Generalized minimal principle for rotor filaments

To a reaction-diffusion medium with an inhomogeneous anisotropic diffusion tensor D, we add a fourth spatial dimension such that the determinant of the diffusion tensor is constant in four dimensions. We propose a generalized minimal principle for rotor filaments, stating that the scroll wave filament strives to minimize its surface area in the higher-dimensional space. As a consequence, stationary scroll wave filaments in the original 3D medium are geodesic curves with respect to the metric tensor G = det(D)D-1. The theory is confirmed by numerical simulations for positive and negative filament tension and a model with a non-stationary spiral core. We conclude that filaments in cardiac tissue with positive tension preferentially reside or anchor in regions where cardiac cells are less interconnected, such as portions of the cardiac wall with a large number of cleavage planes

Development of a realistic computer model of the human ventricles for the study of reentrant arrhythmias

De contracties van het hart worden veroorzaakt door elektrische golven van excitatie die door het hartweefsel propageren. De overdracht van informatie door excitatiegolven is een vaak voorkomend fenomeen in de biologie, en vindt plaats in zenuw- en spierweefsel, zoals het hart. Modelleren in de elektrofysiologie is één van de belangrijkste en boeiendste voorbeelden van de toepassing van theoretische en computationele fysica in de geneeskunde en biologie. Deze tak van de wetenschap ontstond meer dan vijftig jaar geleden met het Hodgkin-Huxley model voor de propagatie van excitatie in zenuwcellen [Hodgkin and Huxley 1952], dat de Nobelprijs won in 1963. Later werd het modelleren eveneens toegepast op hartweefsel door Noble [1962] en FitzHugh [1961], en deze modellen werden verder verfijnd naarmate de experimentele technieken om de eigenschappen van celmembranen te onderzoeken, verbeterd werden [Beeler and Reuter 1977, Luo and Rudy 1991, 1994, Noble et al. 1998]. Het bleek dat onregelmatigheden in de pulspropagatie in het hart aan de basis liggen van de gevaarlijkste hartritmestoornissen en plotse hartstilstanden, die één sterfgeval op tien in geïndustrialiseerde landen op hun rekening nemen [Winfree 1994]

Accurate eikonal-curvature relation for wave fronts in locally anisotropic reaction-diffusion systems

The dependency of wave velocity in reaction-diffusion (RD) systems on the local front curvature determines not only the stability of wave propagation, but also the fundamental properties of other spatial configurations such as vortices. This Letter gives the first derivation of a covariant eikonal-curvature relation applicable to general RD systems with spatially varying anisotropic diffusion properties, such as cardiac tissue. The theoretical prediction that waves which seem planar can nevertheless possess a nonvanishing geometrical curvature induced by local anisotropy is confirmed by numerical simulations, which reveal deviations up to 20% from the nominal plane wave speed

3D Source location in optical mapping

International audienceOptical mapping is a display process for cardiac action potentials by fluorescence. So far one considered that experimental measurements represented boundary potentials, although they took into account the interaction of the incident light with the inside of the tissue. Our aim is to reconstruct tridimensional action potentials exploiting this 3D interaction. For each image obtained by optical mapping, we look for a depolarization wave front that fit the data. For now we consider spherical wave fronts, which allows us to locate the position of the excitation. We can also determine the time the excitation took place. It is about solving an inverse problem. To do that we discretised our domain with the finite elements method and implemented BFGS method for the resolution. We present first numerical results of this new approach.La cartographie optique est un procédé de visualisation des potentiels d'action cardiaques par fluorescence. Jusqu'à maintenant, on considérait que les mesures effectuées représentaient des potentiels en surface, bien qu'elles intégraient l'interaction de la lumière avec l'intérieur du tissu. Notre objectif est de reconstruire des potentiels d'action tri-dimensionnels en exploitant au mieux cette interaction 3D. Pour chaque image obtenue par cartographie optique, nous recherchons un front de dépolarisation 3D qui minimise la différence avec les données. Pour le moment nous considérons des fronts sphériques, ce qui nous permet de localiser la position de l'excitation. Nous pouvons également déterminer le temps auquel l'excitation a eu lieu. Il s'agit de résoudre un problème inverse. Pour cela nous avons discrétisé notre domaine avec la méthode des éléments finis et implémenté la méthode BFGS pour la résolution. Nous présentons les premiers résultats numériques de cette nouvelle approche

Attenuation of stretch-induced arrhythmias following chemical ablation of Purkinje fibres, in isolated rabbit hearts

Purkinje fibres (PFs) play an important role in some ventricular arrhythmias and acute ventricular stretch can evoke mechanically-induced arrhythmias. We tested whether Purkinje fibres, play a role in these arrhythmias. Pseudo-ECGs were recorded in isolated, Langendorff-perfused, rabbit hearts in which the left ventricular endocardial surface was also irrigated with Tyrode, via an indwelling catheter placed in the left ventricular lumen. The number and period of ectopic activations was measured during left ventricular lumen inflation via an indwelling fluid-filled balloon (500 μL added over 2 s and maintained for 15 s in total). Mechanically-induced arrhythmias occurred in 70% of balloon inflations: they were maximal in the first 5 s and ceased within 15 s. Brief, (10 s) irrigation of the left ventricular lumen with Lugol solution (IK/I2), via the indwelling catheter, reduced inflation-induced ectopics by 98% (p < 0.05). Ablation of endocardial PFs by Lugol was confirmed by Triphenyltetrazolium Chloride staining. Optical mapping revealed the left ventricular epicardial activation patterns of ectopics could have PF-mediated and focal sources. In silico modelling predicted ectopic sources originating in the endocardial region propagate to and through the Purkinje fibres network. Acute distention-induced ectopics are multi-focal, their attenuation by Lugol, their activation patterns and in silico modelling indicate a participation of Purkinje fibres in these arrhythmias

A comprehensive framework for evaluation of high pacing frequency and arrhythmic optical mapping signals

Introduction: High pacing frequency or irregular activity due to arrhythmia produces complex optical mapping signals and challenges for processing. The objective is to establish an automated activation time-based analytical framework applicable to optical mapping images of complex electrical behavior.Methods: Optical mapping signals with varying complexity from sheep (N = 7) ventricular preparations were examined. Windows of activation centered on each action potential upstroke were derived using Hilbert transform phase. Upstroke morphology was evaluated for potential multiple activation components and peaks of upstroke signal derivatives defined activation time. Spatially and temporally clustered activation time points were grouped in to wave fronts for individual processing. Each activation time point was evaluated for corresponding repolarization times. Each wave front was subsequently classified based on repetitive or non-repetitive events. Wave fronts were evaluated for activation time minima defining sites of wave front origin. A visualization tool was further developed to probe dynamically the ensemble activation sequence.Results: Our framework facilitated activation time mapping during complex dynamic events including transitions to rotor-like reentry and ventricular fibrillation. We showed that using fixed AT windows to extract AT maps can impair interpretation of the activation sequence. However, the phase windowing of action potential upstrokes enabled accurate recapitulation of repetitive behavior, providing spatially coherent activation patterns. We further demonstrate that grouping the spatio-temporal distribution of AT points in to coherent wave fronts, facilitated interpretation of isolated conduction events, such as conduction slowing, and to derive dynamic changes in repolarization properties. Focal origins precisely detected sites of stimulation origin and breakthrough for individual wave fronts. Furthermore, a visualization tool to dynamically probe activation time windows during reentry revealed a critical single static line of conduction slowing associated with the rotation core.Conclusion: This comprehensive analytical framework enables detailed quantitative assessment and visualization of complex electrical behavior

Unanesthetized Rodents Demonstrate Insensitivity of QT Interval and Ventricular Refractory Period to Pacing Cycle Length

Aim: The cardiac electrophysiology of mice and rats has been analyzed extensively, often in the context of pathological manipulations. However, the effects of beating rate on the basic electrical properties of the rodent heart remain unclear. Due to technical challenges, reported electrophysiological studies in rodents are mainly from ex vivo preparations or under deep anesthesia, conditions that might be quite far from the normal physiological state. The aim of the current study was to characterize the ventricular rate-adaptation properties of unanesthetized rats and mice.Methods: An implanted device was chronically implanted in rodents for atrial or ventricular pacing studies. Following recovery from surgery, QT interval was evaluated in rodents exposed to atrial pacing at various frequencies. In addition, the frequency dependence of ventricular refractoriness was tested by conventional ventricular programmed stimulation protocols.Results: Our findings indicate total absence of conventional rate-adaptation properties for both QT interval and ventricular refractoriness. Using monophasic action potential recordings in isolated mice hearts we could confirm the previously reported shortening of the action potential duration at fast pacing rates. However, we found that this mild shortening did not result in similar decrease of ventricular refractory period.Conclusion: Our findings indicate that unanesthetized rodents exhibit flat QT interval and ventricular refractory period rate-dependence. This data argue against empirical use of QT interval correction methods in rodent studies. Our new methodology allowing atrial and ventricular pacing of unanesthetized freely moving rodents may facilitate more appropriate utility of these important animal models in the context of cardiac electrophysiology studies