Fast propagation regions cause self-sustained reentry in excitable media

Spatially Conserved Spiral Wave Activity During Human Atrial Fibrillation

BACKGROUND

Atrial fibrillation is the most common cardiac arrhythmia in the world and increases the risk for stroke and morbidity. During atrial fibrillation, the electric activation fronts are no longer coherently propagating through the tissue and, instead, show rotational activity, consistent with spiral wave activation, focal activity, collision, or partial versions of these spatial patterns. An unexplained phenomenon is that although simulations of cardiac models abundantly demonstrate spiral waves, clinical recordings often show only intermittent spiral wave activity.

METHODS

In silico data were generated using simulations in which spiral waves were continuously created and annihilated and in simulations in which a spiral wave was intermittently trapped at a heterogeneity. Clinically, spatio-temporal activation maps were constructed using 60 s recordings from a 64 electrode catheter within the atrium of N=34 patients (n=24 persistent atrial fibrillation). The location of clockwise and counterclockwise rotating spiral waves was quantified and all intervals during which these spiral waves were present were determined. For each interval, the angle of rotation as a function of time was computed and used to determine whether the spiral wave returned in step or changed phase at the start of each interval.

RESULTS

In both simulations, spiral waves did not come back in phase and were out of step." In contrast, spiral waves returned in step in the majority (68%; P=0.05) of patients. Thus, the intermittently observed rotational activity in these patients is due to a temporally and spatially conserved spiral wave and not due to ones that are newly created at the onset of each interval.

CONCLUSIONS

Intermittency of spiral wave activity represents conserved spiral wave activity of long, but interrupted duration or transient spiral activity, in the majority of patients. This finding could have important ramifications for identifying clinically important forms of atrial fibrillation and in guiding treatment.

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.

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.

Stochastic termination of spiral wave dynamics in cardiac tissue

Rotating spiral waves are self-organized features in spatially extended excitable media and may play an important role in cardiac arrhythmias including atrial fibrillation (AF). In homogeneous media, spiral wave dynamics are perpetuated through spiral wave breakup, leading to the continuous birth and death of spiral waves, but have a finite probability of termination. In non-homogeneous media, however, heterogeneities can act as anchoring sources that result in sustained spiral wave activity. It is thus unclear how and if AF may terminate following the removal of putative spiral wave sources in patients. Here, we address this question using computer simulations in which a stable spiral wave is trapped by an heterogeneity and is surrounded by spiral wave breakup. We show that, following ablation of spatial heterogeneity to render that region of the medium unexcitable, termination of spiral wave dynamics is stochastic and Poisson-distributed. Furthermore, we show that the dynamics can be accurately described by a master equation using birth and death rates. To validate these predictions in vivo, we mapped spiral wave activity in patients with AF and targeted the locations of spiral wave sources using radiofrequency ablation. Targeted ablation was indeed able to terminate AF, but only after a variable delay of up to several minutes. Furthermore, and consistent with numerical simulations, termination was not accompanied by gradual temporal or spatial organization. Our results suggest that spiral wave sources and tissue heterogeneities play a critical role in the maintenance of AF and that the removal of sources results in spiral wave dynamics with a finite termination time, which could have important clinical implications.

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.

Artificially Created Reentry Circuit by Laser Irradiation Causes Atrial Tachycardia to Persist in Murine Atria

BACKGROUND

There is a gradual progression from paroxysmal to persistent atrial fibrillation (AF) in humans. To elucidate the mechanism involved, the creation of an artificial atrial substrate to persist AF in mice was attempted.Methods and Results:This study used wild type (WT) mice, but it is difficult to induce AF in them. A novel antegrade perfusion method from the left ventricle (LV) to enlarge both atria for artificial atrial modification was proposed in this study. Short duration AF was induced by burst pacing under this method. Optical mapping analysis revealed non-sustained focal type and meandering spiral reentrants after short duration AF. A tiny artificial substrate (~1.2 mm in diameter) was added in by laser irradiation to create a critical atrial arrhythmogenic substrate. Burst pacing was performed in a non-laser group (n=8), a circular-shape laser group (n=8), and a wedge-shaped dent laser group (n=8). We defined AF and atrial tachycardia (AT) as atrial arrhythmia (AA). Long-lasting AA was defined as lasting for ≥30 min. Long-lasting AA was observed in 0/8, 0/8, and 6/8 (75%) mice in each group. Optical mapping analysis revealed that the mechanism was AT with a stationary rotor around the irradiated margin.

CONCLUSIONS

Regrettably, this study failed to reproduce persistent AF, but succeeded in creating an arrhythmic substrate that causes sustained AT in WT mice.

The impact of a closed-loop thalamocortical model on the spatiotemporal dynamics of cortical and thalamic traveling waves

Propagation of activity in spatially structured neuronal networks has been observed in awake, anesthetized, and sleeping brains. How these wave patterns emerge and organize across brain structures, and how network connectivity affects spatiotemporal neural activity remains unclear. Here, we develop a computational model of a two-dimensional thalamocortical network, which gives rise to emergent traveling waves similar to those observed experimentally. We illustrate how spontaneous and evoked oscillatory activity in space and time emerge using a closed-loop thalamocortical architecture, sustaining smooth waves in the cortex and staggered waves in the thalamus. We further show that intracortical and thalamocortical network connectivity, cortical excitation/inhibition balance, and thalamocortical or corticothalamic delay can independently or jointly change the spatiotemporal patterns (radial, planar and rotating waves) and characteristics (speed, direction, and frequency) of cortical and thalamic traveling waves. Computer simulations predict that increased thalamic inhibition induces slower cortical frequencies and that enhanced cortical excitation increases traveling wave speed and frequency. Overall, our results provide insight into the genesis and sustainability of thalamocortical spatiotemporal patterns, showing how simple synaptic alterations cause varied spontaneous and evoked wave patterns. Our model and simulations highlight the need for spatially spread neural recordings to uncover critical circuit mechanisms for brain functions.

Emergent dynamics in excitable flow systems

Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a nonlinear relation between current and pressure difference, and can be applied to networks of arbitrary topology. The model displays complex dynamics, including self-sustained oscillations in the absence of any dynamics in the inputs and outputs. In this work we analytically show the origin of self-sustained oscillations for the one-dimensional case. We numerically study the behavior of systems of arbitrary topology under different conditions: we discuss their excitability, the effect of different boundary conditions, and wave propagation when the network has regions of conduits with linear conductance.

Atrial fibrillation and cardiac fibrosis

The understanding of atrial fibrillation (AF) evolved from a sole rhythm disturbance towards the complex concept of a cardiomyopathy based on arrhythmia substrates. There is evidence that atrial fibrosis can be visualized using late gadolinium enhancement cardiac magnetic resonance imaging and that it is a powerful predictor for the outcome of AF interventions. However, a strategy of an individual and fibrosis guided management of AF looks promising but results from prospective multicentre trials are pending. This review gives an overview about the relationship between cardiac fibrosis and AF focusing on translational aspects, clinical observations, and fibrosis imaging to emphasize the concept of personalized paths in AF management taking into account the individual amount and distribution of fibrosis.

Classifying Drugs by their Arrhythmogenic Risk Using Machine Learning

All medications have adverse effects. Among the most serious of these are cardiac arrhythmias. Current paradigms for drug safety evaluation are costly, lengthy, conservative, and impede efficient drug development. Here, we combine multiscale experiment and simulation, high-performance computing, and machine learning to create a risk estimator to stratify new and existing drugs according to their proarrhythmic potential. We capitalize on recent developments in machine learning and integrate information across 10 orders of magnitude in space and time to provide a holistic picture of the effects of drugs, either individually or in combination with other drugs. We show, both experimentally and computationally, that drug-induced arrhythmias are dominated by the interplay between two currents with opposing effects: the rapid delayed rectifier potassium current and the L-type calcium current. Using Gaussian process classification, we create a classifier that stratifies drugs into safe and arrhythmic domains for any combinations of these two currents. We demonstrate that our classifier correctly identifies the risk categories of 22 common drugs exclusively on the basis of their concentrations at 50% current block. Our new risk assessment tool explains under which conditions blocking the L-type calcium current can delay or even entirely suppress arrhythmogenic events. Using machine learning in drug safety evaluation can provide a more accurate and comprehensive mechanistic assessment of the proarrhythmic potential of new drugs. Our study paves the way toward establishing science-based criteria to accelerate drug development, design safer drugs, and reduce heart rhythm disorders.

Classifying Drugs by their Arrhythmogenic Risk Using Machine Learning

All medications have adverse effects. Among the most serious of these are cardiac arrhythmias. Current paradigms for drug safety evaluation are costly, lengthy, conservative, and impede efficient drug development. Here, we combine multiscale experiment and simulation, high-performance computing, and machine learning to create a risk estimator to stratify new and existing drugs according to their proarrhythmic potential. We capitalize on recent developments in machine learning and integrate information across 10 orders of magnitude in space and time to provide a holistic picture of the effects of drugs, either individually or in combination with other drugs. We show, both experimentally and computationally, that drug-induced arrhythmias are dominated by the interplay between two currents with opposing effects: the rapid delayed rectifier potassium current and the L-type calcium current. Using Gaussian process classification, we create a classifier that stratifies drugs into safe and arrhythmic domains for any combinations of these two currents. We demonstrate that our classifier correctly identifies the risk categories of 22 common drugs exclusively on the basis of their concentrations at 50% current block. Our new risk assessment tool explains under which conditions blocking the L-type calcium current can delay or even entirely suppress arrhythmogenic events. Using machine learning in drug safety evaluation can provide a more accurate and comprehensive mechanistic assessment of the proarrhythmic potential of new drugs. Our study paves the way toward establishing science-based criteria to accelerate drug development, design safer drugs, and reduce heart rhythm disorders.

Chaotic tip trajectories of a single spiral wave in the presence of heterogeneities

Spiral waves have been observed in a variety of physical, chemical, and biological systems. They play a major role in cardiac arrhythmias, including fibrillation, where the observed irregular activation patterns are generally thought to arise from the continuous breakup of multiple unstable spiral waves. Using spatially extended simulations of different electrophysiological models of cardiac tissue, we show that a single spiral wave in the presence of heterogeneities can display chaotic tip trajectories, consistent with fibrillation. We also show that the simulated spiral tip dynamics, including chaotic trajectories, can be captured by a simple particle model which only describes the dynamics of the spiral tip. This shows that spiral wave breakup, or interactions with other waves, are not necessary to initiate chaos in spiral waves.

Controlling excitable wave behaviors through the tuning of three parameters

Excitable systems are a class of dynamical systems that can generate self-sustaining waves of activity. These waves are known to manifest differently under diverse conditions, whereas some travel as planar or radial waves, and others evolve into rotating spirals. Excitable systems can also form stationary stable patterns through standing waves. Under certain conditions, these waves are also known to be reflected at no-flux boundaries. Here, we review the basic characteristics of these four entities: traveling, rotating, standing and reflected waves. By studying their mechanisms of formation, we show how through manipulation of three critical parameters: time-scale separation, space-scale separation and threshold, we can interchangeably control the formation of all the aforementioned wave types.

Extinction dynamics of spiral defect chaos

Spatially extended excitable systems can exhibit spiral defect chaos (SDC) during which spiral waves continuously form and disappear. To address how this dynamical state terminates using simulations can be computationally challenging, especially for large systems. To circumvent this limitation, we treat the number of spiral waves as a stochastic population with a corresponding birth-death equation and use techniques from statistical physics to determine the mean episode duration of SDC. Motivated by cardiac fibrillation, during which the heart's electrical activity becomes disorganized and shows fragmenting spiral waves, we use generic models of cardiac electrophysiology. We show that the duration can be computed in minimal computational time and that it depends exponentially on domain size. Therefore, the approach can result in efficient and accurate predictions of mean episode duration which may be extended to more complex geometries and models.

Spiral wave initiation in excitable media

Spiral waves represent an important example of dissipative structures observed in many distributed systems in chemistry, biology and physics. By definition, excitable media occupy a stationary resting state in the absence of external perturbations. However, a perturbation exceeding a threshold results in the initiation of an excitation wave propagating through the medium. These waves, in contrast to acoustic and optical ones, disappear at the medium's boundary or after a mutual collision, and the medium returns to the resting state. Nevertheless, an initiation of a rotating spiral wave results in a self-sustained activity. Such activity unexpectedly appearing in cardiac or neuronal tissues usually destroys their dynamics which results in life-threatening diseases. In this context, an understanding of possible scenarios of spiral wave initiation is of great theoretical importance with many practical applications.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Spiral wave initiation in excitable media

Spiral waves represent an important example of dissipative structures observed in many distributed systems in chemistry, biology and physics. By definition, excitable media occupy a stationary resting state in the absence of external perturbations. However, a perturbation exceeding a threshold results in the initiation of an excitation wave propagating through the medium. These waves, in contrast to acoustic and optical ones, disappear at the medium's boundary or after a mutual collision, and the medium returns to the resting state. Nevertheless, an initiation of a rotating spiral wave results in a self-sustained activity. Such activity unexpectedly appearing in cardiac or neuronal tissues usually destroys their dynamics which results in life-threatening diseases. In this context, an understanding of possible scenarios of spiral wave initiation is of great theoretical importance with many practical applications.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Electrocardiogram phenotypes in hypertrophic cardiomyopathy caused by distinct mechanisms: apico-basal repolarization gradients vs. Purkinje-myocardial coupling abnormalities

AIMS

To identify key structural and electrophysiological features explaining distinct electrocardiogram (ECG) phenotypes in hypertrophic cardiomyopathy (HCM).

METHODS AND RESULTS

Human heart-torso anatomical models were constructed from cardiac magnetic resonance (CMR) images of HCM patients, representative of ECG phenotypes identified previously. High performance computing simulations using bidomain models were conducted to dissect key features explaining the ECG phenotypes with increased HCM Risk-SCD scores, namely Group 1A, characterized by normal QRS but inverted T waves laterally and coexistence of apical and septal hypertrophy; and Group 3 with marked QRS abnormalities (deep and wide S waves laterally) and septal hypertrophy. Hypertrophic cardiomyopathy abnormalities characterized from CMR, such as hypertrophy, tissue microstructure alterations, abnormal conduction system, and ionic remodelling, were selectively included to assess their influence on ECG morphology. Electrocardiogram abnormalities could not be explained by increased wall thickness nor by local conduction abnormalities associated with fibre disarray or fibrosis. Inverted T wave with normal QRS (Group 1A) was obtained with increased apico-basal repolarization gradient caused by ionic remodelling in septum and apex. Lateral QRS abnormalities (Group 3) were only recovered with abnormal Purkinje-myocardium coupling.

CONCLUSION

Two ECG-based HCM phenotypes are explained by distinct mechanisms: ionic remodelling and action potential prolongation in hypertrophied apical and septal areas lead to T wave inversion with normal QRS complexes, whereas abnormal Purkinje-myocardial coupling causes abnormal QRS morphology in V4-V6. These findings have potential implications for patients' management as they point towards different arrhythmia mechanisms in different phenotypes.

Paradoxical Onset of Arrhythmic Waves from Depolarized Areas in Cardiac Tissue Due to Curvature-Dependent Instability

The generation of abnormal excitations in pathological regions of the heart is a main trigger for lethal cardiac arrhythmias. Such abnormal excitations, also called ectopic activity, often arise from areas with local tissue heterogeneity or damage accompanied by localized depolarization. Finding the conditions that lead to ectopy is important to understand the basic biophysical principles underlying arrhythmia initiation and might further refine clinical procedures. In this study, we are the first to address the question of how geometry of the abnormal region affects the onset of ectopy using a combination of experimental, in silico, and theoretical approaches. We paradoxically find that, for any studied geometry of the depolarized region in optogenetically modified monolayers of cardiac cells, primary ectopic excitation originates at areas of maximal curvature of the boundary, where the stimulating electrotonic currents are minimal. It contradicts the standard critical nucleation theory applied to nonlinear waves in reaction-diffusion systems, where a higher stimulus is expected to produce excitation more easily. Our in silico studies reveal that the nonconventional ectopic activity is caused by an oscillatory instability at the boundary of the damaged region, the occurrence of which depends on the curvature of that boundary. The onset of this instability is confirmed using the Schrödinger equation methodology proposed by Rinzel and Keener [SIAM J. Appl. Math. 43, 907 (1983)]. Overall, we show distinctively novel insight into how the geometry of a heterogeneous cardiac region determines ectopic activity, which can be used in the future to predict the conditions that can trigger cardiac arrhythmias.

Spiral waves and vertebrate embryonic handedness

During early embryonic development, the vertebrate main body axis is segmented from head-to-tail into somites. Somites emerge sequentially from the presomitic mesoderm (PSM) as a consequence of oscillatory waves of genetic activity, called somitogenesis waves. Here, we discuss the implications of the dynamic patterns of early X-Delta-2 expression in the prospective somites (somitomeres) of Xenopus laevis. We report that right somitomeres normally emerge before left to form chiral structures (i.e. structures having clockwise or counter-clockwise handedness). From our observations, we infer that somitogenesis waves are normally counter-clockwise spirals, a novel dynamic mechanism for the control of handedness development in Xenopus. We propose that the same mechanism could control handedness development in all vertebrate embryos, providing a dynamical basis for the current asymmetric molecular transport model for generating left-right asymmetry.

Laser catheter ablation of long- lasting persistent atrial fibrillation: Longterm results

Catheter ablation of atrial fibrillation (AF) is a current therapeutic option but its efficacy for the treatment of long-lasting persistent AF (l-lpAF) remains suboptimal. We tested the laser method as an alternative for catheter ablation of l-lpAF by using an open-irrigated electrode laser mapping and ablation (ELMA) catheter. Laser ablation was attempted in 48 patients aged 50-81 years (69 ± 7.6 y, female = 28) with drug resistant (3.5 trials) l-lpAF (≥12 months). All of the patients had comorbidities: congestive heart failure NYHA II-III (100%), hypertension 29 (60%), coronary artery disease 19 (40%), and heart valve defect 17 (35%). None of the patients had diabetes or obstructive sleep apnea. All were in AF at the beginning of the procedure. Continuous wave (cw) 1064nm Nd:YAG laser applications at 15W/10-20s (14-26/patient) were applied via the ELMA catheter until local electrical activity displayed on the monitor in the bipolar focused local electrograms (LEG) recorded via the pin electrodes from the tip of the catheter was abolished permanently and sinus rhythm was achieved. Online monitoring of electrical potential amplitudes in the focused LEG recorded via the pin-electrodes of the ELMA catheter allowed for validation of ablation success. Procedure duration ranged from 82-175 min (118 ± 72 min), number of lesions were14-26 (19 ± 4) per patient and X-ray exposure times ranged from 15-82 min (23.2 ± 12 min). Interventions were without complications. After the ablation procedure all the patients were in sinus rhythm, off medication, however, 12 (25%) needed a repeat study for various arrhythmias. During followup of 9 months to 29.3 years (8.2 ± 6.5 years) patients' quality of life improved significantly and during final follow-up control all except two were off medication still in sinus rhythm (lifelong success rate = 96%). As compared to other catheter ablation methods the laser method is an intriguing alternative for catheter ablation of l-lpAF.

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

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

Geometrical factors in propagation block and spiral wave initiation

Many theoretical and experimental studies indicate that a propagation block represents an important factor in spiral wave initiation in excitable media. The analytical and numerical results we obtained for a generic two-component reaction-diffusion system demonstrate quantitative conditions for the propagation block in a one-dimensional and a two-dimensional medium due to a sharp spatial increase of the medium's excitability or the coupling strength above a certain critical value. Here, we prove that this critical value strongly depends on the medium parameters and the geometry of the inhomogeneity. For an exemplary two-dimensional medium, we show how the propagation block can be used to initiate spiral waves by a specific choice of the size and shape of the medium's inhomogeneity.