Origin of complex behaviour of spatially discordant alternans in a transgenic rabbit model of type 2 long QT syndrome

Ziv, Ohad; Morales, Eduardo; Song, Yoon Kyu; Peng, Xuwen; Odening, Katja E.; Buxton, Alfred E.; Karma, Alain; Koren, Gideon; Choi, Bum Rak

doi:10.1113/jphysiol.2009.175018

Cited by 52 publications

(65 citation statements)

References 64 publications

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“…For instance, in canine ventricles, a pacing-down protocol (with pacing interval decreased in steps of 50 ms to 10 ms) produced a different stationary pattern of alternans than a protocol with constant pacing rate applied to quiescent tissue, for the same asymptotic rate 29 . Similar dependence was found in normal rabbit hearts 30 : while decreasing the pacing interval by 10 ms steps failed to induce discordant alternans, this state was reached by using smaller steps of 5 ms to 2 ms.…”

Section: Introductionsupporting

confidence: 74%

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Memory effects, transient growth, and wave breakup in a model of paced atrium

Garzón

Grigoriev

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The mechanisms underlying cardiac fibrillation have been investigated for over a century, but we are still finding surprising results that change our view of this phenomenon. The present study focuses on the transition from normal rhythm to atrial fibrillation associated with a gradual increase in the pacing rate. While some of our findings are consistent with existing experimental, numerical, and theoretical studies of this problem, one result appears to contradict the accepted picture. Specifically we show that, in a two-dimensional model of paced homogeneous atrial tissue, transition from discordant alternans to conduction block, wave breakup, reentry, and spiral wave chaos is associated with transient growth of finite amplitude disturbances rather than a conventional instability. It is mathematically very similar to subcritical, or bypass, transition from laminar fluid flow to turbulence, which allows many of the tools developed in the context of fluid turbulence to be used for improving our understanding of cardiac arrhythmias.Atrial fibrillation is a common type of cardiac arrhythmia characterized by spatially uncoordinated high-frequency patterns of electrical excitation waves. Several different explanations of how fibrillation arises from a highly coordinated and regular normal rhythm have been offered. The most common is a dynamical scenario that involves several stages. First, a milder type of arrhythmia known as alternans, characterized by regular spatial and temporal modulation in the duration of the excitation, is created as a result of a period doubling or Hopf bifurcation. In the second stage, the modulation grows until some portion of an excitation wave fails to propagate (which is known as conduction block), producing wave breakup. In later stages, spiral waves segments, or wavelets, form and undergo subsequent breakups until a complicated dynamical equilibrium is established, with wavelets continually annihilating and reemerging. The current paradigm is that each of these stages represents a separate bifurcation that leads to either a change in the stability, or the disappearance, of the solution describing a previous stage. Our analysis of a simple model of paced cardiac tissue shows that transitions between different stages can happen without any bifurcations taking place. In particular, conduction block can be caused by strong transient amplification of finite amplitude disturbances, which is a flip side of a very well-known memory effect that describes the sensitivity of the asymptotic dynamics of paced cardiac tissue to the entire pacing history.

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Section: Introductionsupporting

confidence: 74%

“…Consider the pacing protocol A: T [1,10] = 120 ms, followed by T [11,20] = 110 ms, T [21,30] = 100 ms, T [31,40] = 90 ms, and T [41,80] = 80 ms (cf. Fig.…”

Section: A Wave Breakup Induced By Fast Pacingmentioning

confidence: 99%

Memory effects, transient growth, and wave breakup in a model of paced atrium

Garzón

Grigoriev

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Therefore, premature stimulation or pre-existing heterogeneities help to induce discordant alternans, but CV restitution or dynamical spatial instability is needed to maintain discordant alternans. On the other hand, more complex spatial patterns of discordant APD alternans have been shown in experiments [353, 354], which remain to be elucidated by theories of nonlinear dynamics.…”

Section: Electrical Wave Dynamics In Tissue and Organmentioning

confidence: 99%

Nonlinear and stochastic dynamics in the heart

et al. 2014

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In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

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“…To avoid overestimations of CV, values >1.25 m/s were deleted from the analysis. 13 Time and frequency domains analysis was achieved, as previously described. 14 …”

Section: Induction Of Myocarditismentioning

confidence: 99%