Electrical turbulence in three-dimensional heart muscle

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.

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.

Numerical study of the drift of scroll waves by optical feedback in cardiac tissue

Nonlinear waves were found in various types of physical, chemical, and biological excitable media, e.g., in heart muscle. They can form three-dimensional (3D) vortices, called scroll waves, that are of particular significance in the heart, as they underlie lethal cardiac arrhythmias. Thus controlling the behavior of scroll waves is interesting and important. Recently, the optical feedback control procedure for two-dimensional vortices, called spiral waves, was developed. It can induce directed linear drift of spiral waves in optogenetically modified cardiac tissue. However, the extension of this methodology to 3D scroll waves is nontrivial, as optogenetic signals only penetrate close to the surface of cardiac tissue. Here we present a study of this extension in a two-variable reaction-diffusion model and in a detailed model of cardiac tissue. We show that the success of the control procedure is determined by the tension of the scroll wave filament. In tissue with positive filament tension the control procedure works in all cases. However, in the case of negative filament tension for a sufficiently large medium, instabilities occur and make drift and control of scroll waves impossible. Because in normal cardiac tissue the filament tension is assumed to be positive, we conclude that the proposed optical feedback scheme can be a robust method in inducing the linear drift of scroll waves that can control their positions in cardiac tissue.

Effect of excitability on partially pinned scroll waves in excitable chemical media

We present an investigation of excitability effects on the dynamics of scroll waves partially pinned to inert cylindrical obstacles in three-dimensional Belousov-Zhabotinsky excitable media. We also report on corresponding numerical simulations with the Oregonator model. The excitability varies according to the concentration of sulfuric acid [H_{2}SO_{4}] in the Belousov-Zhabotinsky (BZ) reaction and the parameter ɛ^{-1} in the Oregonator model. Initially, the freely rotating scroll segment rotates faster than the pinned one. The difference in the frequency of the two parts results in a transition from a straight pinned scroll wave to a twisted one, which helically wraps around the entire obstacle. The wave frequency in the whole volume is equal to that of the freely rotating scroll wave. When the excitability is increased, the time for the transition to the twisted wave structure decreases while the average speed s of the development increases. After the transition, the twisted wave remains stable. In media with higher excitability, the helical pitch is shorter but the twist rate ω is higher. Analysis presented in this study together with our previous findings of the effect of the cylindrical obstacle diameter on the wave dynamics results in common features: The average speed s and the twist rate ω of both studies fit well to functions of the difference in the initial frequency Δf of the freely rotating and untwisted pinned waves. We also demonstrate the robustness of the partially pinned scroll waves against perturbations from spontaneous waves emerging during the wave generation in the BZ medium with high [H_{2}SO_{4}]. Even though the scroll wave is partly disturbed at the beginning of the experiment, the spontaneous waves are gradually suppressed and the typical wave structure is finally developed.

Time-delay-induced spiral chimeras on a spherical surface of globally coupled oscillators

We consider globally coupled networks of identical oscillators, located on the surface of a sphere with interaction time delays, and show that the distance-dependent time delays play a key role for the spiral chimeras to occur as a generic state in different systems of coupled oscillators. For the phase oscillator system, we analyze the existence and stability of stationary solutions along the Ott-Antonsen invariant manifold to find the bifurcation structure of the spiral chimera state. We demonstrate via an extensive numerical experiment that the time-delay-induced spiral chimeras are also present for coupled networks of the Stuart-Landau and Van der Pol oscillators in the same parameter regime as that of phase oscillators, with a series of evenly spaced band-type regions. It is found that the spiral chimera state occurs as a consequence of a resonant-type interplay between the intrinsic period of an individual oscillator and the interaction time delay as a topological structure property.

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.

Living myocardial slices: Advancing arrhythmia research

Living myocardial slices (LMS) are ultrathin (150-400 µm) sections of intact myocardium that can be used as a comprehensive model for cardiac arrhythmia research. The recent introduction of biomimetic electromechanical cultivation chambers enables long-term cultivation and easy control of living myocardial slices culture conditions. The aim of this review is to present the potential of this biomimetic interface using living myocardial slices in electrophysiological studies outlining advantages, disadvantages and future perspectives of the model. Furthermore, different electrophysiological techniques and their application on living myocardial slices will be discussed. The developments of living myocardial slices in electrophysiology research will hopefully lead to future breakthroughs in the understanding of cardiac arrhythmia mechanisms and the development of novel therapeutic options.

Topological charge-density-vector method of identifying filaments of scroll waves

Scroll waves have been found in a variety of three-dimensional excitable media, including physical, chemical, and biological origins. Scroll waves in cardiac tissue are of particular significance as they underlie ventricular fibrillation that can cause sudden death. The behavior of a scroll wave is characterized by a line of phase singularity at its organizing center, known as a filament. A thorough investigation into the filament dynamics is the key to further exploration of the general theory of scroll waves in excitable media and the mechanisms of ventricular fibrillation. In this paper, we propose a method to identify filaments of scroll waves in excitable media. From the definition of the topological charge of filaments, we obtain the discrete expression of the topological charge-density vector, which is useful in calculating the topological charge vectors at each grid in the space directly. The set of starting points of these topological charge vectors represents a set of phase singularities, thereby forming a line of phase singularity, that is, a filament of a scroll wave.

Reconstruction of three-dimensional scroll waves in excitable media from two-dimensional observations using deep neural networks

Scroll wave dynamics are thought to underlie life-threatening ventricular fibrillation. However, direct observations of three-dimensional electrical scroll waves remain elusive, as there is no direct way to measure action potential wave patterns transmurally throughout the thick ventricular heart muscle. Here we study whether it is possible to reconstruct simulated scroll waves and scroll wave chaos using deep learning. We trained encoding-decoding convolutional neural networks to predict three-dimensional scroll wave dynamics inside bulk-shaped excitable media from two-dimensional observations of the wave dynamics on the bulk's surface. We tested whether observations from one or two opposing surfaces would be sufficient and whether transparency or measurements of surface deformations enhances the reconstruction. Further, we evaluated the approach's robustness against noise and tested the feasibility of predicting the bulk's thickness. We distinguished isotropic and anisotropic, as well as opaque and transparent, excitable media as models for cardiac tissue and the Belousov-Zhabotinsky chemical reaction, respectively. While we demonstrate that it is possible to reconstruct three-dimensional scroll wave dynamics, we also show that it is challenging to reconstruct complicated scroll wave chaos and that prediction outcomes depend on various factors such as transparency, anisotropy, and ultimately the thickness of the medium compared to the size of the scroll waves. In particular, we found that anisotropy provides crucial information for neural networks to decode depth, which facilitates the reconstructions. In the future, deep neural networks could be used to visualize intramural action potential wave patterns from epi- or endocardial measurements.

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.

Dynamic surface patterns on cells

Dynamic pattern formations are commonly observed in multicellular systems, such as cardiac tissue and slime molds, and modeled using reaction–diffusion systems. Recent experiments have revealed dynamic patterns in the concentration profile of various cortical proteins at a much smaller scale, namely, embryos at their single-cell stage. Spiral waves of Rho and F-actin proteins have been reported in Xenopus frog and starfish oocytes [Bement et al., Nat. Cell Biol. 17, 1471 (2015)], while a pulsatile pattern of Rho and myosin proteins has been found in C. elegans embryo [Nishikawa et al., eLife 6, e30537 (2017)]. Here, we propose that these two seemingly distinct dynamic patterns are signatures of a single reaction–diffusion network involving active-Rho, inactive-Rho, actin, and myosin. We show that a small variation in the concentration of other ancillary proteins can give rise to different dynamical states from the same chemical network.

Size matters in atrial fibrillation: the underestimated importance of reduction of contiguous electrical mass underlying the effectiveness of catheter ablation

Evidence has accumulated over the last century of the importance of a critical electrical mass in sustaining atrial fibrillation (AF). AF ablation certainly reduces electrically contiguous atrial mass, but this is not widely accepted to be an important part of its mechanism of action. In this article, we review data showing that atrial size is correlated in many settings with AF propensity. Larger mammals are more likely to exhibit AF. This is seen both in the natural world and in animal models, where it is much easier to create a goat model than a mouse model of AF, for example. This also extends to humans-athletes, taller people, and obese individuals all have large atria and are more likely to exhibit AF. Within an individual, risk factors such as hypertension, valvular disease and ischaemia can enlarge the atrium and increase the risk of AF. With respect to AF ablation, we explore how variations in ablation strategy and the relative effectiveness of these strategies may suggest that a reduction in electrical atrial mass is an important mechanism of action. We counter this with examples in which there is no doubt that mass reduction is less important than competing theories such as ganglionated plexus ablation. We conclude that, when considering future strategies for the ablative therapy of AF, it is important not to discount the possibility that contiguous electrical mass reduction is the most important mechanism despite the disappointing consequence being that enhancing success rates in AF ablation may involve greater tissue destruction.

Scroll wave with negative filament tension in a model of the left ventricle of the human heart and its overdrive pacing

Nonlinear waves of electrical excitation initiate cardiac contraction. Abnormal wave propagation in the heart, e.g., spiral waves, can lead to sudden cardiac arrest. This study analyzed the dynamics of spiral waves under the influence of an instability called negative filament tension, and examined how the spiral waves can be eliminated through high-frequency pacing. A generic anatomical model of the left ventricle of the human heart and the Aliev-Panfilov model for cardiac tissue were used. The study showed that the source of such arrhythmia is elongated filaments with lengths that can be 10-20 times greater than the characteristic thickness of the heart wall. In anisotropic tissue, the filament elongated before it was annihilated at the base of the heart. The spiral waves were eliminated through overdrive pacing with stimulation periods from 0.8 to 0.95 relative to the spiral wave period. The minimum time for the expulsion was about 10 s.

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.

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.

Spectral Analysis and Mutual Information Estimation of Left and Right Intracardiac Electrograms during Ventricular Fibrillation

Ventricular fibrillation (VF) signals are characterized by highly volatile and erratic electrical impulses, the analysis of which is difficult given the complex behavior of the heart rhythms in the left (LV) and right ventricles (RV), as sometimes shown in intracardiac recorded Electrograms (EGM). However, there are few studies that analyze VF in humans according to the simultaneous behavior of heart signals in the two ventricles. The objective of this work was to perform a spectral and a non-linear analysis of the recordings of 22 patients with Congestive Heart Failure (CHF) and clinical indication for a cardiac resynchronization device, simultaneously obtained in LV and RV during induced VF in patients with a Biventricular Implantable Cardioverter Defibrillator (BICD) Contak Renewal IV^TM (Boston Sci.). The Fourier Transform was used to identify the spectral content of the first six seconds of signals recorded in the RV and LV simultaneously. In addition, measurements that were based on Information Theory were scrutinized, including Entropy and Mutual Information. The results showed that in most patients the spectral envelopes of the EGM sources of RV and LV were complex, different, and with several frequency peaks. In addition, the Dominant Frequency (DF) in the LV was higher than in the RV, while the Organization Index (OI) had the opposite trend. The entropy measurements were more regular in the RV than in the LV, thus supporting the spectral findings. We can conclude that basic stochastic processing techniques should be scrutinized with caution and from basic to elaborated techniques, but they can provide us with useful information on the biosignals from both ventricles during VF.

Self-organization of multiarmed spiral waves in excitable media

We present an investigation of self-organized multiarmed spiral waves pinned to unexcitable circular obstacles in a thin layer of the excitable Belousov-Zhabotinsky reaction and in simulations using the Oregonator model. The multiarmed waves are initiated by a series of wave stimuli. In the proximity of the obstacle boundary, the wave rotation around the obstacle causes damped oscillations of the wave periods of all spiral arms. The dynamics of wave periods cause the wave velocities as well as the angular displacements between the adjacent arms to oscillate with decaying amplitudes. Eventually, all displacements approach approximately the same stable value so that all arms are distributed evenly around the obstacle. A further theoretical analysis reveals that the temporal dynamics of the angular displacements can be interpreted as underdamped harmonic oscillations. Far from the obstacles, the wave dynamics are less pronounced. The wave period becomes stable very soon after the initiation. When the number of spiral arms increases, the rotation of individual arms slows down but the wave period of the multiarmed spiral waves decreases. Due to their short period, multiarmed spiral waves emerging in the heart potentially result in severe pathological conditions.

Reconnection of multiple scroll rings in a three-dimensional reaction-diffusion system

Two scroll rings, placed in close proximity, can interact. When they come within one core length of each other, these waves can reconnect to form a single, large filament. In this article we show that three or more scroll rings can also reconnect when they come within the critical distance. Multiple scroll rings form larger vortices of varied filament geometry, depending on their initial sizes and placements. Different filaments, resulting from a reconnection of the same number of scroll rings placed in diverse ways, can have different lifetimes. In experiments with the Belousov-Zhabotinsky reaction and numerical simulations based on a corresponding reaction-diffusion model, we demonstrate the interaction and reconnection of multiple scroll waves and try to elucidate their lifetimes and dynamics.

Synchronization-based reconstruction of electromechanical wave dynamics in elastic excitable media

The heart is an elastic excitable medium, in which mechanical contraction is triggered by nonlinear waves of electrical excitation, which diffuse rapidly through the heart tissue and subsequently activate the cardiac muscle cells to contract. These highly dynamic excitation wave phenomena have yet to be fully observed within the depths of the heart muscle, as imaging technology is unable to penetrate the tissue and provide panoramic, three-dimensional visualizations necessary for adequate study. As a result, the electrophysiological mechanisms that are associated with the onset and progression of severe heart rhythm disorders such as atrial or ventricular fibrillation remain insufficiently understood. Here, we present a novel synchronization-based data assimilation approach with which it is possible to reconstruct excitation wave dynamics within the volume of elastic excitable media by observing spatiotemporal deformation patterns, which occur in response to excitation. The mechanical data are assimilated in a numerical replication of the measured elastic excitable system, and within this replication, the data drive the intrinsic excitable dynamics, which then coevolve and correspond to a reconstruction of the original dynamics. We provide a numerical proof-of-principle and demonstrate the performance of the approach by recovering even complicated three-dimensional scroll wave patterns, including vortex filaments of electrical excitation from within a deformable bulk tissue with fiber anisotropy. In the future, the reconstruction approach could be combined with high-speed imaging of the heart's mechanical contractions to estimate its electrophysiological activity for diagnostic purposes.

Effect of Heart Structure on Ventricular Fibrillation in the Rabbit: A Simulation Study

Ventricular fibrillation (VF) is a lethal condition that affects millions worldwide. The mechanism underlying VF is unstable reentrant electrical waves rotating around lines called filaments. These complex spatio-temporal patterns can be studied using both experimental and numerical methods. Computer simulations provide unique insights including high resolution dynamics throughout the heart and systematic control of quantities such as fiber orientation and cellular kinetics that are not feasible experimentally. Here we study filament dynamics using two bi-ventricular 3-D high-resolution rabbit heart geometries, one with detailed fine structure and another without fine structure. We studied filament dynamics using anisotropic and isotropic conductivities, and with four cellular action potential models with different recovery kinetics. Spiral wave dynamics observed in isotropic two-dimensional sheets were not predictive of the behavior in the whole heart. In 2-D the four cell models exhibited stable reentry, meandering spiral waves, and spiral-wave breakup. In the whole heart with fine structure, all simulation results exhibited complex dynamics reminiscent of fibrillation observed experimentally. In the whole heart without fine structure, anisotropy acted to destabilize filament dynamics although the number of filaments was reduced compared to the heart with structure. In addition, in isotropic hearts without structure the two cell models that exhibited meandering spiral waves in 2-D, stabilized into figure-of-eight surface patterns. We also studied the sensitivity of filament dynamics to computer system configuration and initial conditions. After large simulation times, different macroscopic results sometimes occurred across different system configurations, likely due to a lack of bitwise reproducibility. The study conclusions were insensitive to initial condition perturbations, however, the exact number of filaments over time and their trends were altered by these changes. In summary, we present the following new results. First, we provide a new cell model that resembles the surface patterns of VF in the rabbit heart both qualitatively and quantitatively. Second, filament dynamics in the whole heart cannot be predicted from spiral wave dynamics in 2-D and we identified anisotropy as one destabilizing factor. Third, the exact dynamics of filaments are sensitive to a variety of factors, so we suggest caution in their interpretation and their quantitative analyses.

Simultaneous unpinning of multiple vortices in two-dimensional excitable media

There are many examples of excitable media, such as the heart, that can show complex dynamics and where control is a challenging task. Heavy means like a strong electric shock are nowadays still necessary to control and terminate ventricular fibrillation (VF). It is known that heterogeneities in an excitable medium can stabilize the activity, e.g., spiral waves can pin to such obstacles. This might also be a reason for the persistence of VF and the difficulty to control it. Previous studies investigated systems with a single pinned spiral wave and demonstrated how the spiral can be unpinned. In this article, we extend this case and investigate a generic excitable system with multiple pinned spiral waves. We describe a control technique that allows the simultaneous unpinning of pinned spiral waves. Apart from theoretical considerations, we provide numerical evidence that the proposed technique is superior to the underdrive pacing method that has reportedly high success rates when applied to a single pinned spiral.

Real-time interactive simulations of large-scale systems on personal computers and cell phones: Toward patient-specific heart modeling and other applications

Cardiac dynamics modeling has been useful for studying and treating arrhythmias. However, it is a multiscale problem requiring the solution of billions of differential equations describing the complex electrophysiology of interconnected cells. Therefore, large-scale cardiac modeling has been limited to groups with access to supercomputers and clusters. Many areas of computational science face similar problems where computational costs are too high for personal computers so that supercomputers or clusters currently are necessary. Here, we introduce a new approach that makes high-performance simulation of cardiac dynamics and other large-scale systems like fluid flow and crystal growth accessible to virtually anyone with a modest computer. For cardiac dynamics, this approach will allow not only scientists and students but also physicians to use physiologically accurate modeling and simulation tools that are interactive in real time, thereby making diagnostics, research, and education available to a broader audience and pushing the boundaries of cardiac science.

Twisted scroll wave dynamics: partially pinned waves in excitable chemical media

We present an investigation of the dynamics of scroll waves that are partially pinned to inert cylindrical obstacles of varying lengths and diameters in three-dimensional Belousov-Zhabotinsky excitable media. Experiments are carried out in which a scroll wave is initiated with a special orientation to be partially pinned to the obstacle. Numerical simulations with the Oregonator model are also carried out, where the obstacle is placed in the region of the core of a preexisting freely rotating scroll wave. In both cases, the effect of the obstacle on the wave dynamics is almost immediately observable, such that after the first revolution of the wave, the pinned region of the scroll wave has a longer period than that of the freely rotating scroll wave. The dependence of the scroll wave period on the obstacle position gives rise to a transition from a straight scroll wave to a twisted scroll wave in the pinned region, while the form of the freely rotating wave remains unchanged. The twisted scroll wave arises from the interaction of the freely rotating scroll wave with the obstacle, giving rise to a pinned twisted wave with the same period. The twisted scroll wave gradually advances, displacing the slower untwisted scroll wave until the scroll wave helically wraps around the entire obstacle. At this point, the period of the entire wave has a single value equal to that of the freely rotating scroll wave. The time for the transition to the twisted wave structure increases when either the obstacle length is increased or the obstacle diameter is decreased, while the average speed of the development increases with both the obstacle length and diameter. After the transition, the twisted wave remains stable, with its structure depending on the obstacle diameter - the larger the diameter, the shorter the helical pitch but the higher the twist rate.

Real-time optical manipulation of cardiac conduction in intact hearts

Key points

Although optogenetics has clearly demonstrated the feasibility of cardiac manipulation, current optical stimulation strategies lack the capability to react acutely to ongoing cardiac wave dynamics.

Here, we developed an all‐optical platform to monitor and control electrical activity in real‐time.

The methodology was applied to restore normal electrical activity after atrioventricular block and to manipulate the intraventricular propagation of the electrical wavefront.

The closed‐loop approach was also applied to simulate a re‐entrant circuit across the ventricle.

The development of this innovative optical methodology provides the first proof‐of‐concept that a real‐time all‐optical stimulation can control cardiac rhythm in normal and abnormal conditions.

Abstract

Optogenetics has provided new insights in cardiovascular research, leading to new methods for cardiac pacing, resynchronization therapy and cardioversion. Although these interventions have clearly demonstrated the feasibility of cardiac manipulation, current optical stimulation strategies do not take into account cardiac wave dynamics in real time. Here, we developed an all‐optical platform complemented by integrated, newly developed software to monitor and control electrical activity in intact mouse hearts. The system combined a wide‐field mesoscope with a digital projector for optogenetic activation. Cardiac functionality could be manipulated either in free‐run mode with submillisecond temporal resolution or in a closed‐loop fashion: a tailored hardware and software platform allowed real‐time intervention capable of reacting within 2 ms. The methodology was applied to restore normal electrical activity after atrioventricular block, by triggering the ventricle in response to optically mapped atrial activity with appropriate timing. Real‐time intraventricular manipulation of the propagating electrical wavefront was also demonstrated, opening the prospect for real‐time resynchronization therapy and cardiac defibrillation. Furthermore, the closed‐loop approach was applied to simulate a re‐entrant circuit across the ventricle demonstrating the capability of our system to manipulate heart conduction with high versatility even in arrhythmogenic conditions. The development of this innovative optical methodology provides the first proof‐of‐concept that a real‐time optically based stimulation can control cardiac rhythm in normal and abnormal conditions, promising a new approach for the investigation of the (patho)physiology of the heart.

Although optogenetics has clearly demonstrated the feasibility of cardiac manipulation, current optical stimulation strategies lack the capability to react acutely to ongoing cardiac wave dynamics.

Here, we developed an all‐optical platform to monitor and control electrical activity in real‐time.

The methodology was applied to restore normal electrical activity after atrioventricular block and to manipulate the intraventricular propagation of the electrical wavefront.

The closed‐loop approach was also applied to simulate a re‐entrant circuit across the ventricle.

The development of this innovative optical methodology provides the first proof‐of‐concept that a real‐time all‐optical stimulation can control cardiac rhythm in normal and abnormal conditions.

Interaction of phase singularities on the spiral wave tail: reconsideration of capturing the excitable gap

The action mechanism of stimulation toward spiral waves (SWs) owing to the complex excitation patterns that occur just after point stimulation has not yet been experimentally clarified. This study sought to test our hypothesis that the effect of capturing excitable gap of SWs by stimulation can also be explained as the interaction of original phase singularity (PS) and PSs induced by the stimulation on the wave tail (WT) of the original SW. Phase variance analysis was used to quantitatively analyze the postshock PS trajectories. In a two-dimensional subepicardial layer of Langendorff-perfused rabbit hearts, optical mapping was used to record the excitation pattern during stimulation. After a SW was induced by S1–S2 shock, single biphasic point stimulation S3 was applied. In 70 of the S1-S2-S3 stimulation episodes applied on 6 hearts, the original PS was clearly observed just before the S3 point stimulation in 37 episodes. Pairwise PSs were newly induced by the S3 in 20 episodes. The original PS collided with the newly induced PSs in 16 episodes; otherwise, they did not interact with the original PS. SW shift occurred most efficiently when the S3 shock was applied at the relative refractory period, and PS shifted in the direction of the WT. In conclusion, quantitative tracking of PS clarified that stimulation in desirable conditions induces pairwise PSs on WT and that the collision of PSs causes SW shift along the WT. The results of this study indicate the importance of the interaction of shock-induced excitation with the WT for effective stimulation.

NEW & NOTEWORTHY The quantitative analysis of spiral wave dynamics during stimulation clarified the action mechanism of capturing the excitable gap, i.e., the induction of pairwise phase singularities on the wave tail and spiral wave shift along the wave tail as a result of these interactions. The importance of the wave tail for effective stimulation was revealed.

Electromechanical vortex filaments during cardiac fibrillation

The self-organized dynamics of vortex-like rotating waves, which are also known as scroll waves, are the basis of the formation of complex spatiotemporal patterns in many excitable chemical and biological systems. In the heart, filament-like phase singularities that are associated with three-dimensional scroll waves are considered to be the organizing centres of life-threatening cardiac arrhythmias. The mechanisms that underlie the onset, maintenance and control of electromechanical turbulence in the heart are inherently three-dimensional phenomena. However, it has not previously been possible to visualize the three-dimensional spatiotemporal dynamics of scroll waves inside cardiac tissues. Here we show that three-dimensional mechanical scroll waves and filament-like phase singularities can be observed deep inside the contracting heart wall using high-resolution four-dimensional ultrasound-based strain imaging. We found that mechanical phase singularities co-exist with electrical phase singularities during cardiac fibrillation. We investigated the dynamics of electrical and mechanical phase singularities by simultaneously measuring the membrane potential, intracellular calcium concentration and mechanical contractions of the heart. We show that cardiac fibrillation can be characterized using the three-dimensional spatiotemporal dynamics of mechanical phase singularities, which arise inside the fibrillating contracting ventricular wall. We demonstrate that electrical and mechanical phase singularities show complex interactions and we characterize their dynamics in terms of trajectories, topological charge and lifetime. We anticipate that our findings will provide novel perspectives for non-invasive diagnostic imaging and therapeutic applications.

Dynamics of scroll waves in a cylinder jacket geometry

The dynamics of scroll waves in a narrow cylinder jacket-shaped reactor is investigated experimentally by optical tomography. The fate of the scroll waves of excitation in the Belousov-Zhabotinsky reaction depends on the thickness of the cylinder jacket. While at sufficiently wide cylinder jackets vertically oriented scroll waves remain stable, the probability that the filament of a scroll hits a lateral wall increases as the cylinder jacket narrows. This may lead to the rupture of the initial filament and pinning of the filament ends at the lateral walls. Filaments that pin to opposite lateral walls shrink and reorient to a horizontal orientation; such a reorientation corresponds to a transition from an intramural to a transmural scroll wave. The kinetics of the reorientation and shrinkage of the scrolls were studied. Furthermore, we find that no new filaments were generated upon collision of excitation waves at the side of the cylinder jacket opposite to the scroll wave. Thus, under the studied conditions, we do not observe any new generation of filaments due to a phenomenon like reentry.

Critical phase transitions during ablation of atrial fibrillation

Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia with significant morbidity and mortality. Pharmacological agents are not very effective in the management of AF. Therefore, ablation procedures have become the mainstay of AF management. The irregular and seemingly chaotic atrial activity in AF is caused by one or more meandering spiral waves. Previously, we have shown the presence of sudden rhythm organization during ablation of persistent AF. We hypothesize that the observed transitions from a disorganized to an organized rhythm is a critical phase transition. Here, we explore this hypothesis by simulating ablation in an anatomically-correct 3D AF model. In 722 out of 2160 simulated ablation, at least one sudden transition from AF to an organized rhythm (flutter) was noted (33%). They were marked by a sudden decrease in the cycle length entropy and increase in the mean cycle length. At the same time, the number of reentrant wavelets decreased from 2.99 ± 0.06 in AF to 1.76 ± 0.05 during flutter, and the correlation length scale increased from 13.3 ± 1.0 mm to 196.5 ± 86.6 mm (both P < 0.0001). These findings are consistent with the hypothesis that transitions from AF to an anatomical flutter behave as phase transitions in complex non-equilibrium dynamical systems with flutter acting as an absorbing state. Clinically, the facilitation of phase transition should be considered a novel mechanism of ablation and may help to design effective ablation strategies.

Instantaneous Transfer Entropy for the Study of Cardiovascular and Cardiorespiratory Nonstationary Dynamics

OBJECTIVE

Measures of transfer entropy (TE) quantify the direction and strength of coupling between two complex systems. Standard approaches assume stationarity of the observations, and therefore are unable to track time-varying changes in nonlinear information transfer with high temporal resolution. In this study, we aim to define and validate novel instantaneous measures of TE to provide an improved assessment of complex nonstationary cardiorespiratory interactions.

METHODS

We here propose a novel instantaneous point-process TE (ipTE) and validate its assessment as applied to cardiovascular and cardiorespiratory dynamics. In particular, heartbeat and respiratory dynamics are characterized through discrete time series, and modeled with probability density functions predicting the time of the next physiological event as a function of the past history. Likewise, nonstationary interactions between heartbeat and blood pressure dynamics are characterized as well. Furthermore, we propose a new measure of information transfer, the instantaneous point-process information transfer (ipInfTr), which is directly derived from point-process-based definitions of the Kolmogorov-Smirnov distance.

RESULTS AND CONCLUSION

Analysis on synthetic data, as well as on experimental data gathered from healthy subjects undergoing postural changes confirms that ipTE, as well as ipInfTr measures are able to dynamically track changes in physiological systems coupling.

SIGNIFICANCE

This novel approach opens new avenues in the study of hidden, transient, nonstationary physiological states involving multivariate autonomic dynamics in cardiovascular health and disease. The proposed method can also be tailored for the study of complex multisystem physiology (e.g., brain-heart or, more in general, brain-body interactions).

Dynamics of spatiotemporal line defects and chaos control in complex excitable systems

Spatiotemporal pattern formation governs dynamics and functions in various biological systems. In the heart, excitable waves can form complex oscillatory and chaotic patterns even at an abnormally higher frequency than normal heart beats, which increase the risk of fatal heart conditions by inhibiting normal blood circulation. Previous studies suggested that line defects (nodal lines) play a critical role in stabilizing those undesirable patterns. However, it remains unknown if the line defects are static or dynamically changing structures in heart tissue. Through in vitro experiments of heart tissue observation, we reveal the spatiotemporal dynamics of line defects in rotating spiral waves. We combined a novel signaling over-sampling technique with a multi-dimensional Fourier analysis, showing that line defects can translate, merge, collapse and form stable singularities with even and odd parity while maintaining a stable oscillation of the spiral wave in the tissue. These findings provide insights into a broad class of complex periodic systems, with particular impact to the control and understanding of heart diseases.

Spatiotemporal Progression of Early Human Ventricular Fibrillation

Objectives

The objective of this study was to evaluate the spatio-temporal organization and progression of human ventricular fibrillation (VF) in the left (LV) and right (RV) ventricles.

Background

Studies suggest that localized sources contribute to VF maintenance, but the evolution of VF episodes has not been quantified.

Methods

Synchrony between electrograms recorded from 25 patients with induced VF is computed and used to define the Asynchronous Index (ASI), indicating regions which are out-of-step with surrounding tissue. Computer simulations show that ASI can identify the location of VF-maintaining sources, where larger values of ASI_max correlate with more stable sources.

Results

Automated synchrony analysis shows elevated values of ASI in a majority of self-terminating episodes (LV: 8/9, RV: 7/8) and sustained episodes (LV: 11/11, RV: 12/12). The locations of ASI_max in sustained episodes co-localize with rotor cores when rotational activity is simultaneously present in phase maps (LV: 8/8, RV: 5/7, p<.05). The distribution of ASI_max differentiates self-terminating from sustained episodes (mean ASI_max = 0.60±0.14 and 0.70±0.16, respectively; p=0.01). Across sustained episodes the LV exhibits an increase in ASI_max with time.

Conclusions

Quantitative analysis identifies localized asynchronous regions that correlate with sources in VF, with sustained episodes evolving to exhibit more stable activation in the LV. This successive increase in stability indicates a stabilizing agent may be responsible for perpetuating fibrillation in a "migrate-and-capture" mechanism in the LV.

Arrhythmia Vulnerability in Diabetic Cardiac Tissue is Species-Dependent: Effects of I KATP, Uncoupling, and Connexin Lateralization

Amongst the complications of diabetes is arrhythmia, the risk of which depends on multiple factors. This study was designed to investigate several factors, including the effects of ATP-sensitive potassium current, lateralized connexins, and gap junction uncoupling. ATP-sensitive potassium channel (I _KATP) opening is caused by ischemia, which can occur in diabetic or non-diabetic hearts. I _KATP opening was simulated in this work to determine if the risk of ischemia-induced arrhythmias is affected by diabetes. Simulations were performed using healthy and diabetic models of rat and rabbit ventricle. Results showed that the diabetic rat model is less vulnerable to reentrant arrhythmia than the healthy rat model. The diabetic rabbit model was more vulnerable to reentrant arrhythmia than the healthy rabbit model. In both rabbit models, the vulnerability increased as the gap junctional coupling decreased. Opening of I _KATP resulted in larger window of vulnerability. Conduction reserve was simulated based on 1D simulations for both rat and rabbit models. There was no difference between rat and rabbit conduction reserve. Our results showed that the simulation results are model-dependent, i.e., results from the rabbit model are similar to human clinical data, while the results from the rat model contradict human clinical observations, suggesting a significant species-dependence in arrhythmia vulnerability in the diabetic heart.

Clinical Role of Dominant Frequency Measurements in Atrial Fibrillation Ablation - A Systematic Review

Introduction

Experimental data strongly supports a role for high-frequency sources in the perpetuation of atrial fibrillation, it follows that identification of areas exhibiting spectra containing high dominant frequencies (DF) may represent perpetuating sources and targeted elimination might terminate AF. The aim of this review is to present and critically appraise the literature on DF studied in association with AF ablation.

Methods And Results

A systematic review was done including the PubMed (MEDLINE), Cochrane Central Register of Controlled Trials (Central), Scientific Electronic Library Online (SciELO), and HighWire Press databases. The searches were made by combining the terms "Dominant Frequency", "Atrial Fibrillation", and "Catheter Ablation" and their translations for the English and non-English based databases. Ten articles were selected from a total of 327 articles found after the initial search. The ablation strategy varied, most studies performed pulmonary vein isolation alone or associated with complex fractionated atrial electrogram ablation with or without an additional intervention. The use or not of DF sites as ablation target was distinguishable between the articles. Four articles ablated DF sites as a major intervention or in addition to a traditional approach. The remaining 6 articles assessed DF sites pre and post ablation and associated these data with clinical outcome.

Conclusion

No prior study has systematically comprised information for clinical use of DF. The current literature supports global DF as a useful marker of ablation outcome; however direct intervention targeting DF appears premature with mixed results and too few studies.

Rat Models of Ventricular Fibrillation Following Acute Myocardial Infarction

A number of animal models have been designed in order to unravel the underlying mechanisms of acute ischemia-induced arrhythmias and to test compounds and interventions for antiarrhythmic therapy. This is important as acute myocardial infarction (AMI) continues to be the major cause of sudden cardiac death, and we are yet to discover safe and effective treatments of the lethal arrhythmias occurring in the acute setting. Animal models therefore continue to be relevant for our understanding and treatment of acute ischemic arrhythmias. This review discusses the applicability of the rat as a model for ventricular arrhythmias occurring during the acute phase of AMI. It provides a description of models developed, advantages and disadvantages of rats, as well as an overview of the most important interventions investigated and the relevance for human pathophysiology.

Robustness of free and pinned spiral waves against breakup by electrical forcing in excitable chemical media

We present an investigation on the breakup of free and pinned spiral waves under an applied electrical current in the Belousov-Zhabotinsky reaction. Spiral fronts propagating towards the negative electrode are decelerated. A breakup of the spiral waves occurs when some segments of the fronts are stopped by a sufficiently strong electrical current. In the absence of obstacles (i.e., free spiral waves), the critical value of the electrical current for the wave breakup increases with the excitability of the medium. For spiral waves pinned to circular obstacles, the critical electrical current increases with the obstacle diameter. Analysis of spiral dynamics shows that the enhancement of the robustness against the breakup of both free and pinned spiral waves is originated by the increment of wave speed when either the excitability is strengthened or the obstacle size is enlarged. The experimental findings are reproduced by numerical simulations using the Oregonator model. In addition, the simulations reveal that the robustness against the forced breakup increases with the activator level in both cases of free and pinned spiral waves.

Mechanisms of vortices termination in the cardiac muscle

We propose a solution to a long-standing problem: how to terminate multiple vortices in the heart, when the locations of their cores and their critical time windows are unknown. We scan the phases of all pinned vortices in parallel with electric field pulses (E-pulses). We specify a condition on pacing parameters that guarantees termination of one vortex. For more than one vortex with significantly different frequencies, the success of scanning depends on chance, and all vortices are terminated with a success rate of less than one. We found that a similar mechanism terminates also a free (not pinned) vortex. A series of about 500 experiments with termination of ventricular fibrillation by E-pulses in pig isolated hearts is evidence that pinned vortices, hidden from direct observation, are significant in fibrillation. These results form a physical basis needed for the creation of new effective low energy defibrillation methods based on the termination of vortices underlying fibrillation.

Murine Electrophysiological Models of Cardiac Arrhythmogenesis

Cardiac arrhythmias can follow disruption of the normal cellular electrophysiological processes underlying excitable activity and their tissue propagation as coherent wavefronts from the primary sinoatrial node pacemaker, through the atria, conducting structures and ventricular myocardium. These physiological events are driven by interacting, voltage-dependent, processes of activation, inactivation, and recovery in the ion channels present in cardiomyocyte membranes. Generation and conduction of these events are further modulated by intracellular Ca2+ homeostasis, and metabolic and structural change. This review describes experimental studies on murine models for known clinical arrhythmic conditions in which these mechanisms were modified by genetic, physiological, or pharmacological manipulation. These exemplars yielded molecular, physiological, and structural phenotypes often directly translatable to their corresponding clinical conditions, which could be investigated at the molecular, cellular, tissue, organ, and whole animal levels. Arrhythmogenesis could be explored during normal pacing activity, regular stimulation, following imposed extra-stimuli, or during progressively incremented steady pacing frequencies. Arrhythmic substrate was identified with temporal and spatial functional heterogeneities predisposing to reentrant excitation phenomena. These could arise from abnormalities in cardiac pacing function, tissue electrical connectivity, and cellular excitation and recovery. Triggering events during or following recovery from action potential excitation could thereby lead to sustained arrhythmia. These surface membrane processes were modified by alterations in cellular Ca2+ homeostasis and energetics, as well as cellular and tissue structural change. Study of murine systems thus offers major insights into both our understanding of normal cardiac activity and its propagation, and their relationship to mechanisms generating clinical arrhythmias.

Allometric scaling of electrical excitation and propagation in the mammalian heart

Variations in body mass impose constraints on the structure and function of mammalian species, including those of the cardiovascular system. Numerous biological processes, including cardiovascular parameters, have been shown to scale with body mass (BM) according to the law of allometric scaling: Y=Y =a∙BM^b (Y, biological process; a, normalization constant; b, scaling exponent, which in many instances is a multiple of ¼). These parameters include heart and breathing rates, intervals and subintervals of the electrocardiogram (ECG), action potential duration (APD), metabolic rate, and temporal properties of ventricular fibrillation. For instance, the hierarchical branching networks of the vascular system, and of the specialized conduction system in the heart have been proposed to be important determinants of allometric scaling. A global and unifying molecular mechanism of allometric scaling has not been put forth, but changes in gene expression have been proposed to play an important role. Even though it is accepted that differences in body size have cardiovascular effects, the use of scaling in the clinical setting is limited. An increase in the clinical utilization of scaling is thought to lead to improved cardiovascular disease diagnosis and management in patients.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

In vitro photoacoustic sensing of calcium dynamics with Arsenazo III

Imaging of cellular electric potential via calcium-ion sensitive contrast agents is a useful tool, but current it lacks sufficient depth penetration. We explore contrast-enhanced photoacoustic (PA) imaging, using Arsenazo III dye, to visualize cardiac myocyte depolarization in vitro. Phantom results show strong linearity of PA signal with dye concentration (R ² > 0.95), and agree spectrally with extinction measurements with varying calcium concentration. Cell studies indicate a significant (> 100-fold) increase in PA signal for dye-treated cells, as well as a 10-fold increase in peak-to-peak variation during a 30-second window. This suggests contrast-enhanced PA imaging may have sufficient sensitivity and specificity for depth-resolved visualization of tissue depolarization in real-time.

Linked and knotted chimera filaments in oscillatory systems

While the existence of stable knotted and linked vortex lines has been established in many experimental and theoretical systems, their existence in oscillatory systems and systems with nonlocal coupling has remained elusive. Here, we present strong numerical evidence that stable knots and links such as trefoils and Hopf links do exist in simple, complex, and chaotic oscillatory systems if the coupling between the oscillators is neither too short ranged nor too long ranged. In this case, effective repulsive forces between vortex lines in knotted and linked structures stabilize curvature-driven shrinkage observed for single vortex rings. In contrast to real fluids and excitable media, the vortex lines correspond to scroll wave chimeras [synchronized scroll waves with spatially extended (tubelike) unsynchronized filaments], a prime example of spontaneous synchrony breaking in systems of identical oscillators. In the case of complex oscillatory systems, this leads to a topological superstructure combining knotted filaments and synchronization defect sheets.

Phase-locked scroll waves defy turbulence induced by negative filament tension

Scroll waves in a three-dimensional media may develop into turbulence due to negative tension of the filament. Such negative tension-induced instability of scroll waves has been observed in the Belousov-Zhabotinsky reaction systems. Here we propose a method to restabilize scroll wave turbulence caused by negative tension in three-dimensional chemical excitable media using a circularly polarized (rotating) external field. The stabilization mechanism is analyzed in terms of phase-locking caused by the external field, which makes the effective filament tension positive. The phase-locked scroll waves that have positive tension and higher frequency defy the turbulence and finally restore order. A linear theory for the change of filament tension caused by a generic rotating external field is presented and its predictions closely agree with numerical simulations.

A Computational Study of the Factors Influencing the PVC-Triggering Ability of a Cluster of Early Afterdepolarization-Capable Myocytes

Premature ventricular complexes (PVCs), which are abnormal impulse propagations in cardiac tissue, can develop because of various reasons including early afterdepolarizations (EADs). We show how a cluster of EAD-generating cells (EAD clump) can lead to PVCs in a model of cardiac tissue, and also investigate the factors that assist such clumps in triggering PVCs. In particular, we study, through computer simulations, the effects of the following factors on the PVC-triggering ability of an EAD clump: (1) the repolarization reserve (RR) of the EAD cells; (2) the size of the EAD clump; (3) the coupling strength between the EAD cells in the clump; and (4) the presence of fibroblasts in the EAD clump. We find that, although a low value of RR is necessary to generate EADs and hence PVCs, a very low value of RR leads to low-amplitude EAD oscillations that decay with time and do not lead to PVCs. We demonstrate that a certain threshold size of the EAD clump, or a reduction in the coupling strength between the EAD cells, in the clump, is required to trigger PVCs. We illustrate how randomly distributed inexcitable obstacles, which we use to model collagen deposits, affect PVC-triggering by an EAD clump. We show that the gap-junctional coupling of fibroblasts with myocytes can either assist or impede the PVC-triggering ability of an EAD clump, depending on the resting membrane potential of the fibroblasts and the coupling strength between the myocyte and fibroblasts. We also find that the triggering of PVCs by an EAD clump depends sensitively on factors like the pacing cycle length and the distribution pattern of the fibroblasts.

A Computer Simulation Study of Anatomy Induced Drift of Spiral Waves in the Human Atrium

The interaction of spiral waves of excitation with atrial anatomy remains unclear. This simulation study isolates the role of atrial anatomical structures on spiral wave spontaneous drift in the human atrium. We implemented realistic and idealised 3D human atria models to investigate the functional impact of anatomical structures on the long-term (∼40 s) behaviour of spiral waves. The drift of a spiral wave was quantified by tracing its tip trajectory, which was correlated to atrial anatomical features. The interaction of spiral waves with the following idealised geometries was investigated: (a) a wedge-like structure with a continuously varying atrial wall thickness; (b) a ridge-like structure with a sudden change in atrial wall thickness; (c) multiple bridge-like structures consisting of a bridge connected to the atrial wall. Spiral waves drifted from thicker to thinner regions and along ridge-like structures. Breakthrough patterns caused by pectinate muscles (PM) bridges were also observed, albeit infrequently. Apparent anchoring close to PM-atrial wall junctions was observed. These observations were similar in both the realistic and the idealised models. We conclude that spatially altering atrial wall thickness is a significant cause of drift of spiral waves. PM bridges cause breakthrough patterns and induce transient anchoring of spiral waves.

Activator-inhibitor coupling between Rho signalling and actin assembly makes the cell cortex an excitable medium

Animal cell cytokinesis results from patterned activation of the small GTPase Rho, which directs assembly of actomyosin in the equatorial cortex. Cytokinesis is restricted to a portion of the cell cycle following anaphase onset in which the cortex is responsive to signals from the spindle. We show that shortly after anaphase onset oocytes and embryonic cells of frogs and echinoderms exhibit cortical waves of Rho activity and F-actin polymerization. The waves are modulated by cyclin-dependent kinase 1 (Cdk1) activity and require the Rho GEF (guanine nucleotide exchange factor), Ect2. Surprisingly, during wave propagation, while Rho activity elicits F-actin assembly, F-actin subsequently inactivates Rho. Experimental and modeling results show that waves represent excitable dynamics of a reaction diffusion system with Rho as the activator and F-actin the inhibitor. We propose that cortical excitability explains fundamental features of cytokinesis including its cell cycle regulation.

A patient-specific model of virtual ablation for atrial fibrillation

The purpose of this study was to propose a patient-specific model of atrial fibrillation (AF) and apply it to virtual radiofrequency ablation (RFA). We obtained patient-specific geometries of the left atrium (LA) from CT data and constructed three-dimensional (3D) simulation models. A bidomain Courtemanche model was used to simulate the 3D electric waves on the LA surface, and an S1-S2 protocol was applied to induce AF in the model. To identify scar areas in the models, we converted clinically measured voltage data on the LA surface to the scar maps of the simulation model. Then, after initiation of AF, we applied the virtual ablation scheme to the model and investigated whether the AF was terminated by the scheme. The computed results of AF and ablation were similar to those of clinical observation, providing a clinically important simulation method for preclinical virtual trials of AF treatment.