Computer simulation of arrhythmias in a network of coupled excitable elements.

Capelle, F J van; Durrer, D

doi:10.1161/01.res.47.3.454

Cited by 200 publications

(52 citation statements)

References 31 publications

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“…Interestly, Eqs. (83,84), give a very good prediction of the distribution of twist even for fast spatial changes of excitability. The onset of sproing in this case can be calculated from the absolute instability spectrum [160], giving rise to a spatial modulation in the amplitude of the helix resulting from sproing.…”

Section: Equations For Filament Motionmentioning

confidence: 94%

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Nonlinear physics of electrical wave propagation in the heart: a review

2016

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Abstract. The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.

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Section: Equations For Filament Motionmentioning

confidence: 94%

“…Other two-variable cardiac models were employed for the incipient simulations of cardiac arrhythmias [83] and the first descriptions of spiral breakup [84].…”

Section: 32mentioning

confidence: 99%

Nonlinear physics of electrical wave propagation in the heart: a review

2016

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“…The excitation wavefront of the premature stimulus will therefore bend and, under favourable circumstances, can initiate spiral wave reentry around a functionally unexcitable core (see Figure 5). 25,26 Thus, rotor formation requires areas of non-uniform repolarisation, either due to fixed tissue inhomogeneity, or transient repolarisation non-uniformities due to the delivery of premature stimuli from multiple sites.…”

Section: Functional Reentry Due To Rotors/spiral Wavesmentioning

confidence: 99%

Mechanisms of Atrial Fibrillation – Reentry, Rotors and Reality

Waks

Josephson²

2014

Arrhythmia &Amp; Electrophysiology Review

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Atrial fibrillation (AF), the most common sustained arrhythmia, is a leading cause of stroke, and is associated with significant morbidity and mortality worldwide. Despite its frequency, clinical importance, and advances in technology and our knowledge of the molecular, ionic and physiological fundamentals of cardiac electrophysiology, our limited understanding of the mechanisms that initiate and sustain AF has prevented us from being able to truly cure this arrhythmia with antiarrhythmic drugs and/or ablation. This contrasts with other arrhythmias, such as AV nodal tachycardia or circus movement tachycardia using an accessory pathway, which have well-defined mechanisms and circuits that can be safely targeted with high rates of cure. The observations that AF may have different mechanisms in different patients, and that paroxysmal, persistent and permanent forms of AF may differ in how they are initiated and sustained, only serves to reinforce our lack of understanding of this ubiquitous arrhythmia. Historical Mechanisms of Atrial Fibrillation and the Multiple Wavelet HypothesisInterest and understanding of the mechanism of AF began to take form in the early 1900s. Given the chaotic and irregular nature of AF on the surface electrocardiogram, rapid firing of automatic atrial foci was considered a potential mechanism. However, after the seminal work of Mayer 1 , Mines 2 and Garrey 3 in laying the foundation for describing and understanding reentrant arrhythmias, atrial reentrant circuits emerged as the likely drivers of AF.4-7 Although these theories were conceptually sound, it was impossible to prove a specific mechanism with the technology of the time. Moe et al. demonstrated that it was probabilistically unlikely that a large number of simultaneous wavefronts would all die out simultaneously, and AF would therefore perpetuate. However, if the number of simultaneous wavelets were small and/or below a critical value (between 15 and 30 in Moe's computer model), 9 at some point all reentrant wavefronts would be simultaneously extinguished, and AF would therefore terminate. 8,9 Allessie et al. provided experimental evidence supporting this mechanism in a canine heart model of AF where four to six simultaneous reentrant wavelets were needed to sustain arrhythmia. 10 Further evidence supporting multiple wavelets in AF was demonstrated in a separate model, which evaluated the effect of various antiarrhythmic drugs on canine myocardium. This model demonstrated that termination of AF was associated with a reduction AbstractAtrial fibrillation (AF) is the most common sustained arrhythmia encountered in clinical practice, yet our understanding of the mechanisms that initiate and sustain this arrhythmia remains quite poor. Over the last 50 years, various mechanisms of AF have been proposed, yet none has been consistently observed in both experimental studies and in humans. Recently, there has been increasing interest in understanding how spiral waves or rotors -which are specific, organised forms of functional reentry -su...

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“…If we assume a barrier of length bl+b2 and thickness T, then there are two possible paths consisting of three separate segments between the pacing and recording sites (Figure 1). The conduction time in the presence of a barrier will then be the minimum of CT, and CT2 of Equation 3 and Equation 4 below.…”

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confidence: 99%

Interaction of fiber orientation and direction of impulse propagation with anatomic barriers in anisotropic canine myocardium.

et al. 1988

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We developed a computer model of the interaction of impulse propagation with anatomic barriers in uniformly anisotropic tissue. Its predictions were confirmed experimentally by using an in vitro cut to create a 6x 1-mm anatomic barrier in 12 canine epicardial strips. The model predicted that long, thin barriers located parallel to the direction of impulse propagation would have little effect in delaying conduction regardless of the arrangement of cardiac fibers. In this situation, the mean experimental ratio of postcut to control conduction times across the barrier was 1.05:1.00 in 10 tissues. When impulses were proceeding perpendicular to an anatomic barrier, significant distal conduction delay was predicted and found to occur only when the conduction from pacing to recording sites was initially longitudinal to fiber orientation (mean experimental ratio, 2.34: 1.00 in five tissues) but not transverse to fiber orientation (ratio, 1.08: 1.00 in five tissues). We conclude that the direction of initial impulse propagation and the orientation of myocardial fibers have large effects on the degree to which anatomic barriers delay activation in cardiac tissue. These findings may have implications for the participation of anatomic barriers in reentrant circuits. (Circulation 1988;78:1478-1494 S low conduction and unidirectional block are requirements for reentrant pathways.1-9 In addition to slow conduction because of a decrease in the rate of rise of the intracellular potential, differences in cell-to-cell coupling and the geometric arrangement of fibers in cardiac tissue may also produce slow conduction. [10][11][12][13][14][15] pathway defined by fixed areas of block could provide a long enough conduction pathway to allow sufficient time for an impulse conducting at a normal velocity to return to fully recovered cardiac tissue. The extent of increased conduction time distal to anatomic barriers in cardiac tissue has not been extensively investigated. In addition, the consequences of the interrelation of fixed anatomic barriers and tissue anisotropy are unknown. Such activation delay distal to a barrier may have important implications for the participation of a barrier in reentrant circuits.Therefore, we developed a computer model of the interaction of fixed anatomic barriers with conduction in anisotropic tissue. Our goals were to verify the hypotheses that the direction of impulse propagation and the orientation of fibers relative to a fixed anatomic area of block were crucial in determining the degree of conduction delay and perturbation of activation patterns produced distal to the block. We then validated the predictions of this computer analysis in a simple model of anatomic barrier in canine epicardium produced by a thin surgical cut in an in vitro preparation. Materials and Methods Model of Conduction and Anisotropic TissueDirectional differences in conduction velocity in canine myocardium related to fiber orientation have

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Computer simulation of arrhythmias in a network of coupled excitable elements.

Cited by 200 publications

References 31 publications

Nonlinear physics of electrical wave propagation in the heart: a review

Nonlinear physics of electrical wave propagation in the heart: a review

Mechanisms of Atrial Fibrillation – Reentry, Rotors and Reality

Interaction of fiber orientation and direction of impulse propagation with anatomic barriers in anisotropic canine myocardium.

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