Impact of Combined Modulation of Two Potassium Ion Currents on Spiral Waves and Turbulent States in the Heart.

In the realm of cardiac research, the control of spiral waves and turbulent states has been a persistent focus for scholars. Among various avenues of investigation, the modulation of ion currents represents a crucial direction. It has been proved that the methods involving combined control of currents are superior to singular approaches. While previous studies have proposed some combination strategies, further reinforcement and supplementation are required, particularly in the context of controlling arrhythmias through the combined regulation of two potassium ion currents. This study employs the Luo-Rudy phase I cardiac model, modulating the maximum conductance of the time-dependent potassium current and the time-independent potassium current, to investigate the effects of this combined modulation on spiral waves and turbulent states. Numerical simulation results indicate that, compared to modulating a single current, combining reductions in the conductance of two potassium ion currents can rapidly control spiral waves and turbulent states in a short duration. This implies that employing blockers for both potassium ion currents concurrently represents a more efficient control strategy. The control outcomes of this study represent a novel and effective combination for antiarrhythmic interventions, offering potential avenues for new antiarrhythmic drug targets.

Controlling periodic long-range signalling to drive a morphogenetic transition.

Cells use signal relay to transmit information across tissue scales. However, the production of information carried by signal relay remains poorly characterised. To determine how the coding features of signal relay are generated, we used the classic system for long-range signalling: the periodic cAMP waves that drive Dictyostelium collective migration. Combining imaging and optogenetic perturbation of cell signalling states, we find that migration is triggered by an increase in wave frequency generated at the signalling centre. Wave frequency is regulated by cAMP wave circulation, which organises the long-range signal. To determine the mechanisms modulating wave circulation, we combined mathematical modelling, the general theory of excitable media, and mechanical perturbations to test competing models. Models in which cell density and spatial patterning modulate the wave frequency cannot explain the temporal evolution of signalling waves. Instead, our evidence leads to a model where wave circulation increases the ability for cells to relay the signal, causing further increase in the circulation rate. This positive feedback between cell state and signalling pattern regulates the long-range signal coding that drives morphogenesis.

Rotor mechanism and its mapping in atrial fibrillation.

Treatment of atrial fibrillation (AF) remains challenging despite significant progress in understanding its underlying mechanisms. The first detailed, quantitative theory of functional re-entry, the 'leading circle' model, was developed more than 40 years ago. Subsequently, in decades of study, an alternative paradigm based on spiral waves has long been postulated to drive AF. The rotor as a 'spiral wave generator' is a curved 'vortex' formed by spin motion in the two-dimensional plane, identified using advanced mapping methods in experimental and clinical AF. However, it is challenging to achieve complementary results between experimental results and clinical studies due to the limitation in research methods and the complexity of the rotor mechanism. Here, we review knowledge garnered over decades on generation, electrophysiological properties, and three-dimensional (3D) structure diversity of the rotor mechanism and make a comparison among recent clinical approaches to identify rotors. Although initial studies of rotor ablation at many independent centres have achieved promising results, some inconclusive outcomes exist in others. We propose that the clinical rotor identification might be substantially influenced by (i) non-identical surface activation patterns, which resulted from a diverse 3D form of scroll wave, and (ii) inadequate resolution of mapping techniques. With rapidly advancing theoretical and technological developments, future work is required to resolve clinically relevant limitations in current basic and clinical research methodology, translate from one to the other, and resolve available mapping techniques.

A Phase Defect Framework for the Analysis of Cardiac Arrhythmia Patterns.

During cardiac arrhythmias, dynamical patterns of electrical activation form and evolve, which are of interest to understand and cure heart rhythm disorders. The analysis of these patterns is commonly performed by calculating the local activation phase and searching for phase singularities (PSs), i.e., points around which all phases are present. Here we propose an alternative framework, which focuses on phase defect lines (PDLs) and surfaces (PDSs) as more general mechanisms, which include PSs as a specific case. The proposed framework enables two conceptual unifications: between the local activation time and phase description, and between conduction block lines and the central regions of linear-core rotors. A simple PDL detection method is proposed and applied to data from simulations and optical mapping experiments. Our analysis of ventricular tachycardia in rabbit hearts (n = 6) shows that nearly all detected PSs were found on PDLs, but the PDLs had a significantly longer lifespan than the detected PSs. Since the proposed framework revisits basic building blocks of cardiac activation patterns, it can become a useful tool for further theory development and experimental analysis.

Arrhythmia Mechanism and Dynamics in a Humanized Mouse Model of Inherited Cardiomyopathy Caused by Phospholamban R14del Mutation.

BACKGROUND: Arginine (Arg) 14 deletion (R14del) in the calcium regulatory protein phospholamban (hPLNR14del) has been identified as a disease-causing mutation in patients with an inherited cardiomyopathy. Mechanisms underlying the early arrhythmogenic phenotype that predisposes carriers of this mutation to sudden death with no apparent structural remodeling remain unclear. METHODS: To address this, we performed high spatiotemporal resolution optical mapping of intact hearts from adult knock-in mice harboring the human PLNWT (wildtype [WT], n=12) or the heterozygous human PLNR14del mutation (R14del, n=12) before and after ex vivo challenge with isoproterenol and rapid pacing. RESULTS: Adverse electrophysiological remodeling was evident in the absence of significant structural or hemodynamic changes. R14del hearts exhibited increased arrhythmia susceptibility compared with wildtype. Underlying this susceptibility was preferential right ventricular action potential prolongation that was unresponsive to ß-adrenergic stimulation. A steep repolarization gradient at the left ventricular/right ventricular interface provided the substrate for interventricular activation delays and ultimately local conduction block during rapid pacing. This was followed by the initiation of macroreentrant circuits supporting the onset of ventricular tachycardia. Once sustained, these circuits evolved into high-frequency rotors, which in their majority were pinned to the right ventricle. These rotors exhibited unique spatiotemporal dynamics that promoted their increased stability in R14del compared with wildtype hearts. CONCLUSIONS: Our findings highlight the crucial role of primary electric remodeling caused by the hPLNR14del mutation. These inherently arrhythmogenic features form the substrate for adrenergic-mediated VT at early stages of PLNR14del induced cardiomyopathy.

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

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

A move in the light direction.

Computer simulations show how low-intensity illumination can be used to terminate cardiac arrhythmias.

Efficiency of semi-implicit alternating direction implicit methods for solving cardiac monodomain model.

It is well known that numerical simulations of the cardiac monodomain model require fine mesh resolution, which increases the computational resources required. In this paper, we construct three operator-splitting alternating direction implicit (ADI) schemes to efficiently solve the nonlinear cardiac monodomain model. The main objective of the proposed methods is to reduce the computational time and memory consumed for solving electrocardiology models, compared to standard numerical methods. The proposed methods have second-order accuracy in both space and time while evaluating the ionic model only once per time-step. Several examples using regular wave, spiral wave reentry, and nonsymmetrical scroll wave are conducted, and the efficiency of the proposed ADI methods is compared to the standard semi-implicit Crank-Nicolson/Adams-Bashforth method. Large-scale two- and three-dimensional simulations are performed.

Spatial phase discontinuity at the center of moving cardiac spiral waves.

BACKGROUND: Precise analysis of cardiac spiral wave (SW) dynamics is essential for effective arrhythmia treatment. Although the phase singularity (PS) point in the spatial phase map has been used to determine the cardiac SW center for decades, quantitative detection algorithms that assume PS as a point fail to trace complex and rapid PS dynamics. Through a detailed analysis of numerical simulations, we examined our hypothesis that a boundary of spatial phase discontinuity induced by a focal conduction block exists around the moving SW center in the phase map. METHOD: In a numerical simulation model of a 2D cardiac sheet, three different types of SWs (short wavelength; long wavelength; and low excitability) were induced by regulating ion channels. Discontinuities of all boundaries among adjacent cells at each instance were evaluated by calculating the phase bipolarity (PB). The total amount of phase transition (PTA) in each cell during the study period was evaluated. RESULTS: Pivoting, drifting, and shifting SWs were observed in the short-wavelength, low-excitability, and long-wavelength models, respectively. For both the drifting and shifting cases, long high-PB edges were observed on the SW trajectories. In all cases, the conduction block (CB) was observed at the same boundaries. These were also identical to the boundaries in the PTA maps. CONCLUSIONS: The analysis of the simulations revealed that the conduction block at the center of a moving SW induces discontinuous boundaries in spatial phase maps that represent a more appropriate model of the SW center than the PS point.

The transient outward potassium current plays a key role in spiral wave breakup in ventricular tissue.

Spiral wave reentry as a mechanism of lethal ventricular arrhythmias has been widely demonstrated in animal experiments and recordings from human hearts. It has been shown that in structurally normal hearts spiral waves are unstable, breaking up into multiple wavelets via dynamical instabilities. However, many of the second-generation action potential models give rise only to stable spiral waves, raising issues regarding the underlying mechanisms of spiral wave breakup. In this study, we carried out computer simulations of two-dimensional homogeneous tissues using five ventricular action potential models. We show that the transient outward potassium current (Ito), although it is not required, plays a key role in promoting spiral wave breakup in all five models. As the maximum conductance of Ito increases, it first promotes spiral wave breakup and then stabilizes the spiral waves. In the absence of Ito, speeding up the L-type calcium kinetics can prevent spiral wave breakup, however, with the same speedup kinetics, spiral wave breakup can be promoted by increasing Ito. Increasing Ito promotes single-cell dynamical instabilities, including action potential duration alternans and chaos, and increasing Ito further suppresses these action potential dynamics. These cellular properties agree with the observation that increasing Ito first promotes spiral wave breakup and then stabilizes spiral waves in tissue. Implications of our observations to spiral wave dynamics in the real hearts and action potential model improvements are discussed.NEW & NOTEWORTHY Spiral wave breakup manifesting as multiple wavelets is a mechanism of ventricular fibrillation. It has been known that spiral wave breakup in cardiac tissue can be caused by a steeply sloped action potential duration restitution curve, a property mainly determined by the recovery of L-type calcium current. Here, we show that the transient outward potassium current (Ito) is another current that plays a key role in spiral wave breakup, that is, spiral waves can be stable for low and high maximum Ito conductance but breakup occurs for intermediate maximum Ito conductance. Since Ito is present in normal hearts of many species and required for Brugada syndrome, it may play an important role in the spiral wave stability and arrhythmogenesis under both normal condition and Brugada syndrome.

Standardizing Single-Frame Phase Singularity Identification Algorithms and Parameters in Phase Mapping During Human Atrial Fibrillation.

PURPOSE: Recent investigations failed to reproduce the positive rotor-guided ablation outcomes shown by initial studies for treating persistent atrial fibrillation (persAF). Phase singularity (PS) is an important feature for AF driver detection, but algorithms for automated PS identification differ. We aim to investigate the performance of four different techniques for automated PS detection. METHODS: 2048-channel virtual electrogram (VEGM) and electrocardiogram signals were collected for 30 s from 10 patients undergoing persAF ablation. QRST-subtraction was performed and VEGMs were processed using sinusoidal wavelet reconstruction. The phase was obtained using Hilbert transform. PSs were detected using four algorithms: (1) 2D image processing based and neighbor-indexing algorithm; (2) 3D neighbor-indexing algorithm; (3) 2D kernel convolutional algorithm estimating topological charge; (4) topological charge estimation on 3D mesh. PS annotations were compared using the structural similarity index (SSIM) and Pearson's correlation coefficient (CORR). Optimized parameters to improve detection accuracy were found for all four algorithms using F ß score and 10-fold cross-validation compared with manual annotation. Local clustering with density-based spatial clustering of applications with noise (DBSCAN) was proposed to improve algorithms 3 and 4. RESULTS: The PS density maps created by each algorithm with default parameters were poorly correlated. Phase gradient threshold and search radius (or kernels) were shown to affect PS detections. The processing times for the algorithms were significantly different (p < 0.0001). The F ß scores for algorithms 1, 2, 3, 3 + DBSCAN, 4 and 4 + DBSCAN were 0.547, 0.645, 0.742, 0.828, 0.656, and 0.831. Algorithm 4 + DBSCAN achieved the best classification performance with acceptable processing time (2.0 ± 0.3 s). CONCLUSION: AF driver identification is dependent on the PS detection algorithms and their parameters, which could explain some of the inconsistencies in rotor-guided ablation outcomes in different studies. For 3D triangulated meshes, algorithm 4 + DBSCAN with optimal parameters was the best solution for real-time, automated PS detection due to accuracy and speed. Similarly, algorithm 3 + DBSCAN with optimal parameters is preferred for uniform 2D meshes. Such algorithms - and parameters - should be preferred in future clinical studies for identifying AF drivers and minimizing methodological heterogeneities. This would facilitate comparisons in rotor-guided ablation outcomes in future works.

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

INTRODUCTION: Successful initiation of spiral wave reentry in the neonatal rat ventricular myocyte (NRVM) monolayer implicitly assumes the presence of spatial dispersion of repolarization (DR), which is difficult to quantify. We recently introduced a NRVM monolayer that utilizes anthopleurin-A to impart a prolonged plateau to the NRVM action potential. This was associated with a significant degree of spatial DR that lends itself to accurate quantification. METHODS AND RESULTS: We utilized the monolayer and fluorescence optical mapping of intracellular calcium transients (FCai ) to systematically study and compare the contribution of spatial dispersion of the duration of FCai (as a surrogate of DR) to induction of spiral wave reentry around a functional core versus reentry around a fixed anatomical obstacle. We show that functional reentry could be initiated by a premature stimulus acting on a substrate of spatial DR resulting in a functional line of propagation block. Subsequent wave fronts circulated around a central core of functional obstacle created by sustained depolarization from the circulating wave front. Both initiation and termination of spiral wave reentry around an anatomical obstacle consistently required participation of a region of functional propagation block. This region was similarly based on spatial DR. Spontaneous termination of spiral wave reentry also resulted from block in the functional component of the circuit obstacle, usually preceded by beat-to-beat slowing of propagation. CONCLUSIONS: The study demonstrates the critical contribution of DR to spiral wave reentry around a purely functional core as well as reentry around a fixed anatomical core.

Defects formation and spiral waves in a network of neurons in presence of electromagnetic induction.

Complex anatomical and physiological structure of an excitable tissue (e.g., cardiac tissue) in the body can represent different electrical activities through normal or abnormal behavior. Abnormalities of the excitable tissue coming from different biological reasons can lead to formation of some defects. Such defects can cause some successive waves that may end up to some additional reorganizing beating behaviors like spiral waves or target waves. In this study, formation of defects and the resulting emitted waves in an excitable tissue are investigated. We have considered a square array network of neurons with nearest-neighbor connections to describe the excitable tissue. Fundamentally, electrophysiological properties of ion currents in the body are responsible for exhibition of electrical spatiotemporal patterns. More precisely, fluctuation of accumulated ions inside and outside of cell causes variable electrical and magnetic field. Considering undeniable mutual effects of electrical field and magnetic field, we have proposed the new Hindmarsh-Rose (HR) neuronal model for the local dynamics of each individual neuron in the network. In this new neuronal model, the influence of magnetic flow on membrane potential is defined. This improved model holds more bifurcation parameters. Moreover, the dynamical behavior of the tissue is investigated in different states of quiescent, spiking, bursting and even chaotic state. The resulting spatiotemporal patterns are represented and the time series of some sampled neurons are displayed, as well.

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.

Impact of number of co-existing rotors and inter-electrode distance on accuracy of rotor localization.

BACKGROUND: Conflicting evidence exists on the efficacy of focal impulse and rotor modulation on atrial fibrillation ablation. A potential explanation is inaccurate rotor localization from multiple rotors coexistence and a relatively large (9-11mm) inter-electrode distance (IED) of the multi-electrode basket catheter. METHODS AND RESULTS: We studied a numerical model of cardiac action potential to reproduce one through seven rotors in a two-dimensional lattice. We estimated rotor location using phase singularity, Shannon entropy and dominant frequency. We then spatially downsampled the time series to create IEDs of 2-30mm. The error of rotor localization was measured with reference to the dynamics of phase singularity at the original spatial resolution (IED=1mm). IED has a significant impact on the error using all the methods. When only one rotor is present, the error increases exponentially as a function of IED. At the clinical IED of 10mm, the error is 3.8mm (phase singularity), 3.7mm (dominant frequency), and 11.8mm (Shannon entropy). When there are more than one rotors, the error of rotor localization increases 10-fold. The error based on the phase singularity method at the clinical IED of 10mm ranges from 30.0mm (two rotors) to 96.1mm (five rotors). CONCLUSIONS: The magnitude of error of rotor localization using a clinically available basket catheter, in the presence of multiple rotors might be high enough to impact the accuracy of targeting during AF ablation. Improvement of catheter design and development of high-density mapping catheters may improve clinical outcomes of FIRM-guided AF ablation.

A method for quantifying recurrent patterns of local wavefront direction during atrial fibrillation.

INTRODUCTION: Spiral wave reentry is a potential mechanism of atrial fibrillation (AF), but is difficult to differentiate clinically from multiple wavelet breakup using standard bipolar recordings. We developed a new methodology using bipolar recordings to estimate the direction of local activation wavefronts during AF by calculating the electrogram conformation (Egm-C). We subsequently used recurrence quantification analysis (RQA) of Egm-C to differentiate regions of spiral wave reentry from wavelet breakup. METHODS: A 2D computer simulation was created with regions containing a stable spiral wave and also regions of wavebreak. A grid of 40 × 40 unipolar electrodes was superimposed. At each site, the actual wavefront direction (WD) was determined by comparing relative activation timings of the local intracellular recordings, and the estimated wavefront direction (Egm-C) was determined from the morphology of the local bipolar electrogram. RQA of Egm-C was compared to RQA of actual WD in order to differentiate AF mechanisms. RESULTS: RQA of actual WD and Egm-C both distinguished regions of spiral wave reentry from wavelet breakup with high correlation between the two methods (recurrence rate, r = 0.96; determinism, r = 0.61; line max, r = 0.95; entropy, r = 0.84; p < 0.001 for all). In areas of stable spiral wave reentry, the recurrence plots of both Egm-C and actual WD demonstrated stable, periodic dynamics, while regions of wavelet breakup demonstrated chaotic behavior largely devoid of repetitive activation patterns. CONCLUSION: Calculation of Egm-C allows RQA to be performed on bipolar electrograms during AF and differentiates regions of spiral wave reentry from multiple wavelet breakup.

Elimination of spiral waves in a locally connected chaotic neural network by a dynamic phase space constraint.

In this study, a method is proposed that eliminates spiral waves in a locally connected chaotic neural network (CNN) under some simplified conditions, using a dynamic phase space constraint (DPSC) as a control method. In this method, a control signal is constructed from the feedback internal states of the neurons to detect phase singularities based on their amplitude reduction, before modulating a threshold value to truncate the refractory internal states of the neurons and terminate the spirals. Simulations showed that with appropriate parameter settings, the network was directed from a spiral wave state into either a plane wave (PW) state or a synchronized oscillation (SO) state, where the control vanished automatically and left the original CNN model unaltered. Each type of state had a characteristic oscillation frequency, where spiral wave states had the highest, and the intra-control dynamics was dominated by low-frequency components, thereby indicating slow adjustments to the state variables. In addition, the PW-inducing and SO-inducing control processes were distinct, where the former generally had longer durations but smaller average proportions of affected neurons in the network. Furthermore, variations in the control parameter allowed partial selectivity of the control results, which were accompanied by modulation of the control processes. The results of this study broaden the applicability of DPSC to chaos control and they may also facilitate the utilization of locally connected CNNs in memory retrieval and the exploration of traveling wave dynamics in biological neural networks.

Anatomical and spiral wave reentry in a simplified model for atrial electrophysiology.

For modeling the propagation of action potentials in the human atria, various models have been developed in the past, which take into account in detail the influence of the numerous ionic currents flowing through the cell membrane. Aiming at a simplified description, the Bueno-Orovio-Cherry-Fenton (BOCF) model for electric wave propagation in the ventricle has been adapted recently to atrial physiology. Here, we study this adapted BOCF (aBOCF) model with respect to its capability to accurately generate spatio-temporal excitation patterns found in anatomical and spiral wave reentry. To this end, we compare results of the aBOCF model with the more detailed one proposed by Courtemanche, Ramirez and Nattel (CRN model). We find that characteristic features of the reentrant excitation patterns seen in the CRN model are well captured by the aBOCF model. This opens the possibility to study origins of atrial fibrillation based on a simplified but still reliable description.