Feedback-Controlled Dynamics of Meandering Spiral Waves

Grill, Stephan W.; Zykov, V. S.; Müller, Stefan

doi:10.1103/physrevlett.75.3368

Cited by 131 publications

(83 citation statements)

References 18 publications

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“…Resonant drift of spiral waves in cardiac tissue has not been studied experimentally in biological tissues but has been shown to exist in detailed ionic models of cardiac tissue (28), as well as in experiments involving BZ reactions (26). Therefore, it is likely that these effects of mechanics on spiral wave dynamics also could be reproduced by using more detailed experimental and modeling studies in cardiac tissue and in BZ reaction.…”

Section: Discussionmentioning

confidence: 99%

“…As demonstrated in ref. 26, a periodical variation of the properties of an excitable medium in synchrony with the period of a spiral wave resulted in drift and subsequent stable meandering of the spiral wave tip. In our model, deformation of the medium also produced a periodical modulation of the tissue properties in synchrony with the spiral wave period as a result of the excitation-contraction coupling.…”

Section: Spiral Wave Breakupmentioning

confidence: 99%

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Drift and breakup of spiral waves in reaction–diffusion–mechanics systems

Panfilov

Keldermann

Nash

2007

Proc. Natl. Acad. Sci. U.S.A.

105

131

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Rotating spiral waves organize excitation in various biological, physical, and chemical systems. They underpin a variety of important phenomena, such as cardiac arrhythmias, morphogenesis processes, and spatial patterns in chemical reactions. Important insights into spiral wave dynamics have been obtained from theoretical studies of the reaction–diffusion (RD) partial differential equations. However, most of these studies have ignored the fact that spiral wave rotation is often accompanied by substantial deformations of the medium. Here, we show that joint consideration of the RD equations with the equations of continuum mechanics for tissue deformations (RD–mechanics systems), yield important effects on spiral wave dynamics. We show that deformation can induce the breakup of spiral waves into complex spatiotemporal patterns. We also show that mechanics leads to spiral wave drift throughout the medium approaching dynamical attractors, which are determined by the parameters of the model and the size of the medium. We study mechanisms of these effects and discuss their applicability to the theory of cardiac arrhythmias. Overall, we demonstrate the importance of RD–mechanics systems for mathematics applied to life sciences.

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Section: Discussionmentioning

confidence: 99%

Section: Spiral Wave Breakupmentioning

confidence: 99%

Drift and breakup of spiral waves in reaction–diffusion–mechanics systems

Panfilov

Keldermann

Nash

2007

Proc. Natl. Acad. Sci. U.S.A.

105

131

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“…The period-2 nature of T-wave alternans suggests that, like AV-nodal alternans, it may be amenable to nonlinear-dynamical control techniques. However, because T-wave alternans is distributed spatially over the surface of the ventricles (unlike the spatially localized AV-nodal alternans controlled in this study), nonlinear-dynamical methods applied to it must be capable of spatiotemporal control (25,26,(77)(78)(79)(80)(81). If such control is successful, a potential route to a sustained ventricular arrhythmia may be eliminated (72)(73)(74)(75)(76) thereby preventing the onset of a potentially deadly arrhythmic event.…”

Section: Discussionmentioning

confidence: 98%

Nonlinear-dynamical arrhythmia control in humans

Christini

Steín²,

Markowitz³

et al. 2001

Proc. Natl. Acad. Sci. U.S.A.

114

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Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52͞54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.I ncreasingly, it is recognized that many cardiac arrhythmias can be characterized on the basis of the physical principles of nonlinear dynamics (1, 2). A nonlinear-dynamical system is one that changes with time and cannot be broken down into a linear sum of its individual components. For certain nonlinear systems, known as chaotic systems, behavior is aperiodic and long-term prediction is impossible, even though the dynamics are entirely deterministic (i.e., the dynamics of the system are completely determined from known inputs and the previous state of the system, with no influence from random inputs). Importantly, such determinism actually can be exploited to control the dynamics of a chaotic system. To this end, a variety of nonlineardynamical control techniques, also known as chaos control, ‡ have been developed (3, 4) and applied successfully to a wide range of physical systems (5)(6)(7)(8)(9)(10)(11)(12)(13)(14). Such techniques are modelindependent, i.e., they require no a priori knowledge of the underlying equations of a system and are therefore appropriate for systems that are essentially ''black boxes.''The success of nonlinear-dynamical control techniques in stabilizing physical systems, together with the facts that many physiological systems are nonlinear (e.g., the cardiac conduction system, because of its numerous complex nonlinear component interactions) and lack the detailed analytical system models required for model-based control techniques, have fostered widespread interest in applying these model-independent techniques to biological dynamical systems (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26). In a pioneering application, Garfinkel et al. (15) stabilized drug-induced irregular cardiac rhythms by means of dynamically timed electrical stimulation in an in vitro rabbit ventricular-tissue preparation. That work was an important demonstration that the physical principles of nonlinear-dynamical control could be extended into the realm of cardiac dynamics. Although extension of that work to the control of fibrill...

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“…Entrainment of spiral wave meandering [5] and the formation of labyrinthine patterns [6] have been found with periodic forcing. Resonance attractors [7] and oscillatory cluster patterns [8] were recently reported in photosensitive BZ systems with different types of global feedback.We study the photosensitive BZ reaction with nonlocal coupling over a wide range of length scales, from much larger than the characteristic reaction-diffusion length scale to length scales that are comparable. The kernel of the feedback alternates from positive (activatory) for short distances to negative (inhibitory) for larger distances.…”

mentioning

confidence: 91%

mentioning

confidence: 91%

Spatial Symmetry Breaking in the Belousov-Zhabotinsky Reaction with Light-Induced Remote Communication

2001

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Domains containing spiral waves form on a stationary background in a photosensitive BelousovZhabotinsky reaction with light-induced alternating nonlocal feedback. Complex behavior of colliding and splitting wave fragments is found with feedback radii comparable to the spiral wavelength. A linear stability analysis of the uniform stationary states in an Oregonator model reveals a spatial symmetry breaking instability. Numerical simulations show behavior in agreement with that found experimentally and also predict a variety of other new patterns. DOI: 10.1103/PhysRevLett.87.088303 PACS numbers: 82.40.Ck, 05.65. +b, 47.54. +r, 82.30.Vy Physicochemical systems with coupled processes on different length scales often exhibit stationary spatially periodic structures arising from symmetry breaking instabilities [1][2][3]. In nonequilibrium systems, such structures occur in activator-inhibitor systems with short-range activation and long-range inhibition [1], while in equilibrium systems they arise from the competition of short-range attractive interactions and long-range repulsion [2]. Recent investigations also revealed spatial symmetry breaking arising from the interplay between short-range attractive interactions and a long-range reaction-diffusion process [3]. In this Letter, we report on novel spatiotemporal patterns in the photosensitive Belousov-Zhabotinsky (BZ) reaction [4] arising from a nonlocal feedback that imposes short-range activation and long-range inhibition.The photosensitive BZ reaction has proven to be an ideal model system for studies of perturbed excitable media. The medium excitability can be precisely controlled by exposure to 460 nm light, enabling the application of a wide variety of external perturbations. Entrainment of spiral wave meandering [5] and the formation of labyrinthine patterns [6] have been found with periodic forcing. Resonance attractors [7] and oscillatory cluster patterns [8] were recently reported in photosensitive BZ systems with different types of global feedback.We study the photosensitive BZ reaction with nonlocal coupling over a wide range of length scales, from much larger than the characteristic reaction-diffusion length scale to length scales that are comparable. The kernel of the feedback alternates from positive (activatory) for short distances to negative (inhibitory) for larger distances. We show below that such a feedback gives rise to a "Turinglike" instability, and, as a result, patterns with more than one characteristic length scale are formed.Experiments were carried out with the catalyst of the light-sensitive BZ reaction, Ru͑bpy͒ 21 3 , immobilized in a thin slab of silica gel. The gel was continuously fed with a fresh, catalyst-free BZ solution in a reactor thermostated at 23.0 ± C to maintain constant, nonequilibrium conditions [9]. The silica gel medium was prepared by acidifying a solution of 10% (w͞w) Na 2 SiO 3 and 2.0 mM Ru͑bpy͒ 21 3 with H 2 SO 4 and by casting a uniform 0.3 3 20.0 3 25.6 mm 3 layer onto a microscope slide. Prior to each experim...

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Feedback-Controlled Dynamics of Meandering Spiral Waves

Cited by 131 publications

References 18 publications

Drift and breakup of spiral waves in reaction–diffusion–mechanics systems

Drift and breakup of spiral waves in reaction–diffusion–mechanics systems

Nonlinear-dynamical arrhythmia control in humans

Spatial Symmetry Breaking in the Belousov-Zhabotinsky Reaction with Light-Induced Remote Communication

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