Low-energy control of electrical turbulence in the heart

Experimental studies of spiral wave teleportation in a light sensitive Belousov-Zhabotinsky system

Cardiac arrythmias are a form of heart disease that contributes toward making heart disease a significant cause of death globally. Irregular rhythms associated with cardiac arrythmias are thought to arise due to singularities in the heart tissue that generate reentrant waves in the underlying excitable medium. A normal approach to removing such singularities is to apply a high voltage electric shock, which effectively resets the phase of the cardiac cells. A concern with the use of this defibrillation technique is that the high-energy shock can cause lasting damage to the heart tissue. Various theoretical works have investigated lower-energy alternatives to defibrillation. In this work, we demonstrate the effectiveness of a low-energy defibrillation method in an experimental 2D Belousov-Zhabotinsky (BZ) system. When implemented as a 2D spatial reaction, the BZ reaction serves as an effective analog of general excitable media and supports regular and reentrant wave activity. The defibrillation technique employed involves targeted low-energy perturbations that can be used to "teleport" and/or annihilate singularities present in the excitable BZ medium.

Chaos control in cardiac dynamics: terminating chaotic states with local minima pacing

Current treatments of cardiac arrhythmias like ventricular fibrillation involve the application of a high-energy electric shock, that induces significant electrical currents in the myocardium and therefore involves severe side effects like possible tissue damage and post-traumatic stress. Using numerical simulations on four different models of 2D excitable media, this study demonstrates that low energy pulses applied shortly after local minima in the mean value of the transmembrane potential provide high success rates. We evaluate the performance of this approach for ten initial conditions of each model, ten spatially different stimuli, and different shock amplitudes. The investigated models of 2D excitable media cover a broad range of dominant frequencies and number of phase singularities, which demonstrates, that our findings are not limited to a specific kind of model or parameterization of it. Thus, we propose a method that incorporates the dynamics of the underlying system, even during pacing, and solely relies on a scalar observable, which is easily measurable in numerical simulations.

In silico thermal control of spiral wave dynamics in excitable cardiac tissue

Self-organizing spiral waves of excitation occur in many complex excitable systems. In the heart, for example, they are associated with the occurrence of fatal cardiac arrhythmias such as tachycardia and fibrillation, which can lead to sudden cardiac death. The control of these waves is therefore necessary for the treatment of the disease. In this letter, I present an innovative approach to control cardiac arrhythmias using low (nonfreezing) temperatures. This approach differs from all previous established techniques in that it involves no drugs, no genetic modification, no injection of foreign bodies, no application of voltage shocks (high or low, single or pulsed), and no curative damage to the heart. It relies on regional cooling of cardiac tissue to create a transient inhomogeneity in the electrophysiological properties. This inhomogeneity can then be manipulated to control the dynamics of the reentrant waves. This approach is, to my knowledge, the most sustainable theoretical proposal for the treatment of cardiac arrhythmias in the clinic.

Optimal phase-selective entrainment of electrochemical oscillators with different phase response curves

We investigate the entrainment of electrochemical oscillators with different phase response curves (PRCs) using a global signal: the goal is to achieve the desired phase configuration using a minimum-power waveform. Establishing the desired phase relationships in a highly nonlinear networked system exhibiting significant heterogeneities, such as different conditions or parameters for the oscillators, presents a considerable challenge because different units respond differently to the common global entraining signal. In this work, we apply an optimal phase-selective entrainment technique in both a kinetic model and experiments involving electrochemical oscillators in achieving phase synchronized states. We estimate the PRCs of the oscillators at different circuit potentials and external resistance, and entrain pairs and small sets of four oscillators in various phase configurations. We show that for small PRC variations, phase assignment can be achieved using an averaged PRC in the control design. However, when the PRCs are sufficiently different, individual PRCs are needed to entrain the system with the expected phase relationships. The results show that oscillator assemblies with heterogeneous PRCs can be effectively entrained to desired phase configurations in practical settings. These findings open new avenues to applications in biological and engineered oscillator systems where synchronization patterns are essential for system performance.

Emergent Synchronous Volumetric Oscillation in Hierarchically Structured Self-Oscillating Gel Clusters

Emergent properties accompanying synchronization among oscillators are vital characteristics in biological systems. Belousov-Zhabotinsky (BZ) oscillators are an artificial model to study the emergence and synchronization in life. This research represents a self-oscillating gel system with clusterable properties to experimentally examine synchronous and emergent properties at a fundamental hierarchical level. Incorporating acrylic acid (AAc) moieties within the gel network facilitates cluster formation through hydrogen bonding in an acidic BZ substrate solution. Upon clustering, both homogeneous and heterogeneous gel assemblies─ranging from double to quadruple clusters─exhibit increased and synchronized periods and amplitudes during the BZ reaction. Notably, in heterogeneous clusters, gel units with initially short periods and small volumetric amplitudes display a significant increase, aligning with the lonfger periods and larger amplitudes of other elements within the cluster, an emergent property. This research can pave the way for a better understanding of synchronous and emergent properties in biological oscillators such as cardiomyocytes.

Efficient termination of cardiac arrhythmias using optogenetic resonant feedback pacing

Malignant cardiac tachyarrhythmias are associated with complex spatiotemporal excitation of the heart. The termination of these life-threatening arrhythmias requires high-energy electrical shocks that have significant side effects, including tissue damage, excruciating pain, and worsening prognosis. This significant medical need has motivated the search for alternative approaches that mitigate the side effects, based on a comprehensive understanding of the nonlinear dynamics of the heart. Cardiac optogenetics enables the manipulation of cellular function using light, enhancing our understanding of nonlinear cardiac function and control. Here, we investigate the efficacy of optically resonant feedback pacing (ORFP) to terminate ventricular tachyarrhythmias using numerical simulations and experiments in transgenic Langendorff-perfused mouse hearts. We show that ORFP outperforms the termination efficacy of the optical single-pulse (OSP) approach. When using ORFP, the total energy required for arrhythmia termination, i.e., the energy summed over all pulses in the sequence, is 1 mJ. With a success rate of 50%, the energy per pulse is 40 times lower than with OSP with a pulse duration of 10 ms. We demonstrate that even at light intensities below the excitation threshold, ORFP enables the termination of arrhythmias by spatiotemporal modulation of excitability inducing spiral wave drift.

Spiking at the edge: Excitability at interfaces in reaction-diffusion systems

Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations where the amplifying and suppressing forces necessary for spiking coexist at every point in space. In this case, spikes arise due to local bistabilities, which require a fine-tuned ratio between local amplification and suppression strengths. But, in nature and engineered systems, these forces can be segregated in space, forming structures like interfaces and boundaries. Here, we show how boundaries can generate and protect spiking when the reacting components can spread out: Even arbitrarily weak diffusion can cause spiking at the edge between two non-excitable media. This edge spiking arises due to a global bistability, which can occur even if amplification and suppression strengths do not allow spiking when mixed. We analytically derive a spiking phase diagram that depends on two parameters: i) the ratio between the system size and the characteristic diffusive length-scale and ii) the ratio between the amplification and suppression strengths. Our analysis explains recent experimental observations of action potentials at the interface between two non-excitable bioelectric tissues. Beyond electrophysiology, we highlight how edge spiking emerges in predator-prey dynamics and in oscillating chemical reactions. Our findings provide a theoretical blueprint for a class of interfacial excitations in reaction-diffusion systems, with potential implications for spatially controlled chemical reactions, nonlinear waveguides and neuromorphic computation, as well as spiking instabilities, such as cardiac arrhythmias, that naturally occur in heterogeneous biological media.

Pulsating Active Matter

We reveal that the mechanical pulsation of locally synchronized particles is a generic route to propagate deformation waves. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual. The dynamics is inspired by biological tissues where cells consume fuel to sustain active deformation. We show that the competition between repulsion and synchronization triggers an instability which promotes a wealth of dynamical patterns, ranging from spiral waves to defect turbulence. We identify the mechanisms underlying the emergence of patterns, and characterize the corresponding transitions. By coarse-graining the dynamics, we propose a hydrodynamic description of an assembly of pulsating particles, and discuss an analogy with reaction-diffusion systems.

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.

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.

Low-energy defibrillation using a base-apex epicardial electrode

BACKGROUND

Current implantable cardioverter defibrillators (ICDs) require electric conduction with high voltage and high energy, which can impair cardiac function and induce another malignant arrhythmia. As a result, there has been a demand for an ICD that can effectively operate with lower energy to mitigate the risks of a strong electric shock.

METHODS

A pair of sheet-shaped electrodes covering the heart were analyzed in three configurations (top-bottom, left-right, and front-back) using a heart simulator. We also varied the distance between the two electrodes (clearance) to identify the electrode shape with the lowest defibrillation threshold (DFT). We also investigated the ICD shock waveform, shock direction, and the effect of the backside insulator of the electrode.

RESULTS

The DFT was high when the clearance was too small and the DFT was high even when the clearance was too large, suggesting that an optimal value clearance. The top-bottom electrodes with optimal clearance showed the lowest DFT when the biphasic shocks set the top electrode to a high potential first and then the bottom electrode was set to a high potential. An interval between a first shock waveform and a second shock waveform should be provided for low-energy defibrillation. Because the insulator prevents unnecessary current flow to the backside, the DFT of the electrodes with insulators is less than those without insulators.

CONCLUSION

Painless defibrillation using sheet-shaped electrodes on the epicardium is predicated on the basis of results using a heart simulator.

Reordering and synchronization of electrical turbulence in cardiac tissue through global and partial optogenetical illumination

Electrical turbulence in the heart is considered the culprit of cardiac disease, including the fatal ventricular fibrillation. Optogenetics is an emerging technology that has the capability to produce action potentials of cardiomyocytes to affect the electric wave propagation in cardiac tissue, thereby possessing the potential to control the turbulence, by shining a rotating spiral pattern onto the tissue. In this paper, we present a method to reorder and synchronize electrical turbulence through optogenetics. A generic two-variable reaction-diffusion model and a simplified three-variable ionic cardiac model are used. We discuss cases involving either global or partial illumination.

Optogenetic Modulation of Arrhythmia Triggers: Proof-of-Concept from Computational Modeling

Introduction

Early afterdepolarizations (EADs) are secondary voltage depolarizations associated with reduced repolarization reserve (RRR) that can trigger lethal arrhythmias. Relating EADs to triggered activity is difficult to study, so the ability to suppress or provoke EADs would be experimentally useful. Here, we use computational simulations to assess the feasibility of subthreshold optogenetic stimulation modulating the propensity for EADs (cell-scale) and EAD-associated ectopic beats (organ-scale).

Methods

We modified a ventricular ionic model by reducing rapid delayed rectifier potassium (0.25-0.1 × baseline) and increasing L-type calcium (1.0-3.5 × baseline) currents to create RRR conditions with varying severity. We ran simulations in models of single cardiomyocytes and left ventricles from post-myocardial infarction patient MRI scans. Optogenetic stimulation was simulated using either ChR2 (depolarizing) or GtACR1 (repolarizing) opsins.

Results

In cell-scale simulations without illumination, EADs were seen for 164 of 416 RRR conditions. Subthreshold stimulation of GtACR1 reduced EAD incidence by up to 84.8% (25/416 RRR conditions; 0.1 μW/mm2); in contrast, subthreshold ChR2 excitation increased EAD incidence by up to 136.6% (388/416 RRR conditions; 50 μW/mm2). At the organ scale, we assumed simultaneous, uniform illumination of the epicardial and endocardial surfaces. GtACR1-mediated suppression (10-50 μW/mm2) and ChR2-mediated unmasking (50-100 μW/mm2) of EAD-associated ectopic beats were feasible in three distinct ventricular models.

Conclusions

Our findings suggest that optogenetics could be used to silence or provoke both EADs and EAD-associated ectopic beats. Validation in animal models could lead to exciting new experimental regimes and potentially to novel anti-arrhythmia treatments.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-023-00781-z.

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%).

A Goodwin Model Modification and Its Interactions in Complex Networks

The global economy cannot be understood without the interaction of smaller-scale economies. We addressed this issue by considering a simplified economic model that still preserves the basic features, and analyzed the interaction of a set of such economies and the collective emerging dynamic. The topological structure of the economies' network appears to correlate with the collective properties observed. In particular, the strength of the coupling between the different networks as well as the specific connectivity of each node happen to play a crucial role in the determination of the final state.

Theory and experiments of spiral unpinning in the Belousov-Zhabotinsky reaction using a circularly polarized electric field

We present the first experimental study of unpinning an excitation wave using a circularly polarized electric field. The experiments are conducted using the excitable chemical medium, the Belousov-Zhabotinsky (BZ) reaction, which is modeled with the Oregenator model. The excitation wave in the chemical medium is charged so that it can directly interact with the electric field. This is a unique feature of the chemical excitation wave. The mechanism of wave unpinning in the BZ reaction with a circularly polarized electric field is investigated by varying the pacing ratio, the initial phase of the wave, and field strength. The chemical wave in the BZ reaction unpins when the electric force opposite the direction of the spiral is equal to or above a threshold. We developed an analytical relation of the unpinning phase with the initial phase, the pacing ratio, and the field strength. This is then verified in experiments and simulations.

Electrical Stimulation for Low-Energy Termination of Cardiac Arrhythmias: a Review

Cardiac arrhythmias are a leading cause of morbidity and mortality in the developed world, estimated to be responsible for hundreds of thousands of deaths annually. Our understanding of the electrophysiological mechanisms of such arrhythmias has grown since they were formally characterized in the late nineteenth century, and this has led to the development of numerous devices and therapies that have markedly improved outcomes for patients affected by such conditions. Despite these advancements, the application of a single large shock remains the clinical standard for treating deadly tachyarrhythmias. Such defibrillating shocks are undoubtedly effective in terminating such arrhythmias; however, they are applied without forewarning, contributing to the patient's stress and anxiety; they can be intensely painful; and they can have adverse psychological and physiological effects on patients. In recent years, there has been interest in developing defibrillation protocols that can terminate arrhythmias without crossing the human pain threshold for energy delivery, generally estimated to be between 0.1 and 1 J. In this article, we review existing literature on the development of such low-energy defibrillation methods and their underlying mechanisms, in an attempt to broadly describe the current landscape of these technologies.

Drift of sparse and dense spiral waves under joint external forces

Many methods have been employed to investigate the drift behaviors of spiral waves in an effort to understand and control their dynamics. Drift behaviors of sparse and dense spirals induced by external forces have been investigated, yet they remain incompletely understood. Here we employ joint external forces to study and control the drift dynamics. First, sparse and dense spiral waves are synchronized by the suitable external current. Then, under another weak current or heterogeneity, the synchronized spirals undergo a directional drift, and the dependence of their drift velocity on the strength and frequency of the joint external force is studied.

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.

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

Removal of spiral turbulence by virtual electrodes through the use of a circularly polarized electric field

Heart disease is the leading cause of death and is often accompanied by cardiac fibrillation. Defibrillation using the virtual electrode effects is a promising alternative compared to using the high-voltage electric shock in the clinic. Our earlier works [S. L. Murphy, K. D. Kochanek, J. Xu, and E. Arias, NCHS Data Brief 427 (2021); R. A. Gray, A. M. Pertsov, and J. Jalife, Nature 392, 75-78 (1998); F. X. Witkowski, L. J. Leon, P. A. Penkoske, W. R. Giles, M. L. Spano, W. L. Ditto, and A. T. Winfree, Nature 392, 78-82 (1998); M. Santini, C. Pandozi, G. Altamura, G. Gentilucci, M. Villani, M. C. Scianaro, A. Castro, F. Ammirati, and B. Magris, J. Interv. Card. Electrophysiol. 3, 45-51 (1999).] prove that, compared with other external electric fields, a low voltage circularly polarized electric field is more efficient in turning non-excitable defects in cardiac tissue into virtual electrodes. It, therefore, needs lower voltage to stimulate the excitation waves and causes less harm to reset the spiral turbulence of cardiac excitation for defibrillation. In this paper, we investigate the virtual electrode effect of multiple defects by the circularly polarized electric field for the removal of spiral turbulence. Considering different shapes, sizes, and distributions of multiple defects, we reveal the phase locking of stimulated excitations around multiple virtual electrodes. Furthermore, the circularly polarized electric field parameters are optimized to remove the spiral turbulence.

Non-monotonous dose response function of the termination of spiral wave chaos

The conventional termination technique of life threatening cardiac arrhythmia like ventricular fibrillation is the application of a high-energy electrical defibrillation shock, coming along with severe side-effects. In order to improve the current treatment reducing these side-effects, the application of pulse sequences of lower energy instead of a single high-energy pulse are promising candidates. In this study, we show that in numerical simulations the dose-response function of pulse sequences applied to two-dimensional spiral wave chaos is not necessarily monotonously increasing, but exhibits a non-trivial frequency dependence. This insight into crucial phenomena appearing during termination attempts provides a deeper understanding of the governing termination mechanisms in general, and therefore may open up the path towards an efficient termination of cardiac arrhythmia in the future.

Terminating spiral waves with a single designed stimulus: Teleportation as the mechanism for defibrillation

We identify and demonstrate a universal mechanism for terminating spiral waves in excitable media using an established topological framework. This mechanism dictates whether high- or low-energy defibrillation shocks succeed or fail. Furthermore, this mechanism allows for the design of a single minimal stimulus capable of defibrillating, at any time, turbulent states driven by multiple spiral waves. We demonstrate this method in a variety of computational models of cardiac tissue ranging from simple to detailed human models. The theory described here shows how this mechanism underlies all successful defibrillation and can be used to further develop existing and future low-energy defibrillation strategies.

Optimal entrainment for removal of pinned spiral waves

Cardiac fibrillation is caused by self-sustaining spiral waves that occur in the myocardium, some of which can be pinned to anatomical obstacles, making them more difficult to eliminate. A small electrical stimulation is often sufficient to unpin these spirals but only if it is applied during the vulnerable unpinning window. Even if these unpinning windows can be inferred from data, when multiple pinned spirals exist, their unpinning windows will not generally overlap. Using phase-based reduction techniques, we formulate and solve an optimal control problem to yield a time-varying external voltage gradient that can synchronize a collection of spiral waves that are pinned to a collection of heterogeneous obstacles. Upon synchronization, the unpinning windows overlap so that they can be simultaneously unpinned by applying an external voltage gradient pulse at an appropriate moment. Numerical validation is presented in bidomain model simulations. Results represent a proof-of-concept illustration of the proposed unpinning strategy which explicitly incorporates heterogeneity in the problem formulation and requires no real-time feedback about the system state.

During Early VF in Rabbit Hearts, His Bundle Pacing is Less Effective Than Working Myocardial Pacing in Modulating Left Ventricular Activation Rates

PURPOSE

The potential of pacing and capturing the His-Purkinje system (HPS) to synchronize VF wavefronts is not known even though the HPS is thought to be electrically linked during VF. In this study the effect of selective His Bundle (HB) pacing was compared with nearby working myocardial (WM) pacing on the left ventricular (LV) endocardial activation rates.

METHODS

Rabbit hearts (n = 9) were explanted and Langendorff perfused. Electrodes directly on the HB were identified and paced subsequently using an electrode array. The WM was paced through a silver wire inserted in the right ventricular septal wall. After VF was induced, the HB was paced at rates faster than the intrinsic HB activation rate (n = 18 episodes) and also at rates faster than the LV activation rate (n = 16). A basket array inserted in the LV was used to record electrograms before and during each pacing episode. Activation rates at five LV electrodes each from the earliest and latest activating sinus rhythm regions were analyzed before and during pacing.

RESULTS

Both HB and WM pacing reduced LV activation rates during pacing, but WM pacing was more effective (p < 0.005). WM pacing events were more effective (p < 0.05) in reducing LV activation rates than HB pacing in episodes which were faster than LV activation rates.

CONCLUSION

This study provides evidence that during early VF in rabbit hearts, the HPS cannot be driven to effectively modulate the LV activation rates.

Interaction of multiple spiral rotors in a reaction-diffusion system

Rotors of reaction and diffusion are phase singularities that give rise to spiral waves of chemical activity, which are very similar to spatiotemporal patterns observed across several excitable media. Here we carry out experiments with the Belousov-Zhabotinsky reaction system and numerical simulations based on a reaction-diffusion model to show the possible interactions of multiple spiral rotors. When the cores of two spirals come very close to each other, they could either repel, attract, or remain stationary, depending on their relative chirality, phase, and distance separating them. Multiple pairs of spiral waves, in proximity to each other, could alter the paths of the individual rotors. A spiral core will be influenced most by the rotor that is closest to it, depending on the nature of the corresponding spiral wave arm. We observed rotors lying within a limiting distance of each other attract and annihilate. Otherwise, they push each other away until they reach a critical distance, beyond which all interactions seem to cease. We have established a relationship of this critical distance to the properties of the spiral wave. We also observed spontaneous symmetry-breaking instability for a system of up to eight rotors. Our experiments with the Belousov-Zhabotinsky reaction have successfully demonstrated the validity of the numerical results. A thorough understanding of the dynamics of several spiral rotors within a small area could help us perceive the nature of such excitation waves in cardiac tissue and cell membranes.

Control of spiral waves in optogenetically modified cardiac tissue by periodic optical stimulation

Resonant drift of nonlinear spiral waves occurs in various types of excitable media under periodic stimulation. Recently a novel methodology of optogenetics has emerged, which allows to affect excitability of cardiac cells and tissues by optical stimuli. In this paper we study if resonant drift of spiral waves in the heart can be induced by a homogeneous weak periodic optical stimulation of cardiac tissue. We use a two-variable and a detailed model of cardiac tissue and add description of depolarizing and hyperpolarizing optogenetic ionic currents. We show that weak periodic optical stimulation at a frequency equal to the natural rotation frequency of the spiral wave induces resonant drift for both depolarizing and hyperpolarizing optogenetic currents. We quantify these effects and study how the speed of the drift and its direction depend on the initial conditions. We also derive analytical formulas based on the response function theory which correctly predict the drift velocity and its trajectory. We conclude that optogenetic methodology can be used for control of spiral waves in cardiac tissue and discuss its possible applications.

Patterned Illumination Techniques in Optogenetics: An Insight Into Decelerating Murine Hearts

Much has been reported about optogenetic based cardiac arrhythmia treatment and the corresponding characterization of photostimulation parameters, but still, our capacity to interact with the underlying spatiotemporal excitation patterns relies mainly on electrical and/or pharmacological approaches. However, these well-established treatments have always been an object of somehow heated discussions. Though being acutely life-saving, they often come with potential side-effects leading to a decreased functionality of the complex cardiac system. Recent optogenetic studies showed the feasibility of the usage of photostimulation as a defibrillation method with comparatively high success rates. Although, these studies mainly concentrated on the description as well as on the comparison of single photodefibrillation approaches, such as locally focused light application and global illumination, less effort was spent on the description of excitation patterns during actual photostimulation. In this study, the authors implemented a multi-site photodefibrillation technique in combination with Multi-Lead electrocardiograms (ECGs). The technical connection of real-time heart rhythm measurements and the arrhythmia counteracting light control provides a further step toward automated arrhythmia classification, which can lead to adaptive photodefibrillation methods. In order to show the power effectiveness of the new approach, transgenic murine hearts expressing channelrhodopsin-2 ex vivo were investigated using circumferential micro-LED and ECG arrays. Thus, combining the best of two methods by giving the possibility to illuminate either locally or globally with differing pulse parameters. The optical technique presented here addresses a number of challenges of technical cardiac optogenetics and is discussed in the context of arrhythmic development during photostimulation.

Control of the chirality of spiral waves and recreation of spatial excitation patterns through optogenetics

Spiral waves lead to dangerous arrhythmias in the cardiac system. In 2015 Burton et al. demonstrated the reversal of the spiral wave chirality through the rotating spiral-shaped illumination on the optogenetically modified cardiac monolayers. We show that this process entails the recreation of a spiral wave. We show how this methodology can be used to control and create the desired spatial excitation pattern. We found that the control is sensitive to the area of illuminated region but independent of the phase difference of the existing spiral wave and the applied spiral-shaped light. We also discovered that our methodology can temporarily resynchronize a turbulent system. The results offer numerical evidence for the control of spatial pattern in biological excitable systems with optogenetics.

The role of pulse timing in cardiac defibrillation

Life-threatening cardiac arrhythmias require immediate defibrillation. For state-of-the-art shock treatments, a high field strength is required to achieve a sufficient success rate for terminating the complex spiral wave (rotor) dynamics underlying cardiac fibrillation. However, such high energy shocks have many adverse side effects due to the large electric currents applied. In this study, we show, using 2D simulations based on the Fenton-Karma model, that also pulses of relatively low energy may terminate the chaotic activity if applied at the right moment in time. In our simplified model for defibrillation, complex spiral waves are terminated by local perturbations corresponding to conductance heterogeneities acting as virtual electrodes in the presence of an external electric field. We demonstrate that time series of the success rate for low energy shocks exhibit pronounced peaks which correspond to short intervals in time during which perturbations aiming at terminating the chaotic fibrillation state are (much) more successful. Thus, the low energy shock regime, although yielding very low temporal average success rates, exhibits moments in time for which success rates are significantly higher than the average value shown in dose-response curves. This feature might be exploited in future defibrillation protocols for achieving high termination success rates with low or medium pulse energies.

Intermittent trapping of spiral waves in a cardiac model

Spiral waves are found in many excitable systems and are thought to play a role in the incoherent electrical activation that underlies cardiac arrhythmias. It is well-known that spiral waves can be permanently trapped by local heterogeneities. In this paper, we demonstrate that spiral waves can also be intermittently trapped by such heterogeneities. Using simulations of a cardiac model in two dimensions, we show that a tissue heterogeneity of sufficient strength or size can result in a spiral wave that is trapped for a few rotations, after which it dislodges and meanders away from the heterogeneity. We also show that these results can be captured by a particle model in which the particle represents the spiral wave tip. For both models, we construct a phase diagram which quantifies which parameter combinations of heterogeneity size and strength result in permanent, intermittent, or no trapping. Our results are consistent with clinical observations in patients with atrial fibrillation that showed that spiral wave reentry can be intermittent.

Optical Ultrastructure of Large Mammalian Hearts Recovers Discordant Alternans by In Silico Data Assimilation

Understanding and predicting the mechanisms promoting the onset and sustainability of cardiac arrhythmias represent a primary concern in the scientific and medical communities still today. Despite the long-lasting effort in clinical and physico-mathematical research, a critical aspect to be fully characterized and unveiled is represented by spatiotemporal alternans patterns of cardiac excitation. The identification of discordant alternans and higher-order alternating rhythms by advanced data analyses as well as their prediction by reliable mathematical models represents a major avenue of research for a broad and multidisciplinary scientific community. Current limitations concern two primary aspects: 1) robust and general-purpose feature extraction techniques and 2) in silico data assimilation within reliable and predictive mathematical models. Here, we address both aspects. At first, we extend our previous works on Fourier transformation imaging (FFI), applying the technique to whole-ventricle fluorescence optical mapping. Overall, we identify complex spatial patterns of voltage alternans and characterize higher-order rhythms by a frequency-series analysis. Then, we integrate the optical ultrastructure obtained by FFI analysis within a fine-tuned electrophysiological mathematical model of the cardiac action potential. We build up a novel data assimilation procedure demonstrating its reliability in reproducing complex alternans patterns in two-dimensional computational domains. Finally, we prove that the FFI approach applied to both experimental and simulated signals recovers the same information, thus closing the loop between the experiment, data analysis, and numerical simulations.

An in-silico assessment of efficacy of two novel intra-cardiac electrode configurations versus traditional anti-tachycardia pacing therapy for terminating sustained ventricular tachycardia

The implanted cardioverter defibrillator (ICD) is an effective direct therapy for the treatment of cardiac arrhythmias, including ventricular tachycardia (VT). Anti-tachycardia pacing (ATP) is often applied by the ICD as the first mode of therapy, but is often found to be ineffective, particularly for fast VTs. In such cases, strong, painful and damaging backup defibrillation shocks are applied by the device. Here, we propose two novel electrode configurations: "bipolar" and "transmural" which both combine the concept of targeted shock delivery with the advantage of reduced energy required for VT termination. We perform an in silico study to evaluate the efficacy of VT termination by applying one single (low-energy) monophasic shock from each novel configuration, comparing with conventional ATP therapy. Both bipolar and transmural configurations are able to achieve a higher efficacy (93% and 85%) than ATP (45%), with energy delivered similar to and two orders of magnitudes smaller than conventional ICD defibrillation shocks, respectively. Specifically, the transmural configuration (which applies the shock vector directly across the scar substrate sustaining the VT) is most efficient, requiring typically less than 1 J shock energy to achieve a high efficacy. The efficacy of both bipolar and transmural configurations are higher when applied to slow VTs (100% and 97%) compared to fast VTs (57% and 29%). Both novel electrode configurations introduced are able to improve electrotherapy efficacy while reducing the overall number of required therapies and need for strong backup shocks.

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

Finding type and location of the source of cardiac arrhythmias from the averaged flow velocity field using the determinant-trace method

Life threatening cardiac arrhythmias result from abnormal propagation of nonlinear electrical excitation waves in the heart. Finding the locations of the sources of these waves remains a challenging problem. This is mainly due to the low spatial resolution of electrode recordings of these waves. Also, these recordings are subjected to noise. In this paper, we develop a different approach: the AFV-DT method based on an averaged flow velocity (AFV) technique adopted from the analysis of optical flows and the determinant-trace (DT) method used for vector field analysis of dynamical systems. This method can find the location and determine all important types of sources found in excitable media such as focal activity, spiral waves, and waves rotating around obstacles. We test this method on in silico data of various wave excitation patterns obtained using the Luo-Rudy model for cardiac tissue. We show that the method works well for data with low spatial resolutions (up to 8×8) and is stable against noise. Finally, we apply it to two clinical cases and show that it can correctly identify the arrhythmia type and location. We discuss further steps on the development and improvement of this approach.

Detecting spiral wave tips using deep learning

The chaotic spatio-temporal electrical activity during life-threatening cardiac arrhythmias like ventricular fibrillation is governed by the dynamics of vortex-like spiral or scroll waves. The organizing centers of these waves are called wave tips (2D) or filaments (3D) and they play a key role in understanding and controlling the complex and chaotic electrical dynamics. Therefore, in many experimental and numerical setups it is required to detect the tips of the observed spiral waves. Most of the currently used methods significantly suffer from the influence of noise and are often adjusted to a specific situation (e.g. a specific numerical cardiac cell model). In this study, we use a specific type of deep neural networks (UNet), for detecting spiral wave tips and show that this approach is robust against the influence of intermediate noise levels. Furthermore, we demonstrate that if the UNet is trained with a pool of numerical cell models, spiral wave tips in unknown cell models can also be detected reliably, suggesting that the UNet can in some sense learn the concept of spiral wave tips in a general way, and thus could also be used in experimental situations in the future (ex-vivo, cell-culture or optogenetic experiments).

Electroporation safety factor of 300 nanosecond and 10 millisecond defibrillation in Langendorff-perfused rabbit hearts

AIMS

Recently, a new defibrillation modality using nanosecond pulses was shown to be effective at much lower energies than conventional 10 millisecond monophasic shocks in ex vivo experiments. Here we compare the safety factors of 300 nanosecond and 10 millisecond shocks to assess the safety of nanosecond defibrillation.

METHODS AND RESULTS

The safety factor, i.e. the ratio of median effective doses (ED50) for electroporative damage and defibrillation, was assessed for nanosecond and conventional (millisecond) defibrillation shocks in Langendorff-perfused New Zealand white rabbit hearts. In order to allow for multiple shock applications in a single heart, a pair of needle electrodes was used to apply shocks of varying voltage. Propidium iodide (PI) staining at the surface of the heart showed that nanosecond shocks had a slightly lower safety factor (6.50) than millisecond shocks (8.69), p = 0.02; while PI staining cross-sections in the electrode plane showed no significant difference (5.38 for 300 ns shocks and 6.29 for 10 ms shocks, p = 0.22).

CONCLUSIONS

In Langendorff-perfused rabbit hearts, nanosecond defibrillation has a similar safety factor as millisecond defibrillation, between 5 and 9, suggesting that nanosecond defibrillation can be performed safely.

A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics

Cardiac electrophysiology modeling deals with a complex network of excitable cells forming an intricate syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as cardiac alternans, featuring multiscale emerging behavior. On these grounds, we propose a novel mathematical formulation for cardiac electrophysiology modeling and simulation incorporating spatially non-local couplings within a physiological reaction-diffusion scenario. In particular, we formulate, a space-fractional electrophysiological framework, extending and generalizing similar works conducted for the monodomain model. We characterize one-dimensional excitation patterns by performing an extended numerical analysis encompassing a broad spectrum of space-fractional derivative powers and various intra- and extracellular conductivity combinations. Our numerical study demonstrates that (i) symmetric properties occur in the conductivity parameters' space following the proposed theoretical framework, (ii) the degree of non-local coupling affects the onset and evolution of discordant alternans dynamics, and (iii) the theoretical framework fully recovers classical formulations and is amenable for parametric tuning relying on experimental conduction velocity and action potential morphology.

Thermal effects on cardiac alternans onset and development: A spatiotemporal correlation analysis

Alternans of cardiac action potential duration represent critical precursors for the development of life-threatening arrhythmias and sudden cardiac death. The system's thermal state affects these electrical disorders requiring additional theoretical and experimental efforts to improve a patient-specific clinical understanding. In such a scenario, we generalize a recent work from Loppini et al. [Phys. Rev. E 100, 020201(R) (2019)PREHBM2470-004510.1103/PhysRevE.100.020201] by performing an extended spatiotemporal correlation study. We consider high-resolution optical mapping recordings of canine ventricular wedges' electrical activity at different temperatures and pacing frequencies. We aim to recommend the extracted characteristic length as a potential predictive index of cardiac alternans onset and evolution within a wide range of system states. In particular, we show that a reduction of temperature results in a drop of the characteristic length, confirming the impact of thermal instabilities on cardiac dynamics. Moreover, we theoretically investigate the use of such an index to identify and predict different alternans regimes. Finally, we propose a constitutive phenomenological law linking conduction velocity, characteristic length, and temperature in view of future numerical investigations.

Novel Low-Voltage MultiPulse Therapy to Terminate Atrial Fibrillation

OBJECTIVES

This first-in-human feasibility study was undertaken to translate the novel low-voltage MultiPulse Therapy (MPT) (Cardialen, Inc., Minneapolis, Minnesota), which was previously been shown to be effective in preclinical studies in terminating atrial fibrillation (AF), into clinical use.

BACKGROUND

Current treatment options for AF, the most common arrhythmia in clinical practice, have limited success. Previous attempts at treating AF by using implantable devices have been limited by the painful nature of high-voltage shocks.

METHODS

Forty-two patients undergoing AF ablation were recruited at 6 investigational centers worldwide. Before ablation, electrode catheters were placed in the coronary sinus, right and/or left atrium, for recording and stimulation. After the induction of AF, MPT, which consists of up to a 3-stage sequence of far- and near-field stimulation pulses of varied amplitude, duration, and interpulse timing, was delivered via temporary intracardiac leads. MPT parameters and delivery methods were iteratively optimized.

RESULTS

In the 14 patients from the efficacy phase, MPT terminated 37 of 52 (71%) of AF episodes, with the lowest median energy of 0.36 J (interquartile range [IQR]: 0.14 to 1.21 J) and voltage of 42.5 V (IQR: 25 to 75 V). Overall, 38% of AF terminations occurred within 2 seconds of MPT delivery (p < 0.0001). Shorter time between AF induction and MPT predicted success of MPT in terminating AF (p < 0.001).

CONCLUSIONS

MPT effectively terminated AF at voltages and energies known to be well tolerated or painless in some patients. Our results support further studies of the concept of implanted devices for early AF conversion to reduce AF burden, symptoms, and progression.

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

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

Drift and termination of spiral waves in optogenetically modified cardiac tissue at sub-threshold illumination

The development of new approaches to control cardiac arrhythmias requires a deep understanding of spiral wave dynamics. Optogenetics offers new possibilities for this. Preliminary experiments show that sub-threshold illumination affects electrical wave propagation in the mouse heart. However, a systematic exploration of these effects is technically challenging. Here, we use state-of-the-art computer models to study the dynamic control of spiral waves in a two-dimensional model of the adult mouse ventricle, using stationary and non-stationary patterns of sub-threshold illumination. Our results indicate a light-intensity-dependent increase in cellular resting membrane potentials, which together with diffusive cell-cell coupling leads to the development of spatial voltage gradients over differently illuminated areas. A spiral wave drifts along the positive gradient. These gradients can be strategically applied to ensure drift-induced termination of a spiral wave, both in optogenetics and in conventional methods of electrical defibrillation.

Turbulent pattern in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction

Chemical turbulence was observed experimentally in the 1,4-cyclohexanedione Belousov-Zhabotinsky (CHD-BZ) reaction in a double layer consisting of a catalyst-loaded gel and uncatalyzed liquid on a Petri dish. The chemical patterns in the CHD-BZ reaction occur spontaneously in various forms as follows: the initial, regular, transient, and turbulent patterns, subsequently. These four patterns are characterized by using the two-dimensional Fourier transform (2D-FT). Mechanism of the onset of the turbulence in the CHD-BZ reaction is proposed. Turbulence in the CHD-BZ reaction is reproducible under a well defined protocol and it exists for a period of time of about 50 minutes, which is sufficiently long to offer a good opportunity to study and control the turbulence in the future. Two models of the BZ reaction were used to simulate the spiral breakup. Both are capable of producing spiral turbulence from initially regular patterns in each layer and reflect certain features of dynamics observed in experiments.

Cardiac optogenetics: a decade of enlightenment

The electromechanical function of the heart involves complex, coordinated activity over time and space. Life-threatening cardiac arrhythmias arise from asynchrony in these space-time events; therefore, therapies for prevention and treatment require fundamental understanding and the ability to visualize, perturb and control cardiac activity. Optogenetics combines optical and molecular biology (genetic) approaches for light-enabled sensing and actuation of electrical activity with unprecedented spatiotemporal resolution and parallelism. The year 2020 marks a decade of developments in cardiac optogenetics since this technology was adopted from neuroscience and applied to the heart. In this Review, we appraise a decade of advances that define near-term (immediate) translation based on all-optical electrophysiology, including high-throughput screening, cardiotoxicity testing and personalized medicine assays, and long-term (aspirational) prospects for clinical translation of cardiac optogenetics, including new optical therapies for rhythm control. The main translational opportunities and challenges for optogenetics to be fully embraced in cardiology are also discussed.

On the Role of Ionic Modeling on the Signature of Cardiac Arrhythmias for Healthy and Diseased Hearts

Computational cardiology is rapidly becoming the gold standard for innovative medical treatments and device development. Despite a worldwide effort in mathematical and computational modeling research, the complexity and intrinsic multiscale nature of the heart still limit our predictability power raising the question of the optimal modeling choice for large-scale whole-heart numerical investigations. We propose an extended numerical analysis among two different electrophysiological modeling approaches: a simplified phenomenological one and a detailed biophysical one. To achieve this, we considered three-dimensional healthy and infarcted swine heart geometries. Heterogeneous electrophysiological properties, fine-tuned DT-MRI -based anisotropy features, and non-conductive ischemic regions were included in a custom-built finite element code. We provide a quantitative comparison of the electrical behaviors during steady pacing and sustained ventricular fibrillation for healthy and diseased cases analyzing cardiac arrhythmias dynamics. Action potential duration (APD) restitution distributions, vortex filament counting, and pseudo-electrocardiography (ECG) signals were numerically quantified, introducing a novel statistical description of restitution patterns and ventricular fibrillation sustainability. Computational cost and scalability associated with the two modeling choices suggests that ventricular fibrillation signatures are mainly controlled by anatomy and structural parameters, rather than by regional restitution properties. Finally, we discuss limitations and translational perspectives of the different modeling approaches in view of large-scale whole-heart in silico studies.

Overdrive pacing of spiral waves in a model of human ventricular tissue

High-voltage electrical defibrillation remains the only reliable method of quickly controlling life-threatening cardiac arrhythmias. This paper is devoted to studying an alternative approach, low-voltage cardioversion (LVC), which is based on ideas from non-linear dynamics and aims to remove sources of cardiac arrhythmias by applying high-frequency stimulation to cardiac tissue. We perform a detailed in-silico study of the elimination of arrhythmias caused by rotating spiral waves in a TP06 model of human cardiac tissue. We consider three parameter sets with slopes of the APD restitution curve of 0.7, 1.1 and 1.4, and we study LVC at the baseline and under the blocking of INa and ICaL and under the application of the drugs verapamil and amiodarone. We show that pacing can remove spiral waves; however, its efficiency can be substantially reduced by dynamic instabilities. We classify these instabilities and show that the blocking of INa and the application of amiodarone increase the efficiency of the method, while the blocking of ICaL and the application of verapamil decrease the efficiency. We discuss the mechanisms and the possible clinical applications resulting from our study.

Spatial heterogeneities shape the collective behavior of signaling amoeboid cells

In its natural habitat in the forest soil, the cellular slime mold Dictyostelium discoideum is exposed to obstacles. Starving Dictyostelium cells secrete cAMP, which is the key extracellular signaling molecule that promotes the aggregation process required for their long-term survival. Here, we investigated the influence of environmental inhomogeneities on the signaling and pattern formation of Dictyostelium cells. We present experimental data and numerical simulations on the pattern formation of signaling Dictyostelium cells in the presence of periodic arrays of millimeter-sized pillars. We observed concentric cAMP waves that initiated almost synchronously at the pillars and propagated outward. In response to these circular waves, the Dictyostelium cells streamed toward the pillars, forming aggregates arranged in patterns that reflected the periodicity of the lattice of pillars. Our results suggest that, in nature, the excitability threshold and synchronization level of the cells are two key parameters that control the nature of the interaction between cells and spatial heterogeneities in their environment.

Personalized Low-Energy Defibrillation Through Feedback Based Resynchronization Therapy

AIMS

Defibrillation shocks may cause AV node burnout, scar formation, and pain. In this study, we present a real-time feedback-based control of ventricular fibrillation (VF) with a series of low-energy shocks using ventricular electrical activity as the feedback input.

METHODS

Isolated rabbit hearts were Langendorff perfused and stained with a fluorescent Vm dye. The ventricular activity was measured with a pair of photodiodes, and processed with a feedback controller to calculate defibrillation shock parameters in real-time. Shock timing was based on desynchronized activation of the left and right ventricles during VF, and the strength was proportional to the amplitude difference of the photodiode signals. Shocks were delivered with a custom-developed arbitrary waveform trans-conductance amplifier.

RESULTS

Feedback based resynchronization therapy converts VT to MT before sinus rhythm is restored with a reduction of defibrillation energy, compared to a single biphasic shock.

CONCLUSIONS

Feedback based resynchronization therapy is based on real-time sensing of ventricular activity, while a series of low-energy shocks are delivered, reducing the risk of associated side effects.

In-silico study of the cardiac arrhythmogenic potential of biomaterial injection therapy

Biomaterial injection is a novel therapy to treat ischemic heart failure (HF) that has shown to reduce remodeling and restore cardiac function in recent preclinical studies. While the effect of biomaterial injection in reducing mechanical wall stress has been recently demonstrated, the influence of biomaterials on the electrical behavior of treated hearts has not been elucidated. In this work, we developed computational models of swine hearts to study the electrophysiological vulnerability associated with biomaterial injection therapy. The propagation of action potentials on realistic biventricular geometries was simulated by numerically solving the monodomain electrophysiology equations on anatomically-detailed models of normal, HF untreated, and HF treated hearts. Heart geometries were constructed from high-resolution magnetic resonance images (MRI) where the healthy, peri-infarcted, infarcted and gel regions were identified, and the orientation of cardiac fibers was informed from diffusion-tensor MRI. Regional restitution properties in each case were evaluated by constructing a probability density function of the action potential duration (APD) at different cycle lengths. A comparative analysis of the ventricular fibrillation (VF) dynamics for every heart was carried out by measuring the number of filaments formed after wave braking. Our results suggest that biomaterial injection therapy does not affect the regional dispersion of repolarization when comparing untreated and treated failing hearts. Further, we found that the treated failing heart is more prone to sustain VF than the normal heart, and is at least as susceptible to sustained VF as the untreated failing heart. Moreover, we show that the main features of VF dynamics in a treated failing heart are not affected by the level of electrical conductivity of the biogel injectates. This work represents a novel proof-of-concept study demonstrating the feasibility of computer simulations of the heart in understanding the arrhythmic behavior in novel therapies for HF.

Feedforward attractor targeting for non-linear oscillators using a dual-frequency driving technique

A feedforward control technique is presented to steer a harmonically driven, non-linear system between attractors in the frequency-amplitude parameter plane of the excitation. The basis of the technique is the temporary addition of a second harmonic component to the driving. To illustrate this approach, it is applied to the Keller-Miksis equation describing the radial dynamics of a single spherical gas bubble placed in an infinite domain of liquid. This model is a second-order, non-linear ordinary differential equation, a non-linear oscillator. With a proper selection of the frequency ratio of the temporary dual-frequency driving and with the appropriate tuning of the excitation amplitudes, the trajectory of the system can be smoothly transformed between specific attractors; for instance, between period-3 and period-5 orbits. The transformation possibilities are discussed and summarized for attractors originating from the subharmonic resonances and the equilibrium state (absence of external driving) of the system.