Waves In Cardiac Tissue Research Articles

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.

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.

Tracing the elimination of reentry spiral waves in defibrillation: Temperature effects

The presence of spiral waves in cardiac tissue causes ventricular fibrillation (VF). Clinical studies have demonstrated that reducing the blood temperature to hypothermia can improve the success rate of electrical defibrillation when VF occurs. In this paper, the Hodgkin-Huxley-style model is used to simulate the effects of temperature and electric shock on the spiral waves present in mammalian tissues, and the phase singularity (PS) identification methods are used to track the wave behaviors in network, finally the Luo-Rudy model is used to test the applicability of our results for cardiac tissues. The results show that temperature modulates the optimal parameters for defibrillation: (1) Arnold's tongue structure shows that an alternating electric field close to the tissue natural frequency (e.g.: cardiac sinus rhythm) allows the nodes to be phase-locked or PS directionally drift at a smaller intensity, thus eliminating spiral waves more effectively than a constant electric field. (2) The average node frequency increases with temperature whether the network is synchronized or present spiral waves, and the statistics show that the robustness of electric defibrillation can be enhanced when the tissue is at moderate hypothermia. (3) More interestingly, we define the defibrillation score (DFS) and find that moderate hypothermia is a balance to improves defibrillation success, which may provide some insights for practical defibrillation studies.

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

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

Spiral wave drift under optical feedback in cardiac tissue.

Spiral waves occur in various types of excitable media and their dynamics determine the spatial excitation patterns. An important type of spiral wave dynamics is drift, as it can control the position of a spiral wave or eliminate a spiral wave by forcing it to the boundary. In theoretical and experimental studies of the Belousov-Zhabotinsky reaction, it was shown that the most direct way to induce the controlled drift of spiral waves is by application of an external electric field. Mathematically such drift occurs due to the onset of additional gradient terms in the Laplacian operator describing excitable media. However, this approach does not work for cardiac excitable tissue, where an external electric field does not result in gradient terms. In this paper, we propose a method of how to induce a directed linear drift of spiral waves in cardiac tissue, which can be realized as an optical feedback control in tissue where photosensitive ion channels are expressed. We illustrate our method by using the FitzHugh-Nagumo model for cardiac tissue and the generic model of photosensitive ion channels. We show that our method works for continuous and discrete light sources and can effectively move spiral waves in cardiac tissue, or eliminate them by collisions with the boundary or with another spiral wave. We finally implement our method by using a biophysically motivated photosensitive ion channel model included to the Luo-Rudy model for cardiac cells and show that the proposed feedback control also induces directed linear drift of spiral waves in a wide range of light intensities.

Interaction of multiple spiral rotors in a reaction-diffusion system.

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

Control of spiral waves in optogenetically modified cardiac tissue by periodic optical stimulation

Resonant drift of nonlinear spiral waves occurs in various types of excitable media under periodic stimulation. Recently a novel methodology of optogenetics has emerged, which allows to affect excitability of cardiac cells and tissues by optical stimuli. In this paper we study if resonant drift of spiral waves in the heart can be induced by a homogeneous weak periodic optical stimulation of cardiac tissue. We use a two-variable and a detailed model of cardiac tissue and add description of depolarizing and hyperpolarizing optogenetic ionic currents. We show that weak periodic optical stimulation at a frequency equal to the natural rotation frequency of the spiral wave induces resonant drift for both depolarizing and hyperpolarizing optogenetic currents. We quantify these effects and study how the speed of the drift and its direction depend on the initial conditions. We also derive analytical formulas based on the response function theory which correctly predict the drift velocity and its trajectory. We conclude that optogenetic methodology can be used for control of spiral waves in cardiac tissue and discuss its possible applications.

Efficiency of parallel anisotropic mesh adaptation for the solution of the bidomain model in cardiac tissue

Electrocardiology models are nonlinear reaction–diffusion type systems, where the numerical simulation requires extremely fine meshes to accurately compute the heart’s electrical activity. Anisotropic mesh adaptation methods have been proven to be efficient for simulating cardiac dynamic by many authors and showed a considerable improvement in the numerical accuracy while reducing the computational expenses. However, the efficiency of these techniques in parallel computing environments has not been shown yet, especially when compared to the performance of parallel uniform meshes. In this paper, we demonstrate the efficiency of a parallel anisotropic mesh adaptation method for the solution of the bidomain model in cardiac tissue. The technique is based on an efficient error estimator appropriate for second or higher order numerical solutions. To demonstrate the effectiveness of the developed methodology, comparisons between the numerical simulations on parallel adapted meshes with those on parallel uniform meshes are presented. The computational efficiency is assessed by computing spiral and scroll waves in cardiac tissue.

Predicting the duration of chaotic transients in excitable media

The spatiotemporal dynamics of excitable media may exhibit chaotic transients. We investigate this transient chaos in the 2D Fenton–Karma model describing the propagation of electrical excitation waves in cardiac tissue and compute the average duration of chaotic transients in dependence on model parameter values. Furthermore, other characteristics like the dominant frequency, the size of the excitable gap, pseudo ECGs, the number of phase singularities and parameters characterizing the action potential duration restitution curve are determined and it is shown that these quantities can be used to predict the average transient time using polynomial regression.

Dynamic behaviors of spiral waves in cardiac tissue under electromagnetic radiation

A new modified Fitzhugh–Nagumo model is proposed to study the dynamic behaviors of spiral waves in cardiac tissue under fixed or periodic electromagnetic radiation. The effects of fixed electromagnetic radiation and the amplitude and frequency of periodic electromagnetic radiation on the pattern transitions of the spiral waves are investigated, respectively. Our numerical results show that although spiral waves can normally propagate with slight deformation under weaker fixed or periodic electromagnetic radiation, stronger fixed or periodic electromagnetic radiation can terminate the spiral waves, cause the drift of the spirals and turbulence, and magnetize the spiral waves to the homogeneous state. Extensive comparative analysis results confirm that fixed electromagnetic radiation is more helpful to modify and magnetize the spiral waves to the homogeneous state, but the spiral waves more easily change to the chaotic state under periodic electromagnetic radiation. The simulation results also show that both increasing the amplitude and decreasing the frequency can block the rotating spiral waves and cause turbulence, but our considerable numerical results find that lower frequency more easily develops spatiotemporal chaos from the media.

Data-Driven Modeling and Prediction of Complex Spatio-Temporal Dynamics in Excitable Media

Spatio-temporal chaotic dynamics in a two-dimensional excitable medium is (cross-) estimated using a machine learning method based on a convolutional neural network combined with a conditional random field. The performance of this approach is demonstrated using the four variables of the Bueno-Orovio-Fenton-Cherry model describing electrical excitation waves in cardiac tissue. Using temporal sequences of two-dimensional fields representing the values of one or more of the model variables as input the network successfully cross-estimated all variables and provides excellent forecasts when applied iteratively.

Elimination of spiral waves in excitable media by magnetic induction

The formation of spiral waves in excitable media is a fascinating example of the beauty of nonlinear dynamics in spatiotemporal systems. Apart from the beauty of the patterns, the subject also has many practical application. For example, the emergence of spiral waves in cardiac tissue can lead to arrhythmias. Cortical spiral waves are also involved in epileptic seizures. Motivated by this, we here study the effects of magnetic induction on the formation of spiral waves in excitable media. An external sinusoidal magnetic induction with different amplitudes and angular frequencies is applied in order to study whether spiral waves could be eliminated. We use a network of coupled neurons as a model for the excitable medium. The four-variable magnetic Hindmarsh–Rose model is used for the local dynamics of each isolated neuron. The distribution of the cell membrane potential over time, affected by magnetic induction, is determined and the results are depicted as snapshots of the 2D network. Our research reveals that the continuance of rotating spiral seeds is impaired by high-amplitude magnetic induction. Moreover, we show that low-frequency induction is not capable of breaking the reorganizing rhythm of the spiral seeds, while much higher frequencies can be too fast to overcome this special rhythm.

The dynamics of spiral tip adjacent to inhomogeneity in cardiac tissue

Rotating spiral waves in cardiac tissue are implicated in life threatening cardiac arrhythmias. Experimental and theoretical evidences suggest the inhomogeneities in cardiac tissue play a significant role in the dynamics of spiral waves. Based on a modified 2D cardiac tissue model, the interaction of inhomogeneity on the nearby rigidly rotating spiral wave is numerically studied. The adjacent area of the inhomogeneity is divided to two areas, when the initial rotating center of the spiral tip is located in the two areas, the spiral tip will be attracted and anchor on the inhomogeneity finally, or be repulsed away. The width of the area is significantly dependent on the intensity and size of the inhomogeneity. Our numerical study sheds some light on the mechanism of the interaction of inhomogeneity on the spiral wave in cardiac tissue.

Impact of Bounded Noise and Rewiring on the Formation and Instability of Spiral Waves in a Small-World Network of Hodgkin-Huxley Neurons.

Spiral waves are observed in the chemical, physical and biological systems, and the emergence of spiral waves in cardiac tissue is linked to some diseases such as heart ventricular fibrillation and epilepsy; thus it has importance in theoretical studies and potential medical applications. Noise is inevitable in neuronal systems and can change the electrical activities of neuron in different ways. Many previous theoretical studies about the impacts of noise on spiral waves focus an unbounded Gaussian noise and even colored noise. In this paper, the impacts of bounded noise and rewiring of network on the formation and instability of spiral waves are discussed in small-world (SW) network of Hodgkin-Huxley (HH) neurons through numerical simulations, and possible statistical analysis will be carried out. Firstly, we present SW network of HH neurons subjected to bounded noise. Then, it is numerically demonstrated that bounded noise with proper intensity σ, amplitude A, or frequency f can facilitate the formation of spiral waves when rewiring probability p is below certain thresholds. In other words, bounded noise-induced resonant behavior can occur in the SW network of neurons. In addition, rewiring probability p always impairs spiral waves, while spiral waves are confirmed to be robust for small p, thus shortcut-induced phase transition of spiral wave with the increase of p is induced. Furthermore, statistical factors of synchronization are calculated to discern the phase transition of spatial pattern, and it is confirmed that larger factor of synchronization is approached with increasing of rewiring probability p, and the stability of spiral wave is destroyed.

Mathematical analysis of cardiac electromechanics with physiological ionic model

This paper is concerned with the mathematical analysis of a coupled elliptic-parabolic system modeling the interaction between the propagation of electric potential coupled with general physiological ionic models and subsequent deformation of the cardiac tissue. A prototype system belonging to this class is provided by the electromechanical bidomain model, which is frequently used to study and simulate electrophysiological waves in cardiac tissue. The coupling between muscle contraction, biochemical reactions and electric activity is introduced with a so-called active strain decomposition framework, where the material gradient of deformation is split into an active (electrophysiology-dependent) part and an elastic (passive) one. We prove existence of weak solutions to the underlying coupled electromechanical bidomain model under the assumption of linearized elastic behavior and a truncation of the updated nonlinear diffu-sivities. The proof of the existence result, which constitutes the main thrust of this paper, is proved by means of a non-degenerate approximation system, the Faedo-Galerkin method, and the compactness method.

Scanning and resetting the phase of a pinned spiral wave using periodic far field pulses

Spiral waves in cardiac tissue can pin to tissue heterogeneities and form stable pinned waves. These waves can be unpinned by electric stimuli applied close to the pinning center during the vulnerable window of the spiral. Using a phase transition curve (PTC), we quantify the response of a pinned wave in a cardiac monolayer to secondary excitations generated electric field pulses. The PTC can be used to construct a one-dimensional map that faithfully predicts the pinned wave’s response to periodic field stimuli. Based on this 1D map, we predict that pacing at a frequency greater than the spiral frequency, over drive pacing, leads to phase locking of the spiral to the stimulus, which hinders unpinning. In contrast, under drive pacing can lead to scanning of the phase window of the spiral, which facilitates unpinning. The predicted mechanisms of phase scanning and phase locking are experimentally tested and confirmed in the same monolayers that were used to obtain the PTC. Our results have the potential to help choose optimal parameters for low energy antifibrillation pacing schemes.

Controlling spiral wave and spatiotemporal chaos in cardiac tissues by slowing sodium channel activation and inactivation

Much evidence shows that the appearance and instability of the spiral wave in cardiac tissue can be linked to a kind of heart disease. Therefore there needs a method of controlling spiral wave more safely and effectively. The intelligent modification of specific ion channel to achieve desired control is the future direction of gene therapy in heart disease. The key question that has to be answered is which ion channel is the best candidate for controlling spiral wave. Modern biological technology has been able to make the mutation of sodium channel gene to change its relaxation time constant. In this paper, we adopt the Luo-Rudy phase I model to investigate how to regulate the relaxation time constant of sodium channel gate to control spiral wave and spatiotemporal chaos in cardiac tissues. We suggest a control strategy which slows down the rate of sodium current activation and inactivation by increasing the relaxation time constant of the sodium activation gate by up to times while its fast inactivation gate is clamped to 0.77. Numerical simulation results show that a gradual increase of will cause the activation gate of sodium current to reach maximum more slowly, and its amplitude is gradually reduced, so that the amplitude and duration of the action potential of cardiomyocyte are gradually reduced. When the factor is large enough, the spiral wave and spatiotemporal chaos cannot propagate in the medium except planar wave with low frequency. The reason is that the excitabilities of medium and wave speed significantly decrease. Therefore, the spiral waves and spatiotemporal chaos can be effectively eliminated when the control time is properly selected and the factor is large enough. Spiral wave and spatiotemporal chaos disappear mainly due to conduction obstacle. In some cases, spiral wave can disappear through the transition from spiral wave to target wave or tip retraction. Spatiotemporal chaos disappears after spatiotemporal chaos has evolved into meandering spiral wave. When the parameters are chosen properly, the phenomenon that spiral wave evolves into a self-sustained target wave is also observed. The corresponding target wave source is the pair of spiral waves with opposite rotation directions. These results can provide useful information for gene therapy in heart disease.

Optical control of excitation waves in cardiac tissue.

In nature, macroscopic excitation waves1,2 are found in a diverse range of settings including chemical reactions, metal rust, yeast, amoeba and the heart and brain. In the case of living biological tissue, the spatiotemporal patterns formed by these excitation waves are different in healthy and diseased states2,3. Current electrical and pharmacological methods for wave modulation lack the spatiotemporal precision needed to control these patterns. Optical methods have the potential to overcome these limitations, but to date have only been demonstrated in simple systems, such as the Belousov-Zhabotinsky chemical reaction4. Here, we combine dye-free optical imaging with optogenetic actuation to achieve dynamic control of cardiac excitation waves. Illumination with patterned light is demonstrated to optically control the direction, speed and spiral chirality of such waves in cardiac tissue. This all-optical approach offers a new experimental platform for the study and control of pattern formation in complex biological excitable systems.

Suppression of the spiral wave in cardiac tissue by using forcing currents with diversity

Forcing currents are generated by using two types of constant currents to stimulate different areas of a medium. The external current is mapped into transmembrane current and stable gradient force is induced to drive the stable rotating spiral wave. The medium becomes homogeneous when the spiral wave is removed and the time series of sampled membrane potentials becomes stable value without considering noise. The scheme is confirmed to be effective in the presence of Gaussian white noise.

New index for categorising cardiac reentrant wave: in silico evaluation

Based on the similarity between a reentrant wave in cardiac tissue and a vortex in fluid dynamics, the authors hypothesised that a new non-dimensional index, like the Reynolds number in fluid dynamics, may play a critical role in categorising reentrant wave dynamics. Therefore the goal of the present study is to devise a new index to characterise electric wave conduction in cardiac tissue and examined whether this index can be used as a biomarker for categorising the reentrant wave pattern in cardiac tissue. Similar to the procedure used to derive the Reynolds number in fluid dynamics, the authors used a non-dimensionalisation technique to obtain the new index. Its usefulness was verified using a two-dimensional simulation model of electrical wave propagation in cardiac tissue. The simulation results showed that electrical waves in cardiac tissue move into an unstable region when the index exceeds a threshold value.