Electrical Wave Propagation Research Articles

Finding type and location of the source of cardiac arrhythmias from the averaged flow velocity field using the determinant-trace method.

Life threatening cardiac arrhythmias result from abnormal propagation of nonlinear electrical excitation waves in the heart. Finding the locations of the sources of these waves remains a challenging problem. This is mainly due to the low spatial resolution of electrode recordings of these waves. Also, these recordings are subjected to noise. In this paper, we develop a different approach: the AFV-DT method based on an averaged flow velocity (AFV) technique adopted from the analysis of optical flows and the determinant-trace (DT) method used for vector field analysis of dynamical systems. This method can find the location and determine all important types of sources found in excitable media such as focal activity, spiral waves, and waves rotating around obstacles. We test this method on in silico data of various wave excitation patterns obtained using the Luo-Rudy model for cardiac tissue. We show that the method works well for data with low spatial resolutions (up to 8×8) and is stable against noise. Finally, we apply it to two clinical cases and show that it can correctly identify the arrhythmia type and location. We discuss further steps on the development and improvement of this approach.

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.

Climatology of super‐refraction and trapping layers conditions over Central and West Africa

AbstractThe propagation of radio electric waves emitted from ground‐based meteorological instruments is determined through stratification of the atmosphere. In super‐refractive cases characterized by strong temperature inversions or strong vertical moisture gradients, the radar beam can be deflected towards the ground (trapping). This phenomenon often results in spurious returned echoes and misinterpretation of radar images such as erroneous precipitation, wind, and temperature detection. In this study, a 5‐year Central and West Africa (CWA) climatology of the frequency of super‐refractive and trapping‐layer base height has been produced using refractivity computations from European Centre for Medium‐Range Weather Forecasts (ECMWF) analyses at a 40‐km horizontal resolution and 60 levels in the vertical direction. The aim of this climatology is to improve the understanding on how frequent such anomalous propagations conditions are, which is a prerequisite for fully benefiting from radar data information for the multiple purposes of model validation, precipitation analysis, and data assimilation. First, the main climatological features are summarized for the whole CWA: Sahara and inlands seldom experience super‐refraction, whereas coastal areas are strongly affected, especially in regions where the temperature inversion and the trade winds are intense lying near the surface. Over land, seasonal averages of super‐refraction frequencies reach 80% (40%) over moist areas year‐round but remain below 40% (15%) in most other regions. Seasonal statistics exhibit a pronounced diurnal cycle of super‐refraction occurrences, with averaged frequencies peaking at 60% in summer late afternoon over the areas located on the Atlantic Ocean border but inlands region are less affected with super‐refractive cases by midday.

Efficacy of Patient-Specific Strategy: Catheter Ablation Strategy of Persistent Atrial Fibrillation Based on Morphological Repetitiveness by Periodicity and Similarity

Efficacy of Patient-Specific Strategy: Catheter Ablation Strategy of Persistent Atrial Fibrillation Based on Morphological Repetitiveness by Periodicity and Similarity

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

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

Combining Ultrafast Ultrasound and High-Density EMG to Assess Local Electromechanical Muscle Dynamics: A Feasibility Study

Skeletal muscles generate force, enabling movement through a series of fast electro-mechanical activations coordinated by the central nervous system. Understanding the underlying mechanism of such fast muscle dynamics is essential in neuromuscular diagnostics, rehabilitation medicine and sports biomechanics. The unique combination of electromyography (EMG) and ultrafast ultrasound imaging (UUI) provides valuable insights into both electrical and mechanical activity of muscle fibers simultaneously, the excitation-contraction (E-C) coupling. In this feasibility study we propose a novel non-invasive method to simultaneously track the propagation of both electrical and mechanical waves in muscles using high-density electromyography and ultrafast ultrasound imaging (5000 fps). Mechanical waves were extracted from the data through an axial tissue velocity estimator based on one-lag autocorrelation. The E-C coupling in electrically evoked twitch contractions of the Biceps Brachii in healthy participants could successfully be tracked. The excitation wave (i.e. action potential) had a velocity of 3.9±0.5ms <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> and the subsequent mechanical (i.e. contraction) wave had a velocity of 3.5±0.9ms <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> . The experiment showed evidence that contracting sarcomeres that were already activated by the action potential (AP) pull on sarcomeres that were not yet reached by the AP, which was corroborated by simulated contractions of a newly developed multisegmental muscle fiber model, consisting of 500 sarcomeres in series. In conclusion, our method can track the electromechanical muscle dynamics with high spatio-temporal resolution. Ultimately, characterizing E-C coupling in patients with neuromuscular diseases (e.g. Duchenne or Becker muscular dystrophy) may assess contraction efficiency, monitor the progression of the disease, and determine the efficacy of new treatment options.

Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks.

Electroanatomical maps are a key tool in the diagnosis and treatment of atrial fibrillation. Current approaches focus on the activation times recorded. However, more information can be extracted from the available data. The fibers in cardiac tissue conduct the electrical wave faster, and their direction could be inferred from activation times. In this work, we employ a recently developed approach, called physics informed neural networks, to learn the fiber orientations from electroanatomical maps, taking into account the physics of the electrical wave propagation. In particular, we train the neural network to weakly satisfy the anisotropic eikonal equation and to predict the measured activation times. We use a local basis for the anisotropic conductivity tensor, which encodes the fiber orientation. The methodology is tested both in a synthetic example and for patient data. Our approach shows good agreement in both cases and it outperforms a state of the art method in the patient data. The results show a first step towards learning the fiber orientations from electroanatomical maps with physics-informed neural networks.

Ultra-fast current differential protection with high-sensitivity for HVDC transmission lines

Protection of transmission lines is the most important defense against faults in multi-terminal HVDC system. Up until now, no single protection can balance the operation speed and sensitivity needed for all fault types. To solve this problem, a novel current differential protection for HVDC transmission line is proposed in this paper. The intrinsic properties of a HVDC transmission line are analyzed first. Then, essence of ideal current differential protection is revealed and fundamental relations between line models and performance degradation of existing differential protections are discussed. Based on this analysis, a novel current differential protection scheme, including fault detection and faulty pole selection, is developed, and Bergeron model is used to describe the electrical wave propagation process along line, resulting in only simple computations are needed in each calculation cycle. Finally, a simulation model of Wudongde ± 800 kV HVDC project in China is established in PSCAD/EMTDC for verification. By discussing diversified faults and transient processes, simulation results prove that regardless of fault type, distance and transition impedance, the proposed differential protection can respond correctly. Main contribution of this paper is reducing the operation time of differential protection from hundreds of milliseconds to several milliseconds.

Surface Waves in a Nonlinear Metamaterial Rod

AbstractWe consider propagation of surface Transverse Electric (TE) waves in a rod filled with nonlinear metamaterial medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear surface TE waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. New propagation regimes are discovered.

Gaussian Process-Based Spatiotemporal Modeling of Electrical Wave Propagation in Human Atrium.

Rhythm regularity of the heart depends on how electrical impulses spread through the cardiac conduction system. Any abnormal activities in the electrical impulses can lead to serious cardiac disorders or sudden death. It is important to understand the electrical activities of the human heart in both healthy and diseased conditions to determine the cause of cardiac disorders and explore the best therapeutic designs. Mathematical models calibrated with clinical and/or in-vitro data are popularly used to study cardiac function and investigate treatment effects. Most of the current human heart models are highly integrated and couple over a hundred equations across different organizational scales of ion channel, cell, and muscle. The model complex poses a significant computational challenge on cardiac simulation. This study developed a metamodel to replace the time-consuming simulation model. Specifically, Gaussian Process (GP) is used to reconstruct the spatiotemporal variations of the cell membrane potential in left atrium. Four different covariance functions were used to infer the potential distributions. The GP model provides an accurate estimation of the spatiotemporal propagation of electrical waves with a small set of data and shows great advantage in computations as compared to traditional models.

Anisotropic shortening in the wavelength of electrical waves promotes onset of electrical turbulence in cardiac tissue: An in silico study

Several pathological conditions introduce spatial variations in the electrical properties of cardiac tissue. These variations occur as localized or distributed gradients in ion-channel functionality over extended tissue media. Electrical waves, propagating through such affected tissue, demonstrate distortions, depending on the nature of the ionic gradient in the diseased substrate. If the degree of distortion is large, reentrant activity may develop, in the form of rotating spiral (2d) and scroll (3d) waves of electrical activity. These reentrant waves are associated with the occurrence of lethal cardiac rhythm disorders, known as arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), which are believed to be common precursors of sudden cardiac arrest. By using state-of-the-art mathematical models for generic, and ionically-realistic (human) cardiac tissue, we study the detrimental effects of these ionic gradients on electrical wave propagation. We propose a possible mechanism for the development of instabilities in reentrant wave patterns, in the presence of ionic gradients in cardiac tissue, which may explain how one type of arrhythmia (VT) can degenerate into another (VF). Our proposed mechanism entails anisotropic reduction in the wavelength of the excitation waves because of anisotropic variation in its electrical properties, in particular the action potential duration (APD). We find that the variation in the APD, which we induce by varying ion-channel conductances, imposes a spatial variation in the spiral- or scroll-wave frequency ω. Such gradients in ω induce anisotropic shortening of wavelength of the spiral or scroll arms and eventually leads to instabilitites.

A Two-Stage Model Identification Method for Simulation of Electrical Wave Propagation in Heart Tissue

Computer modeling and simulation is fast-moving towards clinical applications to advance cardiac diagnosis and aid treatment planning. As cardiac models become more popular and useful, the need to tailor these models for individual subjects has grown. Therefore, model identification becomes an important step of cardiac modeling. Cardiac model identification is a challenging task, particularly for simulation in high organizational scales such as tissue and organ scales, as the models are nonlinear and involve hidden ion channel gating variables. In this study, we proposed a two-stage model calibration algorithm to estimate the parameters of cardiac tissue model using membrane potential data. Specifically, an ensemble Kalman Filter (EnKF) is used in the first stage to track the membrane potentials and the hidden ion channel gating variables; the outputs from the EnKF are used as the initial values to calculate forward prediction in the second stage. The optimization algorithm minimizes the sum of squared errors in both stages through a coarse and a fine optimization. The proposed method is validated through multiple simulation designs, which shows good accuracy and efficiency.

Optical mapping of electromechanics in intact organs.

Optical mapping has become a widely used and important method in cardiac electrophysiology. The method typically uses voltage-sensitive fluorescent dyes and high-speed cameras to image propagation of electrical waves. However, signals are highly susceptible to artifact caused by motion of the target organ. Consequently, cardiac optical mapping is traditionally performed in isolated, perfused organs whose contraction has been pharmacologically arrested. This has prevented optical mapping from being used to study interactions between electrical and mechanical motion. However, recently, a number of groups have developed methods to implement cardiac optical mapping in the presence of motion. These methods employ two basic strategies: (1) compensate for motion by measuring it or (2) ratiometry. In ratiometry, two signals are recorded from each site. The signals have differing sensitivity to membrane potential, but common motion artifact, which can be cancelled by taking the ratio of the two signals. Some methods use both of these strategies. Methods that measure motion have the additional advantage that this information can be used to quantify the organ’s mechanical function. Doing so enables combined “electromechanical mapping,” which allows optical study of electromechanical interactions. By allowing recording in the presence of motion, the new methods open the door to optical recording in in-vivo preparations. In addition, it is possible to implement electromechanical optical mapping techniques in organ systems other than the heart. For example, it was recently shown that optical mapping of slow wave propagation in the swine stomach is feasible. Such studies have the potential to uncover new information on the role of dysrhythmic slow wave propagation in gastric motility disorders. Impact statement Electrical and mechanical functions in the heart are bidirectionally coupled, yet are usually studied separately because of the different instrumentation technologies that are used in the two areas. Optical mapping is a powerful and widespread tool for imaging electrical propagation, but has traditionally required mechanical function to be arrested. Recently new methods have been devised that enable optical mapping to be performed in beating hearts and also to simultaneously quantify mechanical function. These new technologies promise to yield new information about electromechanical interactions in normal and pathological settings. They are also beginning to find application in other organ systems such as the gastrointestinal tract where they may provide new insight into motility disorders.

Corporate Feed, Compact 2X2 Array Antenna With Enhanced Radiation Characteristics using Metamaterial Structure

In current study, mushroom type metamaterial substrate is designed to operate at ISM band and is embedded in 2X2 array as a ground. Unique properties of mushroom type metamaterial substrate like as high impedance surface (HIS) helped in design of low aperture antenna, Artificial magnetic conductor (AMC) helps in enhancing the radiation characteristics and Forbidden band gap (FBG) helps in suppressing transverse electric (TE) and transverse magnetic (TM) wave propagation hence point of mutual coupling and side lobe levels are reduced. So, 2X2 array antenna with corporate feed resonating at 2.5GHz is embedded by array of mushroom type metamaterial unit cells is designed in HFSS and obtained results are compared with 2X2 array resonating at 2.5GHz on conventional conducting ground results. An enhancement in impedance band width of 2.47%, gain of 2.91dB and with lowered side lobe reduction of 3.74dB.

Three-Dimensional Heart Model-Based Screening of Proarrhythmic Potential by in silico Simulation of Action Potential and Electrocardiograms.

The proarrhythmic risk is a major concern in drug development. The Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative has proposed the JTpeak interval on electrocardiograms (ECGs) and qNet, an in silico metric, as new biomarkers that may overcome the limitations of the hERG assay and QT interval. In this study, we simulated body-surface ECGs from patch-clamp data using realistic models of the ventricles and torso to explore their suitability as new in silico biomarkers for cardiac safety. We tested seven drugs in this study: dofetilide (high proarrhythmic risk), ranolazine, verapamil (QT increasing, but safe), bepridil, cisapride, mexiletine, and diltiazem. Human ventricular geometry was reconstructed from computed tomography (CT) images, and a Purkinje fiber network was mapped onto the endocardial surface. The electrical wave propagation in the ventricles was obtained by solving a reaction-diffusion equation using finite-element methods. The body-surface ECG data were calculated using a torso model that included the ventricles. The effects of the drugs were incorporated in the model by partly blocking the appropriate ion channels. The effects of the drugs on single-cell action potential (AP) were examined first, and three-dimensional (3D) body-surface ECG simulations were performed at free Cmax values of 1×, 5×, and 10×. In the single-cell and ECG simulations at 5× Cmax, dofetilide, but not verapamil or ranolazine, caused arrhythmia. However, the non-increasing JTpeak caused by verapamil and ranolazine that has been observed in humans was not reproduced in our simulation. Our results demonstrate the potential of 3D body-surface ECG simulation as a biomarker for evaluation of the proarrhythmic risk of candidate drugs.

Generalized thermoelasticity of a piezoelectric layer

In the present research, the response of a one-dimensional piezoelectric layer is investigated using the generalized thermoelasticity theory of Lord and Shulman. The layer is subjected to thermal shock on one surface. Three coupled equations, namely, motion equation, energy equation and Maxwell equation in terms of displacement, temperature, and electric potential are established. Using the proper transformation, the mentioned equations are given in a dimensionless form. These equations are discretized by means of the generalized differential quadrature method and traced in time by means of the Newmark time marching scheme. Numerical examples are provided to show the propagation and reflection of thermal, mechanical and electrical waves in a layer. It is shown that under the Lord and Shulman theory, temperature propagates with a finite speed, similar to mechanical displacement wave. However, the electric displacement and potential propagate with infinite speed.

Blow-up solutions of Helmholtz equation for a Kerr slab with a complex linear and nonlinear permittivity

We show that the Helmholtz equation describing the propagation of transverse electric waves in a Kerr slab with a complex linear permittivity εl and a complex Kerr coefficient σ admits blow-up solutions, provided that the real part of σ is negative, i.e., the slab is defocusing. This result applies to homogeneous as well as inhomogeneous Kerr slabs if εl and σ are continuous functions of the transverse coordinate, and the real part of σ is bounded above by a negative number. It shows that a recently reported nonlinear optical amplification effect, which relies on the existence of blow-up solutions, persists the presence of losses and transverse inhomogeneities.

Perfectly Matched Layers for time-harmonic transverse electric wave propagation in cylindrical and toroidal gyrotropic media

In this paper we implement the stretched-coordinate Perfectly Matched Layer (PML) technique in [28] to emulate full power absorption outside the simulation domain for time-harmonic electromagnetic wave propagation in presence of gyrotropic dielectric tensor and curved geometry relevant for magnetized plasma devices. We recall the PML formulation as an artificial inhomogeneous lossy medium, following the stretching into the complex plane of a general system of three orthogonal curvilinear coordinates. We apply the general method in cylindrical and toroidal geometries. We then assess this technique in a simple case combining gyrotropy and coordinate curvature. Our test problem analytically quantifies the reflection of Transverse Electric (TE) cylindrical eigenmodes in a gyrotropic medium by a radial PML in cylindrical geometry. The obtained reflection coefficient involves wave, PML and geometric parameters at the PML location. The new coefficient generalizes the one obtained earlier with Cartesian coordinates, and becomes equivalent when the effects of the local cylindrical curvature at the PML (stretched) location can be neglected. These curvature effects are outlined and the limitations they impose on the properties of the PML are quantified as a function of the relevant parameters. Peculiarities related to the gyrotropy are also highlighted. Finite element calculations of the test problem in two-dimensional cylindrical geometry are exploited to verify these properties numerically. Indications are finally given on how to choose the PML parameters in order to obtain a minimal wave reflection at given numerical cost, taking into account errors associated with the numerical scheme.

Self-organization of conducting pathways explains electrical wave propagation in cardiac tissues with high fraction of non-conducting cells

Cardiac fibrosis occurs in many forms of heart disease and is considered to be one of the main arrhythmogenic factors. Regions with a high density of fibroblasts are likely to cause blocks of wave propagation that give rise to dangerous cardiac arrhythmias. Therefore, studies of the wave propagation through these regions are very important, yet the precise mechanisms leading to arrhythmia formation in fibrotic cardiac tissue remain poorly understood. Particularly, it is not clear how wave propagation is organized at the cellular level, as experiments show that the regions with a high percentage of fibroblasts (65-75%) are still conducting electrical signals, whereas geometric analysis of randomly distributed conducting and non-conducting cells predicts connectivity loss at 40% at the most (percolation threshold). To address this question, we used a joint in vitro-in silico approach, which combined experiments in neonatal rat cardiac monolayers with morphological and electrophysiological computer simulations. We have shown that the main reason for sustainable wave propagation in highly fibrotic samples is the formation of a branching network of cardiomyocytes. We have successfully reproduced the morphology of conductive pathways in computer modelling, assuming that cardiomyocytes align their cytoskeletons to fuse into cardiac syncytium. The electrophysiological properties of the monolayers, such as conduction velocity, conduction blocks and wave fractionation, were reproduced as well. In a virtual cardiac tissue, we have also examined the wave propagation at the subcellular level, detected wavebreaks formation and its relation to the structure of fibrosis and, thus, analysed the processes leading to the onset of arrhythmias.

Conversion of Ca2+ oscillation into propagative electrical signals by Ca2+-activated ion channels and connexin as a reconstituted Ca2+ clock model for the pacemaker activity

Conversion of intracellular Ca2+ signals to electrical activity results in multiple and differing physiological impacts depending on cell types. In some organs such as gastrointestinal and urinary systems, spontaneous Ca2+ oscillation in pacermaker cells can function essentially as a Ca2+ clock mechanism, which has been originally found in pacemaking in sinoatrial node cell of the heart. The conversion of discrete Ca2+ clock events to spontaneous electrical activity is an essential step for the initiation and propagation of pacemaker activity through the multicellular organs resulting in synchronized physiological functions. Here, a model of intracellular signal transduction from a Ca2+ oscillation to initiation of electrical slow waves and their propagation were reconstituted in HEK293 cells. This was accomplished based on ryanodine receptor (RyR) type 3, Ca2+-activated ion channels, i.e. small conductance Ca2+-activated K+ channel (SK2) or Ca2+-activated Cl− channel (TMEM16A), and connexin43 being heterologously co-expressed. The propagation of electrical waves was abolished or substantially reduced by treatment with selective blockers of the expressed channels and 18β-glycyrrhetinic acid, a gap junction inhibitor, respectively. Thus, we demonstrated that the conversion of Ca2+ oscillation to electrical signals with cell to cell propagation can be reconstituted as a model of Ca2+ clock pacemaker activity by combinational expression of critical elements in heterologous expression system.