Reentrant Wave Research Articles

Scaling properties of conduction velocity in heterogeneous excitable media

Waves of excitation through excitable media, such as cardiac tissue, can propagate as plane waves or break up to form reentrant spiral waves. In diseased hearts reentrant waves can be associated with fatal cardiac arrhythmias. In this paper we investigate the conditions that lead to wave break, reentry, and propagation failure in mathematical models of heterogeneous excitable media. Two types of heterogeneities are considered: sinks are regions in space in which the voltage is fixed at its rest value, and breaks are nonconducting regions with no-flux boundary conditions. We find that randomly distributed heterogeneities in the medium have a decremental effect on the velocity, and above a critical density of such heterogeneities the conduction fails. Using numerical and analytical methods we derive the general relationship among the conduction velocity, density of heterogeneities, diffusion coefficient, and the rise time of the excitation in both two and three dimensions. This work helps us understand the factors leading to reduced propagation velocity and the formation of spiral waves in heterogeneous excitable media.

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.

Virtual tissue engineering of the human atrium: Modelling pharmacological actions on atrial arrhythmogenesis

Computational models of human atrial cells, tissues and atria have been developed. Cell models, for atrial wall, crista terminalis, appendage, Bachmann’s bundle and pectinate myocytes are characterised by action potentials, ionic currents and action potential duration (APD) restitution. The principal effect of the ion channel remodelling of persistent atrial fibrillation (AF), and a mutation producing familial AF, was APD shortening at all rates. Electrical alternans was abolished by the modelled action of Dronedarone. AF induced gap junctional remodelling slows propagation velocity at all rates. Re-entrant spiral waves in 2-D models are characterised by their frequency, wavelength, meander and stability. For homogenous models of normal tissue, spiral waves self-terminate, due to meander to inexcitable boundaries, and by dissipation of excitation. AF electrical remodelling in these homogenous models led to persistence of spiral waves, and AF fibrotic remodelling to their breakdown into fibrillatory activity. An anatomical model of the atria was partially validated by the activation times of normal sinus rhythm. The use of tissue geometry from clinical MRI, and tissue anisotropy from ex vivo diffusion tensor magnetic resonance imaging is outlined. In the homogenous model of normal atria, a single scroll breaks down onto spatio-temporal irregularity (electrical fibrillation) that is self-terminating; while in the AF remodelled atria the fibrillatory activity is persistent. The persistence of electrical AF can be dissected in the model in terms of ion channel and intercellular coupling processes, that can be modified pharmacologically; the effects of anatomy, that can be modified by ablation; and the permanent effects of fibrosis, that need to be prevented.

The electrifying stomach

The stomach is electrified and subject to eurhythmic and dysrhythmic electrical events - much like the heart. The normal human slow wave ranges from 2.5 to 3.75 cycles per min (cpm), tachygastrias range from 3.75 cpm to 10.0 cpm and bradygastrias from .5 to 2.5 cpm, the gastric dysrhythmias of men and women. In this issue of Neurogastroenterology & Motility, O'Grady, etal. describe the gastric dysrhythmias of pigs in electrocardiology terms. Printed circuit boards (PCB) with multi-electrode arrays (160-192 electrodes) were attached to the stomach serosa. Gastric dysrhythmias occurred in eight of the 16 anesthetized pigs and were analysed by manually and by computer. The patterns of dysrhythmias were reminiscent of cardiac dysrhythmias: conduction blocks, ectopic foci, re-entrant wave fronts, premature and aberrant slow waves and regular and irregular tachygastrias. The authors suggest gastric dysrhythmias recorded in pigs may be relevant to human gastric dysrhythmias and electricity-based therapies. The categories of porcine gastric dysrhythmias may help to understand the spectrum of gastric dysrhythmias of men and women recorded over the past 25 years. Analogies between gastric and cardiac neuromuscular disorders are explored because Neurogastroenterology is evolving as a clinical and therapeutic field utilizing knowledge of gastric rhythmicity and electro-contractile events. Interstitial cells of Cajal are the pacemaker cells of the stomach and loss of cells or faulty circuitry appear to be key pathways to gastric dysrhythmias. Gastric electrophysiology (EP) labs, human and animal, are needed to test hypotheses and advance understanding of human gastric dysrhythmias and upper GI symptoms.

Effects of boundaries and geometry on the spatial distribution of action potential duration in cardiac tissue

Increased dispersion of action potential duration across cardiac tissue has long been considered an important substrate for the development of most electrical arrhythmias. Although this dispersion has been studied previously by characterizing the static intrinsic gradients in cellular electrophysiology and dynamical gradients generated by fast pacing, few studies have concentrated on dispersions generated solely by structural effects. Here we show how boundaries and geometry can produce spatially dependent changes in action potential duration (APD) in homogeneous and isotropic tissue, where all the cells have the same APD in the absence of diffusion. Electrotonic currents due to coupling within the tissue and at the tissue boundaries can generate dispersion, and the profile of this dispersion can change dramatically depending on tissue size and shape, action potential morphology, tissue dimensionality, and stimulus frequency and location. The dispersion generated by pure geometrical effects can be on the order of tens of milliseconds, enough under certain conditions to produce conduction blocks and initiate reentrant waves.

3D virtual human atria: A computational platform for studying clinical atrial fibrillation

Despite a vast amount of experimental and clinical data on the underlying ionic, cellular and tissue substrates, the mechanisms of common atrial arrhythmias (such as atrial fibrillation, AF) arising from the functional interactions at the whole atria level remain unclear. Computational modelling provides a quantitative framework for integrating such multi-scale data and understanding the arrhythmogenic behaviour that emerges from the collective spatio-temporal dynamics in all parts of the heart. In this study, we have developed a multi-scale hierarchy of biophysically detailed computational models for the human atria – the 3D virtual human atria. Primarily, diffusion tensor MRI reconstruction of the tissue geometry and fibre orientation in the human sinoatrial node (SAN) and surrounding atrial muscle was integrated into the 3D model of the whole atria dissected from the Visible Human dataset. The anatomical models were combined with the heterogeneous atrial action potential (AP) models, and used to simulate the AP conduction in the human atria under various conditions: SAN pacemaking and atrial activation in the normal rhythm, break-down of regular AP wave-fronts during rapid atrial pacing, and the genesis of multiple re-entrant wavelets characteristic of AF. Contributions of different properties of the tissue to mechanisms of the normal rhythm and arrhythmogenesis were investigated. Primarily, the simulations showed that tissue heterogeneity caused the break-down of the normal AP wave-fronts at rapid pacing rates, which initiated a pair of re-entrant spiral waves; and tissue anisotropy resulted in a further break-down of the spiral waves into multiple meandering wavelets characteristic of AF. The 3D virtual atria model itself was incorporated into the torso model to simulate the body surface ECG patterns in the normal and arrhythmic conditions. Therefore, a state-of-the-art computational platform has been developed, which can be used for studying multi-scale electrical phenomena during atrial conduction and AF arrhythmogenesis. Results of such simulations can be directly compared with electrophysiological and endocardial mapping data, as well as clinical ECG recordings. The virtual human atria can provide in-depth insights into 3D excitation propagation processes within atrial walls of a whole heart in vivo, which is beyond the current technical capabilities of experimental or clinical set-ups.

Experiment-model interaction for analysis of epicardial activation during human ventricular fibrillation with global myocardial ischaemia

We describe a combined experiment-modelling framework to investigate the effects of ischaemia on the organisation of ventricular fibrillation in the human heart. In a series of experimental studies epicardial activity was recorded from 10 patients undergoing routine cardiac surgery. Ventricular fibrillation was induced by burst pacing, and recording continued during 2.5 min of global cardiac ischaemia followed by 30 s of coronary reflow. Modelling used a 2D description of human ventricular tissue. Global cardiac ischaemia was simulated by (i) decreased intracellular ATP concentration and subsequent activation of an ATP sensitive K+ current, (ii) elevated extracellular K+ concentration, and (iii) acidosis resulting in reduced magnitude of the L-type Ca2+ current ICa,L. Simulated ischaemia acted to shorten action potential duration, reduce conduction velocity, increase effective refractory period, and flatten restitution. In the model, these effects resulted in slower re-entrant activity that was qualitatively consistent with our observations in the human heart. However, the flattening of restitution also resulted in the collapse of many re-entrant waves to several stable re-entrant waves, which was different to the overall trend we observed in the experimental data. These findings highlight a potential role for other factors, such as structural or functional heterogeneity in sustaining wavebreak during human ventricular fibrillation with global myocardial ischaemia.

Erratum: Simulation of Reentrant Wave Dynamics in Cardiac Tissue According to the Severity of Fibrosis

This study investigated the spiral wave dynamics in cardiac tissue according to the severity of fibrosis in the hypertrophic human ventricle by simulating propagation of the electric wave. We used a model of the human ventricular cell to describe the cellular electrophysiology and a twodimensional monodomain method to compute the electric wave propagation in ventricular tissue using finite element approximation. To delineate the eect of fibrosis on the wave dynamics, a model of hypertrophic cardiac tissue with randomly distributed fibroblasts was simulated. The electrical conductivity of the fibroblasts was estimated from the experimental data. In the fibrotic cardiac tissue, we generated a reentrant wave and predicted its dynamic variation according to the severity of fibrosis. Compared to the reentrant wave in normal tissue, a conduction delay was observed in the fibrotic tissue. Furthermore, one spiral wave broke into several waves when fibroblasts constituted 40 % of the tissue, causing cardiac fibrillation.

Analysis of the mechanisms initiating random wave propagation at the onset of atrial fibrillation using noncontact mapping: Role of complex fractionated electrogram region

The complex fractionated atrial electrogram (CFAE) region has been suggested to contribute to the maintenance of atrial fibrillation (AF), but its role for the initiation of AF has not been clarified. We analyzed the mechanisms of the initiation of random reentrant wave propagation at AF onset, especially in relation to CFAE region. Endocardial mapping of the left atrium using a 3-dimensional noncontact mapping system was performed in 19 patients. Thirty-two spontaneous AF onset episodes, which were initiated by the focal repetitive discharges (9 ± 9 beats), deriving from the pulmonary veins (PV) (n = 17) and from non-PV CFAE regions (n = 15) were observed. The coupling intervals of the focal discharges that initiated AF (AF-D) were significantly shorter than those that did not initiate AF (non-AF-D) (179 ± 33 ms vs. 217 ± 45 ms, P = .0005). After the AF-D, localized conduction blocks occurred in the CFAE region. Subsequently, the waves propagated to the remainder of the atrium, accompanying the anchored activation around the localized conduction block lines in the CFAE regions. Left atrial activation times of AF-D were significantly longer than those of non-AF-D (151 ± 35 ms vs. 83 ± 17 ms, P < .0001). These longer activation times after AF-D enabled the waves to reenter the previously blocked CFAE region from the opposite direction, and thus the meandering reentrant wave propagation was initiated. Unidirectional conduction block in the CFAE region and subsequent prolonged left atrial activation time following short coupled premature discharge were the underlying mechanisms of AF initiation, suggesting the importance of the CFAE region as the substrate for AF onset.

Study of Parallel Algorithm Based on OpenMP in Myocardial Simulation

Computer simulation is an important method in the study of cardiac electrophysiology. However, complicated studies in tissues are difficult because of the long computation time. In order to speed up the simulation, in this paper a parallel algorithm based on OpenMP was studied on a multi-core computer. The Noble 91 mathematical model was used to develop a two-dimensional tissue. By initiating a reentrant wave, properties of the conventional sequential program, programs of the data parallelism and functional parallelism were analyzed and compared. The results showed that the execution time of the data parallelism was only about one-fourth of the sequential execution time and its efficiency was high, however, the execution time of the functional parallelism was approximately ten times of the sequential execution time and its efficiency became low. Therefore, the method of the data parallelism could significantly reduce the computation time and was suggested to be a good choice in the myocardial simulation.

17 Quantification of spatial dynamics of cardiac arrhythmias

The 1987 Lambeth conventions identify an arrhythmia from time series recordings of cardiac electrical activity. All cardiac arrhythmias are spatio-temporal and involve anisotropic and orthotropic propagation in heterogeneous tissue. Spatial...

Atrial defibrillation voltage: Falling to a new low

Atrial defibrillation voltage: Falling to a new low

Effects of Ibutilide on Inhibiting Heart Rate and Rapidly Terminating Atrial Flutter in Canine

Ibutilide is a newer class-III antiarrhythmic agent approved for clinical use. We sought to investigate its electrophysiological effects in canines and also the underlying mechanism of conversion of atrial flutter (AFL). For this purpose, 15 male mongrel dogs were anesthetized, intubated with tracheal tube, and heart was exposed and connected to electrodes. Electrophysiologic variables were measured with and without ibutilide (10-min infusion-dose: 0.10mg/kg; 30-min later, maintaining dose: 0.01mg/min) which included heart rate, conduction of intra- and inter-atrium, conduction ratio of isthmus, and ERP. Ibutilide had a significant inhibitory effect on sinus atrial node, peak response time was 20-30min, and heart rate returned to the baseline after 2h. One canine had 5s sinus pause, and the other had 2:1 atrioventricular conduction post-administration. Atrial, ventricular, and pulmonary vein ERP was significantly prolonged (P<0.05). No significant differences were observed regarding conduction of intra-atrium, inter-atrium, and isthmus. It was, therefore, concluded that ibutilide had suppressive effect on sinus atrial and atrioventricular nodes. Ibutilide rapidly terminated AFL due to the reentrant wave front's inability to proceed as the refractory period was protracted and hence caused the whole excitable gap of the reentrant circuit to be affected by refractoriness.

Drug-Induced Arrhythmia

Prolongation of the QTc interval has been associated with proarrhythmia resulting from a potentially fatal form of polymorphic ventricular tachycardia called torsades de pointes (TdP). Genetic forms of the long-QT syndrome (LQTS) associated with high arrhythmic risk have been causally related to mutations in ion channels responsible for the cardiac action potential; genetic factors associated with milder degrees of QTc prolongation and arrhythmic risk have also been described. Acquired forms of QTc prolongation and proarrhythmia, particularly related to drug therapy, are frequently related to drug effects on the same ion channels involved in genetic forms of LQTS. As is true for genetic forms of LQTS, there is a wide spectrum of potential drug effects on the QTc interval ranging from trivial to potentially lethal. Drug-induced QTc prolongation is a complicated phenomenon related not just to the properties or dose of a particular drug but also to drug-drug interactions and a variety of patient factors, including age, gender, the presence and severity of underlying heart disease, and genetic predisposition. Additionally, drug effects on other ion channels, including blockade of sodium channels (causing prolongation of the QRS interval rather than the QTc interval), are an important cause of drug-induced proarrhythmia. The purpose of this review is to summarize the available data related to acquired forms of LQTS, with particular focus on drug-related LQTS and proarrhythmia. A brief summary is presented here of genetic LQTS because the relevant genes and proteins form the basis for an understanding of the causes of acquired LQTS, and in any given patient, the QTc is determined by genetic, substrate, and environmental factors. Emphasis is placed on practical strategies for clinicians, with the goal of minimizing the risk of dangerous proarrhythmia related to the use of both cardiac and noncardiac drugs with the potential for QTc prolongation. Genetic …

Stimulus-induced response patterns of medium-embedded neurons

Neuronal ensembles in living organisms are often embedded in a media that provides additional interaction pathways and autoregulation. The underlying mechanisms include but are not limited to modulatory activity of some distantly propagated neuromediators like serotonin, variation of extracellular potassium concentration in brain tissue, and calcium waves propagation in networks of astrocytes. Interaction of these diverse processes can lead to formation of complex spatiotemporal patterns, both self-sustained or triggered by external signal. Besides network effects, many dynamical features of such systems originate from reciprocal interaction between single neuron and surrounding medium. In the present paper we study the response of such systems to the application of a single stimulus pulse. We use a minimal mathematical model representing a forced excitable unit that is embedded in a diffusive or (spatially inhomogeneous) excitable medium. We illustrate three different mechanisms for the formation of response patterns: (i) self-sustained depolarization, (ii) propagation of depolarization due to “nearest-neighbor” networks, and (iii) re-entrant waves.

Phase-2 reentry in cardiac tissue: Role of the slow calcium pulse

Phase-2 re-entry is thought to underlie many causes of idiopathic ventricular arrhythmias as, for instance, those occurring in Brugada syndrome. In this paper, we study under which circumstances a region of depolarized tissue can re-excite adjacent regions that exhibit shorter action potential duration (APD), eventually inducing reentry. For this purpose, we use a simplified ionic model that reproduces well the ventricular action potential. With the help of this model, we analyze the conditions that lead to very short action potentials (APs), as well as possible mechanisms for re-excitation in a cable. We then study the induction of re-entrant waves (spiral waves) in simulations of AP propagation in the heart ventricles. We show that re-excitation takes place via a slow pulse produced by calcium current that propagates into the region of short APs until it encounters excitable tissue. We calculate analytically the speed of the slow pulse, and also give an estimate of the minimal tissue size necessary for allowing reexcitation to take place.

Transmural Ultrasound-based Visualization of Patterns of Action Potential Wave Propagation in Cardiac Tissue

The pattern of action potential propagation during various tachyarrhythmias is strongly suspected to be composed of multiple re-entrant waves, but has never been imaged in detail deep within myocardial tissue. An understanding of the nature and dynamics of these waves is important in the development of appropriate electrical or pharmacological treatments for these pathological conditions. We propose a new imaging modality that uses ultrasound to visualize the patterns of propagation of these waves through the mechanical deformations they induce. The new method would have the distinct advantage of being able to visualize these waves deep within cardiac tissue. In this article, we describe one step that would be necessary in this imaging process—the conversion of these deformations into the action potential induced active stresses that produced them. We demonstrate that, because the active stress induced by an action potential is, to a good approximation, only nonzero along the local fiber direction, the problem in our case is actually overdetermined, allowing us to obtain a complete solution. Use of two- rather than three-dimensional displacement data, noise in these displacements, and/or errors in the measurements of the fiber orientations all produce substantial but acceptable errors in the solution. We conclude that the reconstruction of action potential-induced active stress from the deformation it causes appears possible, and that, therefore, the path is open to the development of the new imaging modality.

Utilizing the eikonal relationship in strategies for reentrant wave termination in excitable media

Obstacle-anchored vortices can be terminated by the application of high-frequency wave trains in excitable media. We theoretically derived the dependency between the obstacle radius and the maximum unpinning period through reinterpretation of the well-known eikonal equation. Our theoretical result was confirmed by experiments with cardiomyocyte monolayers. This result may be useful for improving the stimulation protocol of implantable cardiac pacemakers.

Electromechanical wavebreak in a model of the human left ventricle

In the present report, we introduce an integrative three-dimensional electromechanical model of the left ventricle of the human heart. Electrical activity is represented by the ionic TP06 model for human cardiac cells, and mechanical activity is represented by the Niederer-Hunter-Smith active contractile tension model and the exponential Guccione passive elasticity model. These models were embedded into an anatomic model of the left ventricle that contains a detailed description of cardiac geometry and the fiber orientation field. We demonstrated that fiber shortening and wall thickening during normal excitation were qualitatively similar to experimental recordings. We used this model to study the effect of mechanoelectrical feedback via stretch-activated channels on the stability of reentrant wave excitation. We found that mechanoelectrical feedback can induce the deterioration of an otherwise stable spiral wave into turbulent wave patterns similar to that of ventricular fibrillation. We identified the mechanisms of this transition and studied the three-dimensional organization of this mechanically induced ventricular fibrillation.

Dronedarone in the management of atrial fibrillation.

Atrial fibrillation is the most common type of tachyarrhythmia caused by multiple re-entrant wave forms within the atria and bombarding the atrioventricular node several times making it beat in a rapid, disorganized fashion termed "fibrillation". In atrial fibrillation, atria beat more than 300 times per minute. The arrhythmatous condition needs to be controlled, as humans cannot withstand this rapid and chaotic beating of the heart. New investigational drugs like Dronedarone(®) are being used. Dronedarone is the most recent antiarrhythmic drugs. It was approved by US-FDA on July 2nd 2009 and is available in the USA as Multaq tablets (400 mg). Dronedarone falls under the category of multiple ion channel blocker. It mainly targets the repolarization currents, making them less active and hence prolonging the action potential duration (APD). Dronedarone also exhibits antiadrenergic activity, thus reducing the pace of the pacemaker. Dronedarone has been proven to be a safer and efficacious AAD, evidenced by both animal and human studies. These studies showed that there was prolongation of the APD and absence of QT interval prolongation with long term administration of the drug. Also there was reduced thyroid hormone receptor expression. Dronedarone is significantly safer and effective in maintaining the sinus rhythm and reducing the ventricular proarrhythmias, justifying it for the long term treatment of atrial fibrillation compared to other antiarrhythmic drugs.