Measurement and structure of spiral wave response functions

Dierckx, Hans; Verschelde, Henri; Panfilov, Alexander V.

doi:10.1063/1.4999606

Cited by 13 publications

(14 citation statements)

References 31 publications

(32 reference statements)

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“…In [58] we considered the case below but not too close to phase-locking threshold, and used Fourier series. For the case E ≲ E crit , this does not work, so we resort to the more robust method, by sliding averages.…”

Section: Regime Close To Phase-lockingmentioning

confidence: 99%

“…3, we can in a first step integrate Eqs. (58) to find the net displacement in space, time and rotation angle during the single meander cycle, say the n-th. At the start of this cycle, taking place at t = t n the collective coordinates of the spiral are denoted X a n , Φ n , Ψ n .…”

Section: E Average Drift Speed Of a Non-phase-locked Meandering Spiralmentioning

confidence: 99%

“…These laws can be further simplified if one averages in time over rotation cycles of the spiral or scroll waves [36]. For non-stationary spiral or scroll waves, a possible averaging method is to analyse the motion in a Fourier series and only keep the non-oscillating, secularly growing terms [57,58]. Some recent works have computed the leading order eigenmodes in the laboratory frame of reference [15,59].…”

Section: Introductionmentioning

confidence: 99%

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Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves

et al. 2019

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In many oscillatory or excitable systems, dynamical patterns emerge which are stationary or periodic in a moving frame of reference. Examples include traveling waves or spiral waves in chemical systems or cardiac tissue. We present a unified theoretical framework for the drift of such patterns under small external perturbations, in terms of overlap integrals between the perturbation and the adjoint critical eigenfunctions of the linearised operator (i.e. 'response functions'). For spiral waves, the finite radius of the spiral tip trajectory as well as spiral wave meander are taken into account. Different coordinates systems can be chosen, depending on whether one wants to predict the motion of the spiral wave tip, the time-averaged tip path, or the center of the meander flower. The framework is applied to analyse the drift of a meandering spiral wave in a constant external field in different regimes.

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Section: Regime Close To Phase-lockingmentioning

confidence: 99%

Section: E Average Drift Speed Of a Non-phase-locked Meandering Spiralmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves

et al. 2019

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“…However, meandering spirals with 'linear' cores, as in Fig. 1b, may be the building blocks of ventricular fibrillation, which motivated recent work to calculate their leading eigenmodes [25][26][27]. In this Letter, we derive equations of motion for biperiodic meandering 2D spirals and 3D scroll waves, without restriction to a particular shape of meander.…”

mentioning

confidence: 99%

Filament Tension and Phase Locking of Meandering Scroll Waves

et al. 2017

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Meandering spiral waves are often observed in excitable media such as the Belousov-Zhabotinsky reaction and cardiac tissue. We derive a theory for drift dynamics of meandering rotors in general reaction-diffusion systems and apply it to two types of external disturbances: an external field and curvature-induced drift in three dimensions. We find two distinct regimes: with small filament curvature, meandering scroll waves exhibit filament tension, whose sign determines the stability and drift direction. In the regimes of strong external fields or meandering motion close to resonance, however, phase locking of the meander pattern is predicted and observed.

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“…Interestingly, for rigidly rotating, as well as meandering, spirals the response functions were numerically found to be localized in the space around the spiral core. This localization area was identified as the key determinant of the region where external perturbation could affect spiral wave dynamics [42][43][44]. It would be interesting to apply response function theory to the problem of anchoring.…”

Section: Discussionmentioning

confidence: 99%

In silico optical control of pinned electrical vortices in an excitable biological medium

2020

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Vortices of excitation are generic to any complex excitable system. In the heart, they occur as rotors, spirals (2D) and scroll waves (3D) of electrical activity that are associated with rhythm disorders, known as arrhythmias. Lethal cardiac arrhythmias often result in sudden death, which is one of the leading causes of mortality in the industrialized world. Irrespective of the nature of the excitable medium, the rotation of a rotor is driven by its dynamics at the (vortex) core. In a recent study, Majumder et al (2018 eLife 7 e41076) demonstrated, using in silico and in vitro cardiac optogenetics, that light-guided manipulation of the core of free rotors can be used to establish real-time spatiotemporal control over the position, number and rotation of these rotors in cardiac tissue. Strategic application of this method, called 'Attract-Anchor-Drag' (AAD) can also be used to eliminate free rotors from the heart and stop cardiac arrhythmias. However, rotors in excitable systems, can pin (anchor) around local heterogeneities as well, thereby limiting their dynamics and possibility for spatial control. Here, we expand our results and numerically demonstrate, that AAD method can also detach anchored vortices from inhomogeneities and subsequently control their dynamics in excitable systems. Thus, overall we demonstrate that AAD control is one of the first universal methods that can be applied to both free and pinned vortices, to ensure their spatial control and removal from the heart and, possibly, other excitable systems.

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Measurement and structure of spiral wave response functions

Cited by 13 publications

References 31 publications

Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves

Response function framework for the dynamics of meandering or large-core spiral waves and modulated traveling waves

Filament Tension and Phase Locking of Meandering Scroll Waves

In silico optical control of pinned electrical vortices in an excitable biological medium

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