Propagation In Cardiac Tissue Research Articles

Reordering and synchronization of electrical turbulence in cardiac tissue through global and partial optogenetical illumination.

Electrical turbulence in the heart is considered the culprit of cardiac disease, including the fatal ventricular fibrillation. Optogenetics is an emerging technology that has the capability to produce action potentials of cardiomyocytes to affect the electric wave propagation in cardiac tissue, thereby possessing the potential to control the turbulence, by shining a rotating spiral pattern onto the tissue. In this paper, we present a method to reorder and synchronize electrical turbulence through optogenetics. A generic two-variable reaction-diffusion model and a simplified three-variable ionic cardiac model are used. We discuss cases involving either global or partial illumination.

Classification of mechanisms underlying cardiac arrhythmias by deep learning

This work presents the development and comparison of classifiers based on both traditional classifiers and more advanced deep learning techniques to identify different types of bioelectric propagation in cardiac tissue, which are the mechanisms underlying arrhythmias. The classification uses energy maps obtained from the magnetic field generated by three possible bioelectric models of propagations through simulated cardiac cells (classes), consisting of a linear path, a reentrant circuit around an inexcitable obstacle, and a spiral trajectory. Different classifiers were implemented and compared in regard to their accuracies, aiming to associate each energy map to its respective class. These classifiers were evaluated both on a test set composed by images without noise and on a more challenging “noise test set,” composed by images meant to test the generalization powers of the models in the presence of noise. A Monte Carlo cross-validation approach was used to evaluate the averaged behavior of the classifiers over 10 runs. The classifiers compared include conventional decision support tools as decision trees and random forests, a simple multi-layer perceptron, and deep learning architectures such as a simple Convolutional Neural Network, ResNet50, and InceptionV3. These last two had the best performances on the noise test set, with averaged accuracies of 0.852 and 0.827 over 10 runs, and standard deviations of 0.036 and 0.048, respectively. The use of handcrafted features, specifically histograms of oriented gradients, was also shown to substantially improve results for the classifiers that do not use convolutions, to the point of surpassing the results of the deeper neural networks. The comparative performance of the studied classifiers elucidates some of the properties of this classification problem. ResNet50 and InceptionV3 seem to be promising candidate models for initial tests with real-life data. The study of handcrafted features might also prove useful, especially if the availability of real images is scarce. The use of this automated classification may contribute to the efficacy of diagnostics in a future use of biomagnetic mappings in a medical-hospital environment.

Muscular Thin Films for Label-Free Mapping of Excitation Propagation in Cardiac Tissue.

Muscular thin films (MTFs), have already found a variety of applications in cardiac tissue engineering and in building of lab-on-a-chip systems. Here we present a novel approach to label-free mapping of excitation waves in the cardiomyocyte cell cultures with the use of MTFs. Neonatal rat ventricular cardiomyocytes were cultured on polydimethylsiloxane (PDMS) thin films and observed by means of off-axis illumination. Inflexions of the membrane created by the contraction of cardiomyocytes led to formation of patterns of bright and dark areas on the surface of the membrane. These patterns were recorded and analyzed for the monitoring of the contraction propagation. The method was compared with a standard optical mapping technique based on the use of a Ca2+-sensitive fluorescent dye. A good consistency of the results obtained by these two methods was demonstrated. The proposed method is non-toxic and might be of particular interest for the purpose of continuous monitoring in test systems based on human induced pluripotent stem cells.

Modified bidomain model with passive periodic heterogeneities

<p style='text-indent:20px;'>In this paper we study how mesoscopic heterogeneities affect electrical signal propagation in cardiac tissue. The standard model used in cardiac electrophysiology is a bidomain model - a system of degenerate parabolic PDEs, coupled with a set of ODEs, representing the ionic behviour of the cardiac cells. We assume that the heterogeneities in the tissue are periodically distributed diffusive regions, that are significantly larger than a cardiac cell. These regions represent the fibrotic tissue, collagen or fat, that is electrically passive. We give a mathematical setting of the model. Using semigroup theory we prove that such model has a uniformly bounded solution. Finally, we use two–scale convergence to find the limit problem that represents the average behviour of the electrical signal in this setting.

Observing spatio-temporal dynamics of excitable media using reservoir computing.

We present a dynamical observer for two dimensional partial differential equation models describing excitable media, where the required cross prediction from observed time series to not measured state variables is provided by Echo State Networks receiving input from local regions in space, only. The efficacy of this approach is demonstrated for (noisy) data from a (cubic) Barkley model and the Bueno-Orovio-Cherry-Fenton model describing chaotic electrical wave propagation in cardiac tissue.

A gap junction-based cardiac electromechanics model.

Action potential propagation in cardiac tissue is mainly governed by highly resistive gap junctions, which causes the tissue to behave as a network of active cell nodes interconnected by resistors. This property causes the action potential propagation to be less dependent on the level of mechanical deformation. This study proposes that the electrical conductivity in cardiac electromechanical simulations should be held fixed relative to the material frame, reproducing the dominant effect of intercellular gap junctions on the tissue electrical resistance instead of the more commonly employed spatial frame. Our simulations showed that the implementation of gap junction-based conductivity resulted in similar activation times at given material point, irrespective of the level of deformation. In contrast, the activation time of a given material point using spatial-based conductivity was dependent on the deformation experienced by the tissue. These findings have implication on more complex electromechanical simulations such as spiral wave since gap junction-based conductivity is independent of contraction, in contrast to spatial-based conductivity. Therefore, selection of the appropriate electrical conductivity assumption is highly crucial in electromechanics models of cardiac tissue.

Approximate analytical solutions for excitation and propagation in cardiac tissue.

It is well known that a variety of cardiac arrhythmias are initiated by a focal excitation in heart tissue. At the single cell level these currents are typically induced by intracellular processes such as spontaneous calcium release (SCR). However, it is not understood how the size and morphology of these focal excitations are related to the electrophysiological properties of cardiac cells. In this paper a detailed physiologically based ionic model is analyzed by projecting the excitation dynamics to a reduced one-dimensional parameter space. Based on this analysis we show that the inward current required for an excitation to occur is largely dictated by the voltage dependence of the inward rectifier potassium current (I(K1)), and is insensitive to the detailed properties of the sodium current. We derive an analytical expression relating the size of a stimulus and the critical current required to induce a propagating action potential (AP), and argue that this relationship determines the necessary number of cells that must undergo SCR in order to induce ectopic activity in cardiac tissue. Finally, we show that, once a focal excitation begins to propagate, its propagation characteristics, such as the conduction velocity and the critical radius for propagation, are largely determined by the sodium and gap junction currents with a substantially lesser effect due to repolarizing potassium currents. These results reveal the relationship between ion channel properties and important tissue scale processes such as excitation and propagation.

Mind the Gap: A Semicontinuum Model for Discrete Electrical Propagation in Cardiac Tissue.

Electrical propagation in cardiac tissue is a discrete or discontinuous phenomenon that reflects the complexity of the anatomical structures and their organization in the heart, such as myocytes, gap junctions, microvessels, and extracellular matrix, just to name a few. Discrete models or microscopic and discontinuous models are, so far, the best options to accurately study how structural properties of cardiac tissue influence electrical propagation. These models are, however, inappropriate in the context of large scale simulations, which have been traditionally performed by the use of continuum and macroscopic models, such as the monodomain and the bidomain models. However, continuum models may fail to reproduce many important physiological and physiopathological aspects of cardiac electrophysiology, for instance, those related to slow conduction. In this study, we develop a new mathematical model that combines characteristics of both continuum and discrete models. The new model was evaluated in scenarios of low gap-junctional coupling, where slow conduction is observed, and was able to reproduce conduction block, increase of the maximum upstroke velocity and of the repolarization dispersion. None of these features can be captured by continuum models. In addition, the model overcomes a great disadvantage of discrete models, as it allows variation of the spatial resolution within a certain range.

Does Ephaptic Coupling Contribute to Propagation in Cardiac Tissue?

Does Ephaptic Coupling Contribute to Propagation in Cardiac Tissue?

Simulation of Action Potential Propagation in Cardiac Ventricular Tissue Using an Efficient PDE Model

Signal transmission in the form of propagating waves of electrical excitation is a fast type of communication and coordination between cells that is known in cardiac tissue as the action potential.In this article we used an efficient model of cardiac ventricular cell that is based on partial differential equations(PDE).After that a computational algorithm for action potential propagation was represented that according to this algorithm and proposed efficient model, We demonstrated action potential propagation in one-dimensional (1D) and two-dimensional (2D) space lattices using the central finite-difference method.In addition we investigated the effect of obstacles on the propagation of normal action potential using represented 2D excitable medium.Our results show that proposed efficient model, represented algorithm and excitable media are suitable for simulation of action potential propagation in cardiac tissue. Traveling waves transmit information through space and always an excitable medium serves to promote propagation. an excitable medium is typically comprised of a continuous set of locally excitable regions,which can be both inde- pendently stimulated and inhibited.these media exhibit a sensitivity threshold blow which the media persist undis- turbed at a stable resting state.while subthreshold perturba- tions are rapidly diminished, greater than threshold signals induce an abrupt local transformation within a portion of the medium. shortly after this change occurs, the region becomes transiently refractory to further perturbation, after which it relaxes to the resting state. The bioelectric activity of cardiac cells results from the transport processes of ionic species across the membrane through voltage-gated ion channels. The ion channels act as gates that regulate the permeabilities of sodium, potassium and calcium ions. At rest, the cell maintains a constant, negative transmembrane voltage, called the resting potential. However, if a strong enough depolarizing current is passed through the membrane, the cell departs from equilibrium and responds with a sharp change in the transmembrane voltage followed by a return to the resting state. This rapid course of the transmembrane voltage is called action poten- tial (AP) that is the fastest form of communications in the cardiac excitable tissue. Conduction of AP in the heart occurs by electrotonic mechanisms, in which the local

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.

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.

Acceleration of cardiac tissue simulation with graphic processing units

In this technical note we show the promise of using graphic processing units (GPUs) to accelerate simulations of electrical wave propagation in cardiac tissue, one of the more demanding computational problems in cardiology. We have found that the computational speed of two-dimensional (2D) tissue simulations with a single commercially available GPU is about 30 times faster than with a single 2.0 GHz Advanced Micro Devices (AMD) Opteron processor. We have also simulated wave conduction in the three-dimensional (3D) anatomic heart with GPUs where we found the computational speed with a single GPU is 1.6 times slower than with a 32-central processing unit (CPU) Opteron cluster. However, a cluster with two or four GPUs is faster than the CPU-based cluster. These results demonstrate that a commodity personal computer is able to perform a whole heart simulation of electrical wave conduction within times that enable the investigators to interact more easily with their simulations.

Nicotine, atrial fibrosis, and atrial fibrillation: do microRNAs help to clear the smoke?

Chronic nicotine abuse has clearly been linked to the development and progression of atherosclerosis, myocardial infarction, and heart failure.1 In addition, several studies have also shown that nicotine abuse is associated with the occurrence of cardiac arrhythmias.1–3 The proarrhythmic effect of cigarette smoking seems to depend on the nicotine concentration in the blood.2 Increased nicotine levels raise atrial and ventricular vulnerability to fibrillation.1–4 These profibrillatory effects appear to depend on the inhibition of ion channels and conduction-slowing properties. One factor known to cause a substantial slowing of electrical impulse propagation in cardiac tissue is an increase in the amount of interstitial collagen. Interstitial fibrosis isolates groups of atrial myocytes as well as individual myocytes.4,5 Thus, the development of interstitial fibrosis affects chamber geometry and mechanical performance of the heart and enhances the likelihood of cardiac arrhythmias such as atrial fibrillation (AF). Recently, it was shown that nicotine abuse accelerates atrial collagen accumulation, leading to symptomatic atrial fibrosis at a younger age.6 Experimentally, a linear correlation between nicotine dose and atrial collagen expression was established. Nevertheless, an exact molecular signalling pathway concerning how nicotine induces atrial fibrosis … *Corresponding author: Tel: +49 391 6713225; fax: +49 391 6713202. E-mail address : andreas.goette{at}med.ovgu.de

Modeling cardiac mechano-electrical feedback using reaction-diffusion-mechanics systems

In many practically important cases, wave propagation described by the reaction-diffusion equation initiates deformation of the medium. Mathematically, such processes are described by coupled reaction-diffusion-mechanics (RDM) systems. RDM systems were recently used to study the effects of deformation on wave propagation in cardiac tissue, so called mechano-electrical feedback (MEF). In this article, we review the results of some of these studies, in particular those relating to the effects of deformation on pacemaker activity and spiral wave dynamics in the heart. We also provide brief descriptions of the numerical methods used, and the underlying cardiac physiology.

Connexin40 Imparts Conduction Heterogeneity to Atrial Tissue

Impulse propagation in cardiac tissue is a complex process in which intercellular coupling through gap junction channels is a critical component. Connexin40 (Cx40) is an abundant gap junction protein that is expressed in atrial myocytes. Alterations in the expression of Cx40 have been implicated in atrial arrhythmogenesis. The purpose of the current study was to assess the role of Cx40 in atrial impulse propagation. High-resolution optical mapping was used to study conduction in the right and left atrial appendages of isolated Langendorff-perfused murine hearts. Wild-type (Cx40(+/+)), heterozygous (Cx40(+/-)), and knockout (Cx40(-/-)) mice, both adult and embryonic, were studied to assess the effects of reduced Cx40 expression on sinus node function and conduction velocity at different pacing cycle lengths (100 and 60 ms). In both adult and late-stage embryonic Cx40(+/+) mice, heterogeneity in CV was found between the right and left atrial appendages. Either partial (Cx40(+/-)) or complete (Cx40(-/-)) deletion of Cx40 was associated with the loss of conduction heterogeneity in both adult and embryonic mice. Additionally, sinus node impulse initiation was found to be ectopic in Cx40(-/-) mice at 15.5 days postcoitus, whereas Cx40(+/+) mice showed normal activation occurring near the crista terminalis. Our findings suggest that Cx40 plays an essential role in establishing interatrial conduction velocity heterogeneity in the murine model. Additionally, we describe for the first time a developmental requirement for Cx40 in normal sinus node impulse initiation at 15.5 days postcoitus.

A Phased-Array Stimulator System for Studying Planar and Curved Cardiac Activation Wavefronts

Wavefront propagation in cardiac tissue is affected greatly by the geometry of the wavefront. We describe a computer-controlled stimulator system that creates reproducible wavefronts of a predetermined shape and orientation for the investigation of the effects of wavefront geometry. We conducted demonstration experiments on isolated perfused rabbit hearts, which were stained with the voltage-sensitive dye, di-4-ANEPPS. The wavefronts were imaged using a laser and a charge-coupled device (CCD) camera. The stimulator and imaging systems have been used to characterize the relationship between wavefront velocity and fiber orientation. This approach has potential applications in investigating curvature effects, testing numerical models of cardiac tissue, and creating complex wavefronts using one-, two-, or three-dimensional electrode arrays.

Action Potential Duration Dispersion and Alternans in Simulated Heterogeneous Cardiac Tissue with a Structural Barrier

Structural barriers to wave propagation in cardiac tissue are associated with a decreased threshold for repolarization alternans both experimentally and clinically. Using computer simulations, we investigated the effects of a structural barrier on the onset of spatially concordant and discordant alternans. We used two-dimensional tissue geometry with heterogeneity in selected potassium conductances to mimic known apex-base gradients. Although we found that the actual onset of alternans was similar with and without the structural barrier, the increase in alternans magnitude with faster pacing was steeper with the barrier—giving the appearance of an earlier alternans onset in its presence. This is consistent with both experimental structural barrier findings and the clinical observation of T-wave alternans occurring at slower pacing rates in patients with structural heart disease. In ionically homogeneous tissue, discordant alternans induced by the presence of the structural barrier arose at intermediate pacing rates due to a source-sink mismatch behind the barrier. In heterogeneous tissue, discordant alternans occurred during fast pacing due to a barrier-induced decoupling of tissue with different restitution properties. Our results demonstrate a causal relationship between the presence of a structural barrier and increased alternans magnitude and action potential duration dispersion, which may contribute to why patients with structural heart disease are at higher risk for ventricular tachyarrhythmias.

The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue

Electrical heterogeneities play a role in the initiation of cardiac arrhythmias. In certain pathological conditions such as ischaemia, current sinks can develop in the diseased cardiac tissue. In this study, we investigate the effects of changing the amount of heterogeneity and intercellular coupling on wavefront stability in a cardiac cell culture system and a mathematical model of excitable media. In both systems, we observe three types of behaviour: plane wave propagation without breakup, plane wave breakup into spiral waves and plane wave block. In the theoretical model, we observe a linear decrease in propagation velocity as the number of heterogeneities is increased, followed by a rapid, nonlinear decrease to zero. The linear decrease results from the heterogeneities acting independently on the wavefront. A general scaling argument that considers the degree of system heterogeneity and the properties of the excitable medium is used to derive a dimensionless parameter that describes the interaction of the wavefront with the heterogeneities.

Wave Propagation in Excitable Media with Randomly Distributed Obstacles

We study the effect of small, randomly distributed obstacles on wave propagation in two-dimensional (2D) and 3D excitable media described by the Aliev--Panfilov model. We find that increasing the number of obstacles decreases the conduction velocity of plane waves and decreases the effective diffusion coefficient in the eikonal curvature equation. The presence of obstacles also increases the inducibility of wave breaks and spiral waves in 2D and 3D excitable media, but suppresses spiral breakup induced by a steep restitution curve mechanism. We discuss the mechanisms of the observed effects, the differences between 2D and 3D excitable media, as well as the relevance of our study to processes of wave propagation in cardiac tissue, including arrhythmogenesis in the presence of fibrosis in the myocardium.