Exact coherent structures and chaotic dynamics in a model of cardiac tissue

Byrne, Greg; Marcotte, Christopher D.; Grigoriev, Roman O.

doi:10.1063/1.4915143

Cited by 16 publications

(21 citation statements)

References 40 publications

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“…To our knowledge, the only example where the extensive scaling of the attractor dimension has been shown numerically for an excitable model with a turbulent dynamics stemming from spiral breakup is the work of Strain and Greenside on the Bär-Eiswirth model [337]. An alternative approach to characterize spatio-temporal spiral chaos on the basis of coherent structures was recently suggested by Byrne et al [338]. A second approach builds on the phenomenological classification of electrical turbulence in excitable media as defect-mediated turbulence.…”

Section: Characterization Of Electrical Turbulencementioning

confidence: 99%

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: Characterization Of Electrical Turbulencementioning

confidence: 99%

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

2016

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“…To validate our algorithm, we also implemented and tested its most robust alternative, the Jacobian determinant method 33 . The method essentially identifies PSs with the extrema of the two-dimensional field =ẑ · (∇u| t × ∇u| t+τ ), (10) where τ is an empirically chosen time delay. This method was used to compute PS trajectories for the full resolution (256 × 256) data sets with varying levels of noise, and the results were compared to our benchmark analysis.…”

Section: Comparison With Alternative Approachesmentioning

confidence: 99%

“…An alternative approach relies on the phase-amplitude representation of spiral waves, with the phase singularity (PS) defining the instantaneous center of rotation of the wave. A method for identifying PSs based on the local phase field has become standard in analyzing experimental data 30,31 , although it is also possible to determine the location of PSs using the amplitude field 10 .…”

Section: Introductionmentioning

confidence: 99%

Robust approach for rotor mapping in cardiac tissue

Gurevich

Grigoriev

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The motion of and interaction between phase singularities that lie at the centers of spiral waves captures many qualitative and, in some cases, quantitative features of complex dynamics in excitable systems. Being able to accurately reconstruct their position is thus quite important, even if the data are noisy and sparse, as in electrophysiology studies of cardiac arrhythmias, for instance. A recently proposed global topological approach [Marcotte & Grigoriev, Chaos 27, 093936 (2017)] promises to meaningfully improve the quality of the reconstruction compared with traditional, local approaches. Indeed, we found that this approach is capable of handling noise levels exceeding the range of the signal with minimal loss of accuracy. Moreover, it also works successfully with data sampled on sparse grids with spacing comparable to the mean separation between the phase singularities for complex patterns featuring multiple interacting spiral waves. Keywords: phase singularity, cardiac arrhythmia, spiral wave chaosCatheter ablation has recently emerged as a leading medical treatment for a range of cardiac arrhythmias, especially atrial fibrillation. The premise of the treatment is that certain localized regions of heart tissue can become sources of spiral excitation waves -or rotors -competing with the heart's natural pacemaker, i.e., the sinoatrial node for the atria or the atrio-ventricular node for the ventricles. The success of the ablation procedure then critically depends on the precision with which these sources are located based on electrograms obtained using intra-cardiac multielectrode catheters. This paper explains how the sources of excitation waves in a numerical model of atrial fibrillation can be reliably located with subgrid precision using sparse and noisy measurements of the transmembrane voltage. A similar approach could be used to improve the quality of rotor mapping in a clinical setting.

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“…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%

“…Furthermore, we chose the ionic model introduced by Karma 17 , which captures the essential alternans instability responsible for initiating and maintaining complex arrhythmic behaviors. To make it differentiable, the model has been modified 31,32 such that…”

Section: Model Of Paced Atrial Tissuementioning

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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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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Exact coherent structures and chaotic dynamics in a model of cardiac tissue

Cited by 16 publications

References 40 publications

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

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

Robust approach for rotor mapping in cardiac tissue

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

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