Electrical Excitation Waves Research Articles

Doppler shift during overdrive pacing of spiral waves. Prediction of the annihilation site

Spiral waves of electrical excitation can occur in the heart in cases of dangerous arrhythmias. Low-voltage cardioversion is a treatment method that aims to induce drift and annihilation of the spiral waves. Drift of wave sources causes Doppler shift but it has not been studied for the waves that are interacting with plane wave trains in excitable media. In our numerical research, we made 2D and 3D solitary spiral waves drift by external pacing and studied the Doppler shift using detectors at the tissue boundary. We examined spiral waves with a circular core and meandering waves and tried various external stimulation periods. We observed that the period of the source in the direction of the drift decreased, which could be described quite precisely in 2D by the classical Doppler shift formula. Moreover, the boundary annihilation site of the spiral can be accurately predicted as the location where the minimal period at the boundary is measured.

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.

Rotational Activity around an Obstacle in 2D Cardiac Tissue in Presence of Cellular Heterogeneity

Waves of electrical excitation rotating around an obstacle is one of the important mechanisms of dangerous cardiac arrhythmias occurring in the heart damaged by a post-infarction scar. Such a scar is also surrounded by the region of heterogeneity called a gray zone. In this paper, we perform the first comprehensive numerical study of various regimes of wave rotation around an obstacle surrounded by a gray zone. We use the TP06 cellular ionic model for human cardiomyocytes and study how the period and the pattern of wave rotation depend on the radius of a circular obstacle and the width of a circular gray zone. Our main conclusions are the following. The wave rotation regimes can be subdivided into three main classes: (1) functional rotation, (2) scar rotation and the newly found (3) gray zone rotation regimes. In the scar rotation regime, the wave rotates around the obstacle, while in the gray zone regime, the wave rotates around the gray zone. As a result, the period of rotation is determined by the perimeter of the scar, or gray zone perimeter correspondingly. The transition from the scar to the gray rotation regimes can be determined from the minimal period principle, formulated in this paper. We have also observed additional regimes associated with two types of dynamical instabilities which may affect or not affect the period of rotation. The results of this study can help to identify the factors determining the period of arrhythmias in post-infarction patients.

Scroll wave with negative filament tension in a model of the left ventricle of the human heart and its overdrive pacing.

Nonlinear waves of electrical excitation initiate cardiac contraction. Abnormal wave propagation in the heart, e.g., spiral waves, can lead to sudden cardiac arrest. This study analyzed the dynamics of spiral waves under the influence of an instability called negative filament tension, and examined how the spiral waves can be eliminated through high-frequency pacing. A generic anatomical model of the left ventricle of the human heart and the Aliev-Panfilov model for cardiac tissue were used. The study showed that the source of such arrhythmia is elongated filaments with lengths that can be 10-20 times greater than the characteristic thickness of the heart wall. In anisotropic tissue, the filament elongated before it was annihilated at the base of the heart. The spiral waves were eliminated through overdrive pacing with stimulation periods from 0.8 to 0.95 relative to the spiral wave period. The minimum time for the expulsion was about 10s.

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.

Reconstructing Complex Cardiac Excitation Waves From Incomplete Data Using Echo State Networks and Convolutional Autoencoders

The mechanical contraction of the pumping heart is driven by electrical excitation waves running across the heart muscle due to the excitable electrophysiology of heart cells. With cardiac arrhythmias these waves turn into stable or chaotic spiral waves (also called rotors) whose observation in the heart is very challenging. While mechanical motion can be measured in 3D using ultrasound, electrical activity can (so far) not be measured directly within the muscle and with limited resolution on the heart surface, only. To bridge the gap between measurable and not measurable quantities we use two approaches from machine learning, echo state networks and convolutional autoencoders, to solve two relevant data modelling tasks in cardiac dynamics: Recovering excitation patterns from noisy, blurred or undersampled observations and reconstructing complex electrical excitation waves from mechanical deformation. For the synthetic data sets used to evaluate both methods we obtained satisfying solutions with echo state networks and good results with convolutional autoencoders, both clearly indicating that the data reconstruction tasks can in principle be solved by means of machine learning.

Inverse mechano-electrical reconstruction of cardiac excitation wave patterns from mechanical deformation using deep learning.

The inverse mechano-electrical problem in cardiac electrophysiology is the attempt to reconstruct electrical excitation or action potential wave patterns from the heart's mechanical deformation that occurs in response to electrical excitation. Because heart muscle cells contract upon electrical excitation due to the excitation-contraction coupling mechanism, the resulting deformation of the heart should reflect macroscopic action potential wave phenomena. However, whether the relationship between macroscopic electrical and mechanical phenomena is well-defined and unique enough to be utilized for an inverse imaging technique in which mechanical activation mapping is used as a surrogate for electrical mapping has yet to be determined. Here, we provide a numerical proof-of-principle that deep learning can be used to solve the inverse mechano-electrical problem in phenomenological two- and three-dimensional computer simulations of the contracting heart wall, or in elastic excitable media, with muscle fiber anisotropy. We trained a convolutional autoencoder neural network to learn the complex relationship between electrical excitation, active stress, and tissue deformation during both focal or reentrant chaotic wave activity and, consequently, used the network to successfully estimate or reconstruct electrical excitation wave patterns from mechanical deformation in sheets and bulk-shaped tissues, even in the presence of noise and at low spatial resolutions. We demonstrate that even complicated three-dimensional electrical excitation wave phenomena, such as scroll waves and their vortex filaments, can be computed with very high reconstruction accuracies of about 95% from mechanical deformation using autoencoder neural networks, and we provide a comparison with results that were obtained previously with a physics- or knowledge-based approach.

Induced drift of scroll waves in the Aliev–Panfilov model and in an axisymmetric heart left ventricle

AbstractThe 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.

Role of Oxidation-Dependent CaMKII Activation in the Genesis of Abnormal Action Potentials in Atrial Cardiomyocytes: A Simulation Study

Atrial fibrillation is a common cardiac arrhythmia with an increasing incidence rate. Particularly for the aging population, understanding the underlying mechanisms of atrial arrhythmia is important in designing clinical treatment. Recently, experiments have shown that atrial arrhythmia is associated with oxidative stress. In this study, an atrial cell model including oxidative-dependent Ca2+/calmodulin- (CaM-) dependent protein kinase II (CaMKII) activation was developed to explore the intrinsic mechanisms of atrial arrhythmia induced by oxidative stress. The simulation results showed that oxidative stress caused early afterdepolarizations (EADs) of action potentials by altering the dynamics of transmembrane currents and intracellular calcium cycling. Oxidative stress gradually elevated the concentration of calcium ions in the cytoplasm by enhancing the L-type Ca2+ current and sarcoplasmic reticulum (SR) calcium release. Owing to increased intracellular calcium concentration, the inward Na+/Ca2+ exchange current was elevated which slowed down the repolarization of the action potential. Thus, the action potential was prolonged and the L-type Ca2+ current was reactivated, resulting in the genesis of EAD. Furthermore, based on the atrial single-cell model, a two-dimensional (2D) ideal tissue model was developed to explore the effect of oxidative stress on the electrical excitation wave conduction in 2D tissue. Simulation results demonstrated that, under oxidative stress conditions, EAD hindered the conduction of electrical excitation and caused an unstable spiral wave, which could disrupt normal cardiac rhythm and cause atrial arrhythmia. This study showed the effects of excess reactive oxygen species on calcium cycling and action potential in atrial myocytes and provided insights regarding atrial arrhythmia induced by oxidative stress.

High-Resolution Optical Measurement of Cardiac Restitution, Contraction, and Fibrillation Dynamics in Beating vs. Blebbistatin-Uncoupled Isolated Rabbit Hearts.

Optical mapping is a high-resolution fluorescence imaging technique, that uses voltage- or calcium-sensitive dyes to visualize electrical excitation waves on the heart surface. However, optical mapping is very susceptible to the motion of cardiac tissue, which results in so-called motion artifacts in the fluorescence signal. To avoid motion artifacts, contractions of the heart muscle are typically suppressed using pharmacological excitation-contraction uncoupling agents, such as Blebbistatin. The use of pharmacological agents, however, may influence cardiac electrophysiology. Recently, it has been shown that numerical motion tracking can significantly reduce motion-related artifacts in optical mapping, enabling the simultaneous optical measurement of cardiac electrophysiology and mechanics. Here, we combine ratiometric optical mapping with numerical motion tracking to further enhance the robustness and accuracy of these measurements. We evaluate the method's performance by imaging and comparing cardiac restitution and ventricular fibrillation (VF) dynamics in contracting, non-working vs. Blebbistatin-arrested Langendorff-perfused rabbit hearts (N = 10). We found action potential durations (APD) to be, on average, 25 ± 5% shorter in contracting hearts compared to hearts uncoupled with Blebbistatin. The relative shortening of the APD was found to be larger at higher frequencies. VF was found to be significantly accelerated in contracting hearts, i.e., 9 ± 2Hz with Blebbistatin and 15 ± 4Hz without Blebbistatin, and maintained a broader frequency spectrum. In contracting hearts, the average number of phase singularities was NPS = 11 ± 4 compared to NPS = 6 ± 3 with Blebbistatin during VF on the anterior ventricular surface. VF inducibility was reduced with Blebbistatin. We found the effect of Blebbistatin to be concentration-dependent and reversible by washout. Aside from the electrophysiological characterization, we also measured and analyzed cardiac motion. Our findings may have implications for the interpretation of optical mapping data, and highlight that physiological conditions, such as oxygenation and metabolic demand, must be carefully considered in ex vivo imaging experiments.

Drift of Scroll Waves in a Mathematical Model of a Heterogeneous Human Heart Left Ventricle

Rotating spiral waves of electrical excitation underlie many dangerous cardiac arrhythmias. The heterogeneity of myocardium is one of the factors that affects the dynamics of such waves. In this paper, we present results of our simulations for scroll wave dynamics in a heterogeneous model of the human left ventricle with analytical anatomically based representation of the geometry and anisotropy. We used a set of 18 coupled differential equations developed by ten Tusscher and Panfilov (TP06 model) which describes human ventricular cells based on their measured biophysical properties. We found that apicobasal heterogeneity dramatically changes the scroll wave dynamics. In the homogeneous model, the scroll wave annihilates at the base, but the moderate heterogeneity causes the wave to move to the apex and then continuously rotates around it. The rotation speed increased with the degree of the heterogeneity. However, for large heterogeneity, we observed formation of additional wavebreaks and the onset of complex spatio-temporal patterns. Transmural heterogeneity did not change the dynamics and decreased the lifetime of the scroll wave with an increase in heterogeneity. Results of our numerical experiments show that the apex may be a preferable location of the scroll wave, which may be important for development of clinical interventions.

Terminating transient chaos in spatially extended systems.

In many real-life systems, transient chaotic dynamics plays a major role. For instance, the chaotic spiral or scroll wave dynamics of electrical excitation waves during life-threatening cardiac arrhythmias can terminate by itself. Epileptic seizures have recently been related to the collapse of transient chimera states. Controlling chaotic transients, either by maintaining the chaotic dynamics or by terminating it as quickly as possible, is often desired and sometimes even vital (as in the case of cardiac arrhythmias). We discuss in this study that the difference of the underlying structures in state space between a chaotic attractor (persistent chaos) and a chaotic saddle (transient chaos) may have significant implications for efficient control strategies in real life systems. In particular, we demonstrate that in the latter case, chaotic dynamics in spatially extended systems can be terminated via a relatively low number of (spatially and temporally) localized perturbations. We demonstrate as a proof of principle that control and targeting of high-dimensional systems exhibiting transient chaos can be achieved with exceptionally small interactions with the system. This insight may impact future control strategies in real-life systems like cardiac arrhythmias.

LIVING HEART: USING PREDICTIVE AI/VR MODELS TO REDUCE UNCERTAINTY IN CARDIOVASCULAR DIAGNOSIS AND TREATMENT

The ability to create predictive, validated, multiscale models of the human heart holds promise to minimize speculation in preventing, managing, and treating heart disease by enabling clinicians to determine the optimal treatment for a patient with CVD. Toward this goal, The Living Heart Project has brought together a multidisciplinary team of experts representing research, industry, clinical practice, and regulatory authorities to realize this goal. A predictive heart model, released in 2016, is an anatomically accurate multiphysics model of a healthy human heart with dynamic behavior governed by sound physiological principles. Advanced imaging modalities 3DCTA and DT-MRI were used to define the physical attributes of the heart structure, while the conservation laws of continuum mechanics capture the physical response. The LHM contains well-defined anatomic details including internal structures (e.g., heart valves, chordae tendineae, coronary arteries, and veins) and proximal vasculature (e.g., aortic arch, pulmonary trunk, and SVC). Cardiac contraction is driven by waves of electrical excitation traveling across the heart to generate physiologically observed wave propagation patterns. A closed system of fluid cavities and fluid links models blood flow. The fluid and solid models are directly coupled and the systemic and pulmonary circuits are endowed with vascular compliances and flow resistances that can be modified to simulate exercise, hypertension, and other physiological states. The LHM is thus a dynamic model of a human heart that has been used as a powerful diagnostic and treatment planning tool. Due to the modular nature of the Living Heart Model, it can be modified or extended to simulate a wide range of clinical applications. Using patient-specific data, it can be modified locally or globally to simulate the effects of myocardial infarction or other forms of heart failure. Efficacy of medical devices for improving/restoring cardiac function can be evaluated. The external circulatory system can be enhanced to study peripheral circulation and organ perfusion phenomena using patient-specific flow velocity data, or determine the sensitivity of cardiac function to various peripheral treatment options. The LHM can include models of cellular and subcellular electromechanical phenomena, such as may be required to study arrhythmias and their induction by pharmacological or pathophysiological agents. It is possible to replicate the pre-treatment characteristics of patients with specific congenital or adult cardiac conditions and thus predict patient-specific treatment outcomes.View Large Image Figure ViewerDownload Hi-res image Download (PPT)

Synchronization-based reconstruction of electromechanical wave dynamics in elastic excitable media.

The heart is an elastic excitable medium, in which mechanical contraction is triggered by nonlinear waves of electrical excitation, which diffuse rapidly through the heart tissue and subsequently activate the cardiac muscle cells to contract. These highly dynamic excitation wave phenomena have yet to be fully observed within the depths of the heart muscle, as imaging technology is unable to penetrate the tissue and provide panoramic, three-dimensional visualizations necessary for adequate study. As a result, the electrophysiological mechanisms that are associated with the onset and progression of severe heart rhythm disorders such as atrial or ventricular fibrillation remain insufficiently understood. Here, we present a novel synchronization-based data assimilation approach with which it is possible to reconstruct excitation wave dynamics within the volume of elastic excitable media by observing spatiotemporal deformation patterns, which occur in response to excitation. The mechanical data are assimilated in a numerical replication of the measured elastic excitable system, and within this replication, the data drive the intrinsic excitable dynamics, which then coevolve and correspond to a reconstruction of the original dynamics. We provide a numerical proof-of-principle and demonstrate the performance of the approach by recovering even complicated three-dimensional scroll wave patterns, including vortex filaments of electrical excitation from within a deformable bulk tissue with fiber anisotropy. In the future, the reconstruction approach could be combined with high-speed imaging of the heart's mechanical contractions to estimate its electrophysiological activity for diagnostic purposes.

Spontaneous termination of chaotic spiral wave dynamics in human cardiac ion channel models.

Chaotic spiral or scroll wave dynamics can be found in diverse systems. In cardiac dynamics, spiral or scroll waves of electrical excitation determine the dynamics during life-threatening arrhythmias like ventricular fibrillation. In numerical studies it was found that chaotic episodes of spiral and scroll waves can be transient, thus they terminate spontaneously. We show in this study that this behavior can also be observed using models which describe the ion channel dynamics of human cardiomyocytes (Bueno-Orovio-Cherry-Fenton model and the Ten Tusscher-Noble-Noble-Panfilov model). For both models we find that the average lifetime of the chaotic transients grows exponentially with the system size. With this behavior, we classify the systems into the group of type-II supertransients. We observe a significant difference of the breakup behavior between the models, which results in a distinct dynamics during the final phase just before the termination. The observation of a (temporally) stable single-spiral state affects the prevailing description of the dynamics of type-II supertransients as being “quasi-stationary” and also the feasibility of predicting the spontaneous termination of the spiral wave dynamics. In the long term, the relation between the breakup behavior of spiral waves and properties of chaotic transients like predictability or average transient lifetime may contribute to an improved understanding and classification of cardiac arrhythmias.

Drift of scroll waves in a generic axisymmetric model of the cardiac left ventricle

Abstract Many dangerous cardiac arrhythmias are driven by rotating spiral waves of electrical excitation. The dynamics of these rotating waves determine the properties of the arrhythmia. In this paper, we present a numerical study of the dynamics of scroll waves in generic axisymmetric models of the left ventricle, coupled with an ionic model for human cardiac cells. We find that the most frequent type of dynamic present is annihilation of the scroll waves at the basal boundary of the heart. However, in several cases, the scroll waves stabilised inside the myocardium and rotated around transmural filaments. This behaviour is affected by many parameters, including the thickness of the myocardial wall, the cardiac tissue anisotropy, that is the anisotropy ratio and the directions of the myofibres, the chirality of the scroll waves and the parameters of the cell model. There can be several attractors, and a scroll wave can persist or disappear depending on the initial conditions, for example, S1S2 protocol parameters. However, the exact dependencies are complex and not always monotonic. In this study, we discuss the possible mechanisms underlying these dynamics and the application of our results to cardiac arrhythmias.

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.

The impact of cardiac tissue anisotropy on spiral wave superseding: A simulation study using ionic cell models

Several types of dangerous cardiac arrhythmias, such as paroxysmal tachycardia and fibrillation, are linked with the spiral waves of electrical excitation in the heart muscle. In many cases, these diseases must be cured immediately after their diagnosis. Low-voltage defibrillation and cardioversion are modern treatment methods. Electrotherapy is based on spiral wave superseding by a high-frequency pacing from an electrode. In the present work, we study the influence of the anisotropic myocardial structure and cell-level model on cardioversion results. We use long line and point electrodes. Intervals of effective stimulation periods are determined and compared for two ionic cell-level models. Of all the considered factors, the cell-level model appears to play the greatest role in the results.

Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue.

We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER) of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM). Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of the mechano-electrical feedback in facilitating and promoting atrial fibrillation.

Effect of the form and anisotropy of the left ventricle on the drift of spiral waves

Three-dimensional spiral waves of electrical excitation in the myocardium are sources of dangerous cardiac arrhythmias. In this work, the dynamics of spiral waves of electrical excitation were studied in a symmetric anatomical model of the human heart left ventricle and a realistic ionic cell model of the human ventricular myocardium. Three factors that affect the drift waves in the heart were compared for the first time: the geometry of the heart wall, myocardial anisotropy, and wave chirality. Cardiac anisotropy was identified as a main factor in determining the drift of spiral waves. In the isotropic case, the dynamics were determined by the wall thickness, but did not depend on the wave chirality. In the anisotropic case, chirality was found to play a crucial role.