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A super‐diffusive HBV model with the intracellular time delay and logistic hepatocyte growth is studied. We discuss the local asymptotic stability of the unique positive equilibrium and prove that the intracellular time delay can cause spatial patterns. Furthermore, we find that system undergoes a Hopf bifurcation when the time delay increase to a critical value. By the normal form theory and the center manifold theorem, we investigate the stability and direction of the bifurcating periodic solutions. Finally, we present how the initial condition, time delay, superdiffusion coefficient and the exponent of superdiffusion affect spatial patterns by numerical simulations. [ABSTRACT FROM AUTHOR]

Analysis of Hindmarsh-Rose (HR) neural model and its network dynamics under different inputs or network topologies are the leading research of the structural dynamics of complex networks, but the typical three-variable HR neural model has limitations in describing the complex non-linear features and precise behavior patterns of neuron. Based on an extended HR neural model, the firing patterns and bifurcation behavior are analysed in this paper, and how the newly introduced variable affect discharge modes has also been explored. A two-dimensional lattice is constructed to study the mechanism of spiral wave formation and breakup in the neural network, and to explore its network dynamics and synchronous behavior. Obtained results show that the extended HR neural model has more rich and stable firing properties, and it can be observed that there are multimodal phenomena with both spiking and bursting states simultaneously. If the network topology is changed, the formation and breakup of spiral waves can be observed, and the synchronization factor exhibits a monotonically decreasing relationship with the coupling strength and the control parameters of the newly introduced variable. When HR neurons are in spiking state, the system is more prone to spiral waves, and the coupling strength range for spiral waves is wider. The above results provide valuable ideas to explore the modulation of network group behavior. [ABSTRACT FROM AUTHOR]

In order to figure out the driver effect of a curved scoop on three-dimensional flow field in a gas centrifuge (GC), a double-chamber GC was used as the research object. 3D Navier–Stokes equations were solved by the semidiscrete finite volume method with high precision. Numerical results show that there are a bow-shaped shock wave and a detached-body shock wave being generated around the scoop. After the shock wave enters the separation chamber, it moves along a spiral trajectory, which leads to the disturbance of physical variables. Compared with other positions in the rotor, the gas pressure close to the side wall undergoes a more obvious change. The significant axial velocity disturbance is distributed close to the artificial inner boundary, but the main mass transfer of gas occurs near the side wall. The variation of angular integration of axial mass flux in radial direction indicates that there are 3 axial circulations in the separation chamber. [ABSTRACT FROM AUTHOR]

Optogenetics as an emerging technology can eliminate spiral waves in myocardial tissue. The heat generated during illumination of myocardial tissue is an overlooked influence. Even small fluctuations in temperature may affect the action potentials of cardiomyocyte. In this paper, a minimal ventricular model and a simplified model of optogenetics are employed to study the effects of heat generation by illumination on elimination of spiral waves. The Luo-Rudy model and Channelrhodospin-2 light-sensitive ion channel model are used to validate our conclusions. We induce drift of spiral waves through inhomogeneities generated by discrete gradients of illumination. The inhomogeneity of temperature caused by gradient illumination can inhibit the elimination of spiral waves. Spiral waves in the myocardial medium can be induced to drift more efficiently by controlling temperature changes in the myocardial medium during illumination. We emphasized the importance of temperature factors in optogenetic experiments, hoping that our results could provide guidance for its clinical applications. [ABSTRACT FROM AUTHOR]

Using finite element simulation, we study the main features of rotating wave solutions of the cubic complex Ginzburg–Landau equation. To focus on the characteristics of the waves themselves, we have used a circular domain to avoid the effects of irregular boundaries; we have inhibited the formation of defects using an Archimedean wave centered at the origin as the initial condition, and we have chosen a domain size long enough to contain several spiral arms but not so long as to promote long-wave instabilities. This allows us to focus on the geometric features of the solutions often overlooked in traditional works with random initial conditions in large domains. We show with our simulations that the convective and absolute stabilities differ from those predicted for plane waves. Likewise, we show that the appearance of spirals and anti-spirals can occur in any of the quadrants of the parameter space and depends fundamentally on the initial conditions. Finally, regarding the stability of spiral waves against sideband disturbances, we show that the persistence of two-dimensional spiral waves, if fulfilled, does not correspond to the Eckhaus criterion. Our simulations allow us to corroborate the idea that two-dimensional spirals depend on the size of the domain and that they require new analytical results whose trends are identified in this work. [ABSTRACT FROM AUTHOR]

The changes in cardiomyocyte action potentials are related to variations in intra- and extracellular ion concentrations. Abnormal ion concentrations can lead to irregular action potentials, subsequently affecting wave propagation in myocardial tissue and potentially resulting in the formation of spiral waves. Therefore, timely monitoring of ion concentration changes is essential. This study presents a novel machine learning classification model that predicts ion concentration changes based on action potential variation data. We conducted simulations using a single-cell model, generating a dataset of 850 action potential variations corresponding to different ion concentration changes. The model demonstrated excellent predictive performance, achieving an accuracy of 0.988 on the test set. Additionally, the causes of spontaneous spiral wave generation in the heart are insufficiently studied. This study presents a new mechanism whereby changes in extracellular potassium ion concentration leads to the spontaneous generation of spiral waves. By constructing composite myocardial tissue containing both myocardial and fibroblast cells, we observed that variations in extracellular potassium ion concentration can either trigger or inhibit cardiomyocyte excitation. We developed three tissue structures, and by appropriately adjusting the extracellular potassium ion concentration, we observed the spontaneous generation of single spiral waves, symmetrical spiral wave pairs, and asymmetrical double spiral waves. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The changes in cardiomyocyte action potentials are related to variations in intra- and extracellular ion concentrations. Abnormal ion concentrations can lead to irregular action potentials, subsequently affecting wave propagation in myocardial tissue and potentially resulting in the formation of spiral waves. Therefore, timely monitoring of ion concentration changes is essential. This study presents a novel machine learning classification model that predicts ion concentration changes based on action potential variation data. We conducted simulations using a single-cell model, generating a dataset of 850 action potential variations corresponding to different ion concentration changes. The model demonstrated excellent predictive performance, achieving an accuracy of 0.988 on the test set. Additionally, the causes of spontaneous spiral wave generation in the heart are insufficiently studied. This study presents a new mechanism whereby changes in extracellular potassium ion concentration leads to the spontaneous generation of spiral waves. By constructing composite myocardial tissue containing both myocardial and fibroblast cells, we observed that variations in extracellular potassium ion concentration can either trigger or inhibit cardiomyocyte excitation. We developed three tissue structures, and by appropriately adjusting the extracellular potassium ion concentration, we observed the spontaneous generation of single spiral waves, symmetrical spiral wave pairs, and asymmetrical double spiral waves.

We study the formation and suppression of spiral wave patterns in a lattice of memristive FitzHugh–Nagumo neurons that are connected through chemical coupling. While earlier works focused predominantly on diffusive coupling, we focus on various parameters that determine the properties of chemical synapses, in particular their firing threshold, the sigmoidal slope, and the reversal potential. Based on physiologically plausible scenarios, we also aim to determine the most probable realistic values of these parameters that facilitate the formation of spiral waves. Furthermore, we study the destabilizing impact of external direct and Faradaic currents on spiral wave patterns, showing that they commonly convert into other turbulent patterns or vanish altogether. Interestingly, however, during the destabilization process, counter-rotating spirals that then collide and generate complex patterns can also be observed. [ABSTRACT FROM AUTHOR]

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.

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. [ABSTRACT FROM AUTHOR]

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.

We consider a boundary value problem based on a logistic model with delay and diffusion describing the dynamics of changes in the population density in a planar domain. It has spatially inhomogeneous stable solutions branching off from a spatially homogeneous solution and sharing qualitatively the same dynamical properties. We numerically investigate their phase bifurcations with a significant decrease in the diffusion coefficient. The coexisting stable modes with qualitatively different properties are also constructed numerically. Based on the applied numerical and analytic methods, the solutions of the considered boundary value problem are divided into two types, the first of which includes solutions that inherit the properties of the homogeneous solution and the second includes the so-called self-organization modes. Solutions of the second type are more intricately distributed in space and have properties much more preferable from the standpoint of population dynamics. [ABSTRACT FROM AUTHOR]

This paper deals with a predator–prey model with time delay and constant prey harvesting. We investigate the effect of the time delay on the stability of the coexistence equilibrium and demonstrate that time delay can induce spatial patterns. Furthermore, a Hopf bifurcation occurs when the delay increases to a critical value. By applying normal form theory and the center manifold theorem, we develop the explicit formulae that determines the stability and direction of the bifurcating periodic solutions. Finally, we show how the initial condition affects the types of spatial patterns by numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract. The objective is to study numerically the dynamics of two-dimensional lattice of locally coupled maps of Rulkov. We analyze conditions for the appearance and existence as well as the properties of auto-wave spatio-temporal structures which are represented by spiral and target waves. The influence of noise on the lattice dynamics is explored as the noise intensity and the size of the noise-disturbed region are varied. Methods. In numerical experiments the evolution of the lattice dynamics is directly determined by the corresponding recurrence relations. The numerical data are used to construct spatial distributions of the instantaneous values of the amplitudes for all the network elements, spatio-temporal diagrams for the lattice cross-section at different values of the control parameters of the individual nodes, for various noise intensities and different sizes of the noise-disturbed region. The obtained results are compared. The noise-disturbed region is specified as a square which consists of a small number of oscillators at the lattice center. Results. It is found that for certain values of the control parameters of the maps, of the coupling parameters, and the initial conditions, long-lived spiral and target waves can exist in the lattice. It is shown that the spiral wave regimes are, as a rule, transient, can be observed for a finite time and become long-lived only for certain values of the parameters and the initial conditions. When the noise influences a finite region of the lattice showing spiral waves, the transition to spiral waves with a different structure or to target waves can occur. However, if the noise disturbance is removed, the lattice returns to its original mode or exhibits the transition to coherent dynamics modes. The target waves are more resistant to the noise and are observed for longer times. If the noise causes the target waves to change, the resulting regime continues to exist after removing the noise source. Conclusion. It is shown that the spiral and target waves can be observed in the lattice of locally coupled Rulkov maps. The regions where these waves exist are defined and constructed in the plane of the control parameters of the individual elements. Studying the impact of the relation between the noise intensity and the size of the noise-disturbed region enables one to distinguish the region where the transition from spiral to target waves always occurs, as well as the area inside which this transition depends on the initial states of the lattice elements and the noise realization. The effect of noise on the target waves can induce the appearance of only target wave chimeras which continue to exist even after the noise excitation is turned off.

The stability of rigidly rotating spiral waves is a very important topic in the study of nonlinear reaction-diffusion media. Computer experiments carried out with a slightly modified Barkley model showed that, in addition to one region of instability observed earlier in the original Barkley model, there is another one exhibiting completely different properties. The wave instability in the second region is not related to the Hopf bifurcation. Moreover, hysteresis effects are observed at the boundary of the region. This means that in the vicinity of this region of instability, direct integration of the model equations leads either to a rigidly rotating or meandering spiral, depending on the initial conditions.

Systems of coupled nonlinear oscillators often exhibit states of partial synchrony in which some of the oscillators oscillate coherently while the rest remain incoherent. If such a state emerges spontaneously, in other words, if it cannot be associated with any heterogeneity in the system, it is generally referred to as a chimera state. In planar oscillator arrays, these chimera states can take the form of rotating spiral waves surrounding an incoherent core, resembling those observed in oscillatory or excitable media, and may display complex dynamical behavior. To understand this behavior we study stationary and moving chimera states in planar phase oscillator arrays using a combination of direct numerical simulations and numerical continuation of solutions of the corresponding continuum limit, focusing on the existence and properties of traveling spiral wave chimeras as a function of the system parameters. The oscillators are coupled nonlocally and their frequencies are drawn from a Lorentzian distribution. Two cases are discussed in detail, that of a top-hat coupling function and a two-parameter truncated Fourier approximation to this function in Cartesian coordinates. The latter allows semi-analytical progress, including determination of stability properties, leading to a classification of possible behaviors of both static and moving chimera states. The transition from stationary to moving chimeras is shown to be accompanied by the appearance of complex filamentary structures within the incoherent spiral wave core representing secondary coherence regions associated with temporal resonances. As the parameters are varied the number of such filaments may grow, a process reflected in a series of folds in the corresponding bifurcation diagram showing the drift speed s as a function of the phase-lag parameter α .

There is a special interest to understand the dynamical properties of the accretion disk created around the newly formed black hole due to the supermassive black hole binaries which merge inside the gaseous disk. The newly formed black hole would have a kick velocity up to thousands of km/s that drives a perturbation on a newly accreted torus around the black hole. Some of the observed supermassive black holes at the center of the Active Galactic Nucleus (AGN) move with a certain velocity relative to its broader accretion disk. In this paper, the effects of the kicked black holes onto the infinitesimally thin accreted torus are studied by using the general relativistic hydrodynamical code, focusing on changing the dynamics of the accretion disk during the accretion disk–black hole interaction. We have found that the non-axisymmetric global mode m = 1 inhomogeneity, which causes a spiral-wave-structure, is excited on the torus due to kicked black hole. The higher the perturbation velocity produced by the kicked black hole, the longer the time the torus takes to reach the saturation point. The created spiral density waves which rapidly evolve into the spiral shocks are also observed from the numerical simulations. The spiral shock is responsible for accreting matter toward the black hole. First, the spiral-wave-structure is developed and the accretion through the spiral arms is stopped around the black hole. At the later time of simulation, the formed spiral shocks partly cause the angular momentum loss across the torus. [ABSTRACT FROM AUTHOR]

The controls of chaotic and coexisting attractors and collective dynamics in linear resistive-capacitive-inductive shunted Josephson junction (LRCISJJ) model are investigated in this paper. A single feedback controller is designed to control chaos found in the LRCISJJ model. Analytical calculations and numerical simulations are carried out to show the serviceableness of the designed single controller. In addition, the coexistence between chaotic and limit cycle attractors is ruined and controlled to a desired trajectory by using the linear augmentation control method. Finally, since the LRCISJJ shows spiking and bursting behaviors, a 2D lattice array of the LRCISJJ model is constructed in order to understand its network behavior. The spiral wave formation in the network is studied in the presence of heterogeneity. To further confirm the excitability heterogeneity in the network, the periods of each node are used to show the periodicity pattern in the network. [ABSTRACT FROM AUTHOR]

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.

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. [ABSTRACT FROM AUTHOR]

In this article, we construct an excitable memristive diffusive neuron model by considering a biophysical slow–fast bursting oscillator and study the effects of electromagnetic induction on the dynamics of the single model as well as the coupled systems. We explore various firing regimes such as tonic spiking, bursting, and mixed-mode oscillations depending on the bifurcation structure with different injected current stimuli, then perform a comparative analysis on the synchronization of the coupled oscillators by setting the model into two different network architectures. First, a diffusively coupled network is considered, and later a global network is constructed. The results suggest that the diffusively connected neurons show complete synchronization at higher couplings for bursting and tonic spiking regimes. Furthermore, we show that the extended spatial system can generate spiral-like patterns in the vicinity of a Hopf bifurcation point and observe the impact of Gaussian white noise to study its effects on pattern formation. These types of patterns are robust in the excitable model. Our results might contribute significantly to the dynamical studies of irregular neural computation. [ABSTRACT FROM AUTHOR]

AimsVentricular tachycardia (VT) and fibrillation (VF) are the most lethal cardiac arrhythmias. The degeneration of VT into VF is associated with the breakup of a spiral wave of the action potential in cardiac tissue. β-Adrenergic (βAR) signalling potentiates the L-type Ca current (ICaL) faster than the slow delayed rectifier potassium current (IKs), which transiently prolongs the action potential duration (APD) and promotes early after depolarizations. In this study, we aimed at investigating how βAR signalling affects the transition from VT to VF.Methods and resultsWe used a physiologically detailed computer model of the rabbit ventricular myocyte in a two-dimensional tissue to determine how spiral waves respond to βAR activation following administration of isoproterenol. A simplified mathematical model was also used to investigate the underlying dynamics. We found that the spatiotemporal behaviour of spiral waves strongly depends on the kinetics of βAR activation. When βAR activation is rapid, a stable spiral wave turns into small fragments and its electrocardiogram reveals the transition from VT to VF. This is due to the transiently steepened APD restitution induced by the faster activation of ICaL vs. IKs upon sudden βAR activation. The spiral wave may also disappear if its transient wavelength is too large to be supported by the tissue size upon sudden strong βAR activation that prolongs APD transiently. When βAR activation is gradual, a stable spiral wave remains such, because of more limited increase in both APD and slope of APD restitution due to more contemporaneous ICaL and IKs activation.ConclusionChanges in APD restitution during βAR activation revealed a novel transient spiral wave dynamics; this spatiotemporal characteristic strongly depends on the protocol of isoproterenol application.

Spiral waves in the cardiac tissue may cause life-threatening arrhythmia. Such waves can be anchored to a local heterogeneity and form stable pinned waves, which are difficult to be eliminated. Here, a numerical simulation using the FHN model provides the parameter area of the obstacle size and the perturbation period for successful unpinning and elimination by the method of a periodic perturbation near the boundary. The termination of pinned spirals may be successful when the obstacle size is small, and the optional range of the perturbation period is small. It is also illustrated that the pinned spiral wave can be coincidentally eliminated for individual parameter values outside the area. A new strategy of the periodic perturbation is proposed to liberate pinned spiral waves, where there is no limit to the size of the obstacle. In this approach, a free end is generated near the boundary, and is carried to the obstacle by the wave train, thereby changing the total topological charge around the obstacle and making the pinned spiral be eliminated. To better implement the control scheme, the dynamics of the carried defect is also discussed in detail. [ABSTRACT FROM AUTHOR]

The present work is devoted to the detailed quantification of the transition from spiral waves to spiral wave chimeras in a network of self-sustained oscillators with two-dimensional geometry. The basic elements of the network under consideration are the van der Pol oscillator or the FitzHugh – Nagumo neuron. Both of the models are in the regime of relaxation oscillations. We analyze the regime by using the indices of local sensitivity, which enables us to evaluate the sensitivity of each oscillator at a finite time. Spiral waves are observed in both lattices when the interaction between elements has a local character. The dynamics of all the elements is regular. There are no pronounced high-sensitive regions. We have discovered that, when the coupling becomes nonlocal, the features of the system change significantly. The oscillation regime of the spiral wave center element switches to a chaotic one. Besides, a region with high sensitivity occurs around the wave center oscillator. Moreover, we show that the latter expands in space with elongation of the coupling range. As a result, an incoherence cluster of the spiral wave chimera is formed exactly within this high-sensitive area. A sharp increase in the values of the maximal Lyapunov exponent in the positive region leads to the formation of the incoherence cluster. Furthermore, we find that the system can even switch to a hyperchaotic regime when several Lyapunov exponents become positive. [ABSTRACT FROM AUTHOR]

The low-voltage cardioversion-defibrillation is a modern sparing electrotherapy method for such dangerous heart arrhythmias as paroxysmal tachycardia and fibrillation. In an excitable medium, such arrhythmias relate to appearance of spiral waves of electrical excitation, and the spiral waves are superseded to the electric boundary of the medium in the process of treatment due to high-frequency stimulation from the electrode. In this paper we consider the Aliev–Panfilov myocardial model, which provides a positive tension of three-dimensional scroll waves, and an axisymmetric model of the left ventricle of the human heart. Two relations of anisotropy are considered, namely, isotropy and physiological anisotropy. The periods of stimulation with an apical electrode are found so that the electrode successfully entrains its rhythm in the medium, the spiral wave is superseded to the base of the ventricle, and disappears. The results are compared in two-dimensional and three-dimensional media. The intervals of effective stimulation periods are sufficiently close to each other in the two-dimensional case and in the anatomical model. However, the use of the anatomical model is essential in determination of the time of superseding. [ABSTRACT FROM AUTHOR]

Treatment of atrial fibrillation (AF) remains challenging despite a deep understanding of its underlying mechanisms. The detailed and quantitative description of functional reentry, the famous "leading circle" model, was developed more than 40 years ago. Subsequently, an alternative paradigm based on spiral waves has long been postulated to drive AF in decades of study. Rotor as a "spiral wave generator", is a curved "vortex" formed by spin motion in the two-dimensional plane, which can be identified by using advanced mapping methods in experimental and clinical AF. However, it is difficult to achieve complementary results between basic results and clinical studies due to limited research methods and complexity of rotor mechanism. This paper reviews knowledge garnered over decades on generation, electrophysiological properties and three-dimensional structure diversity of the rotor, and make a comparison among the latest clinical approaches of rotor identification, such as panoramic mapping and local high-density mapping. Although the rotor mapping and ablation perform as a promising therapeutic option for AF, some inclusive outcomes of studies remain existing in either panoramic mapping or local high-density mapping. It is proposed that the clinical rotor identification might be substantially influenced by ( i ) non-identical surface activation patterns n:sulLcd from diverse three-dimensional forms of scroll wave, and ( ii ) inadequate resolution of mapping techniques. With rapidly advancing theoretical and technological developments, future work is required to resolve the clinical limitations in current basic and clinical research methodology, in translation from one to the other, and in resolution of available mapping techniques. [ABSTRACT FROM AUTHOR]

This work deals with the stimulation of cardiac spiral waves in a two-dimensional FitzHugh–Nagumo model through modulational instability phenomenon in the presence of intracellular magnetic flux. The nonlinear generic model is firstly transformed into a two-dimensional complex Ginzburg–Landau equation with a small real damping term. Then, the latter is explored to perform the linear stability analysis and some modulational instability properties are derived and found to be modified with the change of either the magnetic coupling strength or the diffusion coefficient which are set as the control parameters. The bifurcation theory analysis is numerically performed, and the range of values of the stimulation parameter for which firing patterns emerge in cardiac media is well estimated. The recording of membrane potential as well as the magnetic flux as functions of time or spatial coordinates allows to picture some features such as time series, phase portraits and spatial patterns of membrane potential. As a result, diamond-shaped, squared-shaped and spiral-shaped waves are obtained. An elimination process of multi-spiral waves is proposed by exposing such patterns to an external magnetic flux. Thus, for suited values of parameters, the cardiac spiral waves are transmuted into target waves which obviously protect heart against harmful attacks such as ventricular tachycardia and fibrillation. Our results suggest that uncontrolled electromagnetic induction within cardiac tissue may be considered as the principal source of many heart injuries which are the first cause of mortality in the industrial world. [ABSTRACT FROM AUTHOR]

In this paper, we design a memristive system involving magnetic coupling with time-delayed feedback. In a way of autaptic connection, the memristive magnetic coupling feedback is mapped into a neuronal model with ion-channel effect. Compared with the resistive coupling feedback in line with proposed autaptic connection, the memristive magnetic coupling feedback can enhance firing rates more effectively. Furthermore, we analyze collective behaviors of a neural lattice composed of the individual neuronal model connected electrically by bidirectional gap junction. Under the different intensities of gap junction, we find the memristive magnetic coupling feedback can induce a target wave or make a transition from a regular spiral wave to an irregular pattern mixed by both target wave and spiral wave and then to an inverted U-type steady traveling wave. Indeed, the memristive magnetic coupling feedback is able to trigger the transition between different wave patterns. Thereby, we expect that designing the neural lattice with memristive magnetic coupling feedback will be helpful for more advanced applications like neuromorphic circuits. [ABSTRACT FROM AUTHOR]