Dissolution of spiral wave's core using cardiac optogenetics.

Rotating spiral waves in the heart are associated with life-threatening cardiac arrhythmias such as ventricular tachycardia and fibrillation. These arrhythmias are treated by a process called defibrillation, which forces electrical resynchronization of the heart tissue by delivering a single global high-voltage shock directly to the heart. This method leads to immediate termination of spiral waves. However, this may not be the only mechanism underlying successful defibrillation, as certain scenarios have also been reported, where the arrhythmia terminated slowly, over a finite period of time. Here, we investigate the slow termination dynamics of an arrhythmia in optogenetically modified murine cardiac tissue both in silico and ex vivo during global illumination at low light intensities. Optical imaging of an intact mouse heart during a ventricular arrhythmia shows slow termination of the arrhythmia, which is due to action potential prolongation observed during the last rotation of the wave. Our numerical studies show that when the core of a spiral is illuminated, it begins to expand, pushing the spiral arm towards the inexcitable boundary of the domain, leading to termination of the spiral wave. We believe that these fundamental findings lead to a better understanding of arrhythmia dynamics during slow termination, which in turn has implications for the improvement and development of new cardiac defibrillation techniques.

Optical mapping of contracting hearts.

Optical mapping is a widely used tool to record and visualize the electrophysiological properties in a variety of myocardial preparations such as Langendorff-perfused isolated hearts, coronary-perfused wedge preparations, and cell culture monolayers. Motion artifact originating from the mechanical contraction of the myocardium creates a significant challenge to performing optical mapping of contracting hearts. Hence, to minimize the motion artifact, cardiac optical mapping studies are mostly performed on non-contracting hearts, where the mechanical contraction is removed using pharmacological excitation-contraction uncouplers. However, such experimental preparations eliminate the possibility of electromechanical interaction, and effects such as mechano-electric feedback cannot be studied. Recent developments in computer vision algorithms and ratiometric techniques have opened the possibility of performing optical mapping studies on isolated contracting hearts. In this review, we discuss the existing techniques and challenges of optical mapping of contracting hearts.

In silico optical modulation of spiral wave trajectories in cardiac tissue.

Life-threatening cardiac arrhythmias such as ventricular tachycardia and fibrillation are common precursors to sudden cardiac death. They are associated with the occurrence of abnormal electrical spiral waves in the heart that rotate at a high frequency. In severe cases, arrhythmias are combated with a clinical method called defibrillation, which involves administering a single global high-voltage shock to the heart to reset all its activity and restore sinus rhythm. Despite its high efficiency in controlling arrhythmias, defibrillation is associated with several negative side effects that render the method suboptimal. The best approach to optimize this therapeutic technique is to deepen our understanding of the dynamics of spiral waves. Here, we use computational cardiac optogenetics to study and control the dynamics of a single spiral wave in a two-dimensional, electrophysiologically detailed, light-sensitive model of a mouse ventricle. First, we illuminate the domain globally by applying a sequence of periodic optical pulses with different frequencies in the sub-threshold regime where no excitation wave is induced. In doing so, we obtain epicycloidal, hypocycloidal, and resonant drift trajectories of the spiral wave core. Then, to effectively control the wave dynamics, we use a method called resonant feedback pacing. In this approach, each global optical pulse is applied when the measuring electrode positioned on the domain registers a predefined value of the membrane voltage. This enables us to steer the spiral wave in a desired direction determined by the position of the electrode. Our study thus provides valuable mechanistic insights into the success or failure of global optical stimulation in executing efficient arrhythmia control.

Pulsed low-energy stimulation initiates electric turbulence in cardiac tissue.

Interruptions in nonlinear wave propagation, commonly referred to as wave breaks, are typical of many complex excitable systems. In the heart they lead to lethal rhythm disorders, the so-called arrhythmias, which are one of the main causes of sudden death in the industrialized world. Progress in the treatment and therapy of cardiac arrhythmias requires a detailed understanding of the triggers and dynamics of these wave breaks. In particular, two very important questions are: 1) What determines the potential of a wave break to initiate re-entry? and 2) How do these breaks evolve such that the system is able to maintain spatiotemporally chaotic electrical activity? Here we approach these questions numerically using optogenetics in an in silico model of human atrial tissue that has undergone chronic atrial fibrillation (cAF) remodelling. In the lesser studied sub-threshold illumination régime, we discover a new mechanism of wave break initiation in cardiac tissue that occurs for gentle slopes of the restitution characteristics. This mechanism involves the creation of conduction blocks through a combination of wavefront-waveback interaction, reshaping of the wave profile and heterogeneous recovery from the excitation of the spatially extended medium, leading to the creation of re-excitable windows for sustained re-entry. This finding is an important contribution to cardiac arrhythmia research as it identifies scenarios in which low-energy perturbations to cardiac rhythm can be potentially life-threatening.

Taming cardiac arrhythmias: Terminating spiral wave chaos by adaptive deceleration pacing.

Sequences of weak electrical pulses are considered a promising alternative for terminating ventricular and atrial fibrillations while avoiding strong defibrillation shocks with adverse side effects. In this study, using numerical simulations of four different 2D excitable media, we show that pulse trains with increasing temporal intervals between successive pulses (deceleration pacing) provide high success rates at low energies. Furthermore, we propose a simple and robust approach to calculate inter-pulse spacing directly from the frequency spectrum of the dynamics (for instance, computed based on the electrocardiogram), which can be practically used in experiments and clinical applications.

Excitable dynamics in neural and cardiac systems.

The application of mathematics, physics and engineering to medical research is continuously growing; interactions among these disciplines have become increasingly important and have contributed to an improved understanding of clinical and biological phenomena, with implications for disease prevention, diagnosis and treatment. This special issue presents examples of this synergy, with a particular focus on the investigation of cardiac and neural excitability. This issue includes 24 original research papers and covers a broad range of topics related to the physiological and pathophysiological function of the brain and the heart. Studies span scales from isolated neurons and small networks of neurons to whole-organ dynamics for the brain and from cardiac subcellular domains and cardiomyocytes to one-dimensional tissues for the heart. This preface is part of the Special Issue on "Excitable Dynamics in Neural and Cardiac Systems".

Multiscale Modeling of Dyadic Structure-Function Relation in Ventricular Cardiac Myocytes.

Cardiovascular disease is often related to defects of subcellular components in cardiac myocytes, specifically in the dyadic cleft, which include changes in cleft geometry and channel placement. Modeling of these pathological changes requires both spatially resolved cleft as well as whole cell level descriptions. We use a multiscale model to create dyadic structure-function relationships to explore the impact of molecular changes on whole cell electrophysiology and calcium cycling. This multiscale model incorporates stochastic simulation of individual L-type calcium channels and ryanodine receptor channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca2+ and Ca2+-binding molecules in the bulk of the cell. We found action potential duration, systolic, and diastolic [Ca2+] to respond most sensitively to changes in L-type calcium channel current. The ryanodine receptor channel cluster structure inside dyadic clefts was found to affect all biomarkers investigated. The shape of clusters observed in experiments by Jayasinghe et al. and channel density within the cluster (characterized by mean occupancy) showed the strongest correlation to the effects on biomarkers.

Termination of Scroll Waves by Surface Impacts.

Three-dimensional scroll waves direct cell movement and gene expression, and induce chaos in the brain and heart. We found an approach to terminate multiple three-dimensional scrolls. A pulse of a properly configured electric field detaches scroll filaments from the surface. They shrink due to filament tension and disappear. Since wave emission from small heterogeneities is not used, this approach requires a much lower electric field. It is not sensitive to the details of the excitable medium. It may affect future studies of low-energy chaos termination in the heart.

Optogenetic determination of the myocardial requirements for extrasystoles by cell type-specific targeting of ChannelRhodopsin-2.

Extrasystoles lead to several consequences, ranging from uneventful palpitations to lethal ventricular arrhythmias, in the presence of pathologies, such as myocardial ischemia. The role of working versus conducting cardiomyocytes, as well as the tissue requirements (minimal cell number) for the generation of extrasystoles, and the properties leading ectopies to become arrhythmia triggers (topology), in the normal and diseased heart, have not been determined directly in vivo. Here, we used optogenetics in transgenic mice expressing ChannelRhodopsin-2 selectively in either cardiomyocytes or the conduction system to achieve cell type-specific, noninvasive control of heart activity with high spatial and temporal resolution. By combining measurement of optogenetic tissue activation in vivo and epicardial voltage mapping in Langendorff-perfused hearts, we demonstrated that focal ectopies require, in the normal mouse heart, the simultaneous depolarization of at least 1,300-1,800 working cardiomyocytes or 90-160 Purkinje fibers. The optogenetic assay identified specific areas in the heart that were highly susceptible to forming extrasystolic foci, and such properties were correlated to the local organization of the Purkinje fiber network, which was imaged in three dimensions using optical projection tomography. Interestingly, during the acute phase of myocardial ischemia, focal ectopies arising from this location, and including both Purkinje fibers and the surrounding working cardiomyocytes, have the highest propensity to trigger sustained arrhythmias. In conclusion, we used cell-specific optogenetics to determine with high spatial resolution and cell type specificity the requirements for the generation of extrasystoles and the factors causing ectopies to be arrhythmia triggers during myocardial ischemia.

Sensing Cardiac Electrical Activity With a Cardiac Myocyte--Targeted Optogenetic Voltage Indicator.

RATIONALE: Monitoring and controlling cardiac myocyte activity with optogenetic tools offer exciting possibilities for fundamental and translational cardiovascular research. Genetically encoded voltage indicators may be particularly attractive for minimal invasive and repeated assessments of cardiac excitation from the cellular to the whole heart level. OBJECTIVE: To test the hypothesis that cardiac myocyte-targeted voltage-sensitive fluorescence protein 2.3 (VSFP2.3) can be exploited as optogenetic tool for the monitoring of electric activity in isolated cardiac myocytes and the whole heart as well as function and maturity in induced pluripotent stem cell-derived cardiac myocytes. METHODS AND RESULTS: We first generated mice with cardiac myocyte-restricted expression of VSFP2.3 and demonstrated distinct localization of VSFP2.3 at the t-tubulus/junctional sarcoplasmic reticulum microdomain without any signs for associated pathologies (assessed by echocardiography, RNA-sequencing, and patch clamping). Optically recorded VSFP2.3 signals correlated well with membrane voltage measured simultaneously by patch clamping. The use of VSFP2.3 for human action potential recordings was confirmed by simulation of immature and mature action potentials in murine VSFP2.3 cardiac myocytes. Optical cardiograms could be monitored in whole hearts ex vivo and minimally invasively in vivo via fiber optics at physiological heart rate (10 Hz) and under pacing-induced arrhythmia. Finally, we reprogrammed tail-tip fibroblasts from transgenic mice and used the VSFP2.3 sensor for benchmarking functional and structural maturation in induced pluripotent stem cell-derived cardiac myocytes. CONCLUSIONS: We introduce a novel transgenic voltage-sensor model as a new method in cardiovascular research and provide proof of concept for its use in optogenetic sensing of physiological and pathological excitation in mature and immature cardiac myocytes in vitro and in vivo.

Low-energy control of electrical turbulence in the heart.

Controlling the complex spatio-temporal dynamics underlying life-threatening cardiac arrhythmias such as fibrillation is extremely difficult, because of the nonlinear interaction of excitation waves in a heterogeneous anatomical substrate. In the absence of a better strategy, strong, globally resetting electrical shocks remain the only reliable treatment for cardiac fibrillation. Here we establish the relationship between the response of the tissue to an electric field and the spatial distribution of heterogeneities in the scale-free coronary vascular structure. We show that in response to a pulsed electric field, E, these heterogeneities serve as nucleation sites for the generation of intramural electrical waves with a source density ρ(E) and a characteristic time, τ, for tissue depolarization that obeys the power law τ ∝ E(α). These intramural wave sources permit targeting of electrical turbulence near the cores of the vortices of electrical activity that drive complex fibrillatory dynamics. We show in vitro that simultaneous and direct access to multiple vortex cores results in rapid synchronization of cardiac tissue and therefore, efficient termination of fibrillation. Using this control strategy, we demonstrate low-energy termination of fibrillation in vivo. Our results give new insights into the mechanisms and dynamics underlying the control of spatio-temporal chaos in heterogeneous excitable media and provide new research perspectives towards alternative, life-saving low-energy defibrillation techniques.

Extremes of fractional noises: A model for the timings of arrhythmic heart beats in post-infarction patients.

We have analyzed symbol sequences of heart beat annotations obtained from 24-h electrocardiogram recordings of 184 post-infarction patients (from the Cardiac Arrhythmia Suppression Trial database, CAST). In the symbol sequences, each heart beat was coded as an arrhythmic or as a normal beat. The symbol sequences were analyzed with a model-based approach which relies on two-parametric peaks over the threshold (POT) model, interpreting each premature ventricular contraction (PVC) as an extreme event. For the POT model, we explored (i) the Shannon entropy which was estimated in terms of the Lempel-Ziv complexity, (ii) the shape parameter of the Weibull distribution that best fits the PVC return times, and (iii) the strength of long-range correlations quantified by detrended fluctuation analysis (DFA) for the two-dimensional parameter space. We have found that in the frame of our model the Lempel-Ziv complexity is functionally related to the shape parameter of the Weibull distribution. Thus, two complementary measures (entropy and strength of long-range correlations) are sufficient to characterize realizations of the two-parametric model. For the CAST data, we have found evidence for an intermediate strength of long-range correlations in the PVC timings, which are correlated to the age of the patient: younger post-infarction patients have higher strength of long-range correlations than older patients. The normalized Shannon entropy has values in the range 0.5

Emergent dynamics of spatio-temporal chaos in a heterogeneous excitable medium.

Self-organized activation patterns in excitable media such as spiral waves and spatio-temporal chaos underlie dangerous cardiac arrhythmias. While the interaction of single spiral waves with different types of heterogeneity has been studied extensively, the effect of heterogeneity on fully developed spatio-temporal chaos remains poorly understood. We investigate how the complexity and stability properties of spatio-temporal chaos in the Bär-Eiswirth model of excitable media depend on the heterogeneity of the underlying medium. We employ different measures characterizing the chaoticity of the system and find that the spatial arrangement of multiple discrete lower excitability regions has a strong impact on the complexity of the dynamics. Varying the number, shape, and spatial arrangement of the heterogeneities, we observe strong emergent effects ranging from increases in chaoticity to the complete cessation of chaos, contrasting the expectation from the homogeneous behavior. The implications of our findings for the development and treatment of arrhythmias in the heterogeneous cardiac muscle are discussed.

Basin structure of optimization based state and parameter estimation.

Most data based state and parameter estimation methods require suitable initial values or guesses to achieve convergence to the desired solution, which typically is a global minimum of some cost function. Unfortunately, however, other stable solutions (e.g., local minima) may exist and provide suboptimal or even wrong estimates. Here, we demonstrate for a 9-dimensional Lorenz-96 model how to characterize the basin size of the global minimum when applying some particular optimization based estimation algorithm. We compare three different strategies for generating suitable initial guesses, and we investigate the dependence of the solution on the given trajectory segment (underlying the measured time series). To address the question of how many state variables have to be measured for optimal performance, different types of multivariate time series are considered consisting of 1, 2, or 3 variables. Based on these time series, the local observability of state variables and parameters of the Lorenz-96 model is investigated and confirmed using delay coordinates. This result is in good agreement with the observation that correct state and parameter estimation results are obtained if the optimization algorithm is initialized with initial guesses close to the true solution. In contrast, initialization with other exact solutions of the model equations (different from the true solution used to generate the time series) typically fails, i.e., the optimization procedure ends up in local minima different from the true solution. Initialization using random values in a box around the attractor exhibits success rates depending on the number of observables and the available time series (trajectory segment).

Stimulated emission depletion live-cell super-resolution imaging shows proliferative remodeling of T-tubule membrane structures after myocardial infarction.

RATIONALE: Transverse tubules (TTs) couple electric surface signals to remote intracellular Ca(2+) release units (CRUs). Diffraction-limited imaging studies have proposed loss of TT components as disease mechanism in heart failure (HF). OBJECTIVES: Objectives were to develop quantitative super-resolution strategies for live-cell imaging of TT membranes in intact cardiomyocytes and to show that TT structures are progressively remodeled during HF development, causing early CRU dysfunction. METHODS AND RESULTS: Using stimulated emission depletion (STED) microscopy, we characterized individual TTs with nanometric resolution as direct readout of local membrane morphology 4 and 8 weeks after myocardial infarction (4pMI and 8pMI). Both individual and network TT properties were investigated by quantitative image analysis. The mean area of TT cross sections increased progressively from 4pMI to 8pMI. Unexpectedly, intact TT networks showed differential changes. Longitudinal and oblique TTs were significantly increased at 4pMI, whereas transversal components appeared decreased. Expression of TT-associated proteins junctophilin-2 and caveolin-3 was significantly changed, correlating with network component remodeling. Computational modeling of spatial changes in HF through heterogeneous TT reorganization and RyR2 orphaning (5000 of 20 000 CRUs) uncovered a local mechanism of delayed subcellular Ca(2+) release and action potential prolongation. CONCLUSIONS: This study introduces STED nanoscopy for live mapping of TT membrane structures. During early HF development, the local TT morphology and associated proteins were significantly altered, leading to differential network remodeling and Ca(2+) release dyssynchrony. Our data suggest that TT remodeling during HF development involves proliferative membrane changes, early excitation-contraction uncoupling, and network fracturing.

Mechanistic insights into hypothermic ventricular fibrillation: the role of temperature and tissue size.

AIMS: Hypothermia is well known to be pro-arrhythmic, yet it has beneficial effects as a resuscitation therapy and valuable during intracardiac surgeries. Therefore, we aim to study the mechanisms that induce fibrillation during hypothermia. A better understanding of the complex spatiotemporal dynamics of heart tissue as a function of temperature will be useful in managing the benefits and risks of hypothermia. METHODS AND RESULTS: We perform two-dimensional numerical simulations by using a minimal model of cardiac action potential propagation fine-tuned on experimental measurements. The model includes thermal factors acting on the ionic currents and the gating variables to correctly reproduce experimentally recorded restitution curves at different temperatures. Simulations are implemented using WebGL, which allows long simulations to be performed as they run close to real time. We describe (i) why fibrillation is easier to induce at low temperatures, (ii) that there is a minimum size required for fibrillation that depends on temperature, (iii) why the frequency of fibrillation decreases with decreasing temperature, and (iv) that regional cooling may be an anti-arrhythmic therapy for small tissue sizes however it may be pro-arrhythmic for large tissue sizes. CONCLUSION: Using a mathematical cardiac cell model, we are able to reproduce experimental observations, quantitative experimental results, and discuss possible mechanisms and implications of electrophysiological changes during hypothermia.

Local observability of state variables and parameters in nonlinear modeling quantified by delay reconstruction.

Features of the Jacobian matrix of the delay coordinates map are exploited for quantifying the robustness and reliability of state and parameter estimations for a given dynamical model using a measured time series. Relevant concepts of this approach are introduced and illustrated for discrete and continuous time systems employing a filtered Hénon map and a Rössler system.

SAP97 and dystrophin macromolecular complexes determine two pools of cardiac sodium channels Nav1.5 in cardiomyocytes.

RATIONALE: The cardiac sodium channel Na(v)1.5 plays a key role in excitability and conduction. The 3 last residues of Na(v)1.5 (Ser-Ile-Val) constitute a PDZ-domain binding motif that interacts with the syntrophin-dystrophin complex. As dystrophin is absent at the intercalated discs, Na(v)1.5 could potentially interact with other, yet unknown, proteins at this site. OBJECTIVE: The aim of this study was to determine whether Na(v)1.5 is part of distinct regulatory complexes at lateral membranes and intercalated discs. METHODS AND RESULTS: Immunostaining experiments demonstrated that Na(v)1.5 localizes at lateral membranes of cardiomyocytes with dystrophin and syntrophin. Optical measurements on isolated dystrophin-deficient mdx hearts revealed significantly reduced conduction velocity, accompanied by strong reduction of Na(v)1.5 at lateral membranes of mdx cardiomyocytes. Pull-down experiments revealed that the MAGUK protein SAP97 also interacts with the SIV motif of Na(v)1.5, an interaction specific for SAP97 as no pull-down could be detected with other cardiac MAGUK proteins (PSD95 or ZO-1). Furthermore, immunostainings showed that Na(v)1.5 and SAP97 are both localized at intercalated discs. Silencing of SAP97 expression in HEK293 and rat cardiomyocytes resulted in reduced sodium current (I(Na)) measured by patch-clamp. The I(Na) generated by Na(v)1.5 channels lacking the SIV motif was also reduced. Finally, surface expression of Na(v)1.5 was decreased in silenced cells, as well as in cells transfected with SIV-truncated channels. CONCLUSIONS: These data support a model with at least 2 coexisting pools of Na(v)1.5 channels in cardiomyocytes: one targeted at lateral membranes by the syntrophin-dystrophin complex, and one at intercalated discs by SAP97.

Optimising low-energy defibrillation in 2D cardiac tissue with a genetic algorithm.

Sequences of low-energy electrical pulses can effectively terminate ventricular fibrillation (VF) and avoid the side effects of conventional high-energy electrical defibrillation shocks, including tissue damage, traumatic pain, and worsening of prognosis. However, the systematic optimisation of sequences of low-energy pulses remains a major challenge. Using 2D simulations of homogeneous cardiac tissue and a genetic algorithm, we demonstrate the optimisation of sequences with non-uniform pulse energies and time intervals between consecutive pulses for efficient VF termination. We further identify model-dependent reductions of total pacing energy ranging from ∼4% to ∼80% compared to reference adaptive-deceleration pacing (ADP) protocols of equal success rate (100%).

Negative curvature boundaries as wave emitting sites for the control of biological excitable media.

Understanding the interaction of electric fields with the complex anatomy of biological excitable media is key to optimizing control strategies for spatiotemporal dynamics in those systems. On the basis of a bidomain description, we provide a unified theory for the electric-field-induced depolarization of the substrate near curved boundaries of generalized shapes, resulting in the localized recruitment of control sites. Our findings are confirmed in experiments on cardiomyocyte cell cultures and supported by two-dimensional numerical simulations on a cross section of a rabbit ventricle.