The heart as a system of coupled nonlinear oscillators

In various approximations the heart is considered as a system of coupled nonlinear oscillators which are characterized by their phase transition curve (PTC) only. The system exhibits many phenomena which are known from ECG recordings such as multi-level-Wenckebach periodicity, dissociation, induction or removal of a tachycardia by an extrasystole, pseudo-block and the gap phenomenon. All these can be discussed within the model on a quantitative level.     

An uncommon case of spontaneous conversion from AV re-entry tachycardia to AV nodal re-entry tachycardia in a patient with dual tachycardia

We report the case of a 46-year old patient in whom an electrophysiology study (EP) was performed due to paroxysmal supraventricular tachycardia documented in 12-lead ECG. During the EP study, supraventricular tachycardia was induced easily and it corresponded to orthodromic AV reentry tachycardia (AVRT) using a concealed left free wall accessory pathway. However, during the study AVRT spontaneously and repeatedly converted to the typical slow-fast AV node reentry tachycardia (AVNRT). Both accessory and AV nodal slow pathways were ablated, due to the finding that both AVRT and AVNRT were independently inducible during the EP study.     

Simulated Interactions between a Class III Antiarrhythmic Drug and a Figure 8 Reentry

Ventricular Fibrillation is responsible for a majority of sudden cardiac death, but little is known about how ventricular tachycardia (VT) degenerates into ventricular fibrillation. Several clinical studies focused only on preventing VT with a class III antiarrhythmic drug resulted in many deaths. Our simulations investigate the interactions between an antiarrhythmic drug likely to suppress a VT and a Figure 8 reentry. A parameter AAR is introduced to increase the action potential duration and therefore simulate various Class III drugs. Simulations are ran under several conditions (phases of the reentry, values of AAR, durations). They show that a VT can be suppressed whatever the phase of the reentry but it strongly depends on the duration of the effect. It confirms that a drug which can suppress a reentry can also worsen it. It also shows a great variety of activation patterns and thus the complexity of antiarrhythmic drugs effects. Simulations also demonstrate that suppressing VT is an increasing function of AAR.     

Interaction of coupled nonlinear oscillators having different intrinsic resting levels

The interaction among coupled oscillators is governed by oscillator properties (intrinsic frequency and amplitude) and coupling mechanisms. This study considers another oscillator property, the intrinsic resting level, and evaluates its role in governing oscillator interactions. The results of computer experiments on a chain of either three or five bidirectionally coupled nonlinear oscillators, suggest that an intrinsic resting level gradient, if present, is one of the factors governing the interaction between coupled oscillators. If there is no intrinsic frequency gradient, then an intrinsic resting level gradient is sufficient to produce many features of interaction among coupled oscillators. If both intrinsic frequency and intrinsic resting level gradients are present, then both of them determine the manner in which the coupled oscillators interact with each other.     

Mode analysis of a tubular structure of coupled non-linear oscillators for digestive-tract modelling

A commonly accepted mathematical model for the slow-wave electrical activity of the gastro-intestinal tract of humans and animals comprises a set of interconnected nonlinear oscillators. Using a van der Pol oscillator with third-power conductance characteristics as the unit oscillator a number of structures have been analysed using a matrix Krylov-Bogolioubov method linearisation. The mode analysis of one-dimensional chains and two-dimensional arrays has been reported. In this paper the method has been extended to consider a tubular structure which is relevant to modelling small-intestinal rhythms. It is shown that this structure is capable of producing stable single models, non-resonant double modes and degenerated modes. General expressions are obtained for anm×n structure and examples given of two special conditions of 3×4 (i.e. odd numbers of oscillators in a ring) and 4×3 cases. The analytical results obtained for these two cases have been vertified experimentally using an electronic implementation of coupled van der Pol oscillators. Results obtained using fifth-power non-linear oscillators are summarised.     

Adenosine-sensitive perinodal atrial tachycardia. What is the mechanism?

Termination of focal atrial tachycardia with adenosine is considered a defining feature for triggered activity. Recent evidence, however, suggests that the perinodal adenosine-sensitive AT has reentry as the mechanism of tachycardia. In this report, we were able to confirm the mechanism of AT as reentry by observing the response to programmed electrical stimulation and demonstrating the fallacy of traditional teaching that the adenosine responsiveness of AT is a criterion for labeling the mechanism as triggered activity.     

Control of interaction strength in a network of the true slime mold by a microfabricated structure

The plasmodium of the true slime mold, Physarum polycephalum, which shows various nonlinear oscillatory phenomena, for example, in its thickness, protoplasmic streaming and concentration of intracellular chemicals, can be regarded as a collective of nonlinear oscillators. The plasmodial oscillators are interconnected by microscale tubes whose dimensions can be closely related to the strength of interaction between the oscillators. Investigation of the collective behavior of the oscillators under the conditions in which the interaction strength can be systematically controlled gives significant information on the characteristics of the system. In this study, we proposed a living model system of a coupled oscillator system in the Physarum plasmodium. We patterned the geometry and dimensions of the microscale tube structure in the plasmodium by a microfabricated structure (microstructure). As the first step, we constructed a two-oscillator system for the plasmodium that has two wells (oscillator part) and a channel (coupling part). We investigated the oscillation behavior by monitoring the thickness oscillation of the plasmodium in the microstructure with various channel widths. It was found that the oscillation behavior of two oscillators dynamically changed depending on the channel width. Based on the results of measurements of the tube dimensions and the velocity of the protoplasmic streaming in the tube, we discuss how the channel width relates to the interaction strength of the coupled oscillator system.     

Analytical approximations for the amplitude and period of a relaxation oscillator

Background  

Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters.     

Nonlinear dynamics and bifurcations of a coupled oscillator model for calling behavior of Japanese tree frogs (Hyla japonica)

Synchronization has been observed in various systems, including living beings. In a previous study, we reported a new phenomenon with antisynchronization in calling behavior of two interacting Japanese tree frogs. In this paper, we theoretically analyse nonlinear dynamics in a system of three coupled oscillators, which models three interacting frogs, where the oscillators of each pair have the property of antisynchronization; in particular, we perform bifurcation analysis and Lyapunov function analysis.     

Nonlinear dynamics and bifurcations of a coupled oscillator model for calling behavior of Japanese tree frogs (Hyla japonica)

Synchronization has been observed in various systems, including living beings. In a previous study, we reported a new phenomenon with antisynchronization in calling behavior of two interacting Japanese tree frogs. In this paper, we theoretically analyse nonlinear dynamics in a system of three coupled oscillators, which models three interacting frogs, where the oscillators of each pair have the property of antisynchronization; in particular, we perform bifurcation analysis and Lyapunov function analysis.     

ICD discrimination of SVT versus VT with 1:1 V-A conduction: A review of the literature

Inappropriate ICD shocks are associated with increased mortality. They also impair patients'' quality of life, increase hospitalizations, and raise health-care costs. Nearly 80% of inappropriate ICD shocks are caused by supraventricular tachycardia. Here we report the case of a patient who received a single-lead dual-chamber sensing ICD for primary prevention of sudden cardiac death and experienced inappropriate ICD shocks. V-A time, electrogram morphology, and response to antitachycardia pacing suggested atrioventricular nodal reentry tachycardia, which was confirmed in an electrophysiology study. Inspired by this case, we performed a literature review to discuss mechanisms for discrimination of supraventricular tachycardia with 1:1 A:V relationship from ventricular tachycardia with 1:1 retrograde conduction.     

Dynamics of a neural system with a multiscale architecture

The architecture of the brain is characterized by a modular organization repeated across a hierarchy of spatial scales-neurons, minicolumns, cortical columns, functional brain regions, and so on. It is important to consider that the processes governing neural dynamics at any given scale are not only determined by the behaviour of other neural structures at that scale, but also by the emergent behaviour of smaller scales, and the constraining influence of activity at larger scales. In this paper, we introduce a theoretical framework for neural systems in which the dynamics are nested within a multiscale architecture. In essence, the dynamics at each scale are determined by a coupled ensemble of nonlinear oscillators, which embody the principle scale-specific neurobiological processes. The dynamics at larger scales are 'slaved' to the emergent behaviour of smaller scales through a coupling function that depends on a multiscale wavelet decomposition. The approach is first explicated mathematically. Numerical examples are then given to illustrate phenomena such as between-scale bifurcations, and how synchronization in small-scale structures influences the dynamics in larger structures in an intuitive manner that cannot be captured by existing modelling approaches. A framework for relating the dynamical behaviour of the system to measured observables is presented and further extensions to capture wave phenomena and mode coupling are suggested.     

Principles of entrainment: diagnostic utility for supraventricular tachycardia

Entrainment is an important pacing maneuver that can be used to identify reentry as a tachycardia mechanism and define components of the circuit. This review examines how principles of entrainment can be used to arrive at a firm supraventricular tachycardia diagnosis using a simple algorithm and builds a foundation for the application of entrainment to more complex or unknown circuits.     

Coupled Van der Pol oscillators — A model of excitatory and inhibitory neural interactions

A system of mutually coupled Van der Pol equations is derived from an extended version of the Wilson and Cowan model for the dynamics of a number of excitatory and inhibitory neural subsets. In the lowest order of approximation, interactions between excitatory and inhibitory subsets appear as linear elastic coupling, while those within and between excitatory and excitatory subsets appear as nonlinear frictional coupling. The case of two coupled oscillators is investigated by the method of averaging and the stability conditions for two mode oscillations are obtained. Internal resonance is also discussed briefly in the case of identical oscillators.     

Experimental analysis of the formation of macro-reentry in the right atrium of rabbits

The aim of the present study was experimental demonstration of the formation of reentry in isolated preparations of the rabbit's right atrium, including sulcus terminalis, interatrial septum and AV node. Tachycardia was evoked by extrasystolic stimulation of the preparation. Reentry was identified by computerized multichannel mapping of excitation wave propagation. A series of sections performed in the area between the caval veins and the coronary sinus confirmed the presence of reentry pathway round the orifices of caval veins and through AV made zone. Local cooling and sections performed in different parts of the AV node showed that not all areas of AV node were involved in the formation of reentry, but only the perinodal (AN) area. These effects on the AN area terminated tachycardia. Linear dependence between the period of tachycardia and delay in the AV nodal zone was found.     

Substrate Based Ablation of Ventricular Tachycardia Through An Epicardial Approach

Ventricular tachycardia (VT) occurring late after myocardial infarction is often due to reentry circuit in the peri-infarct zone. The circuit is usually located in the sub-endocardium, though subepicardial substrates are known. Activation mapping during VT to identify target regions for ablation can be difficult if VT is non inducible or poorly tolerated. In the latter, a substrate based approach of mapping during sinus rhythm in conjunction with pace mapping helps to define the reentry circuit and select target sites for ablation in majority of patients with hemodynamically unstable VT. Percutaneous epicardial catheter ablation has been attempted as an approach where ablation by a conventional endocardial access has been unsuccessful. We report a case of post myocardial infarction scar VT which could be successfully ablated with a substrate based approach from the epicardial aspect.     

Mechanisms of unpinning and termination of ventricular tachycardia

High-energy defibrillation shock is the only therapy for ventricular tachyarrhythmias. However, because of adverse side effects, lowering defibrillation energy is desirable. We investigated mechanisms of unpinning, destabilization, and termination of ventricular tachycardia (VT) by low-energy shocks in isolated rabbit right ventricular preparations (n = 22). Stable VT was initiated with burst pacing and was optically mapped. Monophasic "unpinning" shocks (10 ms) of different strengths were applied at various phases throughout the reentry cycle. In 8 of 22 preparations, antitachycardia pacing (ATP: 8-20 pulses, 50-105% of period, 0.8-10 mA) was also applied. Termination of reentry by ATP was achieved in only 5 of 8 preparations. Termination by unpinning occurred in all 22 preparations. Rayleigh's test showed a statistically significant unpinning phase window, during which reentry could be unpinned and subsequently terminated with E80 (magnitude at which 80% of reentries were unpinned) = 1.2 V/cm. All reentries were unpinned with field strengths < or = 2.4 V/cm. Unpinning was achieved by inducing virtual electrode polarization and secondary sources of excitation at the core of reentry. Optical mapping revealed the mechanisms of phase-dependent unpinning of reentry. These results suggest that a 20-fold reduction in energy could be achieved compared with conventional high-energy defibrillation and that the unpinning method may be more effective than ATP for terminating stable, pinned reentry in this experimental model.     

Catheter ablation of fascicular ventricular tachycardia

Fascicular ventricular tachycardia (VT) is an idiopathic VT with right bundle branch block morphology and left-axis deviation occuring predominantly in young males. Fascicular tachycardia has been classified into three subtypes namely, left posterior fascicular VT, left anterior fascicular VT and upper septal fascicular VT. The mechanism of this tachycardia is believed to be localized reentry close to the fascicle of the left bundle branch. The reentrant circuit is composed of a verapamil sensitive zone, activated antegradely during tachycardia and the fast conduction Purkinje fibers activated retrogradely during tachycardia recorded as the pre Purkinje and the Purkinje potentials respectively. Catheter ablation is the preferred choice of therapy in patients with fascicular VT. Ablation is carried out during tachycardia, using conventional mapping techniques in majority of the patients, while three dimensional mapping and sinus rhythm ablation is reserved for patients with nonmappable tachycardia.     

Two coupled neural oscillators as a model of the circadian pacemaker

Pittendrigh first found that the circadian rhythm of locomotor activity in nocturnal rodents split into two components. Hoffman then reported that the splitting phenomenon was even more reproducible in the small diurnal primate Tupaia. These “splitting” experiments and many other experiments suggest that two coupled oscillators may constitute the circadian pacemaker system. Pittendrigh proposed a phenomenological two-oscillator model. Daan and Berde developed a quantitative model assuming that the interaction between the two constituent oscillators is by instantaneous resets. Their model system can simulate several qualitative features in the experimental data. As the assumption of instantaneous resets seems to be unnatural, we study two limit cycle oscillators, which are coupled continuously to each other, as a model of the circadian pacemaker. We assume the following points, (i) One oscillator in a resting state does not affect another oscillator, (ii) Two oscillators are identical, (iii) The coupling is symmetrical. By the theory of Hopf bifurcation it is found that the general two-oscillator system has two stable periodic solutions. One is the in-phase solution where the two constituent oscillators oscillate in phase synchrony. Another is the anti-phase solution where the two oscillators oscillate 180 ° out of phase. The former corresponds to a single pattern of locomotor activity and the latter corresponds to a splitting pattern. Furthermore, we study specific two-neural oscillators, which are linearly coupled to each other. By the method of secondary bifurcation we find that the model shows simultaneous stability of the two alternative phase relationships and the hysteresis phenomena found in Tupaia. A natural period of the uncoupled constituent oscillator is longer than that of the in-phase solution but it is shorter than that of the anti-phase solution. This is in agreement with the data of Tupaia.     

Bundle-branch reentry ventricular tachycardia after transcatheter aortic valve replacement

An 83-year-old male suffering from severe symptomatic aortic valve stenosis received an implant of a biological aortic prosthesis through the femoral artery without complications. Seven days after dischargement he experienced a syncope. The patient was wearing an ECG holter monitor that day, which showed a wide QRS complex tachycardia of 300 beats per minute. The electrophysiological study revealed a bundle-branch reentry ventricular tachycardia as the cause of the syncope. Radio-frequency was applied on the right-bundle branch. Twelve months later, the patient has remained asymptomatic.