Role of conduction velocity restitution and short-term memory in the development of action potential duration alternans in isolated rabbit hearts

Extended voltage imaging in cardiomyocytes with a triplet state quencher-stabilized silicon rhodamine

Voltage imaging of cardiac electrophysiology with voltage-sensitive dyes has long been a powerful complement to traditional methods like patch-clamp electrophysiology. Chemically synthesized voltage sensitive fluorophores offer flexibility for imaging in sensitive samples like human induced pluripotent stem cell derived cardiomyocytes (hiPSC-CMs), since they do not require genetic transformation of the sample. One serious concern for any fluorescent voltage indicator, whether chemically synthesized or genetically encoded, is phototoxicity. We have been exploring self-healing fluorophores that use triplet state quenchers (TSQs) as a means to reduce the already low phototoxicity of VoltageFluor dyes developed in our lab. We previously showed that conjugation of the TSQ cyclooctatetraene (COT) to a fluorescein based VoltageFluor dye substantially reduced phototoxicity. Here, we show that this approach can be applied to far-red Silicon rhodamine dyes. COT-conjugated Si-rhodamines show improved photostability and reduced phototoxicity in hiPSC-CMs compared to the unmodified dye. This enables imaging of hiPSC-CMs for up to 30 min with continuous illumination. We show that this effect is mediated by a combination of reduced singlet oxygen production and lower loading in the cellular membrane. We discuss future applications and avenues of improvement for TSQ-stabilized VoltageFluor dyes.

A cross species thermoelectric and spatiotemporal analysis of alternans in live explanted hearts using dual voltage-calcium fluorescence optical mapping

Objective.Temperature plays a crucial role in influencing the spatiotemporal dynamics of the heart. Electrical instabilities due to specific thermal conditions typically lead to early period-doubling bifurcations and beat-to-beat alternans. These pro-arrhythmic phenomena manifest in voltage and calcium traces, resulting in compromised contractile behaviors. In such intricate scenario, dual optical mapping technique was used to uncover unexplored multi-scale and nonlinear couplings, essential for early detection and understanding of cardiac arrhythmia.Approach.We propose a methodological analysis of synchronized voltage-calcium signals for detecting alternans, restitution curves, and spatiotemporal alternans patterns under different thermal conditions, based on integral features calculation. To validate our approach, we conducted a cross-species investigation involving rabbit and guinea pig epicardial ventricular surfaces and human endocardial tissue under pacing-down protocols.Main results.We show that the proposed integral feature, as the area under the curve, could be an easily applicable indicator that may enhance the predictability of the onset and progression of cardiac alternans. Insights into spatiotemporal correlation analysis of characteristic spatial lengths across different heart species were further provided.Significance.Exploring cross-species thermoelectric features contributes to understanding temperature-dependent proarrhythmic regimes and their implications on coupled spatiotemporal voltage-calcium dynamics. The findings provide preliminary insights and potential strategies for enhancing arrhythmia detection and treatment.

Intracellular ion accumulation in the genesis of complex action potential dynamics under cardiac diseases

Intracellular ions, including sodium (Na^{+}), calcium (Ca^{2+}), and potassium (K^{+}), etc., accumulate slowly after a change of the state of the heart, such as a change of the heart rate. The goal of this study is to understand the roles of slow ion accumulation in the genesis of cardiac memory and complex action-potential duration (APD) dynamics that can lead to lethal cardiac arrhythmias. We carry out numerical simulations of a detailed action potential model of ventricular myocytes under normal and diseased conditions, which exhibit memory effects and complex APD dynamics. We develop a low-dimensional iterated map (IM) model to describe the dynamics of Na^{+}, Ca^{2+}, and APD and use it to uncover the underlying dynamical mechanisms. The development of the IM model is informed by simulation results under the normal condition. We then use the IM model to perform linear stability analyses and computer simulations to investigate the bifurcations and complex APD dynamics, which depend on the feedback loops between APD and intracellular Ca^{2+} and Na^{+} concentrations and the steepness of the APD response to the ion concentrations. When the feedback between APD and Ca^{2+} concentration is positive, a Hopf bifurcation leading to periodic oscillatory behavior occurs as the steepness of the APD response to the ion concentrations increases. The negative feedback loop between APD and Na^{+} concentration is required for the Hopf bifurcation. When the feedback between APD and Ca^{2+} concentration is negative, period-doubling bifurcations leading to high periodicity and chaos occurs. In this case, Na^{+} accumulation plays little role in the dynamics. Finally, we carry out simulations of the detailed action potential model under two diseased conditions, which exhibit steep APD responses to ion concentrations. Under both conditions, Hopf bifurcations leading to slow oscillations or period-doubling bifurcations leading to high periodicity and chaotic APD dynamics occur, depending on the strength of the ion pump-Na^{+}-Ca^{2+} exchanger. Using functions reconstructed from the simulation data, the IM model accurately captures the bifurcations and dynamics under the two diseased conditions. In conclusion, besides using computer simulations of a detailed high-dimensional action-potential model to investigate the effects of slow ion accumulation and short-term memory on bifurcations and genesis of complex APD dynamics in cardiac myocytes under diseased conditions, this study also provides a low-dimensional mathematical tool, i.e., the IM model, to allow stability analyses for uncovering the underlying mechanisms.

Ephaptic Coupling as a Resolution to the Paradox of Action Potential Wave Speed and Discordant Alternans Spatial Scales in the Heart

Previous computer simulations have suggested that existing models of action potential wave propagation in the heart are not consistent with observed wave propagation behavior. Specifically, computer models cannot simultaneously reproduce the rapid wave speeds and small spatial scales of discordant alternans patterns measured experimentally in the same simulation. The discrepancy is important, because discordant alternans can be a key precursor to the development of abnormal and dangerous rapid rhythms in the heart. In this Letter, we show that this paradox can be resolved by allowing so-called ephaptic coupling to play a primary role in wave front propagation in place of conventional gap-junction coupling. With this modification, physiological wave speeds and small discordant alternans spatial scales both occur with gap-junction resistance values that are more in line with those observed in experiments. Our theory thus also provides support to the hypothesis that ephaptic coupling plays an important role in normal wave propagation.

Role of ephaptic coupling in discordant alternans domain sizes and action potential propagation in the heart

Discordant alternans, the spatially out-of-phase alternation of the durations of propagating action potentials in the heart, has been linked to the onset of fibrillation, a major cardiac rhythm disorder. The sizes of the regions, or domains, within which these alternations are synchronized are critical in this link. However, computer models employing standard gap junction-based coupling between cells have been unable to reproduce simultaneously the small domain sizes and rapid action potential propagation speeds seen in experiments. Here we use computational methods to show that rapid wave speeds and small domain sizes are possible when a more detailed model of intercellular coupling that accounts for so-called ephaptic effects is used. We provide evidence that the smaller domain sizes are possible, because different coupling strengths can exist on the wavefronts, for which both ephaptic and gap-junction coupling are involved, in contrast to the wavebacks, where only gap-junction coupling plays an active role. The differences in coupling strength are due to the high density of fast-inward (sodium) channels known to localize on the ends of cardiac cells, which are only active (and thus engage ephaptic coupling) during wavefront propagation. Thus, our results suggest that this distribution of fast-inward channels, as well as other factors responsible for the critical involvement of ephaptic coupling in wave propagation, including intercellular cleft spacing, play important roles in increasing the vulnerability of the heart to life-threatening tachyarrhythmias. Our results, combined with the absence of short-wavelength discordant alternans domains in standard gap-junction-dominated coupling models, also provide evidence that both gap-junction and ephaptic coupling are critical in wavefront propagation and waveback dynamics.

Mechanistic insights into spontaneous transition from cellular alternans to ventricular fibrillation

T-wave alternans (TWA) has been used for predicting the risk of malignant cardiac arrhythmias and sudden cardiac death (SCD) in multiple clinical settings; however, possible mechanism(s) underlying the spontaneous transition from cellular alternans reflected by TWA to arrhythmias in impaired repolarization remains unclear. The healthy guinea pig ventricular myocytes under E-4031 blocking IKr (0.1 μM, N = 12; 0.3 μM, N = 10; 1 μM, N = 10) were evaluated using whole-cell patch-clamp. The electrophysiological properties of isolated perfused guinea pig hearts under E-4031 (0.1 μM, N = 5; 0.3 μM, N = 5; 1 μM, N = 5) were evaluated using dual- optical mapping. The amplitude/threshold/restitution curves of action potential duration (APD) alternans and potential mechanism(s) underlying the spontaneous transition of cellular alternans to ventricular fibrillation (VF) were examined. There were longer APD80 and increased amplitude and threshold of APD alternans in E-4031 group compared with baseline group, which was reflected by more pronounced arrhythmogenesis at the tissue level, and were associated with steep restitution curves of the APD and the conduction velocity (CV). Conduction of AP alternans augmented tissue's functional spatiotemporal heterogeneity of regional AP/Ca alternans, as well as the AP/Ca dispersion, leading to localized uni-directional conduction block that spontaneous facilitated the formation of reentrant excitation waves without the need for additional premature stimulus. Our results provide a possible mechanism for the spontaneous transition from cardiac electrical alternans in cellular action potentials and intercellular conduction without the involvement of premature excitations, and explain the increased susceptibility to ventricular arrhythmias in impaired repolarization. In this study, we implemented voltage-clamp and dual-optical mapping approaches to investigate the underlying mechanism(s) for the arrhythmogenesis of cardiac alternans in the guinea pig heart at cellular and tissue levels. Our results demonstrated a spontaneous development of reentry from cellular alternans, arising from a combined actions of restitution properties of action potential duration, conduction velocity of excitation wave and interplay between alternants of action potential and the intracellular Ca handling. We believe this study provides new insights into underlying the mechanism, by which cellular cardiac alternans spontaneously evolves into cardiac arrhythmias.

Cardiac Alternans: From Bedside to Bench and Back

Cardiac alternans arises from dynamical instabilities in the electrical and calcium cycling systems of the heart, and often precedes ventricular arrhythmias and sudden cardiac death. In this review, we integrate clinical observations with theory and experiment to paint a holistic portrait of cardiac alternans: the underlying mechanisms, arrhythmic manifestations and electrocardiographic signatures. We first summarize the cellular and tissue mechanisms of alternans that have been demonstrated both theoretically and experimentally, including 3 voltage-driven and 2 calcium-driven alternans mechanisms. Based on experimental and simulation results, we describe their relevance to mechanisms of arrhythmogenesis under different disease conditions, and their link to electrocardiographic characteristics of alternans observed in patients. Our major conclusion is that alternans is not only a predictor, but also a causal mechanism of potentially lethal ventricular and atrial arrhythmias across the full spectrum of arrhythmia mechanisms that culminate in functional reentry, although less important for anatomic reentry and focal arrhythmias.

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.

Interpretable machine learning of action potential duration restitution kinetics in single-cell models of atrial cardiomyocytes

Action potential duration (APD) restitution curve and its maximal slope (Smax) reflect single cell-level dynamic instability for inducing chaotic heart rhythms. However, conventional parameter sensitivity analysis often fails to describe nonlinear relationships between ion channel parameters and electrophysiological phenotypes, such as Smax. We explored the parameter-phenotype mapping in a population of 5000 single-cell atrial cell models through interpretable machine learning (ML) approaches. Parameter sensitivity analyses could explain the linear relationships between parameters and electrophysiological phenotypes, including APD₉₀, resting membrane potential, Vmax, refractory period, and APD/calcium alternans threshold, but not for Smax. However, neural network models had better prediction performance for Smax. To interpret the ML model, we evaluated the parameter importance at the global and local levels by computing the permutation feature importance and the local interpretable model-agnostic explanations (LIME) values, respectively. Increases in I_CaL, I_NCX, and I_Kr, and decreases in I_K1, I_b,Cl, I_Kur, I_SERCA, and I_to are correlated with higher Smax values. The LIME algorithm determined that I_NaK plays a significant role in determining Smax as well as I_to and I_Kur. The atrial cardiomyocyte population was hierarchically clustered into three distinct groups based on the LIME values and the single-cell simulation confirmed that perturbations in I_NaK resulted in different behaviors of APD restitution curves in three clusters. Our combined top-down interpretable ML and bottom-up mechanistic simulation approaches uncovered the role of I_NaK in heterogeneous behaviors of Smax in the atrial cardiomyocyte population.

Circle Method for Robust Estimation of Local Conduction Velocity High-Density Maps From Optical Mapping Data: Characterization of Radiofrequency Ablation Sites

Conduction velocity (CV) slowing is associated with atrial fibrillation (AF) and reentrant ventricular tachycardia (VT). Clinical electroanatomical mapping systems used to localize AF or VT sources as ablation targets remain limited by the number of measuring electrodes and signal processing methods to generate high-density local activation time (LAT) and CV maps of heterogeneous atrial or trabeculated ventricular endocardium. The morphology and amplitude of bipolar electrograms depend on the direction of propagating electrical wavefront, making identification of low-amplitude signal sources commonly associated with fibrotic area difficulty. In comparison, unipolar electrograms are not sensitive to wavefront direction, but measurements are susceptible to distal activity. This study proposes a method for local CV calculation from optical mapping measurements, termed the circle method (CM). The local CV is obtained as a weighted sum of CV values calculated along different chords spanning a circle of predefined radius centered at a CV measurement location. As a distinct maximum in LAT differences is along the chord normal to the propagating wavefront, the method is adaptive to the propagating wavefront direction changes, suitable for electrical conductivity characterization of heterogeneous myocardium. In numerical simulations, CM was validated characterizing modeled ablated areas as zones of distinct CV slowing. Experimentally, CM was used to characterize lesions created by radiofrequency ablation (RFA) on isolated hearts of rats, guinea pig, and explanted human hearts. To infer the depth of RFA-created lesions, excitation light bands of different penetration depths were used, and a beat-to-beat CV difference analysis was performed to identify CV alternans. Despite being limited to laboratory research, studies based on CM with optical mapping may lead to new translational insights into better-guided ablation therapies.

Synchronization of spatially discordant voltage and calcium alternans in cardiac tissue

The heart is an excitable medium which is excited by membrane potential depolarization and propagation. Membrane potential depolarization brings in calcium (Ca) through the Ca channels to trigger intracellular Ca release for contraction of the heart. Ca also affects voltage via Ca-dependent ionic currents, and thus, voltage and Ca are bidirectionally coupled. It has been shown that the voltage subsystem or the Ca subsystem can generate its own dynamical instabilities which are affected by their bidirectional couplings, leading to complex dynamics of action potential and Ca cycling. Moreover, the dynamics become spatiotemporal in tissue in which cells are diffusively coupled through voltage. A widely investigated spatiotemporal dynamics is spatially discordant alternans (SDA) in which action potential duration (APD) or Ca amplitude exhibits temporally period-2 and spatially out-of-phase patterns, i.e., APD-SDA and Ca-SDA patterns, respectively. However, the mechanisms of formation, stability, and synchronization of APD-SDA and Ca-SDA patterns remain incompletely understood. In this paper, we use cardiac tissue models described by an amplitude equation, coupled iterated maps, and reaction-diffusion equations with detailed physiology (the ionic model) to perform analytical and computational investigations. We show that, when the Ca subsystem is stable, the Ca-SDA pattern always follows the APD-SDA pattern, and thus, they are always synchronized. When the Ca subsystem is unstable, synchronization of APD-SDA and Ca-SDA patterns depends on the stabilities of both subsystems, their coupling strengths, and the spatial scales of the initial Ca-SDA patterns. Spontaneous (initial condition-independent) synchronization is promoted by enhancing APD instability and reducing Ca instability as well as stronger Ca-to-APD and APD-to-Ca coupling, a pattern formation caused by dynamical instabilities. When Ca is more unstable and APD is less unstable or APD-to-Ca coupling is weak, synchronization of APD-SDA and Ca-SDA patterns is promoted by larger initially synchronized Ca-SDA clusters, i.e., initial condition-dependent synchronization. The synchronized APD-SDA and Ca-SDA patterns can be locked in-phase, antiphase, or quasiperiodic depending on the coupling relationship between APD and Ca. These theoretical and simulation results provide mechanistic insights into the APD-SDA and Ca-SDA dynamics observed in experimental studies.

High resolution optical mapping of cardiac electrophysiology in pre-clinical models

Optical mapping of animal models is a widely used technique in pre-clinical cardiac research. It has several advantages over other methods, including higher spatial resolution, contactless recording and direct visualisation of action potentials and calcium transients. Optical mapping enables simultaneous study of action potential and calcium transient morphology, conduction dynamics, regional heterogeneity, restitution and arrhythmogenesis. In this dataset, we have optically mapped Langendorff perfused isolated whole hearts (mouse and guinea pig) and superfused isolated atria (mouse). Raw datasets (consisting of over 400 files) can be combined with open-source software for processing and analysis. We have generated a comprehensive post-processed dataset characterising the baseline cardiac electrophysiology in these widely used pre-clinical models. This dataset also provides reference information detailing the effect of heart rate, clinically used anti-arrhythmic drugs, ischaemia-reperfusion and sympathetic nervous stimulation on cardiac electrophysiology. The effects of these interventions can be studied in a global or regional manner, enabling new insights into the prevention and initiation of arrhythmia.

Cardiac Conduction Velocity, Remodeling and Arrhythmogenesis

Cardiac electrophysiological disorders, in particular arrhythmias, are a key cause of morbidity and mortality throughout the world. There are two basic requirements for arrhythmogenesis: an underlying substrate and a trigger. Altered conduction velocity (CV) provides a key substrate for arrhythmogenesis, with slowed CV increasing the probability of re-entrant arrhythmias by reducing the length scale over which re-entry can occur. In this review, we examine methods to measure cardiac CV in vivo and ex vivo, discuss underlying determinants of CV, and address how pathological variations alter CV, potentially increasing arrhythmogenic risk. Finally, we will highlight future directions both for methodologies to measure CV and for possible treatments to restore normal CV.

Progressive increase in activation delay during premature stimulation is related to ventricular fibrillation in Brugada syndrome

INTRODUCTION

The local conduction delay has been deemed to play an important role in the perpetuation of ventricular fibrillation (VF) in Brugada syndrome (BrS). We evaluated the relationship between the activation delay during programmed stimulation and cardiac events in BrS patients.

METHODS

This study included 47 consecutive BrS patients who underwent an electrophysiological study and received implantable cardiac defibrillator therapy. We divided the patients into two groups based on whether they had developed VF (11 patients) or not (36 patients) during the follow-up period of 89 ± 53 months. The activation delay was assessed using the interval between the stimulus and the QRS onset during programmed stimulation. The mean increase in delay (MID) was used to characterize the conduction curves.

RESULTS

The MID at the right ventricular outflow tract (RVOT) was significantly greater in patients with VF (4.5 ± 1.2 ms) than in those without VF (2.2 ± 0.9 ms) (p < .001). A receiver operating characteristics curve analysis indicated that the optimal cut-off point for discriminating VF occurrence was 3.3 with 88.9% sensitivity and 91.3% specificity. Furthermore, patients with an MID at the RVOT ≥ 3.3 ms showed significantly higher rates of VF recurrence than those with an MID at the RVOT < 3.3 ms (p < .001). The clinical characteristics, including the signal-averaged electrocardiogram measurement and VF inducibility were similar between the two groups.

CONCLUSION

A prolonged MID at the RVOT was associated with VF and maybe an additional electrophysiological risk factor for VF in BrS patients.

Electrophysiological Mechanisms Underlying T-Wave Alternans and Their Role in Arrhythmogenesis

T-wave alternans (TWA) reflects every-other-beat alterations in the morphology of the electrocardiogram ST segment or T wave in the setting of a constant heart rate, hence, in the absence of heart rate variability. It is believed to be associated with the dispersion of repolarization and has been used as a non-invasive marker for predicting the risk of malignant cardiac arrhythmias and sudden cardiac death as numerous studies have shown. This review aims to provide up-to-date review on both experimental and simulation studies in elucidating possible mechanisms underlying the genesis of TWA at the cellular level, as well as the genesis of spatially concordant/discordant alternans at the tissue level, and their transition to cardiac arrhythmia. Recent progress and future perspectives in antiarrhythmic therapies associated with TWA are also discussed.

Detection of Drug-Induced Torsades de Pointes Arrhythmia Mechanisms Using hiPSC-CM Syncytial Monolayers in a High-Throughput Screening Voltage Sensitive Dye Assay

We validated 3 distinct hiPSC-CM cell lines-each of different purity and a voltage sensitive dye (VSD)-based high-throughput proarrhythmia screening assay as a noncore site in the recently completed CiPA Myocyte Phase II Validation Study. Blinded validation was performed using 12 drugs linked to low, intermediate, or high risk for causing Torsades de Pointes (TdP). Commercially sourced hiPSC-CMs were obtained either from Cellular Dynamics International (CDI, Madison, Wisconsin, iCell Cardiomyoyctes2) or Takara Bio (CLS, Cellartis Cardiomyocytes). A third hiPSC-CM cell line (MCH, Michigan) was generated in house. Each cell type had distinct baseline electrophysiological function (spontaneous beat rate, action potential duration, and conduction velocity) and drug responsiveness. Use of VSD and optical mapping enabled the detection of conduction slowing of sodium channel blockers (quinidine, disopyramide, and mexiletine) and drug-induced TdP-like activation patterns (rotors) for some high- and intermediate-risk compounds. Low-risk compounds did not induce rotors in any cell type tested. These results further validate the utility of hiPSC-CMs for predictive proarrhythmia screening and the utility of VSD technology to detect drug-induced APD prolongation, arrhythmias (rotors), and conduction slowing. Importantly, results indicate that different ratios of cardiomyocytes and noncardiomyocytes have important impact on drug response that may be considered during risk assessment of new drugs. Finally, we present the first blinded CiPA hiPSC-CM validation results to simultaneously detect drug-induced conduction slowing, action potential duration prolongation, action potential triangulation, and drug-induced rotors in a proarrhythmia assay.

Stability of spatially discordant repolarization alternans in cardiac tissue

Cardiac alternans, a period-2 behavior of excitation and contraction of the heart, is a precursor of ventricular arrhythmias and sudden cardiac death. One form of alternans is repolarization or action potential duration alternans. In cardiac tissue, repolarization alternans can be spatially in-phase, called spatially concordant alternans, or spatially out-of-phase, called spatially discordant alternans (SDA). In SDA, the border between two out-of-phase regions is called a node in a one-dimensional cable or a nodal line in a two-dimensional tissue. In this study, we investigate the stability and dynamics of the nodes and nodal lines of repolarization alternans driven by voltage instabilities. We use amplitude equation and coupled map lattice models to derive theoretical results, which are compared with simulation results from the ionic model. Both conduction velocity restitution induced SDA and non-conduction velocity restitution induced SDA are investigated. We show that the stability and dynamics of the SDA nodes or nodal lines are determined by the balance of the tensions generated by conduction velocity restitution, convection due to action potential propagation, curvature of the nodal lines, and repolarization and coupling heterogeneities. Our study provides mechanistic insights into the different SDA behaviors observed in experiments.

Delayed global feedback in the genesis and stability of spatiotemporal excitation patterns in paced biological excitable media

Biological excitable media, such as cardiac or neural cells and tissue, exhibit memory in which a change in the present excitation may affect the behaviors in the next excitation. For example, a change in calcium (Ca²⁺) concentration in a cell in the present excitation may affect the Ca²⁺ dynamics in the next excitation via bi-directional coupling between voltage and Ca²⁺, forming a delayed feedback loop. Since the Ca²⁺ dynamics inside the excitable cells are spatiotemporal while the membrane voltage is a global signal, the feedback loop is then a delayed global feedback (DGF) loop. In this study, we investigate the roles of DGF in the genesis and stability of spatiotemporal excitation patterns in periodically-paced excitable media using mathematical models with different levels of complexity: a model composed of coupled FitzHugh-Nagumo units, a 3-dimensional physiologically-detailed ventricular myocyte model, and a coupled map lattice model. We investigate the dynamics of excitation patterns that are temporal period-2 (P2) and spatially concordant or discordant, such as subcellular concordant or discordant Ca²⁺alternans in cardiac myocytes or spatially concordant or discordant Ca²⁺ and repolarization alternans in cardiac tissue. Our modeling approach allows both computer simulations and rigorous analytical treatments, which lead to the following results and conclusions. When DGF is absent, concordant and discordant P2 patterns occur depending on initial conditions with the discordant P2 patterns being spatially random. When the DGF is negative, only concordant P2 patterns exist. When the DGF is positive, both concordant and discordant P2 patterns can occur. The discordant P2 patterns are still spatially random, but they satisfy that the global signal exhibits a temporal period-1 behavior. The theoretical analyses of the coupled map lattice model reveal the underlying instabilities and bifurcations for the genesis, selection, and stability of spatiotemporal excitation patterns.

Understanding the mechanisms of pattern formation in biological systems is of great importance. Here we investigate the dynamical mechanisms by which delayed global feedback affects excitation pattern formation and stability in periodically-paced biological excitable media, such as cardiac or neural cells and tissue. We focus on the formation and stability of the temporal period-2 and spatially in-phase and out-of-phase excitation patterns. Using models of different levels of complexity, we show that when the delayed global feedback is negative, only the spatially in-phase patterns are stable. When the feedback is positive, both spatially in-phase and out-of-phase patterns are stable, and the out-of-phase patterns are spatially random but satisfy that the global signals are temporal period-1 solutions.

High-Resolution Optical Measurement of Cardiac Restitution, Contraction, and Fibrillation Dynamics in Beating vs. Blebbistatin-Uncoupled Isolated Rabbit Hearts

Optical mapping is a high-resolution fluorescence imaging technique, that uses voltage- or calcium-sensitive dyes to visualize electrical excitation waves on the heart surface. However, optical mapping is very susceptible to the motion of cardiac tissue, which results in so-called motion artifacts in the fluorescence signal. To avoid motion artifacts, contractions of the heart muscle are typically suppressed using pharmacological excitation-contraction uncoupling agents, such as Blebbistatin. The use of pharmacological agents, however, may influence cardiac electrophysiology. Recently, it has been shown that numerical motion tracking can significantly reduce motion-related artifacts in optical mapping, enabling the simultaneous optical measurement of cardiac electrophysiology and mechanics. Here, we combine ratiometric optical mapping with numerical motion tracking to further enhance the robustness and accuracy of these measurements. We evaluate the method's performance by imaging and comparing cardiac restitution and ventricular fibrillation (VF) dynamics in contracting, non-working vs. Blebbistatin-arrested Langendorff-perfused rabbit hearts (N = 10). We found action potential durations (APD) to be, on average, 25 ± 5% shorter in contracting hearts compared to hearts uncoupled with Blebbistatin. The relative shortening of the APD was found to be larger at higher frequencies. VF was found to be significantly accelerated in contracting hearts, i.e., 9 ± 2Hz with Blebbistatin and 15 ± 4Hz without Blebbistatin, and maintained a broader frequency spectrum. In contracting hearts, the average number of phase singularities was N_PS = 11 ± 4 compared to N_PS = 6 ± 3 with Blebbistatin during VF on the anterior ventricular surface. VF inducibility was reduced with Blebbistatin. We found the effect of Blebbistatin to be concentration-dependent and reversible by washout. Aside from the electrophysiological characterization, we also measured and analyzed cardiac motion. Our findings may have implications for the interpretation of optical mapping data, and highlight that physiological conditions, such as oxygenation and metabolic demand, must be carefully considered in ex vivo imaging experiments.

In Situ Expansion, Differentiation, and Electromechanical Coupling of Human Cardiac Muscle in a 3D Bioprinted, Chambered Organoid

RATIONALE

One goal of cardiac tissue engineering is the generation of a living, human pump in vitro that could replace animal models and eventually serve as an in vivo therapeutic. Models that replicate the geometrically complex structure of the heart, harboring chambers and large vessels with soft biomaterials, can be achieved using 3-dimensional bioprinting. Yet, inclusion of contiguous, living muscle to support pump function has not been achieved. This is largely due to the challenge of attaining high densities of cardiomyocytes-a notoriously nonproliferative cell type. An alternative strategy is to print with human induced pluripotent stem cells, which can proliferate to high densities and fill tissue spaces, and subsequently differentiate them into cardiomyocytes in situ.

OBJECTIVE

To develop a bioink capable of promoting human induced pluripotent stem cell proliferation and cardiomyocyte differentiation to 3-dimensionally print electromechanically functional, chambered organoids composed of contiguous cardiac muscle.

METHODS AND RESULTS

We optimized a photo-crosslinkable formulation of native ECM (extracellular matrix) proteins and used this bioink to 3-dimensionally print human induced pluripotent stem cell-laden structures with 2 chambers and a vessel inlet and outlet. After human induced pluripotent stem cells proliferated to a sufficient density, we differentiated the cells within the structure and demonstrated function of the resultant human chambered muscle pump. Human chambered muscle pumps demonstrated macroscale beating and continuous action potential propagation with responsiveness to drugs and pacing. The connected chambers allowed for perfusion and enabled replication of pressure/volume relationships fundamental to the study of heart function and remodeling with health and disease.

CONCLUSIONS

This advance represents a critical step toward generating macroscale tissues, akin to aggregate-based organoids, but with the critical advantage of harboring geometric structures essential to the pump function of cardiac muscle. Looking forward, human chambered organoids of this type might also serve as a test bed for cardiac medical devices and eventually lead to therapeutic tissue grafting.

Spatially Discordant Repolarization Alternans in the Absence of Conduction Velocity Restitution

Spatially discordant alternans (SDA) of action potential duration (APD) has been widely observed in cardiac tissue and is linked to cardiac arrhythmogenesis. Theoretical studies have shown that conduction velocity restitution (CVR) is required for the formation of SDA. However, this theory is not completely supported by experiments, indicating that other mechanisms may exist. In this study, we carried out computer simulations using mathematical models of action potentials to investigate the mechanisms of SDA in cardiac tissue. We show that when CVR is present and engaged, such as fast pacing from one side of the tissue, the spatial pattern of APD in the tissue undergoes either spatially concordant alternans or SDA, independent of initial conditions or tissue heterogeneities. When CVR is not engaged, such as simultaneous pacing of the whole tissue or under normal/slow heart rates, the spatial pattern of APD in the tissue can have multiple solutions, including spatially concordant alternans and different SDA patterns, depending on heterogeneous initial conditions or pre-existing repolarization heterogeneities. In homogeneous tissue, curved nodal lines are not stable, which either evolve into straight lines or disappear. However, in heterogeneous itssue, curved nodal lines can be stable, depending on their initial locations and shapes relative to the structure of the heterogeneity. Therefore, CVR-induced SDA and non-CVR-induced SDA exhibit different dynamical properties, which may be responsible for the different SDA properties observed in experimental studies and arrhythmogenesis in different clinical settings.

Restitution metrics in Brugada syndrome: a systematic review and meta-analysis

BACKGROUND

Brugada syndrome (BrS) is an ion channelopathy that predisposes affected subjects to ventricular tachycardia/fibrillation (VT/VF) and sudden cardiac death. Restitution analysis has been examined in BrS patients but not all studies have reported significant differences between BrS patients and controls. Therefore, we conducted a systematic review and meta-analysis to investigate the different restitution indices used in BrS.

METHODS

PubMed and Embase were searched until April 7, 2019, identifying 20 and 27 studies.

RESULTS

A total of ten studies involving 178 BrS (mean age 38 years old, 63% male) and 102 controls (mean age 31 years old, 42% male) were included in this systematic review. Pacing was carried out at the right ventricular outflow tract (RVOT)/right ventricular apex (RPA) (n = 4), RPA (n = 4), or right atrium (RA) (n = 1). Basic cycle lengths of 400 (n = 4), 500 (n = 2), 600 (n = 6) and 750 ms (n = 1) were used. Recording methods include electrograms (n = 4), monophasic action potentials (n = 5), and electrocardiograms (n = 1). Signals were obtained from the RVOT (n = 8), RVA (n = 3), RA (n = 1), or the body surface (n = 1). The maximum restitution slope for endocardial repolarization at the RVOT was 0.87 for BrS patients (n = 5; 95% confidence interval [CI] 0.68-1.07) compared with 0.74 in control subjects (n = 4; 95% CI 0.42-1.06), with a significant mean difference of 0.40 (n = 4; 95% CI 0.11-0.69; P = 0.007).

CONCLUSIONS

Steeper endocardial repolarization restitution slopes are found in BrS patients compared with controls at baseline. Restitution analysis can provide important information for risk stratification in BrS.

Spatiotemporal correlation uncovers characteristic lengths in cardiac tissue

Complex spatiotemporal patterns of action potential duration have been shown to occur in many mammalian hearts due to period-doubling bifurcations that develop with increasing frequency of stimulation. Here, through high-resolution optical mapping experiments and mathematical modeling, we introduce a characteristic spatial length of cardiac activity in canine ventricular wedges via a spatiotemporal correlation analysis, at different stimulation frequencies and during fibrillation. We show that the characteristic length ranges from 40 to 20 cm during one-to-one responses and it decreases to a specific value of about 3 cm at the transition from period-doubling bifurcation to fibrillation. We further show that during fibrillation, the characteristic length is about 1 cm. Another significant outcome of our analysis is the finding of a constitutive phenomenological law obtained from a nonlinear fitting of experimental data which relates the conduction velocity restitution curve with the characteristic length of the system. The fractional exponent of 3/2 in our phenomenological law is in agreement with the domain size remapping required to reproduce experimental fibrillation dynamics within a realistic cardiac domain via accurate mathematical models.

Climent A. Optical imaging of voltage and calcium in isolated hearts: Linking spatiotemporal heterogeneities and ventricular fibrillation initiation

BACKGROUND

Alternans have been associated with the development of ventricular fibrillation and its control has been proposed as antiarrhythmic strategy. However, cardiac arrhythmias are a spatiotemporal phenomenon in which multiple factors are involved (e.g. calcium and voltage spatial alternans or heterogeneous conduction velocity) and how an antiarrhythmic drug modifies these factors is poorly understood.

OBJECTIVE

The objective of the present study is to evaluate the relation between spatial electrophysiological properties (i.e. spatial discordant alternans and conduction velocity) and the induction of ventricular fibrillation (VF) when a calcium blocker is applied.

METHODS

The mechanisms of initiation of VF were studied by simultaneous epicardial voltage and calcium optical mapping in isolated rabbit hearts using an incremental fast pacing protocol. The additional value of analyzing spatial phenomena in the generation of unidirectional blocks and reentries as precursors of VF was depicted. Specifically, the role of action potential duration (APD), calcium transients (CaT), spatial alternans and conduction velocity in the initiation of VF was evaluated during basal conditions and after the administration of verapamil.

RESULTS

Our results enhance the relation between (1) calcium spatial alternans and (2) slow conduction velocities with the dynamic creation of unidirectional blocks that allowed the induction of VF. In fact, the administration of verapamil demonstrated that calcium and not voltage spatial alternans were the main responsible for VF induction.

CONCLUSIONS

VF induction at high activation rates was linked with the concurrence of a low conduction velocity and high magnitude of calcium alternans, but not necessarily related with increases of APD. Verapamil can postpone the development of cardiac alternans and the apparition of ventricular arrhythmias.

Body surface distribution of T wave alternans is modulated by heart rate and ventricular activation sequence in patients with cardiomyopathy

Background

T wave alternans (TWA) is an electrocardiographic marker of heightened sudden death risk from ventricular tachyarrhythmias in patients with cardiomyopathy. TWA is evaluated from the 12-lead electrocardiogram, Frank lead, or Holter lead recordings, however these clinical lead configurations will not record TWA from adjacent regions of the body torso.

Objective

We tested the hypothesis that changing heart rate or ventricular activation may alter the body surface distribution of TWA such that the clinical ECG leads fail to detect TWA in some patients; thereby producing a false-negative test.

Methods

In 28 cardiomyopathy patients (left ventricular ejection fraction 28±6%), 114 unipolar electrograms were recorded across the body torso during incremental atrial pacing, followed by atrioventricular pacing at 100, 110 and 120bpm. TWA was measured from each unipolar electrogram using the spectral method. A clinically positive TWA test was defined as TWA magnitude (V_alt) ≥1.9 uV with k ≥3 at ≤110bpm.

Results

Maximum V_alt (TWA_max) was greater from the body torso than clinical leads during atrial (p<0.005) and atrioventricular pacing (p<0.005). TWA_max was most prevalent in the right lower chest with atrial pacing 100 bpm and shifted to the left lower chest at 120 bpm. TWA_max was most prevalent in left lower chest with atrioventricular pacing at 100 bpm and shifted to the left upper chest at 120 bpm. Using the body torso as a gold standard, the false-negative rate for clinically positive TWA with clinical leads was 21% during atrial and 11% during atrioventricular pacing. Due to TWA signal migration outside the clinical leads, clinically positive TWA became false-negative when pacing mode was switched (atrial→atrioventricular pacing) in 21% of patients.

Conclusions

The body surface distribution of TWA is modulated by heart rate and the sequence of ventricular activation in patients with cardiomyopathy, which can give rise to modest false-negative TWA signal detection using standard clinical leads.

Control of voltage-driven instabilities in cardiac myocytes with memory

Sudden cardiac death is known to be associated with dynamical instabilities in the heart, and thus control of dynamical instabilities is considered a potential therapeutic strategy. Different control methods were developed previously, including time-delayed feedback pacing control and constant diastolic interval pacing control. Experimental, theoretical, and simulation studies have examined the efficacy of these control methods in stabilizing action potential dynamics. In this study, we apply these control methods to control complex action potential (AP) dynamics under two diseased conditions: early repolarization syndrome and long QT syndrome, in which voltage-driven instabilities occur in the presence of short-term cardiac memory. In addition, we also develop a feedback pacing method to stabilize these instabilities. We perform theoretical analyses using iterated map models and carry out numerical simulations of AP models. We show that under the normal condition where the memory effect is minimal, all three methods can effectively control the action potential duration (APD) dynamics. Under the two diseased conditions where the memory effect is exacerbated, constant diastolic pacing control is least effective, while the feedback pacing control is most effective. Under a very strong memory effect, all three methods fail to stabilize the voltage-driven instabilities. The failure of effective control is due to memory and the all-or-none AP dynamics which results in very steep changes in APD.

Synchronization of Triggered Waves in Atrial Tissue

When an atrial cell is paced rapidly, calcium (Ca) waves can form on the cell boundary and propagate to the cell interior. These waves are referred to as "triggered waves" because they are initiated by Ca influx from the L-type Ca channel and occur during the action potential. However, the consequences of triggered waves in atrial tissue are not known. Here, we develop a phenomenological model of Ca cycling in atrial myocytes that accounts for the formation of triggered waves. Using this model, we show that a fundamental requirement for triggered waves to induce abnormal electrical activity in tissue is that these waves must be synchronized over large populations of cells. This is partly because triggered waves induce a long action potential duration (APD) followed by a short APD. Thus, if these events are not synchronized between cells, then they will on average cancel and have minimal effects on the APD in tissue. Using our computational model, we identify two distinct mechanisms for triggered wave synchronization. The first relies on cycle length (CL) variability, which can prolong the CL at a given beat. In cardiac tissue, we show that CL prolongation leads to a substantial amplification of APD because of the synchronization of triggered waves. A second synchronization mechanism applies in a parameter regime in which the cell exhibits stochastic alternans in which a triggered wave fires, on average, only every other beat. In this scenario, we identify a slow synchronization mechanism that relies on the bidirectional feedback between the APD in tissue and triggered wave initiation. On large cables, this synchronization mechanism leads to spatially discordant APD alternans with spatial variations on a scale of hundreds of cells. We argue that these spatial patterns can potentially serve as an arrhythmogenic substrate for the initiation of atrial fibrillation.

Reduced T wave alternans in heart failure responders to cardiac resynchronization therapy: Evidence of electrical remodeling

Background

T-wave alternans (TWA), a marker of electrical instability, can be modulated by cardiac resynchronization therapy (CRT). The relationship between TWA and heart failure response to CRT has not been clearly defined.

Methods and results

In 40-patients (age 65±11 years, left ventricular ejection-fraction [LVEF] 23±7%), TWA was evaluated prospectively at median of 2 months (baseline) and 8 months (follow-up) post-CRT implant. TWA-magnitude (V_alt >0μV, k≥3), its duration (d), and burden (V_alt ·d) were quantified in moving 128-beat segments during incremental atrial (AAI, native-TWA) and atrio-biventricular (DDD-CRT) pacing. The immediate and long-term effect of CRT on TWA was examined. Clinical response to CRT was defined as an increase in LVEF of ≥5%. Native-TWA was clinically significant (V_alt ≥1.9μV, k≥3) in 68% of subjects at baseline. Compared to native-TWA at baseline, DDD-CRT pacing at baseline and follow-up reduced the number of positive TWA segments, peak-magnitude, longest-duration and peak-burden of TWA (44±5 to 33±5 to 28±4%, p = 0.02 and 0.002; 5.9±0.8 to 4.1±0.7 to 3.8±0.7μV, p = 0.01 and 0.01; 97±9 to 76±8 to 67±8sec, p = 0.004 and <0.001; and 334±65 to 178±58 to 146±54μV.sec, p = 0.01 and 0.004). In addition, the number of positive segments and longest-duration of native-TWA diminished during follow-up (44±5 to 35±6%, p = 0.044; and 97±9 to 81±9sec, p = 0.02). Clinical response to CRT was observed in 71% of patients; the reduction in DDD-CRT paced TWA both at baseline and follow-up was present only in responders (interaction p-values <0.1).

Conclusion

Long-term CRT reduces the prevalence and magnitude of TWA. This CRT induced beneficial electrical remodeling is a marker of clinical response after CRT.

Feasibility of visualizing higher regions of Shannon entropy in atrial fibrillation patients

Catheter ablation is associated with limited success rates in patients with persistent atrial fibrillation (AF), which is mostly maintained by rotors that are located outside of pulmonary veins (PV) region. None of the currently available commercial mapping systems can accurately predict the rotor location outside of PV in patients with persistent AF. Experimental verification of the feasibility of using Shannon entropy (SE) based mapping technique based on symbolic dynamics approach to identify pivotal points of rotors in isolated rabbit hearts was performed. This mapping approach was applied to clinical intracardiac electrograms from a patient with persistent AF to construct a 3-dimensional (3D) SE map. Our results demonstrate that SE can correctly predict the pivot point of the rotor in animal model. We also demonstrated the feasibility of generating 3D SE maps using current catheter mapping methods to identify active rotor sites that may maintain AF. Higher SE areas are noted at the base of right atrial appendage. Further clinical studies are needed to validate ablation of areas with high SE with outcomes.

Memory-induced nonlinear dynamics of excitation in cardiac diseases

Excitable cells, such as cardiac myocytes, exhibit short-term memory, i.e., the state of the cell depends on its history of excitation. Memory can originate from slow recovery of membrane ion channels or from accumulation of intracellular ion concentrations, such as calcium ion or sodium ion concentration accumulation. Here we examine the effects of memory on excitation dynamics in cardiac myocytes under two diseased conditions, early repolarization and reduced repolarization reserve, each with memory from two different sources: slow recovery of a potassium ion channel and slow accumulation of the intracellular calcium ion concentration. We first carry out computer simulations of action potential models described by differential equations to demonstrate complex excitation dynamics, such as chaos. We then develop iterated map models that incorporate memory, which accurately capture the complex excitation dynamics and bifurcations of the action potential models. Finally, we carry out theoretical analyses of the iterated map models to reveal the underlying mechanisms of memory-induced nonlinear dynamics. Our study demonstrates that the memory effect can be unmasked or greatly exacerbated under certain diseased conditions, which promotes complex excitation dynamics, such as chaos. The iterated map models reveal that memory converts a monotonic iterated map function into a nonmonotonic one to promote the bifurcations leading to high periodicity and chaos.

Mechanisms linking T-wave alternans to spontaneous initiation of ventricular arrhythmias in rabbit models of long QT syndrome

KEY POINTS

T-wave alternans (TWA) and T-wave lability (TWL) are precursors of ventricular arrhythmias in long QT syndrome; however, the mechanistic link remains to be clarified. Computer simulations show that action potential duration (APD) prolongation and slowed heart rates promote APD alternans and chaos, manifesting as TWA and TWL, respectively. Regional APD alternans and chaos can exacerbate pre-existing or induce de novo APD dispersion, which combines with enhanced I_Ca,L to result in premature ventricular complexes (PVCs) originating from the APD gradient region. These PVCs can directly degenerate into re-entrant arrhythmias without the need for an additional tissue substrate or further exacerbate the APD dispersion to cause spontaneous initiation of ventricular arrhythmias. Experiments conducted in transgenic long QT rabbits show that PVC alternans occurs at slow heart rates, preceding spontaneous intuition of ventricular arrhythmias.

ABSTRACT

T-wave alternans (TWA) and irregular beat-to-beat T-wave variability or T-wave lability (TWL), the ECG manifestations of action potential duration (APD) alternans and variability, are precursors of ventricular arrhythmias in long QT syndromes. TWA and TWL in patients tend to occur at normal heart rates and are usually potentiated by bradycardia. Whether or how TWA and TWL at normal or slow heart rates are causally linked to arrhythmogenesis remains unknown. In the present study, we used computer simulations and experiments of a transgenic rabbit model of long QT syndrome to investigate the underlying mechanisms. Computer simulations showed that APD prolongation and slowed heart rates caused early afterdepolarization-mediated APD alternans and chaos, manifesting as TWA and TWL, respectively. Regional APD alternans and chaos exacerbated pre-existing APD dispersion and, in addition, APD chaos could also induce APD dispersion de novo via chaos desynchronization. Increased APD dispersion, combined with substantially enhanced I_Ca,L , resulted in a tissue-scale dynamical instability that gave rise to the spontaneous occurrence of unidirectionally propagating premature ventricular complexes (PVCs) originating from the APD gradient region. These PVCs could directly degenerate into re-entrant arrhythmias without the need for an additional tissue substrate or could block the following sinus beat to result in a longer RR interval, which further exacerbated the APD dispersion giving rise to the spontaneous occurrence of ventricular arrhythmias. Slow heart rate-induced PVC alternans was observed in experiments of transgenic LQT2 rabbits under isoproterenol, which was associated with increased APD dispersion and spontaneous occurrence of ventricular arrhythmias, in agreement with the theoretical predictions.

Slow Adaptation of Ventricular Repolarization as a Cause of Arrhythmia?

Introduction: This article is part of the Focus Theme of Methods of Information in Medicine on “Biosignal Interpretation: Advanced Methods for Studying Cardiovascular and Respiratory Systems”.

Background: Adaptation of the QT-interval to changes in heart rate reflects on the body-surface electrocardiogram the adaptation of action potential duration (APD) at the cellular level. The initial fast phase of APD adaptation has been shown to modulate the arrhythmia substrate. Whether the slow phase is potentially proarrhythmic remains unclear.

Objectives: To analyze in-vivo human data and use computer simulations to examine effects of the slow APD adaptation phase on dispersion of repolarization and reentry in the human ventricle.

Methods: Electrograms were acquired from 10 left and 10 right ventricle (LV/RV) endocardial sites in 15 patients with normal ventricles during RV pacing. Activation-recovery intervals, as a surrogate for APD, were measured during a sustained increase in heart rate. Observed dynamics were studied using computer simulations of human tissue electrophysiology.

Results: Spatial heterogeneity of rate adaptation was observed in all patients. Inhomogeneity in slow APD adaptation time constants (ΔTs) was greater in LV than RV (ΔTs LV = 31.8 ± 13.2, ΔTs RV = 19.0 ± 12.8 s, P < 0.01). Simulations showed that altering local slow time constants of adaptation was sufficient to convert partial wavefront block to block with successful reentry.

Conclusions: Using electrophysiological data acquired in-vivo in human and computer simulations, we identify heterogeneity in the slow phase of APD adaptation as an important component of arrhythmogenesis.

Stochastic Pacing Inhibits Spatially Discordant Cardiac Alternans

Depressed heart rate variability is a well-established risk factor for sudden cardiac death in survivors of acute myocardial infarction and for those with congestive heart failure. Although measurements of heart rate variability provide a valuable prognostic tool, it is unclear whether reduced heart rate variability itself is proarrhythmic or if it simply correlates with the severity of autonomic nervous system dysfunction. In this work, we investigate a possible mechanism by which heart rate variability could protect against cardiac arrhythmia. Specifically, in numerical simulations, we observe an inverse relationship between the variance of stochastic pacing and the occurrence of spatially discordant alternans, an arrhythmia that is widely believed to facilitate the development of cardiac fibrillation. By analyzing the effects of conduction velocity restitution, cellular dynamics, electrotonic coupling, and stochastic pacing on the nodal dynamics of spatially discordant alternans, we provide intuition for this observed behavior and propose control strategies to inhibit discordant alternans.

Novel Quantitative Analytical Approaches for Rotor Identification and Associated Implications for Mapping

GOAL

Clinical studies identifying rotors and confirming these sites for ablation in treating cardiac arrhythmias have had inconsistent results with the currently available analysis techniques. The aim of this study is to evaluate four new signal analysis approaches-multiscale frequency (MSF), Shannon entropy (SE), Kurtosis (Kt), and multiscale entropy (MSE)-in their ability to identify the pivot point of rotors.

METHODS

Optical mapping movies of ventricular tachycardia were used to evaluate the performance and robustness of SE, Kt, MSF, and MSE techniques with respect to several clinical limitations: decreased time duration, reduced spatial resolution, and the presence of meandering rotors. To quantitatively assess the robustness of the four techniques, results were compared to the "true" rotor(s) identified using optical mapping-based phase maps.

RESULTS

The results demonstrate that MSF, Kt, and MSE accurately identified both stationary and meandering rotors. In addition, these techniques remained accurate under simulated clinical limitations: shortened electrogram duration and decreased spatial resolution. Artifacts mildly affected the performance of MSF, Kt, and MSE, but strongly impacted the performance of SE.

CONCLUSION

These results motivate further validation using intracardiac electrograms to see if these approaches can map rotors in a clinical setting and whether they apply to more complex arrhythmias including atrial or ventricular fibrillation.

SIGNIFICANCE

New techniques providing more accurate rotor localization could improve characterization of arrhythmias and, in turn, offer a means to accurately evaluate whether rotor ablation is a viable and effective treatment for chaotic cardiac arrhythmias.

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.

Memory in a fractional-order cardiomyocyte model alters properties of alternans and spontaneous activity

Cardiac memory is the dependence of electrical activity on the prior history of one or more system state variables, including transmembrane potential (V_m), ionic current gating, and ion concentrations. While prior work has represented memory either phenomenologically or with biophysical detail, in this study, we consider an intermediate approach of a minimal three-variable cardiomyocyte model, modified with fractional-order dynamics, i.e., a differential equation of order between 0 and 1, to account for history-dependence. Memory is represented via both capacitive memory, due to fractional-order V_m dynamics, that arises due to non-ideal behavior of membrane capacitance; and ionic current gating memory, due to fractional-order gating variable dynamics, that arises due to gating history-dependence. We perform simulations for varying V_m and gating variable fractional-orders and pacing cycle length and measure action potential duration (APD) and incidence of alternans, loss of capture, and spontaneous activity. In the absence of ionic current gating memory, we find that capacitive memory, i.e., decreased V_m fractional-order, typically shortens APD, suppresses alternans, and decreases the minimum cycle length (MCL) for loss of capture. However, in the presence of ionic current gating memory, capacitive memory can prolong APD, promote alternans, and increase MCL. Further, we find that reduced V_m fractional order (typically less than 0.75) can drive phase 4 depolarizations that promote spontaneous activity. Collectively, our results demonstrate that memory reproduced by a fractional-order model can play a role in alternans formation and pacemaking, and in general, can greatly increase the range of electrophysiological characteristics exhibited by a minimal model.

Effects of pharmacological gap junction and sodium channel blockade on S1S2 restitution properties in Langendorff-perfused mouse hearts

Gap junctions and sodium channels are the major molecular determinants of normal and abnormal electrical conduction through the myocardium, however, their exact contributions to arrhythmogenesis are unclear. We examined conduction and recovery properties of regular (S1) and extrasystolic (S2) action potentials (APs), S1S2 restitution and ventricular arrhythmogenicity using the gap junction and sodium channel inhibitor heptanol (2 mM) in Langendorff-perfused mouse hearts (n=10). Monophasic action potential recordings obtained during S1S2 pacing showed that heptanol increased the proportion of hearts showing inducible ventricular tachycardia (0/10 vs. 5/8 hearts (Fisher’s exact test, P < 0.05), prolonged activation latencies of S1 and S2 APs, thereby decreasing S2/S1 activation latency ratio (ANOVA, P < 0.05) despite prolonged ventricular effective refractory period (VERP). It did not alter S1 action potential duration at 90% repolarization (APD₉₀) but prolonged S2 APD₉₀ (P < 0.05), thereby increasing S2/S1 APD₉₀ ratio (P < 0.05). It did not alter maximum conduction velocity (CV) restitution gradient or maximum CV reductions but decreased the restitution time constant (P < 0.05). It increased maximal APD₉₀ restitution gradient (P < 0.05) without altering critical diastolic interval or maximum APD₉₀ reductions. Pro-arrhythmic effects of 2 mM heptanol are explicable by delayed conduction and abnormal electrical restitution. We concluded that gap junctions modulated via heptanol (0.05 mM) increased arrhythmogenicity through a delay in conduction, while sodium channel inhibition by a higher concentration of heptanol (2 mM) increased arrhythmogenicity via additional mechanisms, such as abnormalities in APDs and CV restitution.

Role of abnormal repolarization in the mechanism of cardiac arrhythmia

In cardiac patients, life-threatening tachyarrhythmia is often precipitated by abnormal changes in ventricular repolarization and refractoriness. Repolarization abnormalities typically evolve as a consequence of impaired function of outward K⁺ currents in cardiac myocytes, which may be caused by genetic defects or result from various acquired pathophysiological conditions, including electrical remodelling in cardiac disease, ion channel modulation by clinically used pharmacological agents, and systemic electrolyte disorders seen in heart failure, such as hypokalaemia. Cardiac electrical instability attributed to abnormal repolarization relies on the complex interplay between a provocative arrhythmic trigger and vulnerable arrhythmic substrate, with a central role played by the excessive prolongation of ventricular action potential duration, impaired intracellular Ca²⁺ handling, and slowed impulse conduction. This review outlines the electrical activity of ventricular myocytes in normal conditions and cardiac disease, describes classical electrophysiological mechanisms of cardiac arrhythmia, and provides an update on repolarization-related surrogates currently used to assess arrhythmic propensity, including spatial dispersion of repolarization, activation-repolarization coupling, electrical restitution, TRIaD (triangulation, reverse use dependence, instability, and dispersion), and the electromechanical window. This is followed by a discussion of the mechanisms that account for the dependence of arrhythmic vulnerability on the location of the ventricular pacing site. Finally, the review clarifies the electrophysiological basis for cardiac arrhythmia produced by hypokalaemia, and gives insight into the clinical importance and pathophysiology of drug-induced arrhythmia, with particular focus on class Ia (quinidine, procainamide) and Ic (flecainide) Na⁺ channel blockers, and class III antiarrhythmic agents that block the delayed rectifier K⁺ channel (dofetilide).

Assessments of the QT/QRS restitution in perfused guinea-pig heart can discriminate safe and arrhythmogenic drugs

INTRODUCTION

Drug-induced arrhythmia remains a matter of serious clinical concern, partly due to low prognostic value of currently available arrhythmic biomarkers.

METHODS

This study examined whether arrhythmogenic risks can be predicted through assessments of the rate adaptation of QT interval, ventricular effective refractory period (ERP), or the QT/QRS ratio, in perfused guinea-pig hearts.

RESULTS

When the maximum restitution slope was taken as a metric of proarrhythmia, neither QT interval nor ERP measurements at progressively increased pacing rates were found to fully discriminate arrhythmogenic drugs (dofetilide, quinidine, flecainide, and procainamide) from those recognized as safe antiarrhythmics (lidocaine and mexiletine). For example, the slope of QT restitution was increased by dofetilide and quinidine, but remained unchanged by flecainide, procainamide, lidocaine, and mexiletine. With ERP rate adaptation, even though the restitution slope was increased by dofetilide, all class I agents reduced the slope value independently of their safety profile. The QRS measurements revealed variable drug effects, ranging from significant use-dependent conduction slowing (flecainide, quinidine, and procainamide) to only modest increase in QRS (lidocaine and mexiletine), or no change at all (dofetilide). However, with the QT/QRS rate adaptation, the restitution slope was significantly increased by all agents which have been reported to produce proarrhythmic effects (dofetilide, quinidine, flecainide, and procainamide), but not changed by lidocaine and mexiletine.

DISCUSSION

These findings suggest that the slope of the QT/QRS rate adaptation can be considered as a novel electrophysiological biomarker in predicting potential arrhythmic risks associated with pharmacotherapy in cardiac patients.

Mechanism for Amplitude Alternans in Electrocardiograms and the Initiation of Spatiotemporal Chaos

It is widely believed that one major life-threatening transition to chaotic fibrillation occurs via spiral-wave breakup that is preceded by spatiotemporal dispersion of refractoriness due to alternations in the duration of the cardiac action potential (AP). However, recent clinical and experimental evidence suggests that other characteristics of the AP may contribute to, and perhaps drive, this dangerous dynamical instability. To identify the relative roles of AP characteristics, we performed experiments in rabbit hearts under conditions to minimize AP duration dynamics which unmasked pronounced AP amplitude alternans just before the onset of fibrillation. We used a simplified ionic cell model to derive a return map and a stability condition that elucidates a novel underlying mechanism for AP alternans and spiral breakup. We found that inactivation of the sodium current is key to developing amplitude alternans and is directly connected to conduction block and initiation of arrhythmias. Simulations in 2D where AP amplitude alternation led to turbulence confirm our hypothesis.

Memory-Induced Chaos in Cardiac Excitation

Excitable systems display memory, but how memory affects the excitation dynamics of such systems remains to be elucidated. Here we use computer simulation of cardiac action potential models to demonstrate that memory can cause dynamical instabilities that result in complex excitation dynamics and chaos. We develop an iterated map model that correctly describes these dynamics and show that memory converts a monotonic first return map of action potential duration into a nonmonotonic one, resulting in a period-doubling bifurcation route to chaos.

Electrophysiological mechanisms of long and short QT syndromes

The QT interval on the human electrocardiogram is normally in the order of 450 ms, and reflects the summated durations of action potential (AP) depolarization and repolarization of ventricular myocytes. Both prolongation and shortening in the QT interval have been associated with ventricular tachy-arrhythmias, which predispose affected individuals to sudden cardiac death. In this article, the molecular determinants of the AP duration and the causes of long and short QT syndromes (LQTS and SQTS) are explored. This is followed by a review of the recent advances on their arrhythmogenic mechanisms involving reentry and/or triggered activity based on experiments conducted in mouse models. Established and novel clinical risk markers based on the QT interval for the prediction of arrhythmic risk and cardiovascular mortality are presented here. It is concluded by a discussion on strategies for the future rational design of anti-arrhythmic agents.

The effect of electrical conductivity of myocardium on cardiac pumping efficacy: a computational study

Background and aims

The existence of non-excitable cells in the myocardium leads to the increasing conduction non-uniformity and decreasing myocardial electrical conductivity. Slowed myocardial conduction velocity (MCV) believed to enhance the probability of cardiac arryhthmia and alter the cardiac mechanical pumping efficacy, even in sinus rhythm. Though several studies on the correlation between MCV and cardiac electrical instabilities exist, there has been no study concerning correlation or causality between MCV and cardiac mechanical pumping efficacy, due to the limitation in clinical methods to document and evaluate cardiac mechanical responses directly. The goal of this study was to examine quantitatively the cardiac pumping efficacy under various MCV conditions using three-dimensional (3D) electromechanical model of canine’s failing ventricle.

Methods

The electromechanical model used in this study composed of the electrical model coupled with the mechanical contraction model along with a lumped model of the circulatory system. The electrical model consisted of 241,725 nodes and 1,298,751 elements of tetrahedral mesh, whereas the mechanical model consisted of 356 nodes and 172 elements of hexahedral mesh with Hermite basis. First, we performed the electrical simulation for five different MCV conditions, from 30 to 70 cm/s with 10 cm/s interval during sinus pacing. Then, we compared the cardiac electrical and mechanical responses of each MCV condition, such as the electrical activation time (EAT), pressure, volume, and energy consumption of the myocardium. The energy consumption of the myocardium was calculated by integrating ATP consumption rate of each node in myofilament model.

Results

The result showed that under higher MCV conditions, the EAT, energy consumption, end diastolic and systolic volume are gradually decreased. Meanwhile, the systolic pressure, stroke volume, stroke work, and stroke work to ATP are increased as the MCV values increased. The cardiac functions and performances are more efficient under higher MCV conditions by consuming smaller energy (ATP) while carrying more works.

Conclusion

In conclusion, this study reveals that MCV has strong correlation with the cardiac pumping efficacy. The obtained results provide useful information to estimate the effect of MCV on the electro-physiology and hemodynamic responses of the ventricle and can be used for further study about arrhythmogeneis and heart failure.

Interactions between Activation and Repolarization Restitution Properties in the Intact Human Heart: In-Vivo Whole-Heart Data and Mathematical Description

BACKGROUND

The restitution of the action potential duration (APDR) and conduction velocity (CVR) are mechanisms whereby cardiac excitation and repolarization adapt to changes in heart rate. They modulate the vulnerability to dangerous arrhythmia, but the mechanistic link between restitution and arrhythmogenesis remains only partially understood.

METHODS

This paper provides an experimental and theoretical study of repolarization and excitation restitution properties and their interactions in the intact human epicardium. The interdependence between excitation and repolarization dynamic is studied in 8 patients (14 restitution protocols, 1722 restitution curves) undergoing global epicardial mapping with multi-electrode socks before open heart surgery. A mathematical description of the contribution of both repolarization and conduction dynamics to the steepness of the APDR slope is proposed.

RESULTS

This study demonstrates that the APDR slope is a function of both activation and repolarization dynamics. At short cycle length, conduction delay significantly increases the APDR slope by interacting with the diastolic interval. As predicted by the proposed mathematical formulation, the APDR slope was more sensitive to activation time prolongation than to the simultaneous shortening of repolarization time. A steep APDR slope was frequently identified, with 61% of all cardiac sites exhibiting an APDR slope > 1, suggesting that a slope > 1 may not necessarily promote electrical instability in the human epicardium. APDR slope did not change for different activation or repolarization times, and it was not a function of local baseline APD. However, it was affected by the spatial organization of electrical excitation, suggesting that in tissue APDR is not a unique function of local electrophysiological properties. Spatial heterogeneity in both activation and repolarization restitution contributed to the increase in the modulated dispersion of repolarization, which for short cycle length was as high as 250 ms. Heterogeneity in conduction velocity restitution can translate into both activation and repolarization dispersion and increase cardiac instability. The proposed mathematical formulation shows an excellent agreement with the experimental data (correlation coefficient r = 0.94) and provides a useful tool for the understanding of the complex interactions between activation and repolarization restitution properties as well as between their measurements.

Computational rabbit models to investigate the initiation, perpetuation, and termination of ventricular arrhythmia

Current understanding of cardiac electrophysiology has been greatly aided by computational work performed using rabbit ventricular models. This article reviews the contributions of multiscale models of rabbit ventricles in understanding cardiac arrhythmia mechanisms. This review will provide an overview of multiscale modeling of the rabbit ventricles. It will then highlight works that provide insights into the role of the conduction system, complex geometric structures, and heterogeneous cellular electrophysiology in diseased and healthy rabbit hearts to the initiation and maintenance of ventricular arrhythmia. Finally, it will provide an overview on the contributions of rabbit ventricular modeling on understanding the mechanisms underlying shock-induced defibrillation.