Electromechanical vortex filaments during cardiac fibrillation

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.

Optical mapping and optogenetics in cardiac electrophysiology research and therapy: a state-of-the-art review

State-of-the-art innovations in optical cardiac electrophysiology are significantly enhancing cardiac research. A potential leap into patient care is now on the horizon. Optical mapping, using fluorescent probes and high-speed cameras, offers detailed insights into cardiac activity and arrhythmias by analysing electrical signals, calcium dynamics, and metabolism. Optogenetics utilizes light-sensitive ion channels and pumps to realize contactless, cell-selective cardiac actuation for modelling arrhythmia, restoring sinus rhythm, and probing complex cell-cell interactions. The merging of optogenetics and optical mapping techniques for 'all-optical' electrophysiology marks a significant step forward. This combination allows for the contactless actuation and sensing of cardiac electrophysiology, offering unprecedented spatial-temporal resolution and control. Recent studies have performed all-optical imaging ex vivo and achieved reliable optogenetic pacing in vivo, narrowing the gap for clinical use. Progress in optical electrophysiology continues at pace. Advances in motion tracking methods are removing the necessity of motion uncoupling, a key limitation of optical mapping. Innovations in optoelectronics, including miniaturized, biocompatible illumination and circuitry, are enabling the creation of implantable cardiac pacemakers and defibrillators with optoelectrical closed-loop systems. Computational modelling and machine learning are emerging as pivotal tools in enhancing optical techniques, offering new avenues for analysing complex data and optimizing therapeutic strategies. However, key challenges remain including opsin delivery, real-time data processing, longevity, and chronic effects of optoelectronic devices. This review provides a comprehensive overview of recent advances in optical mapping and optogenetics and outlines the promising future of optics in reshaping cardiac electrophysiology and therapeutic strategies.

Non-Gaussian anomalous diffusion of optical vortices

Anomalous diffusion of different particlelike entities, the deviation from typical Brownian motion, is ubiquitous in complex physical and biological systems. While optical vortices move randomly in evolving speckle fields, optical vortices have only been observed to exhibit pure Brownian motion in random speckle fields. Here we present direct experimental evidence of the anomalous diffusion of optical vortices in temporally varying speckle patterns from multiple-scattering viscoelastic media. Moreover, we observe two characteristic features, i.e., the self-similarity and the antipersistent correlation of the optical vortex motion, indicating that the mechanism of the observed subdiffusion of optical vortices can only be attributed to fractional Brownian motion (FBM). We further demonstrate that the vortex displacements exhibit a non-Gaussian heavy-tailed distribution. Additionally, we modulate the extent of subdiffusion, such as diffusive scaling exponents, and the non-Gaussianity of optical vortices by altering the viscoelasticity of samples. The discovery of the complex FBM but non-Gaussian subdiffusion of optical vortices may not only offer insight into certain fundamental physics, including the anomalous diffusion of vortices in fluids and the decoupling between Brownianity and Gaussianity, but also suggest a strong potential for utilizing optical vortices as tracers in microrheology instead of the introduced exogenous probe particles in particle tracking microrheology.

Cardiac multiscale bioimaging: from nano- through micro- to mesoscales

Cardiac multiscale bioimaging is an emerging field that aims to provide a comprehensive understanding of the heart and its functions at various levels, from the molecular to the entire organ. It combines both physiologically and clinically relevant dimensions: from nano- and micrometer resolution imaging based on vibrational spectroscopy and high-resolution microscopy to assess molecular processes in cardiac cells and myocardial tissue, to mesoscale structural investigations to improve the understanding of cardiac (patho)physiology. Tailored super-resolution deep microscopy with advanced proteomic methods and hands-on experience are thus strategically combined to improve the quality of cardiovascular research and support future medical decision-making by gaining additional biomolecular information for translational and diagnostic applications.

Pulsating Active Matter

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

Dissolution of spiral wave's core using cardiac optogenetics

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

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.

Unsupervised deep network for image texture transformation: Improving the quality of cross-correlation analysis and mechanical vortex visualisation during cardiac fibrillation

Visualisation of cardiac fibrillation plays a very considerable role in cardiophysiological study and clinical applications. One of the ways to obtain the image of these phenomena is the registration of mechanical displacement fields reflecting the track from electrical activity. In this work, we read these fields using cross-correlation analysis from the video of open pig's epicardium at the start of fibrillation recorded with electrocardiogram. However, the quality of obtained displacement fields remains low due to the weak pixels heterogeneity of the frames. It disables to see more clearly such interesting phenomena as mechanical vortexes that underline the mechanical dysfunction of fibrillation. The applying of chemical or mechanical markers to solve this problem can affect the course of natural processes and falsify the results. Therefore, we developed a novel scheme of an unsupervised deep neural network that is based on the state-of-art positional coding technology for a multilayer perceptron. This network enables to generate a couple of frames with a more heterogeneous pixel texture, that is more suitable for cross-correlation analysis methods, from two consecutive frames. The novel network scheme was tested on synthetic pairs of images with different texture heterogeneity and frequency of displacement fields and also it was compared with different filters on our cardiac tissue image dataset. The testing showed that the displacement fields obtained with our method are closer to the ground truth than those which were computed only with the cross-correlation analysis in low contrast images case where filtering is impossible. Moreover, our model showed the best results comparing with the one of the popular filter CLAHE on our dataset. As a result, using our approach, it was possible to register more clearly a mechanical vortex on the epicardium at the start of fibrillation continuously for several milliseconds for the first time.

Virtual blebbistatin: A robust and rapid software approach to motion artifact removal in optical mapping of cardiomyocytes

Fluorescent reporters of cardiac electrophysiology provide valuable information on heart cell and tissue function. However, motion artifacts caused by cardiac muscle contraction interfere with accurate measurement of fluorescence signals. Although drugs such as blebbistatin can be applied to stop cardiac tissue from contracting by uncoupling calcium-contraction, their usage prevents the study of excitation-contraction coupling and, as we show, impacts cellular structure. We therefore developed a robust method to remove motion computationally from images of contracting cardiac muscle and to map fluorescent reporters of cardiac electrophysiological activity onto images of undeformed tissue. When validated on cardiomyocytes derived from human induced pluripotent stem cells (iPSCs), in both monolayers and engineered tissues, the method enabled efficient and robust reduction of motion artifact. As with pharmacologic approaches using blebbistatin for motion removal, our algorithm improved the accuracy of optical mapping, as demonstrated by spatial maps of calcium transient decay. However, unlike pharmacologic motion removal, our computational approach allowed direct analysis of calcium-contraction coupling. Results revealed calcium-contraction coupling to be more uniform across cells within engineered tissues than across cells in monolayer culture. The algorithm shows promise as a robust and accurate tool for optical mapping studies of excitation-contraction coupling in heart tissue.

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

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

Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing

The large-scale activity of the human brain exhibits rich and complex patterns, but the spatiotemporal dynamics of these patterns and their functional roles in cognition remain unclear. Here by characterizing moment-by-moment fluctuations of human cortical functional magnetic resonance imaging signals, we show that spiral-like, rotational wave patterns (brain spirals) are widespread during both resting and cognitive task states. These brain spirals propagate across the cortex while rotating around their phase singularity centres, giving rise to spatiotemporal activity dynamics with non-stationary features. The properties of these brain spirals, such as their rotational directions and locations, are task relevant and can be used to classify different cognitive tasks. We also demonstrate that multiple, interacting brain spirals are involved in coordinating the correlated activations and de-activations of distributed functional regions; this mechanism enables flexible reconfiguration of task-driven activity flow between bottom-up and top-down directions during cognitive processing. Our findings suggest that brain spirals organize complex spatiotemporal dynamics of the human brain and have functional correlates to cognitive processing.

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

Simultaneous Widefield Voltage and Dye-Free Optical Mapping Quantifies Electromechanical Waves in Human Induced Pluripotent Stem Cell-Derived Cardiomyocytes

Coupled electromechanical waves define a heart's function in health and diseases. Optical mapping of electrical waves using fluorescent labels offers mechanistic insights into cardiac conduction abnormalities. Dye-free/label-free mapping of mechanical waves presents an attractive non-invasive alternative. In this study, we developed a simultaneous widefield voltage and interferometric dye-free optical imaging methodology that was used as follows: (1) to validate dye-free optical mapping for quantification of cardiac wave properties in human iPSC-cardiomyocytes (CMs); (2) to demonstrate low-cost optical mapping of electromechanical waves in hiPSC-CMs using recent near-infrared (NIR) voltage sensors and orders of magnitude cheaper miniature industrial CMOS cameras; (3) to uncover previously underexplored frequency- and space-varying parameters of cardiac electromechanical waves in hiPSC-CMs. We find similarity in the frequency-dependent responses of electrical (NIR fluorescence-imaged) and mechanical (dye-free-imaged) waves, with the latter being more sensitive to faster rates and showing steeper restitution and earlier appearance of wavefront tortuosity. During regular pacing, the dye-free-imaged conduction velocity and electrical wave velocity are correlated; both modalities are sensitive to pharmacological uncoupling and dependent on gap-junctional protein (connexins) determinants of wave propagation. We uncover the strong frequency dependence of the electromechanical delay (EMD) locally and globally in hiPSC-CMs on a rigid substrate. The presented framework and results offer new means to track the functional responses of hiPSC-CMs inexpensively and non-invasively for counteracting heart disease and aiding cardiotoxicity testing and drug development.

Optical mapping of contracting hearts

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

A Third Angular Momentum of Photons

Photons that acquire orbital angular momentum move in a helical path and are observed as a light ring. During helical motion, if a force is applied perpendicular to the direction of motion, an additional radial angular momentum is introduced, and alternate dark spots appear on the light ring. Here, a third, centrifugal angular momentum has been added by twisting the helical path further according to the three-step hierarchical assembly of helical organic nanowires. Attaining a third angular momentum is the theoretical limit for a photon. The additional angular momentum converts the dimensionless photon to a hollow spherical photon condensate with interactive dark regions. A stream of these photon condensates can interfere like a wave or disintegrate like matter, similar to the behavior of electrons.

Reconstructing in-depth activity for chaotic 3D spatiotemporal excitable media models based on surface data

Motivated by potential applications in cardiac research, we consider the task of reconstructing the dynamics within a spatiotemporal chaotic 3D excitable medium from partial observations at the surface. Three artificial neural network methods (a spatiotemporal convolutional long-short-term-memory, an autoencoder, and a diffusion model based on the U-Net architecture) are trained to predict the dynamics in deeper layers of a cube from observational data at the surface using data generated by the Barkley model on a 3D domain. The results show that despite the high-dimensional chaotic dynamics of this system, such cross-prediction is possible, but non-trivial and as expected, its quality decreases with increasing prediction depth.

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.

Guidelines for assessment of cardiac electrophysiology and arrhythmias in small animals

Cardiac arrhythmias are a major cause of morbidity and mortality worldwide. Although recent advances in cell-based models, including human-induced pluripotent stem cell-derived cardiomyocytes (iPSC-CM), are contributing to our understanding of electrophysiology and arrhythmia mechanisms, preclinical animal studies of cardiovascular disease remain a mainstay. Over the past several decades, animal models of cardiovascular disease have advanced our understanding of pathological remodeling, arrhythmia mechanisms, and drug effects and have led to major improvements in pacing and defibrillation therapies. There exist a variety of methodological approaches for the assessment of cardiac electrophysiology and a plethora of parameters may be assessed with each approach. This guidelines article will provide an overview of the strengths and limitations of several common techniques used to assess electrophysiology and arrhythmia mechanisms at the whole animal, whole heart, and tissue level with a focus on small animal models. We also define key electrophysiological parameters that should be assessed, along with their physiological underpinnings, and the best methods with which to assess these parameters.

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

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

The physics of heart rhythm disorders

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

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

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

Identifying locations susceptible to micro-anatomical reentry using a spatial network representation of atrial fibre maps

Micro-anatomical reentry has been identified as a potential driver of atrial fibrillation (AF). In this paper, we introduce a novel computational method which aims to identify which atrial regions are most susceptible to micro-reentry. The approach, which considers the structural basis for micro-reentry only, is based on the premise that the accumulation of electrically insulating interstitial fibrosis can be modelled by simulating percolation-like phenomena on spatial networks. Our results suggest that at high coupling, where micro-reentry is rare, the micro-reentrant substrate is highly clustered in areas where the atrial walls are thin and have convex wall morphology, likely facilitating localised treatment via ablation. However, as transverse connections between fibres are removed, mimicking the accumulation of interstitial fibrosis, the substrate becomes less spatially clustered, and the bias to forming in thin, convex regions of the atria is reduced, possibly restricting the efficacy of localised ablation. Comparing our algorithm on image-based models with and without atrial fibre structure, we find that strong longitudinal fibre coupling can suppress the micro-reentrant substrate, whereas regions with disordered fibre orientations have an enhanced risk of micro-reentry. With further development, these methods may be useful for modelling the temporal development of the fibrotic substrate on an individualised basis.

A machine-learning approach for long-term prediction of experimental cardiac action potential time series using an autoencoder and echo state networks

Computational modeling and experimental/clinical prediction of the complex signals during cardiac arrhythmias have the potential to lead to new approaches for prevention and treatment. Machine-learning (ML) and deep-learning approaches can be used for time-series forecasting and have recently been applied to cardiac electrophysiology. While the high spatiotemporal nonlinearity of cardiac electrical dynamics has hindered application of these approaches, the fact that cardiac voltage time series are not random suggests that reliable and efficient ML methods have the potential to predict future action potentials. This work introduces and evaluates an integrated architecture in which a long short-term memory autoencoder (AE) is integrated into the echo state network (ESN) framework. In this approach, the AE learns a compressed representation of the input nonlinear time series. Then, the trained encoder serves as a feature-extraction component, feeding the learned features into the recurrent ESN reservoir. The proposed AE-ESN approach is evaluated using synthetic and experimental voltage time series from cardiac cells, which exhibit nonlinear and chaotic behavior. Compared to the baseline and physics-informed ESN approaches, the AE-ESN yields mean absolute errors in predicted voltage 6-14 times smaller when forecasting approximately 20 future action potentials for the datasets considered. The AE-ESN also demonstrates less sensitivity to algorithmic parameter settings. Furthermore, the representation provided by the feature-extraction component removes the requirement in previous work for explicitly introducing external stimulus currents, which may not be easily extracted from real-world datasets, as additional time series, thereby making the AE-ESN easier to apply to clinical data.

Real-Time Optical Mapping of Contracting Cardiac Tissues With GPU-Accelerated Numerical Motion Tracking

Optical mapping of action potentials or calcium transients in contracting cardiac tissues are challenging because of the severe sensitivity of the measurements to motion. The measurements rely on the accurate numerical tracking and analysis of fluorescence changes emitted by the tissue as it moves, and inaccurate or no tracking can produce motion artifacts and lead to imprecise measurements that can prohibit the analysis of the data. Recently, it was demonstrated that numerical motion-tracking and -stabilization can effectively inhibit motion artifacts, allowing highly detailed simultaneous measurements of electrophysiological phenomena and tissue mechanics. However, the field of electromechanical optical mapping is still young and under development. To date, the technique is only used by a few laboratories, the processing of the video data is time-consuming and performed offline post-acquisition as it is associated with a considerable demand for computing power. In addition, a systematic review of numerical motion tracking algorithms applicable to optical mapping data is lacking. To address these issues, we evaluated 5 open-source numerical motion-tracking algorithms implemented on a graphics processing unit (GPU) and compared their performance when tracking and compensating motion and measuring optical traces in voltage- or calcium-sensitive optical mapping videos of contracting cardiac tissues. Using GPU-accelerated numerical motion tracking, the processing times necessary to analyze optical mapping videos become substantially reduced. We demonstrate that it is possible to track and stabilize motion and create motion-compensated optical maps in real-time with low-resolution (128 x 128 pixels) and high resolution (800 x 800 pixels) optical mapping videos acquired at 500 and 40 fps, respectively. We evaluated the tracking accuracies and motion-stabilization capabilities of the GPU-based algorithms on synthetic optical mapping videos, determined their sensitivity to fluorescence signals and noise, and demonstrate the efficacy of the Farnebäck algorithm with recordings of contracting human cardiac cell cultures and beating hearts from 3 different species (mouse, rabbit, pig) imaged with 4 different high-speed cameras. GPU-accelerated processing provides a substantial increase in processing speed, which could open the path for more widespread use of numerical motion tracking and stabilization algorithms during routine optical mapping studies.

Role of interatrial conduction in atrial fibrillation. Mechanistic insights from renewal theory-based fibrillatory dynamic analysis

Background

Interatrial conduction has been postulated to play an important role in atrial fibrillation (AF). The pathways involved in interatrial conduction during AF remain incompletely defined.

Objective

We recently showed physiological assessment of fibrillatory dynamics could be performed using renewal theory, which determines rates of phase singularity formation (λ_f) and destruction (λ_d). Using the renewal approach, we aimed to understand the role of the interatrial septum and other electrically coupled regions during AF.

Method

RENEWAL-AF is a prospective multicenter observational study recruiting AF ablation patients (ACTRN 12619001172190). We studied unipolar electrograms obtained from 16 biatrial locations prior to ablation using a 16-electrode Advisor HD Grid catheter. Renewal rate constants λ_f and λ_d were calculated, and the relationships between these rate constants in regions of interatrial connectivity were examined.

Results

Forty-one AF patients (28.5% female) were recruited. A positive linear correlation was observed between λ_f and λ_d (1) across the interatrial septum (λ_f r² = 0.5, P < .001, λ_d r² = 0.45, P < .001), (2) in regions connected by the Bachmann bundle (right atrial appendage–left atrial appendage λ_f r² = 0.29, P = .001; λ_d r² = 0.2, P = .008), and (3) across the inferior interatrial routes (cavotricuspid isthmus–left atrial septum λ_f r² = 0.67, P < .001; λ_d r² = 0.55, P < .001). Persistent AF status and left atrial volume were found to be important effect modifiers of the degree of interatrial renewal rate statistical correlation.

Conclusion

Our findings support the role of interseptal statistically determined electrical disrelation in sustaining AF. Additionally, renewal theory identified preferential conduction through specific interatrial pathways during fibrillation. These findings may be of importance in identifying clinically significant targets for ablation in AF patients.

Interaction of multiple spiral rotors in a reaction-diffusion system

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

Pacemaking function of two simplified cell models

Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

High resolution optical mapping of cardiac electrophysiology in pre-clinical models

Optical mapping of animal models is a widely used technique in pre-clinical cardiac research. It has several advantages over other methods, including higher spatial resolution, contactless recording and direct visualisation of action potentials and calcium transients. Optical mapping enables simultaneous study of action potential and calcium transient morphology, conduction dynamics, regional heterogeneity, restitution and arrhythmogenesis. In this dataset, we have optically mapped Langendorff perfused isolated whole hearts (mouse and guinea pig) and superfused isolated atria (mouse). Raw datasets (consisting of over 400 files) can be combined with open-source software for processing and analysis. We have generated a comprehensive post-processed dataset characterising the baseline cardiac electrophysiology in these widely used pre-clinical models. This dataset also provides reference information detailing the effect of heart rate, clinically used anti-arrhythmic drugs, ischaemia-reperfusion and sympathetic nervous stimulation on cardiac electrophysiology. The effects of these interventions can be studied in a global or regional manner, enabling new insights into the prevention and initiation of arrhythmia.

KHz-rate volumetric voltage imaging of the whole Zebrafish heart

Fast volumetric imaging is essential for understanding the function of excitable tissues such as those found in the brain and heart. Measuring cardiac voltage transients in tissue volumes is challenging, especially at the high spatial and temporal resolutions needed to give insight to cardiac function. We introduce a new imaging modality based on simultaneous illumination of multiple planes in the tissue and parallel detection with multiple cameras, avoiding compromises inherent in any scanning approach. The system enables imaging of voltage transients in situ, allowing us, for the first time to our knowledge, to map voltage activity in the whole heart volume at KHz rates. The high spatiotemporal resolution of our method enabled the observation of novel dynamics of electrical propagation through the zebrafish atrioventricular canal.

Understanding the origins of the basic equations of statistical fibrillatory dynamics

The mechanisms governing cardiac fibrillation remain unclear; however, it most likely represents a form of spatiotemporal chaos with conservative system dynamics. Renewal theory has recently been suggested as a statistical formulation with governing equations to quantify the formation and destruction of wavelets and rotors in fibrillatory dynamics. In this perspective Review, we aim to explain the origin of the renewal theory paradigm in spatiotemporal chaos. The ergodic nature of pattern formation in spatiotemporal chaos is demonstrated through the use of three chaotic systems: two classical systems and a simulation of cardiac fibrillation. The logistic map and the baker's transformation are used to demonstrate how the apparently random appearance of patterns in classical chaotic systems has macroscopic parameters that are predictable in a statistical sense. We demonstrate that the renewal theory approach developed for cardiac fibrillation statistically predicts pattern formation in these classical chaotic systems. Renewal theory provides governing equations to describe the apparently random formation and destruction of wavelets and rotors in atrial fibrillation (AF) and ventricular fibrillation (VF). This statistical framework for fibrillatory dynamics provides a holistic understanding of observed rotor and wavelet dynamics and is of conceptual significance in informing the clinical and mechanistic research of the rotor and multiple-wavelet mechanisms of AF and VF.

Methodology for Cross-Talk Elimination in Simultaneous Voltage and Calcium Optical Mapping Measurements With Semasbestic Wavelengths

Most cardiac arrhythmias at the whole heart level result from alteration of cell membrane ionic channels and intracellular calcium concentration ([Ca2+] i ) cycling with emerging spatiotemporal behavior through tissue-level coupling. For example, dynamically induced spatial dispersion of action potential duration, QT prolongation, and alternans are clinical markers for arrhythmia susceptibility in regular and heart-failure patients that originate due to changes of the transmembrane voltage (V m) and [Ca2+] i . We present an optical-mapping methodology that permits simultaneous measurements of the V m - [Ca2+] i signals using a single-camera without cross-talk, allowing quantitative characterization of favorable/adverse cell and tissue dynamical effects occurring from remodeling and/or drugs in heart failure. We demonstrate theoretically and experimentally in six different species the existence of a family of excitation wavelengths, we termed semasbestic, that give no change in signal for one dye, and thus can be used to record signals from another dye, guaranteeing zero cross-talk.

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

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

Rotor Localization and Phase Mapping of Cardiac Excitation Waves Using Deep Neural Networks

The analysis of electrical impulse phenomena in cardiac muscle tissue is important for the diagnosis of heart rhythm disorders and other cardiac pathophysiology. Cardiac mapping techniques acquire local temporal measurements and combine them to visualize the spread of electrophysiological wave phenomena across the heart surface. However, low spatial resolution, sparse measurement locations, noise and other artifacts make it challenging to accurately visualize spatio-temporal activity. For instance, electro-anatomical catheter mapping is severely limited by the sparsity of the measurements, and optical mapping is prone to noise and motion artifacts. In the past, several approaches have been proposed to create more reliable maps from noisy or sparse mapping data. Here, we demonstrate that deep learning can be used to compute phase maps and detect phase singularities in optical mapping videos of ventricular fibrillation, as well as in very noisy, low-resolution and extremely sparse simulated data of reentrant wave chaos mimicking catheter mapping data. The self-supervised deep learning approach is fundamentally different from classical phase mapping techniques. Rather than encoding a phase signal from time-series data, a deep neural network instead learns to directly associate phase maps and the positions of phase singularities with short spatio-temporal sequences of electrical data. We tested several neural network architectures, based on a convolutional neural network (CNN) with an encoding and decoding structure, to predict phase maps or rotor core positions either directly or indirectly via the prediction of phase maps and a subsequent classical calculation of phase singularities. Predictions can be performed across different data, with models being trained on one species and then successfully applied to another, or being trained solely on simulated data and then applied to experimental data. Neural networks provide a promising alternative to conventional phase mapping and rotor core localization methods. Future uses may include the analysis of optical mapping studies in basic cardiovascular research, as well as the mapping of atrial fibrillation in the clinical setting.

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.

The inspection paradox: An important consideration in the evaluation of rotor lifetimes in cardiac fibrillation

Background and Objective: Renewal theory is a statistical approach to model the formation and destruction of phase singularities (PS), which occur at the pivots of spiral waves. A common issue arising during observation of renewal processes is an inspection paradox, due to oversampling of longer events. The objective of this study was to characterise the effect of a potential inspection paradox on the perception of PS lifetimes in cardiac fibrillation. Methods: A multisystem, multi-modality study was performed, examining computational simulations (Aliev-Panfilov (APV) model, Courtmanche-Nattel model), experimentally acquired optical mapping Atrial and Ventricular Fibrillation (AF/VF) data, and clinically acquired human AF and VF. Distributions of all PS lifetimes across full epochs of AF, VF, or computational simulations, were compared with distributions formed from lifetimes of PS existing at 10,000 simulated commencement timepoints. Results: In all systems, an inspection paradox led towards oversampling of PS with longer lifetimes. In APV computational simulations there was a mean PS lifetime shift of +84.9% (95% CI, ± 0.3%) (p < 0.001 for observed vs overall), in Courtmanche-Nattel simulations of AF +692.9% (95% CI, ±57.7%) (p < 0.001), in optically mapped rat AF +374.6% (95% CI, ± 88.5%) (p = 0.052), in human AF mapped with basket catheters +129.2% (95% CI, ±4.1%) (p < 0.05), human AF-HD grid catheters 150.8% (95% CI, ± 9.0%) (p < 0.001), in optically mapped rat VF +171.3% (95% CI, ±15.6%) (p < 0.001), in human epicardial VF 153.5% (95% CI, ±15.7%) (p < 0.001). Conclusion: Visual inspection of phase movies has the potential to systematically oversample longer lasting PS, due to an inspection paradox. An inspection paradox is minimised by consideration of the overall distribution of PS lifetimes.

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

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

Stop the beat to see the rhythm: excitation-contraction uncoupling in cardiac research

Optical mapping is an imaging technique that is extensively used in cardiovascular research, wherein parameter-sensitive fluorescent indicators are used to study the electrophysiology and excitation-contraction coupling of cardiac tissues. Despite many benefits of optical mapping, eliminating motion artifacts within the optical signals is a major challenge, as myocardial contraction interferes with the faithful acquisition of action potentials and intracellular calcium transients. As such, excitation-contraction uncoupling agents are frequently used to reduce signal distortion by suppressing contraction. When compared with other uncoupling agents, blebbistatin is the most frequently used, as it offers increased potency with minimal direct effects on cardiac electrophysiology. Nevertheless, blebbistatin may exert secondary effects on electrical activity, metabolism, and coronary flow, and the incorrect administration of blebbistatin to cardiac tissue can prove detrimental, resulting in erroneous interpretation of optical mapping results. In this "Getting It Right" perspective, we briefly review the literature regarding the use of blebbistatin in cardiac optical mapping experiments, highlight potential secondary effects of blebbistatin on cardiac electrical activity and metabolic demand, and conclude with the consensus of the authors on best practices for effectively using blebbistatin in optical mapping studies of cardiac tissue.

Bidomain modeling of electrical and mechanical properties of cardiac tissue

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

Novel Optics-Based Approaches for Cardiac Electrophysiology: A Review

Optical techniques for recording and manipulating cellular electrophysiology have advanced rapidly in just a few decades. These developments allow for the analysis of cardiac cellular dynamics at multiple scales while largely overcoming the drawbacks associated with the use of electrodes. The recent advent of optogenetics opens up new possibilities for regional and tissue-level electrophysiological control and hold promise for future novel clinical applications. This article, which emerged from the international NOTICE workshop in 2018, reviews the state-of-the-art optical techniques used for cardiac electrophysiological research and the underlying biophysics. The design and performance of optical reporters and optogenetic actuators are reviewed along with limitations of current probes. The physics of light interaction with cardiac tissue is detailed and associated challenges with the use of optical sensors and actuators are presented. Case studies include the use of fluorescence recovery after photobleaching and super-resolution microscopy to explore the micro-structure of cardiac cells and a review of two photon and light sheet technologies applied to cardiac tissue. The emergence of cardiac optogenetics is reviewed and the current work exploring the potential clinical use of optogenetics is also described. Approaches which combine optogenetic manipulation and optical voltage measurement are discussed, in terms of platforms that allow real-time manipulation of whole heart electrophysiology in open and closed-loop systems to study optimal ways to terminate spiral arrhythmias. The design and operation of optics-based approaches that allow high-throughput cardiac electrophysiological assays is presented. Finally, emerging techniques of photo-acoustic imaging and stress sensors are described along with strategies for future development and establishment of these techniques in mainstream electrophysiological research.

Ultrafast four-dimensional imaging of cardiac mechanical wave propagation with sparse optoacoustic sensing

Propagation of electromechanical waves in excitable heart muscles follows complex spatiotemporal patterns holding the key to understanding life-threatening arrhythmias and other cardiac conditions. Accurate volumetric mapping of cardiac wave propagation is currently hampered by fast heart motion, particularly in small model organisms. Here we demonstrate that ultrafast four-dimensional imaging of cardiac mechanical wave propagation in entire beating murine heart can be accomplished by sparse optoacoustic sensing with high contrast, ∼115-µm spatial and submillisecond temporal resolution. We extract accurate dispersion and phase velocity maps of the cardiac waves and reveal vortex-like patterns associated with mechanical phase singularities that occur during arrhythmic events induced via burst ventricular electric stimulation. The newly introduced cardiac mapping approach is a bold step toward deciphering the complex mechanisms underlying cardiac arrhythmias and enabling precise therapeutic interventions.

Cardiac Conduction Velocity, Remodeling and Arrhythmogenesis

Cardiac electrophysiological disorders, in particular arrhythmias, are a key cause of morbidity and mortality throughout the world. There are two basic requirements for arrhythmogenesis: an underlying substrate and a trigger. Altered conduction velocity (CV) provides a key substrate for arrhythmogenesis, with slowed CV increasing the probability of re-entrant arrhythmias by reducing the length scale over which re-entry can occur. In this review, we examine methods to measure cardiac CV in vivo and ex vivo, discuss underlying determinants of CV, and address how pathological variations alter CV, potentially increasing arrhythmogenic risk. Finally, we will highlight future directions both for methodologies to measure CV and for possible treatments to restore normal CV.

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.

Quantifying the unknown impact of segmentation uncertainty on image-based simulations

Image-based simulation, the use of 3D images to calculate physical quantities, relies on image segmentation for geometry creation. However, this process introduces image segmentation uncertainty because different segmentation tools (both manual and machine-learning-based) will each produce a unique and valid segmentation. First, we demonstrate that these variations propagate into the physics simulations, compromising the resulting physics quantities. Second, we propose a general framework for rapidly quantifying segmentation uncertainty. Through the creation and sampling of segmentation uncertainty probability maps, we systematically and objectively create uncertainty distributions of the physics quantities. We show that physics quantity uncertainty distributions can follow a Normal distribution, but, in more complicated physics simulations, the resulting uncertainty distribution can be surprisingly nontrivial. We establish that bounding segmentation uncertainty can fail in these nontrivial situations. While our work does not eliminate segmentation uncertainty, it improves simulation credibility by making visible the previously unrecognized segmentation uncertainty plaguing image-based simulation.

Unimapper: An Online Interactive Analyzer/Visualizer of Optical Mapping Experimental Data

Time series of spatially-extended two-dimensional recordings are the cornerstone of basic and clinical cardiac electrophysiology. The data source may be either multipolar catheters, multi-electrode arrays, optical mapping with the help of voltage and calcium-sensitive fluorescent dyes, or the output of simulation studies. The resulting data cubes (usually two spatial and one temporal dimension) are shared either as movie files or, after additional processing, various graphs and tables. However, such data products can only convey a limited view of the data. It will be beneficial if the data consumers can interactively process the data, explore different processing options and change its visualization. This paper presents the Unified Electrophysiology Mapping Framework (Unimapper) to facilitate the exchange of electrophysiology data. Its pedigree includes a Java-based optical mapping application. The core of Unimapper is a website and a collection of JavaScript utility functions for data import and visualization (including multi-channel visualization for simultaneous voltage/calcium mapping), basic image processing (e.g., smoothing), basic signal processing (e.g., signal detrending), and advanced processing (e.g., phase calculation using the Hilbert transform). Additionally, Unimapper can optionally use graphics processing units (GPUs) for computationally intensive operations. The Unimapper ecosystem also includes utility libraries for commonly used scientific programming languages (MATLAB, Python, and Julia) that allow the data producers to convert images and recorded signals into a standard format readable by Unimapper. Unimapper can act as a nexus to share electrophysiology data - whether recorded experimentally, clinically or generated by simulation - and enhance communication and collaboration among researchers.

Topological braiding and virtual particles on the cell membrane

Braiding of topological structures in complex matter fields provides a robust framework for encoding and processing information, and it has been extensively studied in the context of topological quantum computation. In living systems, topological defects are crucial for the localization and organization of biochemical signaling waves, but their braiding dynamics remain unexplored. Here, we show that the spiral wave cores, which organize the Rho-GTP protein signaling dynamics and force generation on the membrane of starfish egg cells, undergo spontaneous braiding dynamics. Experimentally measured world line braiding exponents and topological entropy correlate with cellular activity and agree with predictions from a generic field theory. Our analysis further reveals the creation and annihilation of virtual quasi-particle excitations during defect scattering events, suggesting phenomenological parallels between quantum and living matter.

Reconceptualising Atrial Fibrillation Using Renewal Theory: A Novel Approach to the Assessment of Atrial Fibrillation Dynamics

Despite a century of research, the mechanisms of AF remain unresolved. A universal motif within AF research has been unstable re-entry, but this remains poorly characterised, with competing key conceptual paradigms of multiple wavelets and more driving rotors. Understanding the mechanisms of AF is clinically relevant, especially with regard to treatment and ablation of the more persistent forms of AF. Here, the authors outline the surprising but reproducible finding that unstable re-entrant circuits are born and destroyed at quasi-stationary rates, a finding based on a branch of mathematics known as renewal theory. Renewal theory may be a way to potentially unify the multiple wavelet and rotor theories. The renewal rate constants are potentially attractive because they are temporally stable parameters of a defined probability distribution (the exponential distribution) and can be estimated with precision and accuracy due to the principles of renewal theory. In this perspective review, this new representational architecture for AF is explained and placed into context, and the clinical and mechanistic implications are discussed.

ESC working group on cardiac cellular electrophysiology position paper: relevance, opportunities, and limitations of experimental models for cardiac electrophysiology research

Cardiac arrhythmias are a major cause of death and disability. A large number of experimental cell and animal models have been developed to study arrhythmogenic diseases. These models have provided important insights into the underlying arrhythmia mechanisms and translational options for their therapeutic management. This position paper from the ESC Working Group on Cardiac Cellular Electrophysiology provides an overview of (i) currently available in vitro, ex vivo, and in vivo electrophysiological research methodologies, (ii) the most commonly used experimental (cellular and animal) models for cardiac arrhythmias including relevant species differences, (iii) the use of human cardiac tissue, induced pluripotent stem cell (hiPSC)-derived and in silico models to study cardiac arrhythmias, and (iv) the availability, relevance, limitations, and opportunities of these cellular and animal models to recapitulate specific acquired and inherited arrhythmogenic diseases, including atrial fibrillation, heart failure, cardiomyopathy, myocarditis, sinus node, and conduction disorders and channelopathies. By promoting a better understanding of these models and their limitations, this position paper aims to improve the quality of basic research in cardiac electrophysiology, with the ultimate goal to facilitate the clinical translation and application of basic electrophysiological research findings on arrhythmia mechanisms and therapies.

Synthetic Data in Quantitative Scanning Probe Microscopy

Synthetic data are of increasing importance in nanometrology. They can be used for development of data processing methods, analysis of uncertainties and estimation of various measurement artefacts. In this paper we review methods used for their generation and the applications of synthetic data in scanning probe microscopy, focusing on their principles, performance, and applicability. We illustrate the benefits of using synthetic data on different tasks related to development of better scanning approaches and related to estimation of reliability of data processing methods. We demonstrate how the synthetic data can be used to analyse systematic errors that are common to scanning probe microscopy methods, either related to the measurement principle or to the typical data processing paths.