Computational analysis of the human sinus node action potential: model development and effects of mutations

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.

Pacemaker Channels and the Chronotropic Response in Health and Disease

Loss or dysregulation of the normally precise control of heart rate via the autonomic nervous system plays a critical role during the development and progression of cardiovascular disease-including ischemic heart disease, heart failure, and arrhythmias. While the clinical significance of regulating changes in heart rate, known as the chronotropic effect, is undeniable, the mechanisms controlling these changes remain not fully understood. Heart rate acceleration and deceleration are mediated by increasing or decreasing the spontaneous firing rate of pacemaker cells in the sinoatrial node. During the transition from rest to activity, sympathetic neurons stimulate these cells by activating β-adrenergic receptors and increasing intracellular cyclic adenosine monophosphate. The same signal transduction pathway is targeted by positive chronotropic drugs such as norepinephrine and dobutamine, which are used in the treatment of cardiogenic shock and severe heart failure. The cyclic adenosine monophosphate-sensitive hyperpolarization-activated current (If) in pacemaker cells is passed by hyperpolarization-activated cyclic nucleotide-gated cation channels and is critical for generating the autonomous heartbeat. In addition, this current has been suggested to play a central role in the chronotropic effect. Recent studies demonstrate that cyclic adenosine monophosphate-dependent regulation of HCN4 (hyperpolarization-activated cyclic nucleotide-gated cation channel isoform 4) acts to stabilize the heart rate, particularly during rapid rate transitions induced by the autonomic nervous system. The mechanism is based on creating a balance between firing and recently discovered nonfiring pacemaker cells in the sinoatrial node. In this way, hyperpolarization-activated cyclic nucleotide-gated cation channels may protect the heart from sinoatrial node dysfunction, secondary arrhythmia of the atria, and potentially fatal tachyarrhythmia of the ventricles. Here, we review the latest findings on sinoatrial node automaticity and discuss the physiological and pathophysiological role of HCN pacemaker channels in the chronotropic response and beyond.

A gain-of-function HCN4 mutant in the HCN domain is responsible for inappropriate sinus tachycardia in a Spanish family

In a family with inappropriate sinus tachycardia (IST), we identified a mutation (p.V240M) of the hyperpolarization-activated cyclic nucleotide-gated type 4 (HCN4) channel, which contributes to the pacemaker current (If) in human sinoatrial node cells. Here, we clinically study fifteen family members and functionally analyze the p.V240M variant. Macroscopic (IHCN4) and single-channel currents were recorded using patch-clamp in cells expressing human native (WT) and/or p.V240M HCN4 channels. All p.V240M mutation carriers exhibited IST that was accompanied by cardiomyopathy in adults. IHCN4 generated by p.V240M channels either alone or in combination with WT was significantly greater than that generated by WT channels alone. The variant, which lies in the N-terminal HCN domain, increased the single-channel conductance and opening frequency and probability of HCN4 channels. Conversely, it did not modify the channel sensitivity for cAMP and ivabradine or the level of expression at the membrane. Treatment with ivabradine based on functional data reversed the IST and the cardiomyopathy of the carriers. In computer simulations, the p.V240M gain-of-function variant increases If and beating rate and thus explains the IST of the carriers. The results demonstrate the importance of the unique HCN domain in HCN4, which stabilizes the channels in the closed state.

Mechanistic insight into the functional role of human sinoatrial node conduction pathways and pacemaker compartments heterogeneity: A computer model analysis

The sinoatrial node (SAN), the primary pacemaker of the heart, is responsible for the initiation and robust regulation of sinus rhythm. 3D mapping studies of the ex-vivo human heart suggested that the robust regulation of sinus rhythm relies on specialized fibrotically-insulated pacemaker compartments (head, center and tail) with heterogeneous expressions of key ion channels and receptors. They also revealed up to five sinoatrial conduction pathways (SACPs), which electrically connect the SAN with neighboring right atrium (RA). To elucidate the role of these structural-molecular factors in the functional robustness of human SAN, we developed comprehensive biophysical computer models of the SAN based on 3D structural, functional and molecular mapping of ex-vivo human hearts. Our key finding is that the electrical insulation of the SAN except SACPs, the heterogeneous expression of If, INa currents and adenosine A1 receptors (A1R) across SAN pacemaker-conduction compartments are required to experimentally reproduce observed SAN activation patterns and important phenomena such as shifts of the leading pacemaker and preferential SACP. In particular, we found that the insulating border between the SAN and RA, is required for robust SAN function and protection from SAN arrest during adenosine challenge. The heterogeneity in the expression of A1R within the human SAN compartments underlies the direction of pacemaker shift and preferential SACPs in the presence of adenosine. Alterations of INa current and fibrotic remodelling in SACPs can significantly modulate SAN conduction and shift the preferential SACP/exit from SAN. Finally, we show that disease-induced fibrotic remodeling, INa suppression or increased adenosine make the human SAN vulnerable to pacing-induced exit blocks and reentrant arrhythmia. In summary, our computer model recapitulates the structural and functional features of the human SAN and can be a valuable tool for investigating mechanisms of SAN automaticity and conduction as well as SAN arrhythmia mechanisms under different pathophysiological conditions.

The Action Potential Clamp Technique as a Tool for Risk Stratification of Sinus Bradycardia Due to Loss-of-Function Mutations in HCN4: An In Silico Exploration Based on In Vitro and In Vivo Data

These days, in vitro functional analysis of gene variants is becoming increasingly important for risk stratification of cardiac ion channelopathies. So far, such risk stratification has been applied to SCN5A, KCNQ1, and KCNH2 gene variants associated with Brugada syndrome and long QT syndrome types 1 and 2, respectively, but risk stratification of HCN4 gene variants related to sick sinus syndrome has not yet been performed. HCN4 is the gene responsible for the hyperpolarization-activated 'funny' current If, which is an important modulator of the spontaneous diastolic depolarization underlying the sinus node pacemaker activity. In the present study, we carried out a risk classification assay on those loss-of-function mutations in HCN4 for which in vivo as well as in vitro data have been published. We used the in vitro data to compute the charge carried by If (Qf) during the diastolic depolarization phase of a prerecorded human sinus node action potential waveform and assessed the extent to which this Qf predicts (1) the beating rate of the comprehensive Fabbri-Severi model of a human sinus node cell with mutation-induced changes in If and (2) the heart rate observed in patients carrying the associated mutation in HCN4. The beating rate of the model cell showed a very strong correlation with Qf from the simulated action potential clamp experiments (R2 = 0.95 under vagal tone). The clinically observed minimum or resting heart rates showed a strong correlation with Qf (R2 = 0.73 and R2 = 0.71, respectively). While a translational perspective remains to be seen, we conclude that action potential clamp on transfected cells, without the need for further voltage clamp experiments and data analysis to determine individual biophysical parameters of If, is a promising tool for risk stratification of sinus bradycardia due to loss-of-function mutations in HCN4. In combination with an If blocker, this tool may also prove useful when applied to human-induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) obtained from mutation carriers and non-carriers.

Human Sinoatrial Node Pacemaker Activity: Role of the Slow Component of the Delayed Rectifier K+ Current, IKs

The pacemaker activity of the sinoatrial node (SAN) has been studied extensively in animal species but is virtually unexplored in humans. Here we assess the role of the slowly activating component of the delayed rectifier K+ current (IKs) in human SAN pacemaker activity and its dependence on heart rate and β-adrenergic stimulation. HEK-293 cells were transiently transfected with wild-type KCNQ1 and KCNE1 cDNA, encoding the α- and β-subunits of the IKs channel, respectively. KCNQ1/KCNE1 currents were recorded both during a traditional voltage clamp and during an action potential (AP) clamp with human SAN-like APs. Forskolin (10 µmol/L) was used to increase the intracellular cAMP level, thus mimicking β-adrenergic stimulation. The experimentally observed effects were evaluated in the Fabbri-Severi computer model of an isolated human SAN cell. Transfected HEK-293 cells displayed large IKs-like outward currents in response to depolarizing voltage clamp steps. Forskolin significantly increased the current density and significantly shifted the half-maximal activation voltage towards more negative potentials. Furthermore, forskolin significantly accelerated activation without affecting the rate of deactivation. During an AP clamp, the KCNQ1/KCNE1 current was substantial during the AP phase, but relatively small during diastolic depolarization. In the presence of forskolin, the KCNQ1/KCNE1 current during both the AP phase and diastolic depolarization increased, resulting in a clearly active KCNQ1/KCNE1 current during diastolic depolarization, particularly at shorter cycle lengths. Computer simulations demonstrated that IKs reduces the intrinsic beating rate through its slowing effect on diastolic depolarization at all levels of autonomic tone and that gain-of-function mutations in KCNQ1 may exert a marked bradycardic effect during vagal tone. In conclusion, IKs is active during human SAN pacemaker activity and has a strong dependence on heart rate and cAMP level, with a prominent role at all levels of autonomic tone.

Measuring and modeling the effects of vagus nerve stimulation on heart rate and laryngeal muscles

BACKGROUND

Reduced heart rate (HR) during vagus nerve stimulation (VNS) is associated with therapy for heart failure, but stimulation frequency and amplitude are limited by patient tolerance. An understanding of physiological responses to parameter adjustments would allow differential control of therapeutic and side effects. To investigate selective modulation of the physiological responses to VNS, we quantified the effects and interactions of parameter selection on two physiological outcomes: one related to therapy (reduced HR) and one related to side effects (laryngeal muscle EMG).

METHODS

We applied a broad range of stimulation parameters (mean pulse rates (MPR), intra-burst frequencies, and amplitudes) to the vagus nerve of anesthetized mice. We leveraged the in vivo recordings to parameterize and validate computational models of HR and laryngeal muscle activity across amplitudes and temporal patterns of VNS. We constructed a finite element model of excitation of fibers within the mouse cervical vagus nerve.

RESULTS

HR decreased with increased amplitude, increased MPR, and decreased intra-burst frequency. EMG increased with increased MPR. Preferential HR effects over laryngeal EMG effects required combined adjustments of amplitude and MPR. The model of HR responses highlighted contributions of ganglionic filtering to VNS-evoked changes in HR at high stimulation frequencies. Overlap in activation thresholds between small and large modeled fibers was consistent with the overlap in dynamic ranges of related physiological measures (HR and EMG).

CONCLUSION

The present study provides insights into physiological responses to VNS required for informed parameter adjustment to modulate selectively therapeutic effects and side effects.

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

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

SHOX2 refines the identification of human sinoatrial nodal cell population in the in vitro cardiac differentiation

Introduction

Dysfunction of the sinoatrial node (SAN) cells causes arrhythmias, and many patients require artificial cardiac pacemaker implantation. However, the mechanism of impaired SAN automaticity remains unknown, and the generation of human SAN cells in vitro may provide a platform for understanding the pathogenesis of SAN dysfunction. The short stature homeobox 2 (SHOX2) and hyperpolarization-activated cyclic nucleotide-gated cation channel 4 (HCN4) genes are specifically expressed in SAN cells and are important for SAN development and automaticity. In this study, we aimed to purify and characterize human SAN-like cells in vitro, using HCN4 and SHOX2 as SAN markers.

Methods

We developed an HCN4-EGFP/SHOX2-mCherry dual reporter cell line derived from human induced pluripotent stem cells (hiPSCs), and HCN4 and SHOX2 gene expressions were visualized using the fluorescent proteins EGFP and mCherry, respectively. The dual reporter cell line was established using an HCN4-EGFP bacterial artificial chromosome-based semi-knock-in system and a CRISPR-Cas9-dependent knock-in system with a SHOX2-mCherry targeting vector. Flow cytometry, RT-PCR, and whole-cell patch-clamp analyses were performed to identify SAN-like cells.

Results

Flow cytometry analysis and cell sorting isolated HCN4-EGFP single-positive (HCN4⁺/SHOX2^-) and HCN4-EGFP/SHOX2-mCherry double-positive (HCN4⁺/SHOX2⁺) cells. RT-PCR analyses showed that SAN-related genes were enriched within the HCN4⁺/SHOX2⁺ cells. Further, electrophysiological analyses showed that approximately 70% of the HCN4⁺/SHOX2⁺ cells exhibited SAN-like electrophysiological characteristics, as defined by the action potential parameters of the maximum upstroke velocity and action potential duration.

Conclusions

The HCN4-EGFP/SHOX2-mCherry dual reporter hiPSC system developed in this study enabled the enrichment of SAN-like cells within a mixed HCN4⁺/SHOX2⁺ population of differentiating cardiac cells. This novel cell line is useful for the further enrichment of human SAN-like cells. It may contribute to regenerative medicine, for example, biological pacemakers, as well as testing for cardiotoxic and chronotropic actions of novel drug candidates.

Whole Exome Sequencing Identifies a Heterozygous Variant in the Cav1.3 Gene CACNA1D Associated with Familial Sinus Node Dysfunction and Focal Idiopathic Epilepsy

Cav1.3 voltage-gated L-type calcium channels (LTCCs) are involved in cardiac pacemaking, hearing and hormone secretion, but are also expressed postsynaptically in neurons. So far, homozygous loss of function mutations in CACNA1D encoding the Cav1.3 α₁-subunit are described in congenital sinus node dysfunction and deafness. In addition, germline mutations in CACNA1D have been linked to neurodevelopmental syndromes including epileptic seizures, autism, intellectual disability and primary hyperaldosteronism. Here, a three-generation family with a syndromal phenotype of sinus node dysfunction, idiopathic epilepsy and attention deficit hyperactivity disorder (ADHD) is investigated. Whole genome sequencing and functional heterologous expression studies were used to identify the disease-causing mechanisms in this novel syndromal disorder. We identified a heterozygous non-synonymous variant (p.Arg930His) in the CACNA1D gene that cosegregated with the combined clinical phenotype in an autosomal dominant manner. Functional heterologous expression studies showed that the CACNA1D variant induces isoform-specific alterations of Cav1.3 channel gating: a gain of ion channel function was observed in the brain-specific short CACNA1D isoform (Cav1.3_S), whereas a loss of ion channel function was seen in the long (Cav1.3_L) isoform. The combined gain-of-function (GOF) and loss-of-function (LOF) induced by the R930H variant are likely to be associated with the rare combined clinical and syndromal phenotypes in the family. The GOF in the Cav1.3_S variant with high neuronal expression is likely to result in epilepsy, whereas the LOF in the long Cav1.3_L variant results in sinus node dysfunction.

Characterization of the pace-and-drive capacity of the human sinoatrial node: A 3D in silico study

The sinoatrial node (SAN) is a complex structure that spontaneously depolarizes rhythmically ("pacing") and excites the surrounding non-automatic cardiac cells ("drive") to initiate each heart beat. However, the mechanisms by which the SAN cells can activate the large and hyperpolarized surrounding cardiac tissue are incompletely understood. Experimental studies demonstrated the presence of an insulating border that separates the SAN from the hyperpolarizing influence of the surrounding myocardium, except at a discrete number of sinoatrial exit pathways (SEPs). We propose a highly detailed 3D model of the human SAN, including 3D SEPs to study the requirements for successful electrical activation of the primary pacemaking structure of the human heart. A total of 788 simulations investigate the ability of the SAN to pace and drive with different heterogeneous characteristics of the nodal tissue (gradient and mosaic models) and myocyte orientation. A sigmoidal distribution of the tissue conductivity combined with a mosaic model of SAN and atrial cells in the SEP was able to drive the right atrium (RA) at varying rates induced by gradual If block. Additionally, we investigated the influence of the SEPs by varying their number, length, and width. SEPs created a transition zone of transmembrane voltage and ionic currents to enable successful pace and drive. Unsuccessful simulations showed a hyperpolarized transmembrane voltage (-66 mV), which blocked the L-type channels and attenuated the sodium-calcium exchanger. The fiber direction influenced the SEPs that preferentially activated the crista terminalis (CT). The location of the leading pacemaker site (LPS) shifted toward the SEP-free areas. LPSs were located closer to the SEP-free areas (3.46 ± 1.42 mm), where the hyperpolarizing influence of the CT was reduced, compared with a larger distance from the LPS to the areas where SEPs were located (7.17± 0.98 mm). This study identified the geometrical and electrophysiological aspects of the 3D SAN-SEP-CT structure required for successful pace and drive in silico.

Coupling and heterogeneity modulate pacemaking capability in healthy and diseased two-dimensional sinoatrial node tissue models

Both experimental and modeling studies have attempted to determine mechanisms by which a small anatomical region, such as the sinoatrial node (SAN), can robustly drive electrical activity in the human heart. However, despite many advances from prior research, important questions remain unanswered. This study aimed to investigate, through mathematical modeling, the roles of intercellular coupling and cellular heterogeneity in synchronization and pacemaking within the healthy and diseased SAN. In a multicellular computational model of a monolayer of either human or rabbit SAN cells, simulations revealed that heterogenous cells synchronize their discharge frequency into a unique beating rhythm across a wide range of heterogeneity and intercellular coupling values. However, an unanticipated behavior appeared under pathological conditions where perturbation of ionic currents led to reduced excitability. Under these conditions, an intermediate range of intercellular coupling (900-4000 MΩ) was beneficial to SAN automaticity, enabling a very small portion of tissue (3.4%) to drive propagation, with propagation failure occurring at both lower and higher resistances. This protective effect of intercellular coupling and heterogeneity, seen in both human and rabbit tissues, highlights the remarkable resilience of the SAN. Overall, the model presented in this work allowed insight into how spontaneous beating of the SAN tissue may be preserved in the face of perturbations that can cause individual cells to lose automaticity. The simulations suggest that certain degrees of gap junctional coupling protect the SAN from ionic perturbations that can be caused by drugs or mutations.

Mapping the functional anatomy and topography of the cardiac autonomic innervation for selective cardiac neuromodulation using MicroCT

Background: Vagus nerve stimulation (VNS) has gained great importance as a promising therapy for a myriad of diseases. Of particular interest is the therapy of cardiovascular diseases, such as heart failure or atrial fibrillation using selective cardiac VNS. However, there is still a lack of organ-specific anatomical knowledge about the fascicular anatomy and topography of the cardiac branch (CB), which diminishes the therapeutic possibilities for selective cardiac neuromodulation. Here, we established a topographical and anatomical map of the superior cardiac VN in two animal species to dissect cervical and cardiac VN morphology.

Methods: Autonomic nerves including superior CBs were harvested from domestic pigs and New Zeeland rabbits followed by imaging with microcomputed tomography (µCT) and 3D rendering. The data were analyzed in terms of relevant topographical and anatomical parameters.

Results: Our data showed that cardiac vagal fascicles remained separated from other VN fascicles up to 22.19 mm (IQR 14.02–41.30 mm) in pigs and 7.68 mm (IQR 4.06–12.77 mm) in rabbits from the CB point and then started merging with other fascicles. Exchanges of nerve fascicles between sympathetic trunk (ST) and VN were observed in 3 out of 11 nerves, which might cause additional unwanted effects in unselective VNS. Our 3D rendered digital model of the cardiac fascicles was generated showing that CB first remained on the medial side where it branched off the VN, as also shown in the µCT data of 11 pig nerves, and then migrated towards the ventromedial site the further it was traced cranially.

Conclusion: Our data provided an anatomical map of the cardiac vagal branches including cervical VN and ST for future approaches of selective cardiac neurostimulation, indicating the best position of selective cardiac VNS just above the CB point.

Frequency-Dependent Properties of the Hyperpolarization-Activated Cation Current, If, in Adult Mouse Heart Primary Pacemaker Myocytes

A number of distinct electrophysiological mechanisms that modulate the myogenic spontaneous pacemaker activity in the sinoatrial node (SAN) of the mammalian heart have been investigated extensively. There is agreement that several (3 or 4) different transmembrane ionic current changes (referred to as the voltage clock) are involved; and that the resulting net current interacts with direct and indirect effects of changes in intracellular Ca²⁺ (the calcium clock). However, significant uncertainties, and important knowledge gaps, remain concerning the functional roles in SAN spontaneous pacing of many of the individual ion channel- or exchanger-mediated transmembrane current changes. We report results from patch clamp studies and mathematical modeling of the hyperpolarization-activated current, I_f, in the generation/modulation of the diastolic depolarization, or pacemaker potential, produced by individual myocytes that were enzymatically isolated from the adult mouse sinoatrial node (SAN). Amphotericin-mediated patch microelectrode recordings at 35 °C were made under control conditions and in the presence of 5 or 10 nM isoproterenol (ISO). These sets of results were complemented and integrated with mathematical modeling of the current changes that take place in the range of membrane potentials (−70 to −50 mV), which corresponds to the ‘pacemaker depolarization’ in the adult mouse SAN. Our results reveal a very small, but functionally important, approximately steady-state or time-independent current generated by residual activation of I_f channels that are expressed in these pacemaker myocytes. Recordings of the pacemaker depolarization and action potential, combined with measurements of changes in I_f, and the well-known increases in the L-type Ca²⁺ current, I_CaL, demonstrated that I_CaL activation, is essential for myogenic pacing. Moreover, after being enhanced (approximately 3-fold) by 5 or 10 nM ISO, I_CaL contributes significantly to the positive chronotropic effect. Our mathematical model has been developed in an attempt to better understand the underlying mechanisms for the pacemaker depolarization and action potential in adult mouse SAN myocytes. After being updated with our new experimental data describing I_f, our simulations reveal a novel functional component of I_f in adult mouse SAN. Computational work carried out with this model also confirms that in the presence of ISO the residual activation of I_f and opening of I_CaL channels combine to generate a net current change during the slow diastolic depolarization phase that is essential for the observed accelerated pacemaking rate of these SAN myocytes.

Mechanisms of Sinoatrial Node Dysfunction in Heart Failure With Preserved Ejection Fraction

BACKGROUND

The ability to increase heart rate during exercise and other stressors is a key homeostatic feature of the sinoatrial node (SAN). When the physiological heart rate response is blunted, chronotropic incompetence limits exercise capacity, a common problem in patients with heart failure with preserved ejection fraction (HFpEF). Despite its clinical relevance, the mechanisms of chronotropic incompetence remain unknown.

METHODS

Dahl salt-sensitive rats fed a high-salt diet and C57Bl6 mice fed a high-fat diet and an inhibitor of constitutive nitric oxide synthase (Nω-nitro-L-arginine methyl ester [L-NAME]; 2-hit) were used as models of HFpEF. Myocardial infarction was created to induce HF with reduced ejection fraction. Rats and mice fed with a normal diet or those that had a sham surgery served as respective controls. A comprehensive characterization of SAN function and chronotropic response was conducted by in vivo, ex vivo, and single-cell electrophysiologic studies. RNA sequencing of SAN was performed to identify transcriptomic changes. Computational modeling of biophysically-detailed human HFpEF SAN was created.

RESULTS

Rats with phenotypically-verified HFpEF exhibited limited chronotropic response associated with intrinsic SAN dysfunction, including impaired β-adrenergic responsiveness and an alternating leading pacemaker within the SAN. Prolonged SAN recovery time and reduced SAN sensitivity to isoproterenol were confirmed in the 2-hit mouse model. Adenosine challenge unmasked conduction blocks within the SAN, which were associated with structural remodeling. Chronotropic incompetence and SAN dysfunction were also found in rats with HF with reduced ejection fraction. Single-cell studies and transcriptomic profiling revealed HFpEF-related alterations in both the "membrane clock" (ion channels) and the "Ca2+ clock" (spontaneous Ca2+ release events). The physiologic impairments were reproduced in silico by empirically-constrained quantitative modeling of human SAN function.

CONCLUSIONS

Chronotropic incompetence and SAN dysfunction were seen in both models of HF. We identified that intrinsic abnormalities of SAN structure and function underlie the chronotropic response in HFpEF.

Hypoglycaemia combined with mild hypokalaemia reduces the heart rate and causes abnormal pacemaker activity in a computational model of a human sinoatrial cell

Low blood glucose, hypoglycaemia, has been implicated as a possible contributing factor to sudden cardiac death (SCD) in people with diabetes but it is challenging to investigate in clinical studies. We hypothesized the effects of hypoglycaemia on the sinoatrial node (SAN) in the heart to be a candidate mechanism and adapted a computational model of the human SAN action potential developed by Fabbri et al., to investigate the effects of hypoglycaemia on the pacemaker rate. Using Latin hypercube sampling, we combined the effects of low glucose (LG) on the human ether-a-go-go-related gene channel with reduced blood potassium, hypokalaemia, and added sympathetic and parasympathetic stimulus. We showed that hypoglycaemia on its own causes a small decrease in heart rate but there was also a marked decrease in heart rate when combined with hypokalaemia. The effect of the sympathetic stimulus was diminished, causing a smaller increase in heart rate, with LG and hypokalaemia compared to normoglycaemia. By contrast, the effect of the parasympathetic stimulus was enhanced, causing a greater decrease in heart rate. We therefore demonstrate a potential mechanistic explanation for hypoglycaemia-induced bradycardia and show that sinus arrest is a plausible mechanism for SCD in people with diabetes.

A comparative review on heart ion channels, action potentials and electrocardiogram in rodents and human: extrapolation of experimental insights to clinic

Electrocardiogram (ECG) is a non-invasive valuable diagnostic tool that is used in clinics for investigation and monitoring of heart electrical rhythm/conduction, ischemia/injury of heart, electrolyte disturbances and agents/drugs induced cardiac toxicity. Nowadays using animal models to study heart diseases such as electrical and mechanical disturbance is common. In addition, given to ethical consideration and availability, the use of small rodents has been a top priority for cardiovascular researchers. However, extrapolation of experimental findings from the lab to the clinic needs sufficient basic knowledge of similarities and differences between heart action potential and ECG of rodents and humans in normal and disease conditions. This review compares types of human action potentials, the dominant ion currents during action potential phases, alteration in ion channels activities in channelopathies-induced arrhythmias and the ECG appearance of mouse, rat, guinea pig, rabbit and human. Also, it briefly discusses the responsiveness and alterations in ECG following some interventions such as cardiac injury and arrhythmia induction. Overall, it provides a roadmap for researchers in selecting the best animal model/species whose studies results can be translated into clinical practice. In addition, this study will also be useful to biologists, physiologists, pharmacologists, veterinarians and physicians working in the fields of comparative physiology, pharmacology, toxicology and diseases.

The Functional Role of Hyperpolarization Activated Current (I f) on Cardiac Pacemaking in Human vs. in the Rabbit Sinoatrial Node: A Simulation and Theoretical Study

The cardiac hyperpolarization-activated “funny” current (I_f), which contributes to sinoatrial node (SAN) pacemaking, has a more negative half-maximal activation voltage and smaller fully-activated macroscopic conductance in human than in rabbit SAN cells. The consequences of these differences for the relative roles of I_f in the two species, and for their responses to the specific bradycardic agent ivabradine at clinical doses have not been systematically explored. This study aims to address these issues, through incorporating rabbit and human I_f formulations developed by Fabbri et al. into the Severi et al. model of rabbit SAN cells. A theory was developed to correlate the effect of I_f reduction with the total inward depolarising current (I_total) during diastolic depolarization. Replacing the rabbit I_f formulation with the human one increased the pacemaking cycle length (CL) from 355 to 1,139 ms. With up to 20% I_f reduction (a level close to the inhibition of I_f by ivabradine at clinical concentrations), a modest increase (~5%) in the pacemaking CL was observed with the rabbit I_f formulation; however, the effect was doubled (~12.4%) for the human I_f formulation, even though the latter has smaller I_f density. When the action of acetylcholine (ACh, 0.1 nM) was considered, a 20% I_f reduction markedly increased the pacemaking CL by 37.5% (~27.3% reduction in the pacing rate), which is similar to the ivabradine effect at clinical concentrations. Theoretical analysis showed that the resultant increase of the pacemaking CL is inversely proportional to the magnitude of I_total during diastolic depolarization phase: a smaller I_f in the model resulted in a smaller I_total amplitude, resulting in a slower pacemaking rate; and the same reduction in I_f resulted in a more significant change of CL in the cell model with a smaller I_total. This explained the mechanism by which a low dose of ivabradine slows pacemaking rate more in humans than in the rabbit. Similar results were seen in the Fabbri et al. model of human SAN cells, suggesting our observations are model-independent. Collectively, the results of study explain why low dose ivabradine at clinically relevant concentrations acts as an effective bradycardic agent in modulating human SAN pacemaking.

A Numerical Model of the Acute Cardiac Effects Provoked by Cervical Vagus Nerve Stimulation

OBJECTIVE

Today, the diverse acute cardiac effects of vagus nerve stimulation (VNS) are still not fully understood. Therefore, we propose a numerical model that can predict the acute cardiac responses to VNS and explain the underlying mechanisms on different levels.

METHODS

We integrated a model of vagal nerve fiber recruitment and acetylcholine (ACh) kinetics at vagal nerve terminals into a cardiovascular system model. A sensitivity analysis was performed to identify the most important parameters of vagal cardiac pathways. These parameters were tuned, and the model was validated based on published data of experiments in anesthetized sheep.

RESULTS

The four most important parameters are related to vagus nerve anatomy (electrode-fiber distances, fiber diameters) and ACh kinetics in the vagal neuroeffector junction (rate of ACh release and -hydrolysis) which together explain >53% of the observed variability in acute cardiac responses to VNS. The mean electrode-fiber distance and nerve fiber diameters obtained from tuning are 1.3 0.09 mm, and 4.9 0.25 m; the ACh release and -hydrolysis rate constants are 0.023 s^-1 and 0.77 s^-1 , respectively. With this parameterization, the model could accurately predict published data on the acute cardiac effects of VNS.

CONCLUSIONS

The model can explain the cardiac responses to VNS on multiple levels. The results highlight the importance of four parameters tied to ACh dynamics and vagus nerve anatomy for predicting the cardiac effects of VNS.

SIGNIFICANCE

The model represents a substantial improvement in terms of comprehensibility of the underlying mechanisms of the acute cardiac responses to VNS.

HCN4 current during human sinoatrial node-like action potentials

BACKGROUND

Despite the many studies carried out over the past 40 years, the contribution of the HCN4 encoded hyperpolarization-activated 'funny' current (I_f) to pacemaker activity in the mammalian sinoatrial node (SAN), and the human SAN in particular, is still controversial and not fully established.

OBJECTIVE

To study the contribution of I_f to diastolic depolarization of human SAN cells and its dependence on heart rate, cAMP levels, and atrial load.

METHODS

HCN4 channels were expressed in human cardiac myocyte progenitor cells (CMPCs) and HCN4 currents assessed using perforated patch-clamp in traditional voltage clamp mode and during action potential clamp with human SAN-like action potential waveforms with 500-1500 ms cycle length, in absence or presence of forskolin to mimic β-adrenergic stimulation and a -15 mV command potential offset to mimic atrial load.

RESULTS

Forskolin significantly increased the fully-activated HCN4 current density at -140 mV by 14% and shifted the steady-state activation curve by +7.4 mV without affecting its slope. In addition, forskolin significantly accelerated current activation but slowed deactivation. The HCN4 current did not completely deactivate before the subsequent diastolic depolarization during action potential clamp. The amplitude of HCN4 current increased with increasing cycle length, was significantly larger in the presence of forskolin at all cycle lengths, and was significantly increased upon the negative offset to the command potential.

CONCLUSIONS

I_f is active during a human SAN action potential waveform and its amplitude is modulated by heart rate, β-adrenergic stimulation, and diastolic voltage range, such that I_f is under delicate control.

Model Systems for Addressing Mechanism of Arrhythmogenesis in Cardiac Repair

PURPOSE OF REVIEW

Cardiac cell-based therapy represents a promising approach for cardiac repair. However, one of the main challenges is cardiac arrhythmias associated with stem cell transplantation. The current review summarizes the recent progress in model systems for addressing mechanisms of arrhythmogenesis in cardiac repair.

RECENT FINDINGS

Animal models have been extensively developed for mechanistic studies of cardiac arrhythmogenesis. Advances in human induced pluripotent stem cells (hiPSCs), patient-specific disease models, tissue engineering, and gene editing have greatly enhanced our ability to probe the mechanistic bases of cardiac arrhythmias. Additionally, recent development in multiscale computational studies and machine learning provides yet another powerful tool to quantitatively decipher the mechanisms of cardiac arrhythmias. Advancing efforts towards the integrations of experimental and computational studies are critical to gain insights into novel mitigation strategies for cardiac arrhythmias in cell-based therapy.

Adherens junction engagement regulates functional patterning of the cardiac pacemaker cell lineage

Cardiac pacemaker cells (CPCs) rhythmically initiate the electrical impulses that drive heart contraction. CPCs display the highest rate of spontaneous depolarization in the heart despite being subjected to inhibitory electrochemical conditions that should theoretically suppress their activity. While several models have been proposed to explain this apparent paradox, the actual molecular mechanisms that allow CPCs to overcome electrogenic barriers to their function remain poorly understood. Here, we have traced CPC development at single-cell resolution and uncovered a series of cytoarchitectural patterning events that are critical for proper pacemaking. Specifically, our data reveal that CPCs dynamically modulate adherens junction (AJ) engagement to control characteristics including surface area, volume, and gap junctional coupling. This allows CPCs to adopt a structural configuration that supports their overall excitability. Thus, our data have identified a direct role for local cellular mechanics in patterning critical morphological features that are necessary for CPC electrical activity.

Physiological Roles of the Rapidly Activated Delayed Rectifier K+ Current in Adult Mouse Heart Primary Pacemaker Activity

Robust, spontaneous pacemaker activity originating in the sinoatrial node (SAN) of the heart is essential for cardiovascular function. Anatomical, electrophysiological, and molecular methods as well as mathematical modeling approaches have quite thoroughly characterized the transmembrane fluxes of Na⁺, K⁺ and Ca²⁺ that produce SAN action potentials (AP) and ‘pacemaker depolarizations’ in a number of different in vitro adult mammalian heart preparations. Possible ionic mechanisms that are responsible for SAN primary pacemaker activity are described in terms of: (i) a Ca²⁺-regulated mechanism based on a requirement for phasic release of Ca²⁺ from intracellular stores and activation of an inward current-mediated by Na⁺/Ca²⁺ exchange; (ii) time- and voltage-dependent activation of Na⁺ or Ca²⁺ currents, as well as a cyclic nucleotide-activated current, I_f; and/or (iii) a combination of (i) and (ii). Electrophysiological studies of single spontaneously active SAN myocytes in both adult mouse and rabbit hearts consistently reveal significant expression of a rapidly activating time- and voltage-dependent K⁺ current, often denoted I_Kr, that is selectively expressed in the leading or primary pacemaker region of the adult mouse SAN. The main goal of the present study was to examine by combined experimental and simulation approaches the functional or physiological roles of this K⁺ current in the pacemaker activity. Our patch clamp data of mouse SAN myocytes on the effects of a pharmacological blocker, E4031, revealed that a rapidly activating K⁺ current is essential for action potential (AP) repolarization, and its deactivation during the pacemaker potential contributes a small but significant component to the pacemaker depolarization. Mathematical simulations using a murine SAN AP model confirm that well known biophysical properties of a delayed rectifier K⁺ current can contribute to its role in generating spontaneous myogenic activity.

Reciprocal interaction between IK1 and If in biological pacemakers: A simulation study

Pacemaking dysfunction (PD) may result in heart rhythm disorders, syncope or even death. Current treatment of PD using implanted electronic pacemakers has some limitations, such as finite battery life and the risk of repeated surgery. As such, the biological pacemaker has been proposed as a potential alternative to the electronic pacemaker for PD treatment. Experimentally and computationally, it has been shown that bio-engineered pacemaker cells can be generated from non-rhythmic ventricular myocytes (VMs) by knocking out genes related to the inward rectifier potassium channel current (IK1) or by overexpressing hyperpolarization-activated cyclic nucleotide gated channel genes responsible for the "funny" current (If). However, it is unclear if a bio-engineered pacemaker based on the modification of IK1- and If-related channels simultaneously would enhance the ability and stability of bio-engineered pacemaking action potentials. In this study, the possible mechanism(s) responsible for VMs to generate spontaneous pacemaking activity by regulating IK1 and If density were investigated by a computational approach. Our results showed that there was a reciprocal interaction between IK1 and If in ventricular pacemaker model. The effect of IK1 depression on generating ventricular pacemaker was mono-phasic while that of If augmentation was bi-phasic. A moderate increase of If promoted pacemaking activity but excessive increase of If resulted in a slowdown in the pacemaking rate and even an unstable pacemaking state. The dedicated interplay between IK1 and If in generating stable pacemaking and dysrhythmias was evaluated. Finally, a theoretical analysis in the IK1/If parameter space for generating pacemaking action potentials in different states was provided. In conclusion, to the best of our knowledge, this study provides a wide theoretical insight into understandings for generating stable and robust pacemaker cells from non-pacemaking VMs by the interplay of IK1 and If, which may be helpful in designing engineered biological pacemakers for application purposes.

Evolution of mathematical models of cardiomyocyte electrophysiology

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

Mechanisms underlying pro-arrhythmic abnormalities arising from Pitx2-induced electrical remodelling: an in silico intersubject variability study

Background

Electrical remodelling as a result of the homeodomain transcription factor 2 (Pitx2)-dependent gene regulation induces atrial fibrillation (AF) with different mechanisms. The purpose of this study was to identify Pitx2-induced changes in ionic currents that cause action potential (AP) shortening and lead to triggered activity.

Methods

Populations of computational atrial AP models were developed based on AP recordings from sinus rhythm (SR) and AF patients. Models in the AF population were divided into triggered and untriggered AP groups to evaluate the relationship between each ion current regulated by Pitx2 and triggered APs. Untriggered AP models were then divided into shortened and unshortened AP groups to determine which Pitx2-dependent ion currents contribute to AP shortening.

Results

According to the physiological range of AP biomarkers measured experimentally, populations of 2,885 SR and 4,781 AF models out of the initial pool of 30,000 models were selected. Models in the AF population predicted AP shortening and triggered activity observed in experiments in Pitx2-induced remodelling conditions. The AF models included 925 triggered AP models, 1,412 shortened AP models and 2,444 unshortened AP models. Intersubject variability in I_Ks and I_CaL primarily modulated variability in AP duration (APD) in all shortened and unshortened AP models, whereas intersubject variability in I_K1 and SERCA mainly contributed to the variability in AP morphology in all triggered and untriggered AP models. The incidence of shortened AP was positively correlated with I_Ks and I_K1 and was negatively correlated with I_Na , I_CaL and SERCA, whereas the incidence of triggered AP was negatively correlated with I_Ks and I_K1 and was positively correlated with I_Na , I_CaL and SERCA.

Conclusions

Electrical remodelling due to Pitx2 upregulation may increase the incidence of shortened AP, whereas electrical remodelling arising from Pitx2 downregulation may favor to the genesis of triggered AP.

Mechanistic Insights Into the Reduced Pacemaking Rate of the Rabbit Sinoatrial Node During Postnatal Development: A Simulation Study

Marked age- and development- related differences have been observed in morphology and characteristics of action potentials (AP) of neonatal and adult sinoatrial node (SAN) cells. These may be attributable to a different set of ion channel interactions between the different ages. However, the underlying mechanism(s) have yet to be elucidated. The objective of this study was to determine the mechanisms underlying different spontaneous APs and heart rate between neonatal and adult SAN cells of the rabbit heart by biophysical modeling approaches. A mathematical model of neonatal rabbit SAN cells was developed by modifying the current densities and/or kinetics of ion channels and transporters in an adult cell model based on available experimental data obtained from neonatal SAN cells. The single cell models were then incorporated into a multi-cellular, two-dimensional model of the intact SAN-atrium to investigate the functional impact of altered ion channels during maturation on pacemaking electrical activities and their conduction at the tissue level. Effects of the neurotransmitter acetylcholine on the pacemaking activities in neonatal cells were also investigated and compared to those in the adult. Our results showed: (1) the differences in ion channel properties between neonatal and adult SAN cells are able to account for differences in their APs and the heart rate, providing mechanistic insight into understanding the reduced pacemaking rate of the rabbit sinoatrial node during postnatal development; (2) in the 2D model of the intact SAN-atria, it was shown that cellular changes during postnatal development impaired pacemaking activity through increasing the activation time and reducing the conduction velocity across the SAN; (3) the neonatal SAN model, with its faster beating rates, showed a greater sensitivity to parasympathetic modulation in response to acetylcholine than did the adult model. These results provide novel insights into the understanding of the cellular mechanisms underlying the differences in the cardiac pacemaking activities of the neonatal and adult SAN.

Changes in Resting and Exercise Hemodynamics Early After Heart Transplantation: A Simulation Perspective

Introduction: During heart transplantation (HTx), cardiac denervation is inevitable, thus typically resulting in chronic resting tachycardia and chronotropic incompetence with possible consequences in patient quality of life and clinical outcomes. To this date, knowledge of hemodynamic changes early after HTx is still incomplete. This study aims at providing a model-based description of the complex hemodynamic changes at rest and during exercise in HTx recipients (HTxRs). Materials and Methods: A numerical model of early HTxRs is developed that integrates intrinsic and autonomic heart rate (HR) control into a lumped-parameter cardiovascular system model. Intrinsic HR control is realized by a single-cell sinoatrial (SA) node model. Autonomic HR control is governed by aortic baroreflex and pulmonary stretch reflex and modulates SA node activity through neurotransmitter release. The model is tuned based on published clinical data of 15 studies. Simulations of rest and exercise are performed to study hemodynamic changes associated with HTxRs. Results: Simulations of HTxRs at rest predict a substantially increased HR [93.8 vs. 69.5 beats/min (bpm)] due to vagal denervation while maintaining normal cardiac output (CO) (5.2 vs. 5.6 L/min) through a reduction in stroke volume (SV) (55.4 vs. 82 mL). Simulations of exercise predict markedly reduced peak CO (13 vs. 19.8 L/min) primarily resulting from diminished peak HRs (133.9 vs. 169 bpm) and reduced ventricular contractility. Yet, the model results show that HTxRs can maintain normal CO for low- to medium-intensity exercise by increased SV augmentation through the Frank-Starling mechanism. Conclusion: Relevant hemodynamic changes occur after HTx. Simulations suggest that (1) increased resting HRs solely result from the absence of vagal tone; (2) chronotropic incompetence is the main limiting factor of exercise capacity whereby peripheral factors play a secondary role; and (3) despite the diminished exercise capacity, HTxRs can compensate chronotropic incompetence by a preload-mediated increase in SV augmentation and thus maintain normal CO in low- to medium-intensity exercise.

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.

An Understandable, Extensible, and Reusable Implementation of the Hodgkin-Huxley Equations Using Modelica

The Hodgkin-Huxley model of the squid giant axon has been used for decades as the basis of many action potential models. These models are usually communicated using just a list of equations or a circuit diagram, which makes them unnecessarily complicated both for novices and for experts. We present a modular version of the Hodgkin-Huxley model that is more understandable than the usual monolithic implementations and that can be easily reused and extended. Our model is written in Modelica using software engineering concepts, such as object orientation and inheritance. It retains the electrical analogy, but names and explains individual components in biological terms. We use cognitive load theory to measure understandability as the amount of items that have to be kept in working memory simultaneously. The model is broken down into small self-contained components in human-readable code with extensive documentation. Additionally, it features a hybrid diagram that uses biological symbols in an electrical circuit and that is directly tied to the model code. The new model design avoids many redundancies and reduces the cognitive load associated with understanding the model by a factor of 6. Extensions can be easily applied due to an unifying interface and inheritance from shared base classes. The model can be used in an educational context as a more approachable introduction to mathematical modeling in electrophysiology. Additionally the modeling approach and the base components can be used to make complex Hodgkin-Huxley-type models more understandable and reusable.

Teaching cardiac excitation-contraction coupling using a mathematical computer simulation model of human ventricular myocytes

To understand the excitation-contraction (E-C) coupling of cardiomyocytes, including the electrophysiological mechanism of their characteristically long action potential duration, is one of the major learning goals in medical physiology. However, the integrative interpretation of the responses occurring during the contraction-relaxation cycle is challenging due to the dynamic interaction of underlying factors. Starting in 2017, we adopted the mathematical computer simulation model of human ventricular myocyte (Cardiac E-C_Sim), hypothesizing that this educational technology may facilitate students' learning of cardiac physiology. Here, we describe the overall process for the educational application of Cardiac E-C_Sim in the human physiology practicum of Seoul National University College of Medicine. We also report the results from questionnaires covering detailed assessment of the practicum class. The analysis of results and feedback opinions enabled us to understand how the students had approached the problem-solving process. As a whole, the students could better accomplish the learning goals using Cardiac E-C_Sim, followed by constructive discussions on the complex and dynamic mechanisms of cardiac E-C coupling. We suggest that the combined approach of lecture-based teaching and computer simulations guided by a manual containing clinical context would be broadly applicable in physiology education.

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.

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.

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.

All-Optical Electrophysiology Refines Populations of In Silico Human iPSC-CMs for Drug Evaluation

High-throughput in vitro drug assays have been impacted by recent advances in human induced pluripotent stem cell-derived cardiomyocyte (hiPSC-CM) technology and by contact-free all-optical systems simultaneously measuring action potentials (APs) and Ca2+ transients (CaTrs). Parallel computational advances have shown that in silico simulations can predict drug effects with high accuracy. We combine these in vitro and in silico technologies and demonstrate the utility of high-throughput experimental data to refine in silico hiPSC-CM populations and to predict and explain drug action mechanisms. Optically obtained hiPSC-CM APs and CaTrs were used from spontaneous activity and under optical pacing in control and drug conditions at multiple doses. An updated version of the Paci2018 model was developed to refine the description of hiPSC-CM spontaneous electrical activity; a population of in silico hiPSC-CMs was constructed and calibrated using simultaneously recorded APs and CaTrs. We tested in silico five drugs (astemizole, dofetilide, ibutilide, bepridil, and diltiazem) and compared the outcomes to in vitro optical recordings. Our simulations showed that physiologically accurate population of models can be obtained by integrating AP and CaTr control records. Thus, constructed population of models correctly predicted the drug effects and occurrence of adverse episodes, even though the population was optimized only based on control data and in vitro drug testing data were not deployed during its calibration. Furthermore, the in silico investigation yielded mechanistic insights; e.g., through simulations, bepridil's more proarrhythmic action in adult cardiomyocytes compared to hiPSC-CMs could be traced to the different expression of ion currents in the two. Therefore, our work 1) supports the utility of all-optical electrophysiology in providing high-content data to refine experimentally calibrated populations of in silico hiPSC-CMs, 2) offers insights into certain limitations when translating results obtained in hiPSC-CMs to humans, and 3) shows the strength of combining high-throughput in vitro and population in silico approaches.

The Cardiac Pacemaker Story-Fundamental Role of the Na+/Ca2+ Exchanger in Spontaneous Automaticity

The electrophysiological mechanism of the sinus node automaticity was previously considered exclusively regulated by the so-called "funny current". However, parallel investigations increasingly emphasized the importance of the Ca²⁺-homeostasis and Na⁺/Ca²⁺ exchanger (NCX). Recently, increasing experimental evidence, as well as insight through mechanistic in silico modeling demonstrates the crucial role of the exchanger in sinus node pacemaking. NCX had a key role in the exciting story of discovery of sinus node pacemaking mechanisms, which recently settled with a consensus on the coupled-clock mechanism after decades of debate. This review focuses on the role of the Na⁺/Ca²⁺ exchanger from the early results and concepts to recent advances and attempts to give a balanced summary of the characteristics of the local, spontaneous, and rhythmic Ca²⁺ releases, the molecular control of the NCX and its role in the fight-or-flight response. Transgenic animal models and pharmacological manipulation of intracellular Ca²⁺ concentration and/or NCX demonstrate the pivotal function of the exchanger in sinus node automaticity. We also highlight where specific hypotheses regarding NCX function have been derived from computational modeling and require experimental validation. Nonselectivity of NCX inhibitors and the complex interplay of processes involved in Ca²⁺ handling render the design and interpretation of these experiments challenging.

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.

Impaired neuronal sodium channels cause intranodal conduction failure and reentrant arrhythmias in human sinoatrial node

Mechanisms for human sinoatrial node (SAN) dysfunction are poorly understood and whether human SAN excitability requires voltage-gated sodium channels (Nav) remains controversial. Here, we report that neuronal (n)Nav blockade and selective nNav1.6 blockade during high-resolution optical mapping in explanted human hearts depress intranodal SAN conduction, which worsens during autonomic stimulation and overdrive suppression to conduction failure. Partial cardiac (c)Nav blockade further impairs automaticity and intranodal conduction, leading to beat-to-beat variability and reentry. Multiple nNav transcripts are higher in SAN vs atria; heterogeneous alterations of several isoforms, specifically nNav1.6, are associated with heart failure and chronic alcohol consumption. In silico simulations of Nav distributions suggest that I_Na is essential for SAN conduction, especially in fibrotic failing hearts. Our results reveal that not only cNav but nNav are also integral for preventing disease-induced failure in human SAN intranodal conduction. Disease-impaired nNav may underlie patient-specific SAN dysfunctions and should be considered to treat arrhythmias.

The role of of voltage-gated sodium channels (Nav) in pacemaking and conduction of the human sinoatrial node is unclear. Here, the authors investigate existence and function of neuronal and cardiac Nav in human sinoatrial nodes, and demonstrate their alterations in explanted human diseased hearts.

Inhibitory Effects of Cyclopiazonic Acid on the Pacemaker Current in Sinoatrial Nodal Cells

OBJECTIVE

The spontaneous action potential of isolated sinoatrial node (SAN) cells is regulated by a coupled-clock system of two clocks: the calcium clock and membrane clock. However, it remains unclear whether calcium clock inhibitors have a direct effect on the membrane clock. The purpose of this study was to investigate the direct effect of cyclopiazonic acid (CPA), a selective calcium clock inhibitor, on the function of the membrane clock of SAN cells.

METHODS

at SAN cells were isolated by trypsinization and identified based on morphology and electrophysiology. I_f and HCN currents were recorded via patch clamp technique. The expression of the HCN channel protein was determined by Western blotting analysis.

RESULTS

The diastolic depolarization rate of spontaneous action potentials and the current densities of I_f were reduced by exposure to 10 μM CPA. The inhibitory effect of CPA was concentration-dependent with an IC₅₀ value of 16.3 μM and a Hill coefficient of 0.98. The effect of CPA on I_f current was also time-dependent, and the I_f current amplitude was partially restored after washout. Furthermore, the steady-state activation curve of the I_f current was shifted to a negative potential, indicating that channel activation slowed down. Finally, the protein expression of HCN4 in HEK293 cells was markedly downregulated by CPA.

CONCLUSIONS

These results indicate that the direct inhibition effect of CPA on the I_f current in SAN cells is both concentration- and time-dependent. The underlying mechanisms may involve slowing down steady-state activation and the downregulation of pacemaker channel protein expression.

In silico study of the effects of anti-arrhythmic drug treatment on sinoatrial node function for patients with atrial fibrillation

Sinus node dysfunction (SND) is often associated with atrial fibrillation (AF). Amiodarone is the most frequently used agent for maintaining sinus rhythm in patients with AF, but it impairs the sinoatrial node (SAN) function in one-third of AF patients. This study aims to gain mechanistic insights into the effects of the antiarrhythmic agents in the setting of AF-induced SND. We have adapted a human SAN model to characterize the SND conditions by incorporating experimental data on AF-induced electrical remodelling, and then integrated actions of drugs into the modified model to assess their efficacy. Reductions in pacing rate upon the implementation of AF-induced electrical remodelling associated with SND agreed with the clinical observations. And the simulated results showed the reduced funny current (If) in these remodelled targets mainly contributed to the heart rate reduction. Computational drug treatment simulations predicted a further reduction in heart rate during amiodarone administration, indicating that the reduction was the result of actions of amiodarone on INa, IKur, ICaL, ICaT, If and beta-adrenergic receptors. However, the heart rate was increased in the presence of disopyramide. We concluded that disopyramide may be a desirable choice in reversing the AF-induced SND phenotype.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

Hypocalcemia-Induced Slowing of Human Sinus Node Pacemaking

Each heartbeat is initiated by cyclic spontaneous depolarization of cardiomyocytes in the sinus node forming the primary natural pacemaker. In patients with end-stage renal disease undergoing hemodialysis, it was recently shown that the heart rate drops to very low values before they suffer from sudden cardiac death with an unexplained high incidence. We hypothesize that the electrolyte changes commonly occurring in these patients affect sinus node beating rate and could be responsible for severe bradycardia. To test this hypothesis, we extended the Fabbri et al. computational model of human sinus node cells to account for the dynamic intracellular balance of ion concentrations. Using this model, we systematically tested the effect of altered extracellular potassium, calcium, and sodium concentrations. Although sodium changes had negligible (0.15 bpm/mM) and potassium changes mild effects (8 bpm/mM), calcium changes markedly affected the beating rate (46 bpm/mM ionized calcium without autonomic control). This pronounced bradycardic effect of hypocalcemia was mediated primarily by ICaL attenuation due to reduced driving force, particularly during late depolarization. This, in turn, caused secondary reduction of calcium concentration in the intracellular compartments and subsequent attenuation of inward INaCa and reduction of intracellular sodium. Our in silico findings are complemented and substantiated by an empirical database study comprising 22,501 pairs of blood samples and in vivo heart rate measurements in hemodialysis patients and healthy individuals. A reduction of extracellular calcium was correlated with a decrease of heartrate by 9.9 bpm/mM total serum calcium (p < 0.001) with intact autonomic control in the cross-sectional population. In conclusion, we present mechanistic in silico and empirical in vivo data supporting the so far neglected but experimentally testable and potentially important mechanism of hypocalcemia-induced bradycardia and asystole, potentially responsible for the highly increased and so far unexplained risk of sudden cardiac death in the hemodialysis patient population.

The Ionotropic P2X4 Receptor has Unique Properties in the Heart by Mediating the Negative Chronotropic Effect of ATP While Increasing the Ventricular Inotropy

Background: Mounting evidence indicate that reducing the sinoatrial node (SAN) activity may be a useful therapeutic strategy to control of heart failure. Purines, like ATP and its metabolite adenosine, consistently reduce the SAN spontaneous activity leading to negative cardiac chronotropy, with variable effects on the force of myocardial contraction (inotropy). Apart from adenosine A₁ receptors, the human SAN expresses high levels of ATP-sensitive ionotropic P2X4 receptors (P2X4R), yet their cardiac role is unexplored. Methods: Here, we investigated the activity of P2 purinoceptors on isolated spontaneously beating atria (chronotropy) and on 2 Hz-paced right ventricular (RV, inotropy) strips from Wistar rats. Results: ATP (pEC ₅₀ = 4.05) and its stable analogue ATPγS (pEC ₅₀ = 4.69) concentration-dependently reduced atrial chronotropy. Inhibition of ATP breakdown into adenosine by NTPDases with POM-1 failed to modify ATP-induced negative chronotropy. The effect of ATP on atrial rate was attenuated by a broad-spectrum P2 antagonist, PPADS, as well as by 5-BDBD, which selectively blocks the P2X4R subtype; however, no effect was observed upon blocking the A₁ receptor with DPCPX. The P2X4R positive allosteric modulator, ivermectin, increased the negative chronotropic response of ATP. Likewise, CTP, a P2X agonist that does not generate adenosine, replicated the P2X4R-mediated negative chronotropism of ATP. Inhibition of the Na⁺/Ca²⁺ exchanger (NCX) with KB-R7943 and ORM-10103, but not blockage of the HCN channel with ZD7288, mimicked the effect of the P2X4R blocker, 5-BDBD. In paced RV strips, ATP caused a mild negative inotropic effect, which magnitude was 2 to 3-fold increased by 5-BDBD and KB-R7943. Immunofluorescence confocal microscopy studies confirm that cardiomyocytes of the rat SAN and RV co-express P2X4R and NCX1 proteins. Conclusions: Data suggest that activation of ATP-sensitive P2X4R slows down heart rate by reducing the SAN activity while increasing the magnitude of ventricular contractions. The mechanism underlying the dual effect of ATP in the heart may involve inhibition of intracellular Ca²⁺-extrusion by bolstering NCX function in the reverse mode. Thus, targeting the P2X4R activation may create novel well-tolerated heart-rate lowering drugs with potential benefits in patients with deteriorated ventricular function.

Comparison of in vitro and computational experiments on the relation of inter-beat interval and duration of repolarization in a specific type of human induced pluripotent stem cell-derived cardiomyocytes

We compared a published computational model of the action potential of a specific type of human induced pluripotent stem cell -derived cardiomyocytes (hiPSC-CM) with experimental field potential data with regard to their inter-beat interval and the duration of repolarization. In particular, concomitant changes in inter-beat interval and duration of repolarization were calculated after reduction and/or augmentation of specific ion channel conductances as a surrogate for pharmacological manipulation. The observed mismatches between calculations and experimental data indicate that there is information missing about the cellular test system. Based on our results we hypothesize that, among other currents, the actual I_f (“funny current”) may deviate from the prediction. We show that replacement of the I_f formulation by alternative equations causes the model predictions to change qualitatively, however, none of the available formulations is actually achieving a satisfactory match with experimental data. We suggest a strategy to clarify whether the mismatch can be completely resolved at all using single cell models and, if yes, how this goal could be reached.

Simulation of action potential propagation based on the ghost structure method

In this paper, a ghost structure (GS) method is proposed to simulate the monodomain model in irregular computational domains using finite difference without regenerating body-fitted grids. In order to verify the validity of the GS method, it is first used to solve the Fitzhugh-Nagumo monodomain model in rectangular and circular regions at different states (the stationary and moving states). Then, the GS method is used to simulate the propagation of the action potential (AP) in transverse and longitudinal sections of a healthy human heart, and with left bundle branch block (LBBB). Finally, we analyze the AP and calcium concentration under healthy and LBBB conditions. Our numerical results show that the GS method can accurately simulate AP propagation with different computational domains either stationary or moving, and we also find that LBBB will cause the left ventricle to contract later than the right ventricle, which in turn affects synchronized contraction of the two ventricles.

Genetic variation in GNB5 causes bradycardia by augmenting the cholinergic response via increased acetylcholine-activated potassium current (I K,ACh)

Mutations in GNB5, encoding the G-protein β5 subunit (Gβ5), have recently been linked to a multisystem disorder that includes severe bradycardia. Here, we investigated the mechanism underlying bradycardia caused by the recessive p.S81L Gβ5 variant. Using CRISPR/Cas9-based targeting, we generated an isogenic series of human induced pluripotent stem cell (hiPSC) lines that were either wild type, heterozygous or homozygous for the GNB5 p.S81L variant. These were differentiated into cardiomyocytes (hiPSC-CMs) that robustly expressed the acetylcholine-activated potassium channel [I(KACh); also known as I_K,ACh]. Baseline electrophysiological properties of the lines did not differ. Upon application of carbachol (CCh), homozygous p.S81L hiPSC-CMs displayed an increased acetylcholine-activated potassium current (I _K,ACh) density and a more pronounced decrease of spontaneous activity as compared to wild-type and heterozygous p.S81L hiPSC-CMs, explaining the bradycardia in homozygous carriers. Application of the specific I(KACh) blocker XEN-R0703 resulted in near-complete reversal of the phenotype. Our results provide mechanistic insights and proof of principle for potential therapy in patients carrying GNB5 mutations.This article has an associated First Person interview with the first author of the paper.

Inter-Species Differences in the Response of Sinus Node Cellular Pacemaking to Changes of Extracellular Calcium

Changes of serum and extracellular ion concentrations occur regularly in patients with chronic kidney disease (CKD). Recently, hypocalcaemia, i.e. a decrease of the extracellular calcium concentration [Ca²⁺]_o, has been suggested as potential pathomechanism contributing to the unexplained high rate of sudden cardiac death (SCD) in CKD patients. In particular, there is a hypothesis that hypocalcaemia could slow down natural pacemaking in the human sinus node to fatal degrees. Here, we address the question whether there are inter-species differences in the response of cellular sinus node pacemaking to changes of [Ca²⁺]_o. Towards this end, we employ computational models of mouse, rabbit and human sinus node cells. The Fabbri et al. human model was updated to consider changes of intracellular ion concentrations. We identified crucial inter-species differences in the response of cellular pacemaking in the sinus node to changes of [Ca²⁺]_o with little changes of cycle length in mouse and rabbit models (<; 83 ms) in contrast to a pronounced bradycardic effect in the human model (up to >1000 ms). Our results suggest that experiments with human sinus node cells are required to investigate the potential mechanism of hypocalcaemia-induced bradycardic SCD in CKD patients and small animal models are not well suited.

Resonant model-A new paradigm for modeling an action potential of biological cells

Organ level simulation of bioelectric behavior in the body benefits from flexible and efficient models of cellular membrane potential. These computational organ and cell models can be used to study the impact of pharmaceutical drugs, test hypotheses, assess risk and for closed-loop validation of medical devices. To move closer to the real-time requirements of this modeling a new flexible Fourier based general membrane potential model, called as a Resonant model, is developed that is computationally inexpensive. The new model accurately reproduces non-linear potential morphologies for a variety of cell types. Specifically, the method is used to model human and rabbit sinoatrial node, human ventricular myocyte and squid giant axon electrophysiology. The Resonant models are validated with experimental data and with other published models. Dynamic changes in biological conditions are modeled with changing model coefficients and this approach enables ionic channel alterations to be captured. The Resonant model is used to simulate entrainment between competing sinoatrial node cells. These models can be easily implemented in low-cost digital hardware and an alternative, resource-efficient implementations of sine and cosine functions are presented and it is shown that a Fourier term is produced with two additions and a binary shift.

Investigating the Complex Arrhythmic Phenotype Caused by the Gain-of-Function Mutation KCNQ1-G229D

The congenital long QT syndrome (LQTS) is a cardiac electrophysiological disorder that can cause sudden cardiac death. LQT1 is a subtype of LQTS caused by mutations in KCNQ1, affecting the slow delayed-rectifier potassium current (I Ks), which is essential for cardiac repolarization. Paradoxically, gain-of-function mutations in KCNQ1 have been reported to cause borderline QT prolongation, atrial fibrillation (AF), sinus bradycardia, and sudden death, however, the mechanisms are not well understood. The goal of the study is to investigate the ionic, cellular and tissue mechanisms underlying the complex phenotype of a gain-of-function mutation in KCNQ1, c.686G > A (p.G229D) using computer modeling and simulations informed by in vitro measurements. Previous studies have shown this mutation to cause AF and borderline QT prolongation. We report a clinical description of a family that carry this mutation and that a member of the family died suddenly during sleep at 21 years old. Using patch-clamp experiments, we confirm that KCNQ1-G229D causes a significant gain in channel function. We introduce the effect of the mutation in populations of atrial, ventricular and sinus node (SN) cell models to investigate mechanisms underlying phenotypic variability. In a population of human atrial and ventricular cell models and tissue, the presence of KCNQ1-G229D predominantly shortens atrial action potential duration (APD). However, in a subset of models, KCNQ1-G229D can act to prolong ventricular APD by up to 7% (19 ms) and underlie depolarization abnormalities, which could promote QT prolongation and conduction delays. Interestingly, APD prolongations were predominantly seen at slow pacing cycle lengths (CL > 1,000 ms), which suggests a greater arrhythmic risk during bradycardia, and is consistent with the observed sudden death during sleep. In a population of human SN cell models, the KCNQ1-G229D mutation results in slow/abnormal sinus rhythm, and we identify that a stronger L-type calcium current enables the SN to be more robust to the mutation. In conclusion, our computational modeling experiments provide novel mechanistic explanations for the observed borderline QT prolongation, and predict that KCNQ1-G229D could underlie SN dysfunction and conduction delays. The mechanisms revealed in the study can potentially inform management and treatment of KCNQ1 gain-of-function mutation carriers.