Spiral Waves Research Articles

Adaptive electric shocks control and elimination of spiral waves using dynamic learning based techniques

Adaptive electric shocks control and elimination of spiral waves using dynamic learning based techniques

Disc distortion revisited

Abstract We revisit the dynamics of razor-thin, stone-cold, self-gravitating discs. By recasting the equations into standard cylindrical coordinates, the linearised vertical dynamics of an exponential disc can be followed for several gigayears on a laptop in a few minutes. An initially warped disc rapidly evolves into a flat inner region and an outward-propagating spiral corrugation wave that rapidly winds up and would quickly thicken a disc with non-zero radial velocity dispersion. The Sgr dwarf galaxy generates a similar warp in the Galactic disc as it passes through pericentre, and the warp generated by the dwarf’s last pericentre ∼35 Myr ago is remarkably similar to the warp traced by the Galaxy’s HI disc. The resemblance to the observed warp is fleeting but its timing is perfect. For the adopted parameters the amplitude of the model warp is a factor 3 too small, but there are several reasons for this being so. The marked flaring of our Galaxy’s low-α disc just outside the solar circle can be explained as a legacy of earlier pericentres.

Effects of Anisotropy, Convection, and Relaxation on Nonlinear Reaction-Diffusion Systems

The effects of relaxation, convection, and anisotropy on a two-dimensional, two-equation system of nonlinearly coupled, second-order hyperbolic, advection–reaction–diffusion equations are studied numerically by means of a three-time-level linearized finite difference method. The formulation utilizes a frame-indifferent constitutive equation for the heat and mass diffusion fluxes, taking into account the tensorial character of the thermal diffusivity of heat and mass diffusion. This approach results in a large system of linear algebraic equations at each time level. It is shown that the effects of relaxation are small although they may be noticeable initially if the relaxation times are smaller than the characteristic residence, diffusion, and reaction times. It is also shown that the anisotropy associated with one of the dependent variables does not have an important role in the reaction wave dynamics, whereas the anisotropy of the other dependent variable results in transitions from spiral waves to either large or small curvature reaction fronts. Convection is found to play an important role in the reaction front dynamics depending on the vortex circulation and radius and the anisotropy of the two dependent variables. For clockwise-rotating vortices of large diameter, patterns similar to those observed in planar mixing layers have been found for anisotropic diffusion tensors.

New mapping algorithm SHIM (SVD, Hilbert Identifying Method) for the extraction of phase singularities and spiral waves in cardiac arrhythmias

Background and ObjectiveAtrial fibrillation (AF) is the most prevalent cardiac arrhythmia worldwide. The effectiveness of AF ablation is restricted primarily by inaccuracies in the voltage-map videos (VMVs) acquired through multielectrode catheters. We introduce an innovative algorithm improving map quality and pinpointing the precise locations of action potential singularities. MethodsThe methodology relies on three key operations: singular value decomposition (SVD), Hilbert transform, and identifying the ridge of singularities SHIM (SVD, Hilbert, Identifying Method). To check its feasibility, this approach was used to analyze record sources from two distinct origins: a) cultures of cardiac cells, and b) real-world atrial fibrillation (AF) measurements. Efficacy is exemplified through four illustrative cases, two involving cultures of cardiac cells exposing action potential spirals, and two clinical cases involving basket catheter voltage-map videos. Resolution goodness is measured by a new method of the ratio of the peak’s height divided by the average width at half maximum or the width of the ridge-of-peaks cross-section. ResultsIn the first sample, the driving rotor became evident only following the SVD procedure stage, and its stable center became more pronounced after the H and I stages. In the case of spiral splitting, SHIM extracted all the individual tiny spiral centers. In the VMVs obtained from the basket catheters, even when the image sharpness was suboptimal, distinct singularity ridges were easily discernible with peak intensities larger than 1. ConclusionThe cumulative impact of the three stages of our analysis suggests that our novel method may excel in identifying problematic sources more effectively than previously utilized systems.

Spatiotemporal patterns in a 2D lattice of Hindmarsh–Rose neurons induced by high-amplitude pulses

We present numerical results for the effects of influence by high-amplitude periodic pulse series on a network of nonlocally coupled Hindmarsh–Rose neurons with 2D geometry of the topology. We consider the case when the pulse amplitude is larger than the amplitude of oscillations in the autonomous network for a wide range of pulse frequencies. An initial regime in the network is a spiral wave chimera. We show that the effects of external influence strongly depend on a balance between the pulse frequency and frequencies of the spectral peaks of the autonomous network. Except for the destructive role of the pulses, when they lead to loss of stability of the initial regime, we have also revealed a constructive role. We have found for the first time the emergence of a new type of multi-front spiral waves, when the wavefront represents a set of several close fronts, and the wave dynamics are significantly different from common spiral waves: neurons oscillate independently to the wave rotation, the rotation velocity is in many times less than for the common spiral wave, etc. We have also discovered several types of cluster spatiotemporal structures induced by the pulses.

Short-Period Skyrmion Crystals in Itinerant Body-Centered Tetragonal Magnets

In this study, we investigate the stability of a magnetic skyrmion crystal with short-period magnetic modulations in a centrosymmetric body-centered tetragonal system. By performing the simulated annealing for the spin model, incorporating the effects of the biquadratic interaction and high-harmonic wave–vector interaction in momentum space, we find that the double-Q square skyrmion crystal consisting of two spin density waves is stabilized in an external magnetic field. We also show that double-Q states appear in both low- and high-field regions; the low-field spin configuration is characterized by an anisotropic double-Q modulation consisting of a superposition of the spiral wave and sinusoidal wave, while the high-field spin configuration is characterized by an isotropic double-Q modulation consisting of a superposition of two sinusoidal waves. Furthermore, we show that the obtained multiple-Q instabilities can be realized for various ordering wave vectors. The results provide the possibility of realizing the short-period skyrmion crystals under the body-centered tetragonal lattice structure.

Influence of conduction heterogeneities on transient spatiotemporal chaos in cardiac excitable media

Life-threatening cardiac arrhythmias such as ventricular fibrillation are often based on chaotic spiral or scroll wave dynamics which can be self-terminating. In this work, we investigate the influence of conduction heterogeneities on the duration of such chaotic transients in generic models of excitable cardiac media. We observe that low and medium densities of heterogeneities extend the average transient lifetime, while at high densities very long transients, potentially persistent chaos, and periodic attractors occur. Published by the American Physical Society 2024

Aurorally Driven Supersonic Gravity Waves in Saturn's Atmosphere

AbstractSimulations with the Saturn Thermosphere‐Ionosphere General Circulation Model have revealed global‐scale gravity waves in Saturn's upper atmosphere that have not been observed or predicted before. They are forced by diurnally varying zonally non‐uniform distributions of Joule heating and ion drag at the high‐latitude auroral regions in both hemispheres and propagate outward from the source region. The supersonic zonal phase speed imposed by Saturn's rotation and the subsonic meridional phase velocity of about 800 m form a distinct spiral wave structure. They exhibit features of gravity waves: vertical phase progression opposite to the propagation of wave energy and long vertical wavelengths consistent with the dispersion relation for gravity waves. The amplitudes of the perturbations grow with height, reaching 6%–10% for relative temperature variations and up to 350 m for the meridional velocity perturbations. The main effect of these waves is to accelerate the retrograde westerly jets.

Native mechano-regulative matrix properties stabilize alternans dynamics and reduce spiral wave stabilization in cardiac tissue.

The stability of wave conduction in the heart is strongly related to the proper interplay between the electrophysiological activation and mechanical contraction of myocytes and extracellular matrix (ECM) properties. In this study, we statistically compare bioengineered cardiac tissues cultured on soft hydrogels ( kPa) and rigid glass substrates by focusing on the critical threshold of alternans, network-physiological tissue properties, and the formation of stable spiral waves that manifest after wave breakups. For the classification of wave dynamics, we use an improved signal oversampling technique and introduce simple probability maps to identify and visualize spatially concordant and discordant alternans as V- and X-shaped probability distributions. We found that cardiac tissues cultured on ECM-mimicking soft hydrogels show a lower variability of the calcium transient durations among cells in the tissue. This lowers the likelihood of forming stable spiral waves because of the larger dynamical range that tissues can be stably entrained with to form alternans and larger spatial spiral tip movement that increases the chance of self-termination on the tissue boundary. Conclusively, we show that a dysfunction in the excitation-contraction coupling dynamics facilitates life-threatening arrhythmic states such as spiral waves and, thus, highlights the importance of the network-physiological interplay between contractile myocytes and the ECM.

Isolated Spiral Solutions of the Ginzburg–Landau Equation

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.

The Ithildin library for efficient numerical solution of anisotropic reaction-diffusion problems in excitable media

Ithildin is an open-source library and framework for efficient parallelized simulations of excitable media, written in the C++ programming language. It uses parallelization on multiple CPU processors via the message passing interface (MPI). We demonstrate the library’s versatility through a series of simulations in the context of the monodomain description of cardiac electrophysiology, including the S1S2 protocol, spiral break-up, and spiral waves in ventricular geometry. Our work demonstrates the power of Ithildin as a tool for studying complex wave patterns in cardiac tissue and its potential to inform future experimental and theoretical studies. We publish our full code with this paper in the name of open science.

Horseshoes and spiral waves: capturing the 3D flow induced by a low-mass planet analytically

ABSTRACT The key difficulty faced by 2D models for planet–disc interaction is in appropriately accounting for the impact of the disc’s vertical structure on the dynamics. 3D effects are often mimicked via softening of the planet’s potential; however, the planet-induced flow and torques often depend strongly on the choice of softening length. We show that for a linear adiabatic flow perturbing a vertically isothermal disc, there is a particular vertical average of the 3D equations of motion that exactly reproduces 2D fluid equations for arbitrary adiabatic index. There is a strong connection here with the Lubow–Pringle 2D mode of the disc. Correspondingly, we find a simple, general prescription for the consistent treatment of planetary potentials embedded within ‘2D’ discs. The flow induced by a low-mass planet involves large-scale excited spiral density waves that transport angular momentum radially away from the planet and ‘horseshoe streamlines’ within the coorbital region. We derive simple linear equations governing the flow that locally capture both effects faithfully simultaneously. We present an accurate coorbital flow solution allowing for inexpensive future study of corotation torques, and predict the vertical structure of the coorbital flow and horseshoe region width for different values of adiabatic index, as well as the vertical dependence of the initial shock location. We find strong agreement with the flow computed in 3D numerical simulations, and with 3D one-sided Lindblad torque estimates, which are a factor of 2–3 lower than values from previous 2D simulations.

The Relationship between Cardiomyocyte Action Potentials and Ion Concentrations: Machine Learning Prediction Modeling and Analysis of Spontaneous Spiral Wave Generation Mechanisms

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.

Spatiotemporal patterns in the active cyclic Potts model

Abstract The nonequilibrium dynamics of a cycling three-state Potts model is studied on a square lattice using Monte Carlo simulations and continuum theory. This model is relevant to chemical reactions on a catalytic surface and to molecular transport across a membrane. Several characteristic modes are formed depending on the flipping energies between successive states and the contact energies between neighboring sites. Under cyclic symmetry conditions, cycling homogeneous phases and spiral waves (SW) form at low and high flipping energies, respectively. In the intermediate flipping energy regime, these two modes coexist temporally in small systems and/or at low contact energies. Under asymmetric conditions, we observed small biphasic domains exhibiting amoeba-like locomotion and temporal coexistence of SW and a dominant non-cyclic one-state phase. An increase in the flipping energy between two successive states, say state 0 and state 1, while keeping the other flipping energies constant, induces the formation of the third phase (state 2), owing to the suppression of the nucleation of state 0 domains. Under asymmetric conditions regarding the contact energies, two different modes can appear depending on the initial state, due to a hysteresis phenomenon.

Dreaming of electrical waves: Generative modeling of cardiac excitation waves using diffusion models.

Electrical waves in the heart form rotating spiral or scroll waves during life-threatening arrhythmias, such as atrial or ventricular fibrillation. The wave dynamics are typically modeled using coupled partial differential equations, which describe reaction-diffusion dynamics in excitable media. More recently, data-driven generative modeling has emerged as an alternative to generate spatio-temporal patterns in physical and biological systems. Here, we explore denoising diffusion probabilistic models for the generative modeling of electrical wave patterns in cardiac tissue. We trained diffusion models with simulated electrical wave patterns to be able to generate such wave patterns in unconditional and conditional generation tasks. For instance, we explored the diffusion-based (i) parameter-specific generation, (ii) evolution, and (iii) inpainting of spiral wave dynamics, including reconstructing three-dimensional scroll wave dynamics from superficial two-dimensional measurements. Furthermore, we generated arbitrarily shaped bi-ventricular geometries and simultaneously initiated scroll wave patterns inside these geometries using diffusion. We characterized and compared the diffusion-generated solutions to solutions obtained with corresponding biophysical models and found that diffusion models learn to replicate spiral and scroll wave dynamics so well that they could be used for data-driven modeling of excitation waves in cardiac tissue. For instance, an ensemble of diffusion-generated spiral wave dynamics exhibits similar self-termination statistics as the corresponding ensemble simulated with a biophysical model. However, we also found that diffusion models produce artifacts if training data are lacking, e.g., during self-termination, and "hallucinate" wave patterns when insufficiently constrained.

Experimental studies of spiral wave teleportation in a light sensitive Belousov-Zhabotinsky system.

Cardiac arrythmias are a form of heart disease that contributes toward making heart disease a significant cause of death globally. Irregular rhythms associated with cardiac arrythmias are thought to arise due to singularities in the heart tissue that generate reentrant waves in the underlying excitable medium. A normal approach to removing such singularities is to apply a high voltage electric shock, which effectively resets the phase of the cardiac cells. A concern with the use of this defibrillation technique is that the high-energy shock can cause lasting damage to the heart tissue. Various theoretical works have investigated lower-energy alternatives to defibrillation. In this work, we demonstrate the effectiveness of a low-energy defibrillation method in an experimental 2D Belousov-Zhabotinsky (BZ) system. When implemented as a 2D spatial reaction, the BZ reaction serves as an effective analog of general excitable media and supports regular and reentrant wave activity. The defibrillation technique employed involves targeted low-energy perturbations that can be used to "teleport" and/or annihilate singularities present in the excitable BZ medium.

Unpinning and elimination of spiral waves and turbulence through local optogenetical illumination.

Spiral waves in cardiac tissue have been identified as a significant factor leading to life-threatening arrhythmias and ventricular fibrillation. Consequently, understanding the mechanisms underlying the dynamics of such waves and exploring strategies for their elimination have garnered substantial interest and emerged as crucial research objectives. Spiral waves often become pinned (trapped) at anatomical obstacles in cardiac tissue, resulting in increased stability and posing challenges for their elimination. The unpinning of spiral waves can be achieved through the application of an external electric field and has been the subject of previous research. Recently, optogenetics has emerged as an alternative method to modulate electrical activity by illumination of cardiac tissue. In this paper, we employ mathematical modeling to investigate the potential of utilizing local illumination to unpin and eliminate spiral waves in cardiac tissue. We also extend this methodology to explore the effects of more complex turbulent excitation patterns. We conduct simulations using low-dimensional (Barkley) and ionic (Fenton-Karma) models of cardiac tissue, incorporating optogenetical channels. Our findings demonstrate that local suprathreshold illumination can successfully unpin spiral waves in 100% of cases. Notably, unlike unpinning by electrical field stimulation, this approach does not necessitate precise timing of stimulus application during a specific phase of rotation. Additionally, we demonstrate that periodic optogenetical stimulation can effectively eliminate both unpinned spiral waves and turbulence by moving them toward the boundary via an antitachycardia pacing mechanism.

A geological telescope through the galaxy?

We reside within a relatively interior position within the Milky Way galaxy, which hinders our ability to understand its structure. Nonetheless, astrophysical observations of other galaxies in unison with spectroscopic measurements have produced a model for the Milky Way as a grand design, barred, spiral arm galaxy, with either two or four arms. Viewing through the plane of the Milky Way is not possible with any current astrophysical technique. However, perhaps terrestrial geology can help where current observations of our stellar environment cannot. During the orbit of our Solar System around the galactic centre, Earth will have seen different cosmic surroundings, as a function of the Solar System's orbit (240 km s −1 ) that is faster than the spiral arm's density waves (210 km s −1 ). Specifically, if the terrestrial impact record, or proxies for it, in some cryptic way reflect perturbations on the gravity field of the local Solar System, then Earth may act as a geological orrery, with some interesting implications. Here we explore various models for the design of the Milky Way and compare these with geological proxies proposed by some as indicators for impact flux, through the deep time record within our planet. Isotope signatures in zircon are statistically coherent with a four-armed spiral model. However, even better correspondence is shown between the terrestrial isotopic record and more complex atomic hydrogen models of the galaxy.

Arrhythmogenic Potential of Myocardial Edema: The Interstitial Osmolality Induces Spiral Waves and Multiple Excitation Wavelets.

Myocardial edema is a common symptom of pathological processes in the heart, causing aggravation of cardiovascular diseases and leading to irreversible myocardial remodeling. Patient-based studies show that myocardial edema is associated with arrhythmias. Currently, there are no studies that have examined how edema may influence changes in calcium dynamics in the functional syncytium. We performed optical mapping of calcium dynamics on a monolayer of neonatal rat cardiomyocytes with Fluo-4. The osmolality of the solutions was adjusted using the NaCl content. The initial Tyrode solution contained 140 mM NaCl (1T) and the hypoosmotic solutions contained 105 (0.75T) and 70 mM NaCl (0.5T). This study demonstrated a sharp decrease in the calcium wave propagation speed with a decrease in the solution osmolality. The successive decrease in osmolality also showed a transition from a normal wavefront to spiral wave and multiple wavelets of excitation with wave break. Our study demonstrated that, in a cellular model, hypoosmolality and, as a consequence, myocardial edema, could potentially lead to fatal ventricular arrhythmias, which to our knowledge has not been studied before. At 0.75T spiral waves appeared, whereas multiple wavelets of excitation occurred in 0.5T, which had not been recorded previously in a two-dimensional monolayer under conditions of cell edema without changes in the pacing protocol.

Abstract We015: Modeling Cardiac Arrhythmogenicity of hiPSC-CMs and Cardiac Fibroblasts Nanopatterned Coculture and Machine Learning

Background: Sudden cardiac death is one of the most threatening heart conditions in the U.S. Most individuals have an underlying structural cardiac disease associated with cardiac fibrosis and ventricular arrhythmia. The relationship between fibrosis and arrhythmias is found to be related to cardiovascular cell couplings, especially cardiomyocytes (CMs) and cardiac fibroblasts (CFs). While animal models have been applied to model cardiac arrhythmias, the disparities between animal models and humans limit the accuracy of pro-arrhythmic predictions. The use of human induced pluripotent stem cells (hiPSCs)-derived CMs has permitted highly modular testing conditions, specifically the ratio of CFs to CMs in an engineered coculture system. Moreover, machine learning (ML) has become an emerging tool in cardiology, such as cardiac toxicity and function evaluation and classification, with its unique advantages of high accuracy and efficiency with less human bias and intuition. Hypothesis: We hypothesize that cardiac fibrosis-associated arrhythmia will be modeled by nanopatterned coculture of hiPSC-CMs and CFs at varied ratios, and the arrhythmic samples will be accurately and efficiently classified by ML algorithms. Approach: The hiPSC-CMs were cocultured and nanopatterned with CFs at ratios of 0 to 30% for 7 days. Upon the electrical pacing at 1Hz, the action potential was recorded by live-cell optical mapping with FluoVolt. The recorded membrane potential and electrical propagation were analyzed by Matlab-based Electomap software. Results: The cocultured hiPSC-CMs and CFs were aligned with aligned sarcomeres and uni-directional contraction ( Fig. 1a ). The cardiac arrhythmia was observed in 15% CFs with spiral wave ( Fig. 1b ) in comparison to the hiPSC-CMs with 0% CF. Beat-to-beat and depolarization durations were found significant with top ranks in Feature Importance to facilitate the distinction between arrhythmic and non-arrhythmic samples by the unsupervised K-means Clustering ( Figs. 1c and d ). Conclusions: We have successfully established a nanopatterned coculturing system of hiPSC-CMs and CFs for modeling cardiac fibrosis-induced arrhythmia, which was further analyzed and classified by ML algorithms. This system reveals great potential for better understanding the relationship between cardiac fibrosis-associated arrhythmia and sudden cardiac death and also drug evaluation for anti-cardiac arrhythmia.