Interaction between spiral and paced waves in cardiac tissue

Biomimetic Cardiac Tissue Models for In Vitro Arrhythmia Studies

Cardiac arrhythmias are a major cause of cardiovascular mortality worldwide. Many arrhythmias are caused by reentry, a phenomenon where excitation waves circulate in the heart. Optical mapping techniques have revealed the role of reentry in arrhythmia initiation and fibrillation transition, but the underlying biophysical mechanisms are still difficult to investigate in intact hearts. Tissue engineering models of cardiac tissue can mimic the structure and function of native cardiac tissue and enable interactive observation of reentry formation and wave propagation. This review will present various approaches to constructing cardiac tissue models for reentry studies, using the authors' work as examples. The review will highlight the evolution of tissue engineering designs based on different substrates, cell types, and structural parameters. A new approach using polymer materials and cellular reprogramming to create biomimetic cardiac tissues will be introduced. The review will also show how computational modeling of cardiac tissue can complement experimental data and how such models can be applied in the biomimetics of cardiac tissue.

Conduction of excitation waves and reentry drift on cardiac tissue with simulated photocontrol-varied excitability

The development of new approaches to suppressing cardiac arrhythmias requires a deep understanding of spiral wave dynamics. The study of spiral waves is possible in model systems, for example, in a monolayer of cardiomyocytes. A promising way to control cardiac excitability in vitro is the noninvasive photocontrol of cell excitability mediated by light-sensitive azobenzene derivatives, such as azobenzene trimethylammonium bromide (AzoTAB). The trans-isomer of AzoTAB suppresses spontaneous activity and excitation propagation speed, whereas the cis isomer has no detectable effect on the electrical properties of cardiomyocyte monolayers; cis isomerization occurs under the action of near ultraviolet (UV) light, and reverse isomerization occurs when exposed to blue light. Thus, AzoTAB makes it possible to create patterns of excitability in conductive tissue. Here, we investigate the effect of a simulated excitability gradient in cardiac cell culture on the behavior and termination of reentry waves. Experimental data indicate a displacement of the reentry wave, predominantly in the direction of lower excitability. However, both shifts in the direction of higher excitability and shift absence were also observed. To explain this effect, we reproduced these experiments in a computer model. Computer simulations showed that the explanation of the mechanism of observed drift to a lower excitability area requires not only a change in excitability coefficients (ion currents) but also a change in the diffusion coefficient; this may be the effect of the substance on intercellular connections. In addition, it was found that the drift direction depended on the observation time due to the meandering of the spiral wave. Thus, we experimentally proved the possibility of noninvasive photocontrol and termination of spiral waves with a mechanistic explanation in computer models.

Multicellular In vitro Models of Cardiac Arrhythmias: Focus on Atrial Fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia in clinical practice with a large socioeconomic impact due to its associated morbidity, mortality, reduction in quality of life and health care costs. Currently, antiarrhythmic drug therapy is the first line of treatment for most symptomatic AF patients, despite its limited efficacy, the risk of inducing potentially life-threating ventricular tachyarrhythmias as well as other side effects. Alternative, in-hospital treatment modalities consisting of electrical cardioversion and invasive catheter ablation improve patients' symptoms, but often have to be repeated and are still associated with serious complications and only suitable for specific subgroups of AF patients. The development and progression of AF generally results from the interplay of multiple disease pathways and is accompanied by structural and functional (e.g., electrical) tissue remodeling. Rational development of novel treatment modalities for AF, with its many different etiologies, requires a comprehensive insight into the complex pathophysiological mechanisms. Monolayers of atrial cells represent a simplified surrogate of atrial tissue well-suited to investigate atrial arrhythmia mechanisms, since they can easily be used in a standardized, systematic and controllable manner to study the role of specific pathways and processes in the genesis, perpetuation and termination of atrial arrhythmias. In this review, we provide an overview of the currently available two- and three-dimensional multicellular in vitro systems for investigating the initiation, maintenance and termination of atrial arrhythmias and AF. This encompasses cultures of primary (animal-derived) atrial cardiomyocytes (CMs), pluripotent stem cell-derived atrial-like CMs and (conditionally) immortalized atrial CMs. The strengths and weaknesses of each of these model systems for studying atrial arrhythmias will be discussed as well as their implications for future studies.

Role of spatial dispersion of repolarization in reentry around a functional core versus reentry around a fixed anatomical core

INTRODUCTION

Successful initiation of spiral wave reentry in the neonatal rat ventricular myocyte (NRVM) monolayer implicitly assumes the presence of spatial dispersion of repolarization (DR), which is difficult to quantify. We recently introduced a NRVM monolayer that utilizes anthopleurin-A to impart a prolonged plateau to the NRVM action potential. This was associated with a significant degree of spatial DR that lends itself to accurate quantification.

METHODS AND RESULTS

We utilized the monolayer and fluorescence optical mapping of intracellular calcium transients (F_Cai ) to systematically study and compare the contribution of spatial dispersion of the duration of F_Cai (as a surrogate of DR) to induction of spiral wave reentry around a functional core versus reentry around a fixed anatomical obstacle. We show that functional reentry could be initiated by a premature stimulus acting on a substrate of spatial DR resulting in a functional line of propagation block. Subsequent wave fronts circulated around a central core of functional obstacle created by sustained depolarization from the circulating wave front. Both initiation and termination of spiral wave reentry around an anatomical obstacle consistently required participation of a region of functional propagation block. This region was similarly based on spatial DR. Spontaneous termination of spiral wave reentry also resulted from block in the functional component of the circuit obstacle, usually preceded by beat-to-beat slowing of propagation.

CONCLUSIONS

The study demonstrates the critical contribution of DR to spiral wave reentry around a purely functional core as well as reentry around a fixed anatomical core.

Stable and unstable vortex knots in excitable media

We study the dynamics of knotted vortices in a bulk excitable medium using the FitzHugh-Nagumo model. From a systematic survey of all knots of at most eight crossings we establish that the generic behavior is of unsteady, irregular dynamics, with prolonged periods of expansion of parts of the vortex. The mechanism for the length expansion is a long-range "wave-slapping" interaction, analogous to that responsible for the annihilation of small vortex rings by larger ones. We also show that there are stable vortex geometries for certain knots; in addition to the unknot, trefoil, and figure-eight knots reported previously, we have found stable examples of the Whitehead link and 6_{2} knot. We give a thorough characterization of their geometry and steady-state motion. For the unknot, trefoil, and figure-eight knots we greatly expand previous evidence that FitzHugh-Nagumo dynamics untangles initially complex geometries while preserving topology.

Mathematical approach to unpinning of spiral waves anchored to an obstacle with high-frequency pacing

Spiral waves are observed in wide variety of reaction-diffusion systems. Those observed in cardiac tissues are important since they are related to serious disease that threatens human lives, such as atrial or ventricular fibrillation. We consider the unpinning of spiral waves anchored to a circular obstacle on excitable media using high-frequency pacing. Here, we consider two types of the obstacle; i.e., that without any diffusive interaction with the environment, and that with diffusive interaction. We found that the threshold frequency for success in unpinning is lower for the obstacle with diffusive interaction than for the one without it. We discuss the threshold frequency based on the angular velocity of a chemical wave anchoring the obstacle.

Optogenetics enables real-time spatiotemporal control over spiral wave dynamics in an excitable cardiac system

Propagation of non-linear waves is key to the functioning of diverse biological systems. Such waves can organize into spirals, rotating around a core, whose properties determine the overall wave dynamics. Theoretically, manipulation of a spiral wave core should lead to full spatiotemporal control over its dynamics. However, this theory lacks supportive evidence (even at a conceptual level), making it thus a long-standing hypothesis. Here, we propose a new phenomenological concept that involves artificially dragging spiral waves by their cores, to prove the aforementioned hypothesis in silico, with subsequent in vitro validation in optogenetically modified monolayers of rat atrial cardiomyocytes. We thereby connect previously established, but unrelated concepts of spiral wave attraction, anchoring and unpinning to demonstrate that core manipulation, through controlled displacement of heterogeneities in excitable media, allows forced movement of spiral waves along pre-defined trajectories. Consequently, we impose real-time spatiotemporal control over spiral wave dynamics in a biological system.

From a spinning galaxy to a swarm of honeybees, rotating spirals are widespread in nature. Even within the muscles of the heart, waves of electrical activity sometimes rotate spirally, leading to irregular heart rhythms or arrhythmia – a condition that can be fatal.

Irrespective of where they occur, spiral waves organize around a center or core with different biophysical properties compared to the rest of the medium. The properties of the core determine the overall dynamics of the spiral. This means that, theoretically, it should be possibly to completely control a spiral wave just by manipulating its core.

Now, Majumder, Feola et al. have tested this long-standing hypothesis using a combination of computer modeling and experiments with single layers of rat heart cells grown in a laboratory. First, the heart cells were genetically modified so that their electrical properties could be altered with light; in other words, the cells were put under optical control. Next, by using of a narrow beam of light, Majumder, Feola et al. precisely controlled the electrical properties of a small number of cells, which then attracted and supported a rotating spiral wave by acting as its new core. Moving the light beam allowed the core of the spiral wave to be shifted too, meaning the spiral wave could now be steered along any desired path in the cell layer.

Majumder, Feola et al. hope that these underlying principles may one day provide the basis of new treatments for irregular heartbeats that are more effective and less damaging to the heart than existing options. Yet first, more work is needed to translate these findings from single layers of cells to actual hearts.

Model of electrical activity in cardiac tissue under electromagnetic induction

Complex electrical activities in cardiac tissue can set up time-varying electromagnetic field. Magnetic flux is introduced into the Fitzhugh-Nagumo model to describe the effect of electromagnetic induction, and then memristor is used to realize the feedback of magnetic flux on the membrane potential in cardiac tissue. It is found that a spiral wave can be triggered and developed by setting specific initials in the media, that is to say, the media still support the survival of standing spiral waves under electromagnetic induction. Furthermore, electromagnetic radiation is considered on this model as external stimuli, it is found that spiral waves encounter breakup and turbulent electrical activities are observed, and it can give guidance to understand the occurrence of sudden heart disorder subjected to heavily electromagnetic radiation.

A technical review of optical mapping of intracellular calcium within myocardial tissue

Optical mapping of Ca(2+)-sensitive fluorescence probes has become an extremely useful approach and adopted by many cardiovascular research laboratories to study a spectrum of myocardial physiology and disease conditions. Optical mapping data are often displayed as detailed pseudocolor images, providing unique insight for interpreting mechanisms of ectopic activity, action potential and Ca(2+) transient alternans, tachycardia, and fibrillation. Ca(2+)-sensitive fluorescent probes and optical mapping systems continue to evolve in the ongoing effort to improve therapies that ease the growing worldwide burden of cardiovascular disease. In this technical review we provide an updated overview of conventional approaches for optical mapping of Cai (2+) within intact myocardium. In doing so, a brief history of Cai (2+) probes is provided, and nonratiometric and ratiometric Ca(2+) probes are discussed, including probes for imaging sarcoplasmic reticulum Ca(2+) and probes compatible with potentiometric dyes for dual optical mapping. Typical measurements derived from optical Cai (2+) signals are explained, and the analytics used to compute them are presented. Last, recent studies using Cai (2+) optical mapping to study arrhythmias, heart failure, and metabolic perturbations are summarized.

Removal of pinned scroll waves in cardiac tissues by electric fields in a generic model of three-dimensional excitable media

Spirals or scroll waves pinned to heterogeneities in cardiac tissues may cause lethal arrhythmias. To unpin these life-threatening spiral waves, methods of wave emission from heterogeneities (WEH) induced by low-voltage pulsed DC electric fields (PDCEFs) and circularly polarized electric fields (CPEFs) have been used in two-dimensional (2D) cardiac tissues. Nevertheless, the unpinning of scroll waves in three-dimensional (3D) cardiac systems is much more difficult than that of spiral waves in 2D cardiac systems, and there are few reports on the removal of pinned scroll waves in 3D cardiac tissues by electric fields. In this article, we investigate in detail the removal of pinned scroll waves in a generic model of 3D excitable media using PDCEF, AC electric field (ACEF) and CPEF, respectively. We find that spherical waves can be induced from the heterogeneities by these electric fields in initially quiescent excitable media. However, only CPEF can induce spherical waves with frequencies higher than that of the pinned scroll wave. Such higher-frequency spherical waves induced by CPEF can be used to drive the pinned scroll wave out of the cardiac systems. We hope this remarkable ability of CPEF can provide a better alternative to terminate arrhythmias caused by pinned scroll waves.

Elimination of a spiral wave pinned at an obstacle by a train of plane waves: Effect of diffusion between obstacles and surrounding media

In excitable media such as cardiac tissue and Belousov-Zhabotinsky reaction medium, spiral waves tend to anchor (pin) to local heterogeneities. In general, such pinned waves are difficult to eliminate and may progress to spatio-temporal chaos. Heterogeneities can be classified as either the absence or presence of diffusive interaction with the surrounding medium. In this study, we investigated the difference in the unpinning of spiral waves from obstacles with and without diffusive interaction, and found a profound difference. The pacing period required for unpinning at fixed obstacle size is larger in case of diffusive obstacles. Further, we deduced a generic theoretical framework that can predict the minimal unpinning period. Our results explain the difference in pacing periods between for the obstacles with and without diffusive interaction, and the difference is interpreted in terms of the local decrease of spiral wave velocity close to the obstacle boundary caused in the case of diffusive interaction.

Propagation of spiral waves pinned to circular and rectangular obstacles

We present an investigation of spiral waves pinned to circular and rectangular obstacles with different circumferences in both thin layers of the Belousov-Zhabotinsky reaction and numerical simulations with the Oregonator model. For circular objects, the area always increases with the circumference. In contrast, we varied the circumference of rectangles with equal areas by adjusting their width w and height h. For both obstacle forms, the propagating parameters (i.e., wavelength, wave period, and velocity of pinned spiral waves) increase with the circumference, regardless of the obstacle area. Despite these common features of the parameters, the forms of pinned spiral waves depend on the obstacle shapes. The structures of spiral waves pinned to circles as well as rectangles with the ratio w/h∼1 are similar to Archimedean spirals. When w/h increases, deformations of the spiral shapes are observed. For extremely thin rectangles with w/h≫1, these shapes can be constructed by employing semicircles with different radii which relate to the obstacle width and the core diameter of free spirals.

Functional analysis of the engineered cardiac tissue grown on recombinant spidroin fiber meshes

In the present study, we examined the ability of the recombinant spidroin to serve as a substrate for the cardiac tissue engineering. For this purpose, isolated neonatal rat cardiomyocytes were seeded on the electrospun spidroin fiber matrices and cultured to form the confluent cardiac monolayers. Besides the adhesion assay and immunostaining analysis, we tested the ability of the cultured cardiomyocytes to form a functional cardiac syncytium by studying excitation propagation in the cultured tissue with the aid of optical mapping. It was demonstrated that recombinant spidroin fiber meshes are directly suitable for the adherence and growth of the cardiomyocytes without additional coating with the attachment factors, such as fibronectin.

Influence of excitability on unpinning and termination of spiral waves

Application of electrical forcing to release pinned spiral waves from unexcitable obstacles and to terminate the rotation of free spiral waves at the boundary of excitable media has been investigated in thin layers of the Belousov-Zhabotinsky (BZ) reaction, prepared with different initial concentrations of H_{2}SO_{4}. Increasing [H_{2}SO_{4}] raises the excitability of the reaction and reduces the core diameter of free spiral waves as well as the wave period. An electric current with density stronger than a critical value Junpin causes a pinned spiral wave to drift away from the obstacle. For a given obstacle size, Junpin increases with [H_{2}SO_{4}]. Under an applied electrical current, the rotation center of a free spiral wave drifts along a straight path to the boundary. When the current density is stronger than a critical value Jterm, the spiral tip is forced to hit the boundary, where the spiral wave is terminated. Similar to Junpin for releasing a pinned spiral wave, Jterm also increases with [H_{2}SO_{4}]. These experimental findings were confirmed by numerical simulations using the Oregonator model, in which the excitability was adjusted via the ratio of the excitation rate to the recovery rate of the BZ reaction. Therefore, our investigation shows that decreasing the excitability can facilitate elimination of spiral waves by electrical forcing, either in the presence of obstacles or not.

Arrhythmogenic role of the border between two areas of cardiac cell alignment

The goal of this study is to develop experimental and computational models of the excitation transition between areas of cardiac tissue with different anatomical anisotropy. Alignment of seeded neonatal rat cardiomyocytes was achieved with the aid of guiding polymer (PMGI) nanofibers, and two areas with orthogonal alignment were placed into a contact. It was found that the excitation wave crossing border between the areas with different alignment direction experiences substantial perturbation, up to the complete conduction block. In addition to the experimental study, this effect was analyzed computationally using generic FitzHugh-Nagumo reaction-diffusion model. It was shown that the non-monotonous changes of the excitation wave velocity on this boundary may be explained by the source/sink mismatch. Thus, the border may play pro-arrhythmogenic role.

Influences of periodic mechanical deformation on pinned spiral waves

In a generic model of excitable media, we study the behavior of spiral waves interacting with obstacles and their dynamics under the influences of simple periodic mechanical deformation (PMD). Depending on the characteristics of the obstacles, i.e., size and excitability, the rotation of a pinned spiral wave shows different scenarios, e.g., embedding into or anchoring on an obstacle. Three different drift phenomena induced by PMD are observed: scattering on small partial-excitable obstacles, meander-induced unpinning on big partial-excitable obstacles, and drifting around small unexcitable obstacles. Their underlying mechanisms are discussed. The dependence of the threshold amplitude of PMD on the characteristics of the obstacles to successfully remove pinned spiral waves on big partial-excitable obstacles is studied.

Mechanism of unpinning spirals by a series of stimuli

Antitachycardia pacing (ATP) is widely used to terminate tachycardia before it proceeds to lethal fibrillation. The important prerequisite for successful ATP is unpinning of the spirals anchored to the obstacle by a series of stimuli. Here, to understand the mechanism of unpinning spirals by ATP, we propose a theoretical explanation based on a nonlinear eikonal relation and a kinematical model. The theoretical results are quantitatively consistent with the numerical simulations in both weak and high excitabilities.

Unpinning of spiral waves by electrical forcing in excitable chemical media

We present experimental observations on the electrically forced release of spiral waves pinned to unexcitable circular obstacles in the Belosov-Zhabotinsky reaction. When the applied electric current density reaches the necessary current density J(unpin), the spiral tip is detached and subsequently drifts away from the obstacle. J(unpin) is found to increase with the obstacle diameter d. The growth rate ΔJ(unpin)/Δd is much higher for obstacles larger than the free spiral core compared to that for smaller obstacles. The experimental findings are confirmed by numerical simulations using the Oregonator model. The results imply that it is more difficult to release spiral waves pinned to larger obstacles, especially when the obstacle size exceeds that of the free spiral core.

Fast acceleration of 2D wave propagation simulations using modern computational accelerators

Recent developments in modern computational accelerators like Graphics Processing Units (GPUs) and coprocessors provide great opportunities for making scientific applications run faster than ever before. However, efficient parallelization of scientific code using new programming tools like CUDA requires a high level of expertise that is not available to many scientists. This, plus the fact that parallelized code is usually not portable to different architectures, creates major challenges for exploiting the full capabilities of modern computational accelerators. In this work, we sought to overcome these challenges by studying how to achieve both automated parallelization using OpenACC and enhanced portability using OpenCL. We applied our parallelization schemes using GPUs as well as Intel Many Integrated Core (MIC) coprocessor to reduce the run time of wave propagation simulations. We used a well-established 2D cardiac action potential model as a specific case-study. To the best of our knowledge, we are the first to study auto-parallelization of 2D cardiac wave propagation simulations using OpenACC. Our results identify several approaches that provide substantial speedups. The OpenACC-generated GPU code achieved more than speedup above the sequential implementation and required the addition of only a few OpenACC pragmas to the code. An OpenCL implementation provided speedups on GPUs of at least faster than the sequential implementation and faster than a parallelized OpenMP implementation. An implementation of OpenMP on Intel MIC coprocessor provided speedups of with only a few code changes to the sequential implementation. We highlight that OpenACC provides an automatic, efficient, and portable approach to achieve parallelization of 2D cardiac wave simulations on GPUs. Our approach of using OpenACC, OpenCL, and OpenMP to parallelize this particular model on modern computational accelerators should be applicable to other computational models of wave propagation in multi-dimensional media.

Emitting waves from heterogeneity by a rotating electric field

In a generic model of excitable media, we simulate wave emission from a heterogeneity (WEH) induced by an electric field. Based on the WEH effect, a rotating electric field is proposed to terminate existed spatiotemporal turbulence. Compared with the effects resulted by a periodic pulsed electric field, the rotating electric field displays several improvements, such as lower required intensity, emitting waves on smaller obstacles, and shorter suppression time. Furthermore, due to rotation of the electric field, it can automatically source waves from the boundary of an obstacle with small curvature.

Attractive and repulsive contributions of localized excitability inhomogeneities and elimination of spiral waves in excitable media

The attracting and repelling of spiral waves in a two-dimensional excitable medium in the presence of localized excitability inhomogeneities are studied. The choice of two effects depends on the comparison of excitabilities inside and outside the localized obstacle. We inspect the changes in attracting and repelling behaviors with respect to the size of the obstacle and the initial distance between the center of the spiral core and the obstacle. To understand the occurrence of these phenomena, we investigated the small v-value areas near the tip and the function of the wave velocity as the excitability parameter ε. Considering the attributes of the attractive obstacle, an eliminating scheme of spiral waves is proposed in which the attractive obstacle is rapidly moved at several fixed times. This method can avoid the high-amplitude and high-frequency stimulus in most conventional methods.

Irregular excitation patterns in reaction-diffusion systems due to perturbation by secondary pacemakers

Spatiotemporal excitation patterns in the FitzHugh-Nagumo model are studied, which result from the disturbance of a primary pacemaker by a secondary pacemaker. The primary and secondary pacemakers generate regular waves with frequencies f(pace) and f(pert), respectively. The pacemakers are spatially separated, but waves emanating from them encounter each other via a small bridge. This leads to three different types I-III of irregular excitation patterns in disjunct domains of the f(pace)-f(pert) plane. Types I and II are caused by detachments of waves coming from the two pacemakers at corners of the bridge. Type III irregularities are confined to a boundary region of the system and originate from a partial penetration of the primary waves into a space, where circular wave fronts from the secondary pacemaker prevail. For this type, local frequencies can significantly exceed f(pace) and f(pert). The degree of irregularity found for the three different types is quantified by the entropy of the local frequency distribution and an order parameter for phase coherence.

Attraction and repulsion of spiral waves by inhomogeneity of conduction anisotropy--a model of spiral wave interaction with electrical remodeling of heart tissue

Various forms of heart disease are associated with remodeling of the heart muscle, which results in a perturbation of cell-to-cell electrical coupling. These perturbations may alter the trajectory of spiral wave drift in the heart muscle. We investigate the effect of spatially extended inhomogeneity of transverse cell coupling on the spiral wave trajectory using a simple active media model. The spiral wave was either attracted or repelled from the center of inhomogeneity as a function of cell excitability and gradient of the cell coupling. High levels of excitability resulted in an attraction of the wave to the center of inhomogeneity, whereas low levels resulted in an escape and termination of the spiral wave. The spiral wave drift velocity was related to the gradient of the coupling and the initial position of the wave. In a diseased heart, a region of altered transverse coupling corresponds with local gap junction remodeling that may be responsible for stabilization-destabilization of spiral waves and hence reflect potentially important targets in the treatment of heart arrhythmias.

Pacemaker interactions induce reentrant wave dynamics in engineered cardiac culture

Pacemaker interactions can lead to complex wave dynamics seen in certain types of cardiac arrhythmias. We use experimental and mathematical models of pacemakers in heterogeneous excitable media to investigate how pacemaker interactions can be a mechanism for wave break and reentrant wave dynamics. Embryonic chick ventricular cells are cultured in vitro so as to create a dominant central pacemaker site that entrains other pacemakers in the medium. Exposure of those cultures to a potassium channel blocker, E-4031, leads to emergence of peripheral pacemakers that compete with each other and with the central pacemaker. Waves emitted by faster pacemakers break up over the slower pacemaker to form reentrant waves. Similar dynamics are observed in a modified FitzHugh-Nagumo model of heterogeneous excitable media with two distinct sites of pacemaking. These findings elucidate a mechanism of pacemaker-induced reentry in excitable media.

Optical imaging of arrhythmias in the cardiomyocyte monolayer

In recent years, cultured cardiac cell monolayers have become a contemporary experimental preparation for the study of fundamental mechanisms that underlie normal and pathologic electrophysiology at the tissue level. Ion channels and gap junctions in the cardiomyocyte monolayer may be modulated using drugs that suppress or enhance certain channels/junctions, or by genetic silencing or overexpression. The cardiomyocyte monolayer is particularly well suited for studies of functional electrophysiologic properties of mixtures of cardiac and noncardiac cells (eg, myofibroblasts), which otherwise would be difficult to investigate. Optical mapping of monolayers has provided insight into mechanisms that can set the stage for arrhythmias, such as unidirectional conduction block, gap junction uncoupling, ischemia, alternans, and anisotropy, and continues to enhance our understanding of basic electrophysiologic mechanisms.

GPGPU accelerated cardiac arrhythmia simulations

Computational modeling of cardiac electrophysiology is a powerful tool for studying arrhythmia mechanisms. In particular, cardiac models are useful for gaining insights into experimental studies, and in the foreseeable future they will be used by clinicians to improve therapy for the patients suffering from complex arrhythmias. Such models are highly intricate, both in their geometric structure and in the equations that represent myocyte electrophysiology. For these models to be useful in a clinical setting, cost-effective solutions for solving the models in real time must be developed. In this work, we hypothesized that low-cost GPGPU-based hardware systems can be used to accelerate arrhythmia simulations. We ported a two dimensional monodomain cardiac model and executed it on various GPGPU platforms. Electrical activity was simulated during point stimulation and rotor activity. Our GPGPU implementations provided significant speedups over the CPU implementation: 18X for point stimulation and 12X for rotor activity. We found that the number of threads that could be launched concurrently was a critical factor in optimizing the GPGPU implementations.

Persistent fluctuations in synchronization rate in globally coupled oscillators with periodic external forcing

A system of phase oscillators with repulsive global coupling and periodic external forcing undergoing asynchronous rotation is considered. The synchronization rate of the system can exhibit persistent fluctuations depending on parameters and initial phase distributions, and the amplitude of the fluctuations scales with the system size for uniformly random initial phase distributions. Using the Watanabe-Strogatz transformation that reduces the original system to low-dimensional macroscopic equations, we show that the fluctuations are collective dynamics of the system corresponding to low-dimensional trajectories of the reduced equations. It is argued that the amplitude of the fluctuations is determined by the inhomogeneity of the initial phase distribution, resulting in system-size scaling for the random case.

Electroelastic unpinning of rotating vortices in biological excitable media

Spiral waves in excitable biological media are associated with pathological situations. In the heart an action potential vortex pinned by an obstacle has to be removed through defibrillation protocols fine-tuned theoretically by using electrophysiological nonlinear mathematical models. Cardiac tissue, however, is an electroelastic medium whose electrical properties are strongly affected by large deformations. In this paper we specifically investigate the electroelastic pinning-unpinning mechanism in order to include cardiac contraction in the preexisting theoretically modeled defibrillation scenarios. Based on a two-dimensional minimal electromechanical model, we show numerically the existence of an unpinning band characterized by the size of the obstacle, the pacing site, and the frequency. Similar numerical simulations, performed in the absence of elastic coupling, show small differences in comparison with the electroelastic studies, suggesting for this specific scenario of pinning-unpinning dynamics a nonprominent role of elasticity.

Curvature-Dependent Excitation Propagation in Cultured Cardiac Tissue

The geometry of excitation wave front may play an important role on the propagation block and spiral wave formation. The wave front which is bent over the critical value due to interaction with the obstacles may partially cease to propagate and appearing wave breaks evolve into rotating waves or reentry. This scenario may explain how reentry spontaneously originates in a heart. We studied highly curved excitation wave fronts in the cardiac tissue culture and found that in the conditions of normal, non-inhibited excitability the curvature effects do not play essential role in the propagation. Neither narrow isthmuses nor sharp corners of the obstacles, being classical objects for production of extremely curved wave front, affect non-inhibited wave propagation. The curvature-related phenomena of the propagation block and wave detachment from the obstacle boundary were observed only after partial suppression of the sodium channels with Lidocaine. Computer simulations confirmed the experimental observations. The explanation of the observed phenomena refers to the fact that the heart tissue is made of finite size cells so that curvature radii smaller than the cardiomyocyte size loses sense, and in non-inhibited tissue the single cell is capable to transmit excitation to its neighbors.

Estimating the time scale and anatomical location of atrial fibrillation spontaneous termination in a biophysical model

Due to their transient nature, spontaneous terminations of atrial fibrillation (AF) are difficult to investigate. Apparently, confounding experimental findings about the time scale of this phenomenon have been reported, with values ranging from 1 s to 1 min. We propose a biophysical modeling approach to study the mechanisms of spontaneous termination in two models of AF with different levels of dynamical complexity. 8 s preceding spontaneous terminations were studied and the evolution of cycle length and wavefront propagation were documented to assess the time scale and anatomical location of the phenomenon. Results suggest that termination mechanisms are dependent on the underlying complexity of AF. During simulated AF of low complexity, the total process of spontaneous termination lasted 3,200 ms and was triggered in the left atrium 800 ms earlier than in the right atrium. The last fibrillatory activity was observed more often in the right atrium. These asymmetric termination mechanisms in both time and space were not observed during spontaneous terminations of complex AF simulations, which showed less predictable termination patterns lasting only 1,600 ms. This study contributes to the interpretation of previous clinical observations, and illustrates how computer modeling provides a complementary approach to study the mechanisms of cardiac arrhythmias.

Wave emission on interacting heterogeneities in cardiac tissue

Cardiac arrhythmias, a precursor of fibrillationlike states in the beating heart, are associated with spiral waves, which are likely to become pinned to heterogeneities. Far-field pacing (FFP) is a promising method for terminating such waves by using heterogeneities in the tissue as internal pacing sites. In this study we investigated the role of multiple obstacles and their interaction during FFP. We show that a secondary nearby obstacle can significantly modulate the minimum electrical field in FFP. Further, we show that essentially the same effect can be observed in cardiac tissue culture, which is a powerful experimental model to simulate heart activity. Here, an isotropic cell distribution leads to domain formation of locally distributed depolarization sites. Both secondary obstacles and domain formation of local depolarization sites can modulate energy requirements to originate wave propagation on obstacles. Our theoretical result was confirmed by experiments with cardiomyocyte monolayers. This result may be useful for the future application of FFP to a real beating heart.

Utilizing the eikonal relationship in strategies for reentrant wave termination in excitable media

Obstacle-anchored vortices can be terminated by the application of high-frequency wave trains in excitable media. We theoretically derived the dependency between the obstacle radius and the maximum unpinning period through reinterpretation of the well-known eikonal equation. Our theoretical result was confirmed by experiments with cardiomyocyte monolayers. This result may be useful for improving the stimulation protocol of implantable cardiac pacemakers.

Wave-train-induced termination of weakly anchored vortices in excitable media

A free vortex in excitable media can be displaced and removed by a wave train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached to obstacles smaller than the core radius of the free vortex is possible through pacing. The wave-train frequency necessary for unpinning increases with the obstacle size and we present a geometric explanation of this dependence. Our model-independent results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue.

Unpinning of a spiral wave anchored around a circular obstacle by an external wave train: common aspects of a chemical reaction and cardiomyocyte tissue

It is well known that spiral waves are often stabilized by anchoring to a local heterogeneity ("pinning") and that such pinned waves are rather difficult to eliminate. In the present report, we show that pinned spiral waves can be eliminated through collision with a wave train arriving from the outer region, as confirmed in experiments on the Belousov-Zhabotinsky (BZ) reaction as well as in cardiomyocyte tissue culture. A numerical simulation using the Oregonator, a mathematical model for the BZ reaction, provides the parameter area for successful unpinning. The scenario of unpinning is discussed in terms of the dispersion relation of the wave train by taking into account the curvature effect of the excitation wave.

Zero-refractoriness spirals in phase-coupled excitable media

Effects of excitability and coupling strength on plane and spiral waves in two-dimensional excitable lattices modeled by phase-coupled elements are investigated. The corresponding phase diagrams for stable plane waves and spiral waves are obtained by simulations. The parameters capable of supporting stable spiral waves are sorted out together with the spiral rotation frequencies. This discrete model corresponds to an excitable medium with zero refractoriness and in the continuum limit supports zero-core spiral waves. The associated wave propagating behaviors are also discussed analytically and verified.

Pinned scroll rings in an excitable system

Three-dimensional spiral waves in the Belousov-Zhabotinsky reaction are pinned to unexcitable heterogeneities. This pinning can prevent the collapse of scroll rings even if the heterogeneity does not extend along the entire wave filament. In the latter case, frequency differences create stationary gradients in the rotation phase. These twist patterns and their frequencies agree with algebraic solutions of the forced Burgers equation revealing insights into the phase coupling of scroll waves.

Mechanisms of stretch-induced atrial fibrillation in the presence and the absence of adrenocholinergic stimulation: interplay between rotors and focal discharges

BACKGROUND

Both atrial stretch and combined adrenocholinergic stimulation (ACS) have been shown to favor initiation and maintenance of atrial fibrillation (AF). Their respective contributions to the electrophysiological mechanism remains, however, incompletely understood.

OBJECTIVE

This study endeavored to determine the mechanism of maintenance of stretch-related AF (SRAF) in the presence and absence of ACS and to assess how focal discharges interact with rotors to modify the level of complexity in the activation patterns to perpetuate AF.

METHODS

Video imaging of AF dynamics was carried out using a SRAF model in isolated sheep hearts (n = 24). Pharmacological approaches were used to (1) mimic ACS with acetylcholine (1 microM) plus isoproterenol (0.03 microM), and (2) abolish triggered activity, in response to sarcoplasmic reticulum calcium release, with caffeine (5 mM, CA) or ryanodine (10 to 40 microM, RYA).

RESULTS

In the absence of ACS, on perfusion of CA or RYA, focal discharges were abolished and SRAF was terminated in most of the cases (10 of 13 experiments). In the presence of ACS, multiple drifting rotors as well as a large number of focal discharges were identified and only 1 of 11 AF episodes was terminated.

CONCLUSIONS

In the absence of ACS, SRAF is maintained by high-frequency focal discharges that generate fibrillatory conduction and wave breaks. In the presence of ACS, SRAF dynamics is characterized by multiple high frequency rotors that are rendered unstable by spatially distributed focal discharges.

Coherent wave patterns sustained by a localized inhomogeneity in an excitable medium

The influence of a localized inhomogeneity (oscillatory or stationary) on spatiotemporal chaotic state in an excitable reaction-diffusion system is investigated. We find that various coherent wave patterns, such as spiral waves (including multiarmed) and target wave patterns are able to be created by the inhomogeneity from the chaotic state. Due to the growth of these coherent wave patterns, the previously existing turbulent waves in the absence of inhomogeneity are suppressed. At last, the whole system is entrained by the coherent wave patterns. Closer investigations indicate that the possible mechanisms underlying the inhomogeneity sustained coherent wave patterns seem quite different for oscillatory and stationary inhomogeneities.

Liberation of a pinned spiral wave by a single stimulus in excitable media

The unpinning of a spiral wave from an anatomic obstacle by the application of a single stimulus near the core of the rotating wave was studied experimentally in a cell culture of cardiomyocyte monolayers as well as by computer simulations. It is shown that, with suitable positioning and timing, a single stimulus is sufficient for the successful unpinning of a pinned spiral wave. Successful unpinning is achieved when two conditions are fulfilled: (1) The stimulus is delivered in the vulnerable window of the rotating wave, and (2) the stimulus is delivered in a spatial zone in proximity to the obstacle, where the shape of the zone is defined by the phase of the anchored spiral wave. Two different scenarios for successful unpinning are discussed, which are distinguished by the distance to the stimuli applied to the obstacle.

Eliminating spiral waves pinned to an anatomical obstacle in cardiac myocytes by high-frequency stimuli

The unpinning of spiral waves by the application of high-frequency wave trains was studied in cultured cardiac myocytes. Successful unpinning was observed when the frequency of the paced waves exceeded a critical level. The unpinning process was analyzed by a numerical simulation with a model of cardiac tissue. The mechanism of unpinning by high-frequency stimuli is discussed in terms of local entrainment failure, through a reduction of the two-dimensional spatial characteristics into one dimension.

Generation and escape of local waves from the boundary of uncoupled cardiac tissue

We aim to understand the formation of abnormal waves of activity from myocardial regions with diminished cell-to-cell coupling. En route to this goal, we studied the behavior of a heterogeneous myocyte network in which a sharp coupling gradient was placed under conditions of increasing network automaticity. Experiments were conducted in monolayers of neonatal rat cardiomyocytes using heptanol and isoproterenol as means of altering cell-to-cell coupling and automaticity, respectively. Experimental findings were explained and expanded using a modified Beeler-Reuter numerical model. The data suggest that the combination of a heterogeneous substrate, a gradient of coupling, and an increase in oscillatory activity of individual cells creates a rich set of behaviors associated with self-generated spiral waves and ectopic sources. Spiral waves feature a flattened shape and a pin-unpin drift type of tip motion. These intercellular waves are action-potential based and can be visualized with either voltage or calcium transient measurements. A source/load mismatch on the interface between the boundary and well-coupled layers can lock wavefronts emanating from both ectopic sources and rotating waves within the inner layers of the coupling gradient. A numerical approach allowed us to explore how 1), the spatial distribution of cells, 2), the amplitude and dispersion of cell automaticity, and 3), the speed at which the coupling gradient moves in space affect wave behavior, including its escape into well-coupled tissue.