, and as pacing CLs increase, beat-to-beat concurrences of localized EADs with late-appearing and pointed T-wave morphologies can be observed; (3) under certain conditions, localized EAD events in the midmyocardium may trigger slow uni-directional electric propagation with inverted (antegrade) or upright (retrograde) broad-based T-waves; (4) spatially discordant EADs were typically characterized by desynchronized spontaneous onsets of EAD events between two groups of PVS tissues with biphasic T-wave morphologies, and they can evolve into spatially discordant oscillating EAD patterns with sustained or self-terminated alternating EAD and electrocardiogram (ECG) patterns. Our results provide new insights into the spatiotemporal aspects of the onset and development of EADs and suggest possible mechanistic links between the complex spatial dynamics of EADs and T-wave morphologies.

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

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

Guidelines for assessment of cardiac electrophysiology and arrhythmias in small animals

Cardiac arrhythmias are a major cause of morbidity and mortality worldwide. Although recent advances in cell-based models, including human-induced pluripotent stem cell-derived cardiomyocytes (iPSC-CM), are contributing to our understanding of electrophysiology and arrhythmia mechanisms, preclinical animal studies of cardiovascular disease remain a mainstay. Over the past several decades, animal models of cardiovascular disease have advanced our understanding of pathological remodeling, arrhythmia mechanisms, and drug effects and have led to major improvements in pacing and defibrillation therapies. There exist a variety of methodological approaches for the assessment of cardiac electrophysiology and a plethora of parameters may be assessed with each approach. This guidelines article will provide an overview of the strengths and limitations of several common techniques used to assess electrophysiology and arrhythmia mechanisms at the whole animal, whole heart, and tissue level with a focus on small animal models. We also define key electrophysiological parameters that should be assessed, along with their physiological underpinnings, and the best methods with which to assess these parameters.

Oxytocin exerts harmful cardiac repolarization prolonging effects in drug-induced LQTS

Background

Oxytocin is used therapeutically in psychiatric patients. Many of these also receive anti-depressant or anti-psychotic drugs causing acquired long-QT-syndrome (LQTS) by blocking HERG/I_Kr. We previously identified an oxytocin-induced QT-prolongation in LQT2 rabbits, indicating potential harmful effects of combined therapy. We thus aimed to analyze the effects of dual therapy with oxytocin and fluoxetine/risperidone on cardiac repolarization.

Methods

Effects of risperidone, fluoxetine and oxytocin on QT/QTc, short-term variability (STV) of QT, and APD were assessed in rabbits using in vivo ECG and ex vivo monophasic AP recordings in Langendorff-perfused hearts. Underlying mechanisms were assessed using patch clamp in isolated cardiomyocytes.

Results

Oxytocin, fluoxetine and risperidone prolonged QTc and APD in whole hearts. The combination of fluoxetine + oxytocin resulted in further QTc- and APD-prolongation, risperidone + oxytocin tended to increase QTc and APD compared to monotherapy. Temporal QT instability, STV_QTc was increased by oxytocin, fluoxetine / fluoxetine + oxytocin and risperidone / risperidone + oxytocin. Similar APD-prolonging effects were confirmed in isolated cardiomyocytes due to differential effects of the compounds on repolarizing ion currents: Oxytocin reduced I_Ks, fluoxetine and risperidone reduced I_Kr, resulting in additive effects on I_Ktotal-tail. In addition, oxytocin reduced I_K1, further reducing the repolarization reserve.

Conclusion

Oxytocin, risperidone and fluoxetine prolong QTc / APD. Combined treatment further prolongs QTc/APD due to differential effects on I_Ks and I_K1 (block by oxytocin) and I_Kr (block by risperidone and fluoxetine), leading to pronounced impairment of repolarization reserve. Oxytocin should be used with caution in patients in the context of acquired LQTS.

Positive rate-dependent action potential prolongation by modulating potassium ion channels

Pharmacological agents that prolong action potential duration (APD) to a larger extent at slow rates than at the fast excitation rates typical of ventricular tachycardia exhibit reverse rate dependence. Reverse rate dependence has been linked to the lack of efficacy of class III agents at preventing arrhythmias because the doses required to have an antiarrhythmic effect at fast rates may have pro-arrhythmic effects at slow rates due to an excessive APD prolongation. In this report, we show that, in computer models of the ventricular action potential, APD prolongation by accelerating phase 2 repolarization (by increasing I_Ks ) and decelerating phase 3 repolarization (by blocking I_Kr and I_K1 ) results in a robust positive rate dependence (i.e., larger APD prolongation at fast rates than at slow rates). In contrast, APD prolongation by blocking a specific potassium channel type results in reverse rate dependence or a moderate positive rate dependence. Interventions that result in a strong positive rate dependence tend to decrease the repolarization reserve because they require substantial I_K1 block. However, limiting I_K1 block to ~50% results in a strong positive rate dependence with moderate decrease in repolarization reserve. In conclusion, the use of a combination of I_Ks activators and I_Kr and I_K1 blockers could result in APD prolongation that potentially maximizes antiarrhythmic effects (by maximizing APD prolongation at fast excitation rates) and minimizes pro-arrhythmic effects (by minimizing APD prolongation at slow excitation rates).

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

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

Bifurcations and Proarrhythmic Behaviors in Cardiac Electrical Excitations

The heart is a hierarchical dynamic system consisting of molecules, cells, and tissues, and acts as a pump for blood circulation. The pumping function depends critically on the preceding electrical activity, and disturbances in the pattern of excitation propagation lead to cardiac arrhythmia and pump failure. Excitation phenomena in cardiomyocytes have been modeled as a nonlinear dynamical system. Because of the nonlinearity of excitation phenomena, the system dynamics could be complex, and various analyses have been performed to understand the complex dynamics. Understanding the mechanisms underlying proarrhythmic responses in the heart is crucial for developing new ways to prevent and control cardiac arrhythmias and resulting contractile dysfunction. When the heart changes to a pathological state over time, the action potential (AP) in cardiomyocytes may also change to a different state in shape and duration, often undergoing a qualitative change in behavior. Such a dynamic change is called bifurcation. In this review, we first summarize the contribution of ion channels and transporters to AP formation and our knowledge of ion-transport molecules, then briefly describe bifurcation theory for nonlinear dynamical systems, and finally detail its recent progress, focusing on the research that attempts to understand the developing mechanisms of abnormal excitations in cardiomyocytes from the perspective of bifurcation phenomena.

Exploring the Coordination of Cardiac Ion Channels With Action Potential Clamp Technique

The patch clamp technique underwent continual advancement and developed numerous variants in cardiac electrophysiology since its introduction in the late 1970s. In the beginning, the capability of the technique was limited to recording one single current from one cell stimulated with a rectangular command pulse. Since that time, the technique has been extended to record multiple currents under various command pulses including action potential. The current review summarizes the development of the patch clamp technique in cardiac electrophysiology with special focus on the potential applications in integrative physiology.

Absence of Rgs5 Influences the Spatial and Temporal Fluctuation of Cardiac Repolarization in Mice

Aims

This study investigated the contribution of the regulator of G-protein signaling 5 (Rgs5) knockout to the alteration of the action potential duration (APD) restitution and repolarizing dispersion in ventricle.

Methods and Results

The effects of Rgs5^–/– were investigated by QT variance (QTv) and heart rate variability analysis of Rgs5^–/– mice. Monophasic action potential analysis was investigated in isolated Rgs5^–/– heart. Rgs5^–/– did not promote ventricular remodeling. The 24-h QTv and QT variability index (QTVI) of the Rgs5^–/– mice were higher than those of wild-type (WT) mice (P < 0.01). In WT mice, a positive correlation was found between QTv and the standard deviation of all NN intervals (r = 0.62; P < 0.01), but not in Rgs5^–/– mice (R = 0.01; P > 0.05). The absence of Rgs5 resulted in a significant prolongation of effective refractory period and APD in isolated ventricle. In addition, compared with WT mice, the knockout of Rgs5 significantly deepened the slope of the APD recovery curve at all 10 sites of the heart (P < 0.01) and increased the spatial dispersions of S_max (COV-S_max) (WT: 0.28 ± 0.03, Rgs5^–/–: 0.53 ± 0.08, P < 0.01). Compared with WT heart, Rgs5^–/– increased the induced S1–S2 interval at all sites of heart and widened the window of vulnerability of ventricular tachyarrhythmia (P < 0.05).

Conclusion

Our findings indicate that Rgs5^–/– is an important regulator of ventricular tachyarrhythmia in mice by prolonging ventricular repolarization and increasing spatial dispersion in ventricle.

Adaptation of ventricular repolarization time following abrupt changes in heart rate: comparisons and reproducibility of repeated atrial and ventricular pacing

Adequate adaptation of ventricular repolarization (VR) duration to changes in heart rate (HR) is important for cardiac electromechanical function and electrical stability. We studied the QT and QT_peak adaptation in response to abrupt start and stop of atrial and ventricular pacing on two occasions with an interval of at least 1 mo in 25 study subjects with permanent pacemakers. Frank vectorcardiography was used for data collection. Atrial or ventricular pacing was performed for 8 min aiming at a cycle length (CL) of 500 ms. We measured the immediate response (IR), the time constant (τ) of the exponential phase, and T90 End, the time to reach 90% change of QT and QT_peak from baseline to steady state during and after pacing. During atrial pacing, the CL decreased on average 45% from mean (SD) 944 (120) to 518 (46) ms and QT decreased on average 18% from 388 (20) to 318 (17) ms. For QT, T90 End was 103 (24) s and 126 (15) s after start versus stop of atrial pacing; a difference of 24 (27) s (P = 0.006). The response pattern was similar for τ but IR did not differ significantly between pacing start and stop. The response pattern was similar for QT_peak and also for QT and QT_peak following ventricular pacing start and stop. The coefficients of variation for repeated measures were 7%-21% for T90 End and τ. In conclusion, the adaptation of VR duration was significantly more rapid following increasing than decreasing HR and intraindividually a relatively reproducible process.NEW & NOTEWORTHY We studied the duration of ventricular repolarization (VR) adaptation and its hysteresis, following increasing and decreasing heart rate by abrupt start and stop of 8-min atrial or ventricular pacing in study subjects with permanent pacemakers and repeated the protocol with ≥1 mo interval, a novel approach. VR adaptation was significantly longer following decreasing than increasing heart rate corroborating previous observations. Furthermore, VR adaptation was intraindividually a reproducible and, hence, robust phenomenon, a novel finding.

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.

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.

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 ICaL 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.

Intercellular Sodium Regulates Repolarization in Cardiac Tissue with Sodium Channel Gain of Function

In cardiac myocytes, action potentials are initiated by an influx of sodium (Na⁺) ions via voltage-gated Na⁺ channels. Na⁺ channel gain of function (GOF), arising in both inherited conditions associated with mutation in the gene encoding the Na⁺ channel and acquired conditions associated with heart failure, ischemia, and atrial fibrillation, enhance Na⁺ influx, generating a late Na⁺ current that prolongs action potential duration (APD) and triggering proarrhythmic early afterdepolarizations (EADs). Recent studies have shown that Na⁺ channels are highly clustered at the myocyte intercalated disk, facilitating formation of Na⁺ nanodomains in the intercellular cleft between cells. Simulations from our group have recently predicted that narrowing the width of the intercellular cleft can suppress APD prolongation and EADs in the presence of Na⁺ channel mutations because of increased intercellular cleft Na⁺ ion depletion. In this study, we investigate the effects of modulating multiple extracellular spaces, specifically the intercellular cleft and bulk interstitial space, in a novel computational model and experimentally via osmotic agents albumin, dextran 70, and mannitol. We perform optical mapping and transmission electron microscopy in a drug-induced (sea anemone toxin, ATXII) Na⁺ channel GOF isolated heart model and modulate extracellular spaces via osmotic agents. Single-cell patch-clamp experiments confirmed that the osmotic agents individually do not enhance late Na⁺ current. Both experiments and simulations are consistent with the conclusion that intercellular cleft narrowing or expansion regulates APD prolongation; in contrast, modulating the bulk interstitial space has negligible effects on repolarization. Thus, we predict that intercellular cleft Na⁺ nanodomain formation and collapse critically regulates cardiac repolarization in the setting of Na⁺ channel GOF.

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.

Smeared Multiscale Finite Element Models for Mass Transport and Electrophysiology Coupled to Muscle Mechanics

Mass transport represents the most fundamental process in living organisms. It includes delivery of nutrients, oxygen, drugs, and other substances from the vascular system to tissue and transport of waste and other products from cells back to vascular and lymphatic network and organs. Furthermore, movement is achieved by mechanical forces generated by muscles in coordination with the nervous system. The signals coming from the brain, which have the character of electrical waves, produce activation within muscle cells. Therefore, from a physics perspective, there exist a number of physical fields within the body, such as velocities of transport, pressures, concentrations of substances, and electrical potential, which is directly coupled to biochemical processes of transforming the chemical into mechanical energy and further internal forces for motion. The overall problems of mass transport and electrophysiology coupled to mechanics can be investigated theoretically by developing appropriate computational models. Due to the enormous complexity of the biological system, it would be almost impossible to establish a detailed computational model for the physical fields related to mass transport, electrophysiology, and coupled fields. To make computational models feasible for applications, we here summarize a concept of smeared physical fields, with coupling among them, and muscle mechanics, which includes dependence on the electrical potential. Accuracy of the smeared computational models, also with coupling to muscle mechanics, is illustrated with simple example, while their applicability is demonstrated on a liver model with tumors present. The last example shows that the introduced methodology is applicable to large biological systems.

Transmural and rate-dependent profiling of drug-induced arrhythmogenic risks through in silico simulations of multichannel pharmacology

In vitro human ether-à-go-go related gene (hERG) inhibition assay alone might provide insufficient information to discriminate "safe" from "dangerous" drugs. Here, effects of multichannel inhibition on cardiac electrophysiology were investigated using a family of cardiac cell models (Purkinje (P), endocardial (Endo), mid-myocardial (M) and epicardial (Epi)). We found that: (1) QT prolongation alone might not necessarily lead to early afterdepolarization (EAD) events, and it might be insufficient to predict arrhythmogenic liability; (2) the occurrence and onset of EAD events could be a candidate biomarker of drug-induced arrhythmogenicity; (3) M cells are more vulnerable to drug-induced arrhythmias, and can develop early afterdepolarization (EAD) at slower pacing rates; (4) the application of quinidine can cause EADs in all cell types, while INaL is the major depolarizing current during the generation of drug-induced EAD in P cells, ICaL is mostly responsible in other cell types; (5) drug-induced action potential (AP) alternans with beat-to-beat variations occur at high pacing rates in P cells. These results suggested that quantitative profiling of transmural and rate-dependent properties can be essential to evaluate drug-induced arrhythmogenic risks, and may provide mechanistic insights into drug-induced arrhythmias.

Restitution and Stability of Human Ventricular Action Potential at High and Variable Pacing Rate

Despite the key role of beat-to-beat action potential (AP) variability in the onset of ventricular arrhythmias at high pacing rate, the knowledge of the involved dynamics and of effective prognostic parameters is largely incomplete. Electrical restitution (ER), the way AP duration (APD) senses changes in preceding cycle length (CL), has been used to monitor transition to arrhythmias. The use of standard ER (sER), though, is controversial, not always suitable for in vivo and only rarely for clinical applications. By means of simulations on a human ventricular AP model, I investigate the dynamics of APD at high pacing rate under sinusoidally, saw-tooth, and randomly variable pacing CLs. AP sequences were compared in terms of beat-to-beat restitution (btb-ER) and of the collections of sER curves generated from each beat. A definition of APD stability is also proposed, based on successive APD changes introduced in an AP sequence by a premature beat. The explored CL range includes values leading to APD alternans under constant pacing. Three different types of response to CL variability were found, corresponding to progressively higher rate of beat-to-beat CL changes. Low rates (∼1 ms/beat) generate a btb-ER dominated by steady-state rate dependence of APD (type 1), intermediate rates (∼5 ms/beat) lead to a btb-ER similar to a single sER (type 2), and high rates (∼20 ms/beat) to hysteretic btb-ER under periodic pacing and to a vertically spread btb-ER in the case of random pacing (type 3). Stability of AP repolarization always increases with the rate of CL changes. Thus, rather than looking at sER slope, which requires additional interventions during the recording of cardiac electrical activity, this study provides rationale for the use of btb-ER representations as predictors of repolarization stability under extreme pacing conditions, known to be critical for the arrhythmia development.

Four Ways to Fit an Ion Channel Model

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

Interventricular Differences in Action Potential Duration Restitution Contribute to Dissimilar Ventricular Rhythms in ex vivo Perfused Hearts

Background: Dissimilar ventricular rhythms refer to the occurrence of different ventricular tachyarrhythmias in the right and left ventricles or different rates of the same tachyarrhythmia in the two ventricles. Objective: We investigated the inducibility of dissimilar ventricular rhythms, their underlying mechanisms, and the impact of anti-arrhythmic drugs (lidocaine and amiodarone) on their occurrence. Methods: Ventricular tachyarrhythmias were induced with burst pacing in 28 Langendorff-perfused Sprague Dawley rat hearts (14 control, 8 lidocaine, 6 amiodarone) and bipolar electrograms recorded from the right and left ventricles. Fourteen (6 control, 4 lidocaine, 4 amiodarone) further hearts underwent optical mapping of transmembrane voltage to study interventricular electrophysiological differences and mechanisms of dissimilar rhythms. Results: In control hearts, dissimilar ventricular rhythms developed in 8/14 hearts (57%). In lidocaine treated hearts, there was a lower cycle length threshold for developing dissimilar rhythms, with 8/8 (100%) hearts developing dissimilar rhythms in comparison to 0/6 in the amiodarone group. Dissimilar ventricular tachycardia (VT) rates occurred at longer cycle lengths with lidocaine vs. control (57.1 ± 7.9 vs. 36.6 ± 8.4 ms, p < 0.001). The ratio of LV:RV VT rate was greater in the lidocaine group than control (1.91 ± 0.30 vs. 1.76 ± 0.36, p < 0.001). The gradient of the action potential duration (APD) restitution curve was shallower in the RV compared with LV (Control - LV: 0.12 ± 0.03 vs RV: 0.002 ± 0.03, p = 0.015), leading to LV-to-RV conduction block during VT. Conclusion: Interventricular differences in APD restitution properties likely contribute to the occurrence of dissimilar rhythms. Sodium channel blockade with lidocaine increases the likelihood of dissimilar ventricular rhythms.

Smeared multiscale finite element model for electrophysiology and ionic transport in biological tissue

Basic functions of living organisms are governed by the nervous system through bidirectional signals transmitted from the brain to neural networks. These signals are similar to electrical waves. In electrophysiology the goal is to study the electrical properties of biological cells and tissues, and the transmission of signals. From a physics perspective, there exists a field of electrical potential within the living body, the nervous system, extracellular space and cells. Electrophysiological problems can be investigated experimentally and also theoretically by developing appropriate mathematical or computational models. Due to the enormous complexity of biological systems, it would be almost impossible to establish a detailed computational model of the electrical field, even for only a single organ (e.g. heart), including the entirety of cells comprising the neural network. In order to make computational models feasible for practical applications, we here introduce the concept of smeared fields, which represents a generalization of the previously formulated multiscale smeared methodology for mass transport in blood vessels, lymph, and tissue. We demonstrate the accuracy of the smeared finite element computational models for the electric field in numerical examples. The electrical field is further coupled with ionic mass transport within tissue composed of interstitial spaces extracellularly and by cytoplasm and organelles intracellularly. The proposed methodology, which couples electrophysiology and molecular ionic transport, is applicable to a variety of biological systems.

A bilobal model of Ca2+-dependent inactivation to probe the physiology of L-type Ca2+ channels

L-type calcium channels undergo Ca²⁺-dependent inactivation (CDI) in order to precisely control the entry of Ca²⁺ into cells such as cardiomyocytes. Limpitikul et al. develop a bilobal model of CDI and use it to understand the pathogenesis of arrhythmias associated with mutations in CaM.

L-type calcium channels (LTCCs) are critical elements of normal cardiac function, playing a major role in orchestrating cardiac electrical activity and initiating downstream signaling processes. LTCCs thus use feedback mechanisms to precisely control calcium (Ca²⁺) entry into cells. Of these, Ca²⁺-dependent inactivation (CDI) is significant because it shapes cardiac action potential duration and is essential for normal cardiac rhythm. This important form of regulation is mediated by a resident Ca²⁺ sensor, calmodulin (CaM), which is comprised of two lobes that are each capable of responding to spatially distinct Ca²⁺ sources. Disruption of CaM-mediated CDI leads to severe forms of long-QT syndrome (LQTS) and life-threatening arrhythmias. Thus, a model capable of capturing the nuances of CaM-mediated CDI would facilitate increased understanding of cardiac (patho)physiology. However, one critical barrier to achieving a detailed kinetic model of CDI has been the lack of quantitative data characterizing CDI as a function of Ca²⁺. This data deficit stems from the experimental challenge of uncoupling the effect of channel gating on Ca²⁺ entry. To overcome this obstacle, we use photo-uncaging of Ca²⁺ to deliver a measurable Ca²⁺ input to CaM/LTCCs, while simultaneously recording CDI. Moreover, we use engineered CaMs with Ca²⁺ binding restricted to a single lobe, to isolate the kinetic response of each lobe. These high-resolution measurements enable us to build mathematical models for each lobe of CaM, which we use as building blocks for a full-scale bilobal model of CDI. Finally, we use this model to probe the pathogenesis of LQTS associated with mutations in CaM (calmodulinopathies). Each of these models accurately recapitulates the kinetics and steady-state properties of CDI in both physiological and pathological states, thus offering powerful new insights into the mechanistic alterations underlying cardiac arrhythmias.

Modulation of Cardiac Alternans by Altered Sarcoplasmic Reticulum Calcium Release: A Simulation Study

Background: Cardiac alternans is an important precursor to arrhythmia, facilitating formation of conduction block, and re-entry. Diseased hearts were observed to be particularly vulnerable to alternans, mainly in heart failure or after myocardial infarction. Alternans is typically linked to oscillation of calcium cycling, particularly in the sarcoplasmic reticulum (SR). While the role of SR calcium reuptake in alternans is well established, the role of altered calcium release by ryanodine receptors has not yet been studied extensively. At the same time, there is strong evidence that calcium release is abnormal in heart failure and other heart diseases, suggesting that these changes might play a pro-alternans role.

Aims: To demonstrate how changes to intracellular calcium release dynamics and magnitude affect alternans vulnerability.

Methods: We used the state-of-the-art Heijman–Rudy and O’Hara–Rudy computer models of ventricular myocyte, given their detailed representation of calcium handling and their previous utility in alternans research. We modified the models to obtain precise control over SR release dynamics and magnitude, allowing for the evaluation of these properties in alternans formation and suppression.

Results: Shorter time to peak SR release and shorter release duration decrease alternans vulnerability by improved refilling of releasable calcium within junctional SR; conversely, slow release promotes alternans. Modulating the total amount of calcium released, we show that sufficiently increased calcium release may surprisingly prevent alternans via a mechanism linked to the functional depletion of junctional SR during release. We show that this mechanism underlies differences between “eye-type” and “fork-type” alternans, which were observed in human in vivo and in silico. We also provide a detailed explanation of alternans formation in the given computer models, termed “sarcoplasmic reticulum calcium cycling refractoriness.” The mechanism relies on the steep SR load–release relationship, combined with relatively limited rate of junctional SR refilling.

Conclusion: Both altered dynamics and magnitude of SR calcium release modulate alternans vulnerability. In particular, slow dynamics of SR release, such as those observed in heart failure, promote alternans. Therefore, acceleration of intracellular calcium release, e.g., via synchronization of calcium sparks, may inhibit alternans in failing hearts and reduce arrhythmia occurrence.

Modelling variability in cardiac electrophysiology: a moment-matching approach

The variability observed in action potential (AP) cardiomyocyte measurements is the consequence of many different sources of randomness. Often ignored, this variability may be studied to gain insight into the cell ionic properties. In this paper, we focus on the study of ionic channel conductances and describe a methodology to estimate their probability density function (PDF) from AP recordings. The method relies on the matching of observable statistical moments and on the maximum entropy principle. We present four case studies using synthetic and sets of experimental AP measurements from human and canine cardiomyocytes. In each case, the proposed methodology is applied to infer the PDF of key conductances from the exhibited variability. The estimated PDFs are discussed and, when possible, compared to the true distributions. We conclude that it is possible to extract relevant information from the variability in AP measurements and discuss the limitations and possible implications of the proposed approach.

Slow [Na+]i dynamics impacts arrhythmogenesis and spiral wave reentry in cardiac myocyte ionic model

Accumulation of intracellular Na⁺ is gaining recognition as an important regulator of cardiac myocyte electrophysiology. The intracellular Na⁺ concentration can be an important determinant of the cardiac action potential duration, can modulate the tissue-level conduction of excitation waves, and can alter vulnerability to arrhythmias. Mathematical models of cardiac electrophysiology often incorporate a dynamic intracellular Na⁺ concentration, which changes much more slowly than the remaining variables. We investigated the dependence of several arrhythmogenesis-related factors on [Na⁺]_i in a mathematical model of the human atrial action potential. In cell simulations, we found that [Na⁺]_i accumulation stabilizes the action potential duration to variations in several conductances and that the slow dynamics of [Na⁺]_i impacts bifurcations to pro-arrhythmic afterdepolarizations, causing intermittency between different rhythms. In long-lasting tissue simulations of spiral wave reentry, [Na⁺]_i becomes spatially heterogeneous with a decreased area around the spiral wave rotation center. This heterogeneous region forms a functional anchor, resulting in diminished meandering of the spiral wave. Our findings suggest that slow, physiological, rate-dependent variations in [Na⁺]_i may play complex roles in cellular and tissue-level cardiac dynamics.

Revealing the Concealed Nature of Long-QT Type 3 Syndrome

BACKGROUND

Gain-of-function mutations in the voltage-gated sodium channel (Nav1.5) are associated with the long-QT-3 (LQT3) syndrome. Nav1.5 is densely expressed at the intercalated disk, and narrow intercellular separation can modulate cell-to-cell coupling via extracellular electric fields and depletion of local sodium ion nanodomains. Models predict that significantly decreasing intercellular cleft widths slows conduction because of reduced sodium current driving force, termed "self-attenuation." We tested the novel hypothesis that self-attenuation can "mask" the LQT3 phenotype by reducing the driving force and late sodium current that produces early afterdepolarizations (EADs).

METHODS AND RESULTS

Acute interstitial edema was used to increase intercellular cleft width in isolated guinea pig heart experiments. In a drug-induced LQT3 model, acute interstitial edema exacerbated action potential duration prolongation and produced EADs, in particular, at slow pacing rates. In a computational cardiac tissue model incorporating extracellular electric field coupling, intercellular cleft sodium nanodomains, and LQT3-associated mutant channels, myocytes produced EADs for wide intercellular clefts, whereas for narrow clefts, EADs were suppressed. For both wide and narrow clefts, mutant channels were incompletely inactivated. However, for narrow clefts, late sodium current was reduced via self-attenuation, a protective negative feedback mechanism, masking EADs.

CONCLUSIONS

We demonstrated a novel mechanism leading to the concealing and revealing of EADs in LQT3 models. Simulations predict that this mechanism may operate independent of the specific mutation, suggesting that future therapies could target intercellular cleft separation as a compliment or alternative to sodium channels.

β-Adrenergic receptor stimulation inhibits proarrhythmic alternans in postinfarction border zone cardiomyocytes: a computational analysis

We integrated, for the first time, postmyocardial infarction electrical and autonomic remodeling in a detailed, validated computer model of β-adrenergic stimulation in ventricular cardiomyocytes. Here, we show that β-adrenergic stimulation inhibits alternans and provide novel insights into underlying mechanisms, adding to a recent controversy about pro-/antiarrhythmic effects of postmyocardial infarction hyperinnervation.

The border zone (BZ) of the viable myocardium adjacent to an infarct undergoes extensive autonomic and electrical remodeling and is prone to repolarization alternans-induced cardiac arrhythmias. BZ remodeling processes may promote or inhibit Ca²⁺ and/or repolarization alternans and may differentially affect ventricular arrhythmogenesis. Here, we used a detailed computational model of the canine ventricular cardiomyocyte to study the determinants of alternans in the BZ and their regulation by β-adrenergic receptor (β-AR) stimulation. The BZ model developed Ca²⁺ transient alternans at slower pacing cycle lengths than the control model, suggesting that the BZ may promote spatially heterogeneous alternans formation in an infarcted heart. β-AR stimulation abolished alternans. By evaluating all combinations of downstream β-AR stimulation targets, we identified both direct (via ryanodine receptor channels) and indirect [via sarcoplasmic reticulum (SR) Ca²⁺ load] modulation of SR Ca²⁺ release as critical determinants of Ca²⁺ transient alternans. These findings were confirmed in a human ventricular cardiomyocyte model. Cell-to-cell coupling indirectly modulated the likelihood of alternans by affecting the action potential upstroke, reducing the trigger for SR Ca²⁺ release in one-dimensional strand simulations. However, β-AR stimulation inhibited alternans in both single and multicellular simulations. Taken together, these data highlight a potential antiarrhythmic role of sympathetic hyperinnervation in the BZ by reducing the likelihood of alternans and provide new insights into the underlying mechanisms controlling Ca²⁺ transient and repolarization alternans.

NEW & NOTEWORTHY We integrated, for the first time, postmyocardial infarction electrical and autonomic remodeling in a detailed, validated computer model of β-adrenergic stimulation in ventricular cardiomyocytes. Here, we show that β-adrenergic stimulation inhibits alternans and provide novel insights into underlying mechanisms, adding to a recent controversy about pro-/antiarrhythmic effects of postmyocardial infarction hyperinnervation.

Listen to this article’s corresponding podcast at http://ajpheart.podbean.com/e/%CE%B2-ar-stimulation-and-alternans-in-border-zone-cardiomyocytes/.

Mechanisms Underlying the Emergence of Post-acidosis Arrhythmia at the Tissue Level: A Theoretical Study

Acidosis has complex electrophysiological effects, which are associated with a high recurrence of ventricular arrhythmias. Through multi-scale cardiac computer modeling, this study investigated the mechanisms underlying the emergence of post-acidosis arrhythmia at the tissue level. In simulations, ten Tusscher-Panfilov ventricular model was modified to incorporate various data on acidosis-induced alterations of cellular electrophysiology and intercellular electrical coupling. The single cell models were incorporated into multicellular one-dimensional (1D) fiber and 2D sheet tissue models. Electrophysiological effects were quantified as changes of action potential profile, sink-source interactions of fiber tissue, and the vulnerability of tissue to the genesis of unidirectional conduction that led to initiation of re-entry. It was shown that acidosis-induced sarcoplasmic reticulum (SR) calcium load contributed to delayed afterdepolarizations (DADs) in single cells. These DADs may be synchronized to overcome the source-sink mismatch arising from intercellular electrotonic coupling, and produce a premature ventricular complex (PVC) at the tissue level. The PVC conduction can be unidirectionally blocked in the transmural ventricular wall with altered electrical heterogeneity, resulting in the genesis of re-entry. In conclusion, altered source-sink interactions and electrical heterogeneity due to acidosis-induced cellular electrophysiological alterations may increase susceptibility to post-acidosis ventricular arrhythmias.

The control of cardiac ventricular excitability by autonomic pathways

Central to the genesis of ventricular cardiac arrhythmia are variations in determinants of excitability. These involve individual ionic channels and transporters in cardiac myocytes but also tissue factors such as variable conduction of the excitation wave, fibrosis and source-sink mismatch. It is also known that in certain diseases and particularly the channelopathies critical events occur with specific stressors. For example, in hereditary long QT syndrome due to mutations in KCNQ1 arrhythmic episodes are provoked by exercise and in particular swimming. Thus not only is the static substrate important but also how this is modified by dynamic signalling events associated with common physiological responses. In this review, we examine the regulation of ventricular excitability by signalling pathways from a cellular and tissue perspective in an effort to identify key processes, effectors and potential therapeutic approaches. We specifically focus on the autonomic nervous system and related signalling pathways.

Role of CaMKII and PKA in Early Afterdepolarization of Human Ventricular Myocardium Cell: A Computational Model Study

Early afterdepolarization (EAD) plays an important role in arrhythmogenesis. Many experimental studies have reported that Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) and β-adrenergic signaling pathway are two important regulators. In this study, we developed a modified computational model of human ventricular myocyte to investigate the combined role of CaMKII and β-adrenergic signaling pathway on the occurrence of EADs. Our simulation results showed that (1) CaMKII overexpression facilitates EADs through the prolongation of late sodium current's (I_NaL) deactivation progress; (2) the combined effect of CaMKII overexpression and activation of β-adrenergic signaling pathway further increases the risk of EADs, where EADs could occur at shorter cycle length (2000 ms versus 4000 ms) and lower rapid delayed rectifier K⁺ current (I_Kr) blockage (77% versus 85%). In summary, this study computationally demonstrated the combined role of CaMKII and β-adrenergic signaling pathway on the occurrence of EADs, which could be useful for searching for therapy strategies to treat EADs related arrhythmogenesis.

Perpetuation of torsade de pointes in heterogeneous hearts: competing foci or re-entry?

KEY POINTS

The underlying mechanism of torsade de pointes (TdP) remains of debate: perpetuation may be due to (1) focal activity or (2) re-entrant activity. The onset of TdP correlates with action potential heterogeneities in different regions of the heart. We studied the mechanism of perpetuation of TdP in silico using a 2D model of human cardiac tissue and an anatomically accurate model of the ventricles of the human heart. We found that the mechanism of perpetuation TdP depends on the degree of heterogeneity. If the degree of heterogeneity is large, focal activity alone can sustain a TdP, otherwise re-entrant activity emerges. This result can help to understand the relationship between the mechanisms of TdP and tissue properties and may help in developing new drugs against it.

ABSTRACT

Torsade de pointes (TdP) can be the consequence of cardiac remodelling, drug effects or a combination of both. The mechanism underlying TdP is unclear, and may involve triggered focal activity or re-entry. Recent work by our group has indicated that both cases may exist, i.e. TdPs induced in the chronic atrioventricular block (CAVB) dog model may have a focal origin or are due to re-entry. Also it was found that heterogeneities might play an important role. In the current study we have used computational modelling to further investigate the mechanisms involved in TdP initiation and perpetuation, especially in the CAVB dog model, by the addition of heterogeneities with reduced repolarization reserve in comparison with the surrounding tissue. For this, the TNNP computer model was used for computations. We demonstrated in 2D and 3D simulations that ECGs with the typical TdP morphology can be caused by both multiple competing foci and re-entry circuits as a result of introduction of heterogeneities, depending on whether the heterogeneities have a large or a smaller reduced repolarization reserve in comparison with the surrounding tissue. Large heterogeneities can produce ectopic TdP, while smaller heterogeneities will produce re-entry-type TdP.

The Cardiac Electrophysiology Web Lab

Computational modeling of cardiac cellular electrophysiology has a long history, and many models are now available for different species, cell types, and experimental preparations. This success brings with it a challenge: how do we assess and compare the underlying hypotheses and emergent behaviors so that we can choose a model as a suitable basis for a new study or to characterize how a particular model behaves in different scenarios? We have created an online resource for the characterization and comparison of electrophysiological cell models in a wide range of experimental scenarios. The details of the mathematical model (quantitative assumptions and hypotheses formulated as ordinary differential equations) are separated from the experimental protocol being simulated. Each model and protocol is then encoded in computer-readable formats. A simulation tool runs virtual experiments on models encoded in CellML, and a website (https://chaste.cs.ox.ac.uk/WebLab) provides a friendly interface, allowing users to store and compare results. The system currently contains a sample of 36 models and 23 protocols, including current-voltage curve generation, action potential properties under steady pacing at different rates, restitution properties, block of particular channels, and hypo-/hyperkalemia. This resource is publicly available, open source, and free, and we invite the community to use it and become involved in future developments. Investigators interested in comparing competing hypotheses using models can make a more informed decision, and those developing new models can upload them for easy evaluation under the existing protocols, and even add their own protocols.

Experimentally-Based Computational Investigation into Beat-To-Beat Variability in Ventricular Repolarization and Its Response to Ionic Current Inhibition

Beat-to-beat variability in repolarization (BVR) has been proposed as an arrhythmic risk marker for disease and pharmacological action. The mechanisms are unclear but BVR is thought to be a cell level manifestation of ion channel stochasticity, modulated by cell-to-cell differences in ionic conductances. In this study, we describe the construction of an experimentally-calibrated set of stochastic cardiac cell models that captures both BVR and cell-to-cell differences in BVR displayed in isolated canine action potential measurements using pharmacological agents. Simulated and experimental ranges of BVR are compared in control and under pharmacological inhibition, and the key ionic currents determining BVR under physiological and pharmacological conditions are identified. Results show that the 4-aminopyridine-sensitive transient outward potassium current, I_to1, is a fundamental driver of BVR in control and upon complete inhibition of the slow delayed rectifier potassium current, I_Ks. In contrast, I_Ks and the L-type calcium current, I_CaL, become the major contributors to BVR upon inhibition of the fast delayed rectifier potassium current, I_Kr. This highlights both I_Ks and I_to1 as key contributors to repolarization reserve. Partial correlation analysis identifies the distribution of I_to1 channel numbers as an important independent determinant of the magnitude of BVR and drug-induced change in BVR in control and under pharmacological inhibition of ionic currents. Distributions in the number of I_Ks and I_CaL channels only become independent determinants of the magnitude of BVR upon complete inhibition of I_Kr. These findings provide quantitative insights into the ionic causes of BVR as a marker for repolarization reserve, both under control condition and pharmacological inhibition.

Molecular motions that shape the cardiac action potential: Insights from voltage clamp fluorometry

Very recently, voltage-clamp fluorometry (VCF) protocols have been developed to observe the membrane proteins responsible for carrying the ventricular ionic currents that form the action potential (AP), including those carried by the cardiac Na(+) channel, NaV1.5, the L-type Ca(2+) channel, CaV1.2, the Na(+)/K(+) ATPase, and the rapid and slow components of the delayed rectifier, KV11.1 and KV7.1. This development is significant, because VCF enables simultaneous observation of ionic current kinetics with conformational changes occurring within specific channel domains. The ability gained from VCF, to connect nanoscale molecular movement to ion channel function has revealed how the voltage-sensing domains (VSDs) control ion flux through channel pores, mechanisms of post-translational regulation and the molecular pathology of inherited mutations. In the future, we expect that this data will be of great use for the creation of multi-scale computational AP models that explicitly represent ion channel conformations, connecting molecular, cell and tissue electrophysiology. Here, we review the VCF protocol, recent results, and discuss potential future developments, including potential use of these experimental findings to create novel computational models.

Myokit: A simple interface to cardiac cellular electrophysiology

Myokit is a new powerful and versatile software tool for modeling and simulation of cardiac cellular electrophysiology. Myokit consists of an easy-to-read modeling language, a graphical user interface, single and multi-cell simulation engines and a library of advanced analysis tools accessible through a Python interface. Models can be loaded from Myokit's native file format or imported from CellML. Model export is provided to C, MATLAB, CellML, CUDA and OpenCL. Patch-clamp data can be imported and used to estimate model parameters. In this paper, we review existing tools to simulate the cardiac cellular action potential to find that current tools do not cater specifically to model development and that there is a gap between easy-to-use but limited software and powerful tools that require strong programming skills from their users. We then describe Myokit's capabilities, focusing on its model description language, simulation engines and import/export facilities in detail. Using three examples, we show how Myokit can be used for clinically relevant investigations, multi-model testing and parameter estimation in Markov models, all with minimal programming effort from the user. This way, Myokit bridges a gap between performance, versatility and user-friendliness.

Spatially Discordant Alternans and Arrhythmias in Tachypacing-Induced Cardiac Myopathy in Transgenic LQT1 Rabbits: The Importance of IKs and Ca2+ Cycling

BACKGROUND

Remodeling of cardiac repolarizing currents, such as the downregulation of slowly activating K+ channels (IKs), could underlie ventricular fibrillation (VF) in heart failure (HF). We evaluated the role of Iks remodeling in VF susceptibility using a tachypacing HF model of transgenic rabbits with Long QT Type 1 (LQT1) syndrome.

METHODS AND RESULTS

LQT1 and littermate control (LMC) rabbits underwent three weeks of tachypacing to induce cardiac myopathy (TICM). In vivo telemetry demonstrated steepening of the QT/RR slope in LQT1 with TICM (LQT1-TICM; pre: 0.26±0.04, post: 0.52±0.01, P<0.05). In vivo electrophysiology showed that LQT1-TICM had higher incidence of VF than LMC-TICM (6 of 11 vs. 3 of 11, respectively). Optical mapping revealed larger APD dispersion (16±4 vs. 38±6 ms, p<0.05) and steep APD restitution in LQT1-TICM compared to LQT1-sham (0.53±0.12 vs. 1.17±0.13, p<0.05). LQT1-TICM developed spatially discordant alternans (DA), which caused conduction block and higher-frequency VF (15±1 Hz in LQT1-TICM vs. 13±1 Hz in LMC-TICM, p<0.05). Ca2+ DA was highly dynamic and preceded voltage DA in LQT1-TICM. Ryanodine abolished DA in 5 out of 8 LQT1-TICM rabbits, demonstrating the importance of Ca2+ in complex DA formation. Computer simulations suggested that HF remodeling caused Ca2+-driven alternans, which was further potentiated in LQT1-TICM due to the lack of IKs.

CONCLUSIONS

Compared with LMC-TICM, LQT1-TICM rabbits exhibit steepened APD restitution and complex DA modulated by Ca2+. Our results strongly support the contention that the downregulation of IKs in HF increases Ca2+ dependent alternans and thereby the risk of VF.

Cellular cardiac electrophysiology modeling with Chaste and CellML

Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model code is auto-generated at compile or run time; it never has to be manually edited. We use ontological annotation to identify model variables describing certain biological quantities (membrane voltage, capacitance, etc.) to allow us to import any relevant CellML models into the Chaste framework in consistent units and to interact with them via consistent interfaces. This approach provides a great deal of flexibility for analysing different models of the same system. Chaste provides a wide choice of numerical methods for solving the ordinary differential equations that describe the models. Fixed-timestep explicit and implicit solvers are provided, as discussed in previous work. Here we introduce the Rush–Larsen and Generalized Rush–Larsen integration techniques, made available via symbolic manipulation of the model equations, which are automatically rearranged into the forms required by these approaches. We have also integrated the CVODE solvers, a ‘gold standard’ for stiff systems, and we have developed support for symbolic computation of the Jacobian matrix, yielding further increases in the performance and accuracy of CVODE. We discuss some of the technical details of this work and compare the performance of the available numerical methods. Finally, we discuss how this is generalized in our functional curation framework, which uses a domain-specific language for defining complex experiments as a basis for comparison of model behavior.

Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media.

In Silico Organ Modelling in Predicting Efficacy and Safety of New Medicines

The development of new medicines faces important challenges due to difficulties in the assessment of their efficacy and their safety in the targeted human population. In silico approaches through the use of mathematical modelling and computer simulations are increasingly being used to overcome some of the limitations of current experimental methods used in the development of new medicines. This chapter describes state-of-the-art in silico approaches for the evaluation of the safety and efficacy of medicines targeting important causes of mortality such as cardiovascular disease. Firstly, we describe the in silico multi-scale mathematical models and simulation techniques required to describe drug-induced effects on physiological systems such as the heart from the subcellular to the whole organ level. Then we illustrate the power of in silico approaches used to augment experimental and clinical investigations, by providing the framework to unravel multi-scale mechanisms underlying variability in the response to medicines and to focus on effects in human rather than animal models. We devote the last part of the chapter to discussing the process of validation of in silico models and simulations, which is key in building up their credibility.

Three-dimensional computer model of the right atrium including the sinoatrial and atrioventricular nodes predicts classical nodal behaviours

The aim of the study was to develop a three-dimensional (3D) anatomically-detailed model of the rabbit right atrium containing the sinoatrial and atrioventricular nodes to study the electrophysiology of the nodes. A model was generated based on 3D images of a rabbit heart (atria and part of ventricles), obtained using high-resolution magnetic resonance imaging. Segmentation was carried out semi-manually. A 3D right atrium array model (∼3.16 million elements), including eighteen objects, was constructed. For description of cellular electrophysiology, the Rogers-modified FitzHugh-Nagumo model was further modified to allow control of the major characteristics of the action potential with relatively low computational resource requirements. Model parameters were chosen to simulate the action potentials in the sinoatrial node, atrial muscle, inferior nodal extension and penetrating bundle. The block zone was simulated as passive tissue. The sinoatrial node, crista terminalis, main branch and roof bundle were considered as anisotropic. We have simulated normal and abnormal electrophysiology of the two nodes. In accordance with experimental findings: (i) during sinus rhythm, conduction occurs down the interatrial septum and into the atrioventricular node via the fast pathway (conduction down the crista terminalis and into the atrioventricular node via the slow pathway is slower); (ii) during atrial fibrillation, the sinoatrial node is protected from overdrive by its long refractory period; and (iii) during atrial fibrillation, the atrioventricular node reduces the frequency of action potentials reaching the ventricles. The model is able to simulate ventricular echo beats. In summary, a 3D anatomical model of the right atrium containing the cardiac conduction system is able to simulate a wide range of classical nodal behaviours.

The interrelations among stochastic pacing, stability, and memory in the heart

Low pacing variability in the heart has been clinically reported as a risk factor for lethal cardiac arrhythmias and arrhythmic death. In ia previous simulation study, we demonstrated that stochastic pacing sustains an antiarrhythmic effect by moderating the slope of the action potential duration (APD) restitution curve, by reducing the propensity of APD alternans, converting discordant to concordant alternans, and ultimately preventing wavebreaks. However, the dynamic mechanisms relating pacing stochasticity to tissue stability are not yet known. In this work, we develop a mathematical framework to describe the APD signal using an autoregressive stochastic model, and we establish the interrelations between stochastic pacing, cardiac memory, and cardiac stability, as manifested by the degree of APD alternans. Employing stability analysis tools, we show that increased stochasticity in the ventricular tissue activation sequence works to lower the maximal absolute eigenvalues of the stochastic model, thereby contributing to increased stability. We also show that the memory coefficients of the autoregressive model are modulated by pacing stochasticity in a nonlinear, biphasic way, so that for exceedingly high levels of pacing stochasticity, the antiarrhythmic effect is hampered by increasing APD variance. This work may contribute to establishment of an optimal antiarrhythmic pacing protocol in a future study.