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.

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.

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.

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.

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.

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.

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 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.

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.

Termination of reentrant cardiac action potential propagation using far-field electrical pacing.

Several different types of rapid cardiac rhythm disorders, including atrial and ventricular fibrillation, are likely caused by multiple, rapidly rotating, action potential (AP) waves. Thus, an electrical pacing therapy, whose effectiveness is based on being delivered with a particular timing relative to one of these waves, is unlikely to be useful in terminating the remaining waves. Here, we develop pacing protocols that are designed to terminate rotating waves independently of when the sequences of stimuli are imposed or where each wave is in its rotation at the time the sequences are initiated. These protocols are delivered as far-field stimuli, and therefore are capable of simultaneously influencing all the waves present. The pacing intervals for these protocols are, in general, of unequal duration and are determined through examination of the dynamics of AP propagation in a 1-D ring model. Series of two or three stimuli with interstimulus intervals chosen in this way are shown to be effective in terminating these waves over a wide range of ring circumferences and AP dynamical parameters. Stimulus sequences of this type may form the basis for developing new defibrillation protocols to test in experiments or more realistic models of the electrical heart.

Poincaré plots and tachograms reveal beat patterning in sick sinus syndrome with supraventricular tachycardia and varying AV nodal block.

Using 24-h ambulatory electrocardiography, the RR intervals of all beats were determined in a West Highland white terrier with sick sinus syndrome characterized by long sinus pauses, bradycardia, supraventricular tachycardia (SVT) and varying degrees of atrioventricular (AV) heart block. Distinctive patterns of bradycardia and 1:1, 2:1, 3:1, 4:1 and 5:1 AV block associated with SVT were evident in the tachogram (RR interval distribution over time) and Poincaré plots (short-term heart rate variability plots of RRn versus RRn+1). These patterns differed from those of abrupt alteration in cycle length during long sinus pauses or bursts of supraventricular tachycardia. Recognition of such patterns may direct attention to time points for which close attention to the cardiac rhythm should be evaluated in the full-disclosure of the 24-h ECG recording.

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.

"Zone of avoidance": RR interval distribution in tachograms, histograms, and Poincaré plots of a Boxer dog.

The RR intervals of sinus and ventricular beats were determined by analysis of a 24-h ambulatory electrocardiogram in a Boxer before and after treatment with sotalol. These RR intervals were plotted using tachograms, histograms, and Poincaré plots. The tachogram demonstrated a 'band' wherein a range of RR intervals was infrequent, the histogram did not take the form of a single Gaussian distribution of RR intervals, and the Poincaré plot showed nonhomogeneous beat-to-beat variability. This type of patterning was described as a "zone of avoidance" potentially caused by the clustering of beats within specific ranges. Treatment with sotalol enhanced the "zone of avoidance". Further investigation is needed to understand the mechanism for this observation as well as any clinical implications.

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.

Applications of control theory to the dynamics and propagation of cardiac action potentials.

Sudden cardiac arrest is a widespread cause of death in the industrialized world. Most cases of sudden cardiac arrest are due to ventricular fibrillation (VF), a lethal cardiac arrhythmia. Electrophysiological abnormalities such as alternans (a beat-to-beat alternation in action potential duration) and conduction block have been suspected to contribute to the onset of VF. This study focuses on the use of control-systems techniques to analyze and design methods for suppressing these precursor factors. Control-systems tools, specifically controllability analysis and Lyapunov stability methods, were applied to a two-variable Karma model of the action-potential (AP) dynamics of a single cell, to analyze the effectiveness of strategies for suppressing AP abnormalities. State-feedback-integral (SFI) control was then applied to a Purkinje fiber simulated with the Karma model, where only one stimulating electrode was used to affect the system. SFI control converted both discordant alternans and 2:1 conduction block back toward more normal patterns, over a wider range of fiber lengths and pacing intervals compared with a Pyragas-type chaos controller. The advantages conferred by using feedback from multiple locations in the fiber, and using integral (i.e., memory) terms in the controller, are discussed.

Enhanced Computer Modeling of Cardiac Action Potential Dynamics using Experimental Data-Based Feedback.

Mathematical models of cardiac action potential (AP) dynamics are useful for studying the formation of dynamically significant patterns such as alternans and conduction block. A closed-loop observer is an augmented version of a mathematical model, in which experimental data are supplied to the model through feedback. In this study, tools for observer analysis were applied to a two-variable Karma model of AP dynamics. For a single-cell system, it was confirmed that membrane potential data could be used to reconstruct the system state, and that Luenberger feedback could stabilize the observer. Next an observer with a 1D geometry was tested with microelectrode membrane-potential data from a 2.1cm in vitro canine Purkinje fiber. It was shown that the observer produced more accurate AP duration (APD) estimates than the model by itself. These reconstructed quantities could be used to provide enhanced information to anti-tachyarrhythmic stimulus protocols that depend on real-time measurements.

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.

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.

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.

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.