Ephaptic Coupling as a Resolution to the Paradox of Action Potential Wave Speed and Discordant Alternans Spatial Scales in the Heart.

Previous computer simulations have suggested that existing models of action potential wave propagation in the heart are not consistent with observed wave propagation behavior. Specifically, computer models cannot simultaneously reproduce the rapid wave speeds and small spatial scales of discordant alternans patterns measured experimentally in the same simulation. The discrepancy is important, because discordant alternans can be a key precursor to the development of abnormal and dangerous rapid rhythms in the heart. In this Letter, we show that this paradox can be resolved by allowing so-called ephaptic coupling to play a primary role in wave front propagation in place of conventional gap-junction coupling. With this modification, physiological wave speeds and small discordant alternans spatial scales both occur with gap-junction resistance values that are more in line with those observed in experiments. Our theory thus also provides support to the hypothesis that ephaptic coupling plays an important role in normal wave propagation.

Termination of Scroll Waves by Surface Impacts.

Three-dimensional scroll waves direct cell movement and gene expression, and induce chaos in the brain and heart. We found an approach to terminate multiple three-dimensional scrolls. A pulse of a properly configured electric field detaches scroll filaments from the surface. They shrink due to filament tension and disappear. Since wave emission from small heterogeneities is not used, this approach requires a much lower electric field. It is not sensitive to the details of the excitable medium. It may affect future studies of low-energy chaos termination in the heart.

Theory of the development of alternans in the heart during controlled diastolic interval pacing.

The beat-to-beat alternation in action potential durations (APDs) in the heart, called APD alternans, has been linked to the development of serious cardiac rhythm disorders, including ventricular tachycardia and fibrillation. The length of the period between action potentials, called the diastolic interval (DI), is a key dynamical variable in the standard theory of alternans development. Thus, methods that control the DI may be useful in preventing dangerous cardiac rhythms. In this study, we examine the dynamics of alternans during controlled-DI pacing using a series of single-cell and one-dimensional (1D) fiber models of alternans dynamics. We find that a model that combines a so-called memory model with a calcium cycling model can reasonably explain two key experimental results: the possibility of alternans during constant-DI pacing and the phase lag of APDs behind DIs during sinusoidal-DI pacing. We also find that these results can be replicated by incorporating the memory model into an amplitude equation description of a 1D fiber. The 1D fiber result is potentially concerning because it seems to suggest that constant-DI control of alternans can only be effective over only a limited region in space.

Use of machine learning and Poincaré density grid in the diagnosis of sinus node dysfunction caused by sinoatrial conduction block in dogs.

BACKGROUND: Sinus node dysfunction because of abnormal impulse generation or sinoatrial conduction block causes bradycardia that can be difficult to differentiate from high parasympathetic/low sympathetic modulation (HP/LSM). HYPOTHESIS: Beat-to-beat relationships of sinus node dysfunction are quantifiably distinguishable by Poincaré plots, machine learning, and 3-dimensional density grid analysis. Moreover, computer modeling establishes sinoatrial conduction block as a mechanism. ANIMALS: Three groups of dogs were studied with a diagnosis of: (1) balanced autonomic modulation (n = 26), (2) HP/LSM (n = 26), and (3) sinus node dysfunction (n = 21). METHODS: Heart rate parameters and Poincaré plot data were determined [median (25%-75%)]. Recordings were randomly assigned to training or testing. Supervised machine learning of the training data was evaluated with the testing data. The computer model included impulse rate, exit block probability, and HP/LSM. RESULTS: Confusion matrices illustrated the effectiveness in diagnosing by both machine learning and Poincaré density grid. Sinus pauses >2 s differentiated (P < .0001) HP/LSM (2340; 583-3947 s) from sinus node dysfunction (8503; 7078-10 050 s), but average heart rate did not. The shortest linear intervals were longer with sinus node dysfunction (315; 278-323 ms) vs HP/LSM (260; 251-292 ms; P = .008), but the longest linear intervals were shorter with sinus node dysfunction (620; 565-698 ms) vs HP/LSM (843; 799-888 ms; P < .0001). CONCLUSIONS: Number and duration of pauses, not heart rate, differentiated sinus node dysfunction from HP/LSM. Machine learning and Poincaré density grid can accurately identify sinus node dysfunction. Computer modeling supports sinoatrial conduction block as a mechanism of sinus node dysfunction.

Shock-induced termination of reentrant cardiac arrhythmias: comparing monophasic and biphasic shock protocols.

In this article, we compare quantitatively the efficiency of three different protocols commonly used in commercial defibrillators. These are based on monophasic and both symmetric and asymmetric biphasic shocks. A numerical one-dimensional model of cardiac tissue using the bidomain formulation is used in order to test the different protocols. In particular, we performed a total of 4.8 × 10(6) simulations by varying shock waveform, shock energy, initial conditions, and heterogeneity in internal electrical conductivity. Whenever the shock successfully removed the reentrant dynamics in the tissue, we classified the mechanism. The analysis of the numerical data shows that biphasic shocks are significantly more efficient (by about 25%) than the corresponding monophasic ones. We determine that the increase in efficiency of the biphasic shocks can be explained by the higher proportion of newly excited tissue through the mechanism of direct activation.

Role of ephaptic coupling in discordant alternans domain sizes and action potential propagation in the heart.

Discordant alternans, the spatially out-of-phase alternation of the durations of propagating action potentials in the heart, has been linked to the onset of fibrillation, a major cardiac rhythm disorder. The sizes of the regions, or domains, within which these alternations are synchronized are critical in this link. However, computer models employing standard gap junction-based coupling between cells have been unable to reproduce simultaneously the small domain sizes and rapid action potential propagation speeds seen in experiments. Here we use computational methods to show that rapid wave speeds and small domain sizes are possible when a more detailed model of intercellular coupling that accounts for so-called ephaptic effects is used. We provide evidence that the smaller domain sizes are possible, because different coupling strengths can exist on the wavefronts, for which both ephaptic and gap-junction coupling are involved, in contrast to the wavebacks, where only gap-junction coupling plays an active role. The differences in coupling strength are due to the high density of fast-inward (sodium) channels known to localize on the ends of cardiac cells, which are only active (and thus engage ephaptic coupling) during wavefront propagation. Thus, our results suggest that this distribution of fast-inward channels, as well as other factors responsible for the critical involvement of ephaptic coupling in wave propagation, including intercellular cleft spacing, play important roles in increasing the vulnerability of the heart to life-threatening tachyarrhythmias. Our results, combined with the absence of short-wavelength discordant alternans domains in standard gap-junction-dominated coupling models, also provide evidence that both gap-junction and ephaptic coupling are critical in wavefront propagation and waveback dynamics.

Termination of atrial fibrillation using pulsed low-energy far-field stimulation.

BACKGROUND: Electrically based therapies for terminating atrial fibrillation (AF) currently fall into 2 categories: antitachycardia pacing and cardioversion. Antitachycardia pacing uses low-intensity pacing stimuli delivered via a single electrode and is effective for terminating slower tachycardias but is less effective for treating AF. In contrast, cardioversion uses a single high-voltage shock to terminate AF reliably, but the voltages required produce undesirable side effects, including tissue damage and pain. We propose a new method to terminate AF called far-field antifibrillation pacing, which delivers a short train of low-intensity electric pulses at the frequency of antitachycardia pacing but from field electrodes. Prior theoretical work has suggested that this approach can create a large number of activation sites ("virtual" electrodes) that emit propagating waves within the tissue without implanting physical electrodes and thereby may be more effective than point-source stimulation. METHODS AND RESULTS: Using optical mapping in isolated perfused canine atrial preparations, we show that a series of pulses at low field strength (0.9 to 1.4 V/cm) is sufficient to entrain and subsequently extinguish AF with a success rate of 93% (69 of 74 trials in 8 preparations). We further demonstrate that the mechanism behind far-field antifibrillation pacing success is the generation of wave emission sites within the tissue by the applied electric field, which entrains the tissue as the field is pulsed. CONCLUSIONS: AF in our model can be terminated by far-field antifibrillation pacing with only 13% of the energy required for cardioversion. Further studies are needed to determine whether this marked reduction in energy can increase the effectiveness and safety of terminating atrial tachyarrhythmias clinically.

Reconstructing Cardiac Wave Dynamics From Myocardial Motion Data.

Various models exist to predict the active stresses and membrane potentials within cardiac muscle tissue. However, there exist no methods to reliably measure active stresses, nor do there exist ways to measure transmural membrane potentials that are suitable for in vivo usage. Prior work has devised a linear model to map from the active stresses within the tissue to displacements [1]. In situations where measurements of tissue displacements are entirely precise, we are able to naively solve for the active stresses from the measurements with ease. However, real measurement processes always carry some associated random error and, in the presence of this error, our naive solution to this inverse problem fails. In this work we propose the use of the Ensemble Transform Kalman Filter to more reliably solve this inverse problem. This technique is faster than other related Kalman Filter techniques while still generating high quality estimates which improve on our naive solution. We demonstrate, using in silico simulations, that the Ensemble Transform Kalman Filter produces errors whose standard deviation is an order of magnitude smaller than the least-squares solution.

Dynamic mechanism for initiation of ventricular fibrillation in vivo.

BACKGROUND: Dynamically induced heterogeneities of repolarization may lead to wave-front destabilizations and initiation of ventricular fibrillation (VF). In a computer modeling study, we demonstrated that specific sequences of premature stimuli maximized dynamically induced spatial dispersion of refractoriness and predisposed the heart to the development of conduction block. The purpose of this study was to determine whether the computer model results pertained to the initiation of VF in dogs in vivo. METHODS AND RESULTS: Monophasic action potentials were recorded from right and left ventricular endocardium in anesthetized beagle dogs (n=11) in vivo. Restitution of action potential duration and conduction time and the effective refractory period after delivery of the basic stimulus (S(1)) and each of 3 premature stimuli (S(2), S(3), S(4)) were determined at baseline and during verapamil infusion. The effective refractory period data were used to determine the interstimulus intervals for a sequence of 4 premature stimuli (S(2)S(3)S(4)S(5)=CL(VF)) for which the computer model predicted maximal spatial dispersion of refractoriness. Delivery of CL(VF) was associated with discordant action potential duration alternans and induction of VF in all dogs. Verapamil decreased spatial dispersion of refractoriness by reducing action potential duration and conduction time restitution in a dose-dependent fashion, effects that were associated with reduced inducibility of VF with CL(VF). CONCLUSIONS: Maximizing dynamically induced spatial dispersion of repolarization appears to be an effective method for inducing VF. Reducing spatial dispersion of refractoriness by modulating restitution parameters can have an antifibrillatory effect in vivo.

Origin choice and petal loss in the flower garden of spiral wave tip trajectories.

Rotating spiral waves have been observed in numerous biological and physical systems. These spiral waves can be stationary, meander, or even degenerate into multiple unstable rotating waves. The spatiotemporal behavior of spiral waves has been extensively quantified by tracking spiral wave tip trajectories. However, the precise methodology of identifying the spiral wave tip and its influence on the specific patterns of behavior remains a largely unexplored topic of research. Here we use a two-state variable FitzHugh-Nagumo model to simulate stationary and meandering spiral waves and examine the spatiotemporal representation of the system's state variables in both the real (i.e., physical) and state spaces. We show that mapping between these two spaces provides a method to demarcate the spiral wave tip as the center of rotation of the solution to the underlying nonlinear partial differential equations. This approach leads to the simplest tip trajectories by eliminating portions resulting from the rotational component of the spiral wave.

Toward Quantification and Visualization of Active Stress Waves for Myocardial Biomechanical Function Assessment.

Estimating and visualizing myocardial active stress wave patterns is crucial to understanding the mechanical activity of the heart and provides a potential non-invasive method to assess myocardial function. These patterns can be reconstructed by analyzing 2D and/or 3D tissue displacement data acquired using medical imaging. Here we describe an application that utilizes a 3D finite element formulation to reconstruct active stress from displacement data. As a proof of concept, a simple cubic mesh was used to represent a myocardial tissue "sample" consisting of a 10 × 10 × 10 lattice of nodes featuring different fiber directions that rotate with depth, mimicking cardiac transverse isotropy. In the forward model, tissue deformation was generated using a test wave with active stresses that mimic the myocardial contractile forces. The generated deformation field was used as input to an inverse model designed to reconstruct the original active stress distribution. We numerically simulated malfunctioning tissue regions (experiencing limited contractility and hence active stress) within the healthy tissue. We also assessed model sensitivity by adding noise to the deformation field generated using the forward model. The difference image between the original and reconstructed active stress distribution suggests that the model accurately estimates active stress from tissue deformation data with a high signal-to-noise ratio.

Boundary-induced reentry in homogeneous excitable tissue.

Heterogeneity of cardiac electrical properties can lead to heart rhythm disorders. Numerical studies have shown that stimuli chosen to maximize dynamic heterogeneity terminate wave propagation. However, experimental investigations suggest that similar sequences induce fragmentation of the wave fronts, rather than complete wave block. In this paper we show that an insulating boundary in an otherwise homogeneous medium can disrupt dynamically induced wave block by breaking a symmetry in the spatial pattern of action potential duration, leading to unidirectional block and reentrant activation.

Characterization of multiple spiral wave dynamics as a stochastic predator-prey system.

A perspective on systems containing many action potential waves that, individually, are prone to spiral wave breakup is proposed. The perspective is based on two quantities, "predator" and "prey," which we define as the fraction of the system in the excited state and in the excitable but unexcited state, respectively. These quantities exhibited a number of properties in both simulations and fibrillating canine cardiac tissue that were found to be consistent with a proposed theory that assumes the existence of regions we call "domains of influence," each of which is associated with the activity of one action potential wave. The properties include (i) a propensity to rotate in phase space in the same sense as would be predicted by the standard Volterra-Lotka predator-prey equations, (ii) temporal behavior ranging from near periodic oscillation at a frequency close to the spiral wave rotation frequency ("type-1" behavior) to more complex oscillatory behavior whose power spectrum is composed of a range of frequencies both above and, especially, below the spiral wave rotation frequency ("type-2" behavior), and (iii) a strong positive correlation between the periods and amplitudes of the oscillations of these quantities. In particular, a rapid measure of the amplitude was found to scale consistently as the square root of the period in data taken from both simulations and optical mapping experiments. Global quantities such as predator and prey thus appear to be useful in the study of multiple spiral wave systems, facilitating the posing of new questions, which in turn may help to provide greater understanding of clinically important phenomena such as ventricular fibrillation.

Evaluation of atrial fibrillation induced during anesthesia with fentanyl and pentobarbital in German Shepherd Dogs with inherited arrhythmias.

OBJECTIVE: To determine the type of atrial fibrillation induced by use of 2 pacing protocols during fentanyl and pentobarbital anesthesia before and after administration of atropine and to determine the organization of electrical activity in the left and right atria during atrial fibrillation in German Shepherd Dogs. ANIMALS: 7 German Shepherd Dogs. PROCEDURES: Extrastimulus and pacedown protocols were performed before and after atropine administration. Monophasic action potential spectral entropy and mean dominant frequency were calculated during atrial fibrillation. RESULTS: Atrial fibrillation occurred spontaneously in 6 of 7 dogs. All 7 dogs had atrial fibrillation induced. Sustained atrial fibrillation occurred in 13 of 25 (52%) episodes induced by the extrastimulus protocol and in 2 of 12 episodes of atrial fibrillation induced by pacedown. After atropine administration, sustained atrial fibrillation did not occur, and the duration of the nonsustained atrial fibrillation (6 episodes in 2 dogs of 1 to 26 seconds) was significantly shorter than before atropine administration (25 episodes in 7 dogs of 1 to 474 seconds). The left atrium (3.67 +/- 0.08) had lower spectral entropy than the right atrium (3.81 +/- 0.03), indicating more electrical organization in the left atrium. The mean dominant frequency was higher in the left atrium in 3 dogs. CONCLUSIONS AND CLINICAL RELEVANCE: Atrial fibrillation developed spontaneously and was induced in German Shepherd Dogs under fentanyl and pentobarbital anesthesia. Electrical activity was more organized in the left atrium than in the right atrium as judged by use of spectral entropy.

Discordant Alternans as a Mechanism for Initiation of Ventricular Fibrillation In Vitro.

Background Ventricular tachyarrhythmias are often preceded by short sequences of premature ventricular complexes. In a previous study, a restitution-based computational model predicted which sequences of stimulated premature complexes were most likely to induce ventricular fibrillation in canines in vivo. However, the underlying mechanism, based on discordant-alternans dynamics, could not be verified in that study. The current study seeks to elucidate the mechanism by determining whether the spatiotemporal evolution of action potentials and initiation of ventricular fibrillation in in vitro experiments are consistent with model predictions. Methods and Results Optical mapping voltage signals from canine right-ventricular tissue (n=9) were obtained simultaneously from the entire epicardium and endocardium during and after premature stimulus sequences. Model predictions of action potential propagation along a 1-dimensional cable were developed using action potential duration versus diastolic interval data. The model predicted sign-change patterns in action potential duration and diastolic interval spatial gradients with posterior probabilities of 91.1%, and 82.1%, respectively. The model predicted conduction block with 64% sensitivity and 100% specificity. A generalized estimating equation logistic-regression approach showed that model-prediction effects were significant for both conduction block ( P<1×10-15, coefficient 44.36) and sustained ventricular fibrillation ( P=0.0046, coefficient, 1.63) events. Conclusions The observed sign-change patterns favored discordant alternans, and the model successfully identified sequences of premature stimuli that induced conduction block. This suggests that the relatively simple discordant-alternans-based process that led to block in the model may often be responsible for ventricular fibrillation onset when preceded by premature beats. These observations may aid in developing improved methods for anticipating block and ventricular fibrillation.

Theory of action potential wave block at-a-distance in the heart.

Propagation failure of an action potential wave at a finite distance from its source (so-called type-II block) may cause spiral wave formation or wave breakup in the heart, phenomena that are believed to underlie lethal and nonlethal heart rhythm disorders. In this study, we develop a sufficient condition for this type of block in a homogeneous, spatially one-dimensional system. Using a topological argument, we find that type-II block of a wave will always occur when launched within a finite range of times if the velocity of the trailing edge of the preceding wave, as measured at the stimulus site, is smaller than the velocity of a wave launched with the minimum diastolic interval (DI) for which propagation is possible. This "blocking condition" is robust, remaining valid even when memory and waveback electrotonic effects are included. The condition suggests that type-II block is greatly facilitated when waves are initiated at irregular intervals in time such that (1) the velocities of consecutive waves are as different as possible and (2) the DIs preceding each wave fall on the steeply sloped portion of the action potential duration restitution curve as often as possible. The set of timing intervals between stimuli that are predicted by the blocking condition to produce block are found to be consistent with these guidelines, and also to agree well with a coupled-maps computer simulation model, for the case of waves launched by four rapidly and irregularly timed stimuli.

Cardiac electrical dynamics: maximizing dynamical heterogeneity.

The relationships between key features of the cardiac electrical activity, such as electrical restitution, discordant alternans, wavebreak, and reentry, and the onset of ventricular tachyarrhythmias have been characterized extensively under the condition of constant rapid pacing. However, it is unlikely that this scenario applies directly to the clinical situation, where the induction of ventricular tachycardia (VT) typically is associated with the interruption of normal cardiac rhythm by several premature beats. To address this issue, we have developed a general theory to explain why specific patterns of premature stimuli increase dynamic heterogeneity of repolarization and precipitate conduction block. The theory predicts that conduction block is caused by (1) creation of a spatial gradient in diastolic interval (DI) by waves traveling at slightly different velocities (ie, conduction velocity dispersion) and (2) amplification of the spatial gradient in DI over subsequent action potentials, secondary to a strong dependence of action potential duration on the preceding DI (ie, a steep action potential duration restitution function). Tests of this theory have been conducted in computer models of homogeneous tissue, where increased spatial dispersion of repolarization during premature stimulation can be attributed solely to the development of dynamical heterogeneity, and in a canine model exhibiting spontaneously occurring VT and sudden death. Our results thus far indicate that the probability of inducing ventricular fibrillation (VF) in the animal model is highest for those sequences predicted to cause conduction block in the computer model. An understanding of the mechanisms underlying these observations will help to identify key electrical phenomena in the onset of VT and fibrillation. Drug and electrical therapies can then be improved by targeting these specific phenomena.

Deep entry of defibrillating effects into homogeneous cardiac tissue.

A simple, idealized mathematical model of cardiac tissue is used to show that electrical fields applied with the intent of defibrillating the heart can be effective deep within (that is, many space constants into) cardiac tissue, even in cases when the tissue is assumed to have completely homogeneous electrical properties. This conclusion is drawn from the analysis of the two eigenmodes present in the model, which have fundamentally different characteristics. One mode decays very rapidly with space, implying that the associated membrane potential is only present with appreciable amplitude within a few space constants of the tissue surface. The other mode, however, is not directly dependent on the value of the space constant, and allows deep penetration of the membrane potential and, by implication, its associated defibrillating effects. For deep membrane potentials to be generated by this mechanism, the intracellular and extracellular resistivity anisotropy ratios must be unequal, as is typically the case in cardiac tissue. The model also predicts that this mechanism is most effective for a given applied field strength when the electrode size and separation, or spatial features of the externally applied field at the heart surface, are characterized by scalelengths that are commensurate with approximately two times the heart wall thickness.

A primary mechanism for spiral wave meandering.

The stability and dynamics of spiral wave meandering were studied by examining the behavior of small perturbations to a steadily rotating action potential wave. The disturbances responsible for meandering were found to be generated through an interaction between the unstable local linear dynamics characteristic of the action potential trailing edge near the core and perturbations existing in the region immediately behind this edge. Significantly, for the cases studied, neither wavefront curvature nor head-tail interactions were involved in this process. Study of the generation mechanism using a series of representative mathematical models and computer experiments led to the prediction that the following features of rotating action potentials render them more susceptible to meandering: (1) proximity of the wave tip to the center of rotation, (2) wider action potential leading and trailing edges, and (3) slower wave rotation speeds. Variation of basic tissue properties, including firing threshold potentials and excitability above threshold, affected these properties, and those of the perturbation dynamics, in several ways, producing both stabilizing and destabilizing effects. The nature of the involvement of various tissue and membrane electrical properties is therefore complex, affecting several factors relevant to meandering at once. (c) 2002 American Institute of Physics.

Action Potential Propagation Through Tissue Lacking Gap Junctions: Application to Engrafted Cells in Myocardial Infarcts.

Engraftment of viable, electrically functional cells into a myocardial infarct as a method for restoring functionality is currently a topic of active research interest. Cells implanted in this way can form gap junction connectivity with each other, but often do not connect well with the surrounding tissue outside the infarct. Using a bidomain computer simulation model, we find that activation of these implanted cells by outside propagating action potentials is nevertheless possible, even if no gap junction connectivity to the surrounding tissue exists at all. The mechanism by which this action potential "tunneling" process occurs involves a current path that passes through both the intracellular and extracellular spaces, and is fundamentally spatially two-dimensional in nature. The typically convex boundary of the region occupied by these cells is found to greatly enhance the tunneling process, but unfortunately also hinders the ability of the activation of these cells to terminate reentrant waves propagating around the infarct.