Defibrillation via the Elimination of Spiral Turbulence in a Model for Ventricular Fibrillation

Sinha, Sitabhra; Pande, Ashwin; Pandit, Rahul

doi:10.1103/physrevlett.86.3678

Cited by 107 publications

(94 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Can chaos in our model be controlled so as to stabilize and target [13] these helical states? The control of spatiotemporal chaos in PDEs [13,14] is not nearly as well-developed as that in finite dimensional dynamical systems [13]. Accordingly, it is significant that we are able to stabilize, target, and hence control spatiotemporal chaos in our model, as we now show.…”

mentioning

confidence: 74%

Driven Heisenberg magnets: Nonequilibrium criticality, spatiotemporal chaos and control

2002

View full text Add to dashboard Cite

PACS. 64.60.Cn -Order-disorder transformations; statistical mechanics of model systems. PACS. 05.40.-a -Fluctuation phenomena, random processes, noise, and Brownian motion.Abstract. -We drive a d-dimensional Heisenberg magnet using an anisotropic current. The continuum Langevin equation is analysed using a dynamical renormalization group and numerical simulations. We discover a rich steady-state phase diagram, including a critical point in a new nonequilibrium universality class, and a spatiotemporally chaotic phase. The latter may be 'controlled' in a robust manner to target spatially periodic steady states with helical order.How does an imposed steady current of heat or particles alter the dynamics of the isotropic magnet? To answer this question, we extend the equations of motion for the classical O(3) Heisenberg model [1] to include the effects of a uniform current in one spatial direction while retaining isotropy in the order parameter space. The resulting model is a natural generalization of the driven diffusive models of [2] to the case of a 3-component axial-vector order parameter and, as such, is an important step in the exploration of dynamic universality classes [3] far from equilibrium [4]. The form of the local molecular field in which spins precess in this driven state is strikingly different from that at equilibrium [1], and is responsible for all the remarkable phenomena we predict, including a novel nonequilibrium critical point and, in a certain parameter range, a type of turbulence.Here are our results in brief: (i) Despite O(3) invariance in the order-parameter space, the dynamics does not conserve magnetization; (ii) As a temperature-like parameter is lowered, the paramagnetic phase of the model approaches a nonequilibrium critical point in a new dynamic universality class; (iii) Below this critical point, in mean-field theory without stochastic forcing, paramagnetism, ferromagnetism and helical order are all linearly unstable; (iv) Numerical

show abstract

mentioning

confidence: 74%

Driven Heisenberg magnets: Nonequilibrium criticality, spatiotemporal chaos and control

2002

View full text Add to dashboard Cite

show abstract

“…Firstly, we study the influences of deformation on a certain spiral turbulence initialized from a breakup process of a single spiral without any deformation [23,24]. As shown in [25], the spiral turbulence for this model is a long-lived transient whose lifespan increases rapidly with L, the linear size of the system. We have tested one initial turbulence state with L = 128 ( fig.…”

mentioning

confidence: 99%

The effect of mechanical deformation on spiral turbulence

Zhang

Sheng

et al. 2006

Europhys. Lett.

View full text Add to dashboard Cite

Abstract. -The behavior of spiral turbulence in mechanically deformed excitable media is investigated. Numerical simulations show that when the forcing frequency is chosen around the characteristic frequency of the system, complicated spiral turbulence may be quenched within a shorter evolution time, compared to the case free of mechanical deformation. It is shown that the observed phenomenon occurs due to enhancing the drift of spiral tips induced by mechanical deformation.A wide range of self-organized phenomena exists in spatially distributed systems. One of the most paradigmatic examples of spatiotemporal self-organized structures is a class of spiral waves, which have been observed in a variety of physical [1], chemical [2][3][4][5] and biological systems [6][7][8][9]. The attractiveness of investigating the dynamics of spiral waves is not only because they own a special structure, i.e., the core regarded as a phase-singular in mathematical language, but more important they contribute to the underlying class of cardiac disease also, such as tachycardia and fibrillation [6][7][8][9]. It is thus that, from a practical point of view, controlling the behaviors of spiral waves, particularly eliminating spiral waves and spiral turbulence, is extremely important and meaningful. Up to now, various methods to control two-, and even three-dimensional spiral waves and turbulence have been put forward [10][11][12][13][14][15][16][17][18][19].On the other hand, Munuzuri et al. [20] designed an appropriate elastic excitable medium by incorporating the BZ reaction into a polyacrylamide-silica gel and experimentally studied the influence of periodic mechanical contraction of excitable media on the behavior of rotating spiral waves. Recently, we derived, directly from origin reaction-diffusion equations, a formula of drifting velocity using weak-deformation approximation and explained the drift of spiral waves under resonant frequency [21]. Besides, spiral breakup due to mechanical deformation was studied in our recent work [22]. To our knowledge, however, the influences of mechanical

show abstract

“…An attractive future prospect is to control such modes by exploiting their quantized nature and their sensitivity to boundary conditions. An alternative approach might be to eliminate alternans using multiple dispersed controllers spaced at distances less than the maximum controllable tissue distance [dispersed controller approaches have been used to control spatiotemporal dynamics in physical systems [24][25][26], and in simulated cardiac monolayers for the control of spiral-wave reentry or fibrillation [16,27] ].…”

mentioning

confidence: 99%

Control of Electrical Alternans in Canine Cardiac Purkinje Fibers

et al. 2006

View full text Add to dashboard Cite

Alternation in the duration of consecutive cardiac action potentials (electrical alternans) may precipitate conduction block and the onset of arrhythmias. Consequently, suppression of alternans using properly timed premature stimuli may be antiarrhythmic. To determine the extent to which alternans control can be achieved in cardiac tissue, isolated canine Purkinje fibers were paced from one end using a feedback control method. Spatially uniform control of alternans was possible when alternans amplitude was small. However, control became attenuated spatially as alternans amplitude increased. The amplitude variation along the cable was well described by a theoretically expected standing wave profile that corresponds to the first quantized mode of the one-dimensional Helmholtz equation. These results confirm the wavelike nature of alternans and may have important implications for their control using electrical stimuli.Electrical alternans is a phenomenon characterized by a beat-to-beat alternation in the duration of the cardiac action potential (APD) [1]. Because heart cells are refractory to further stimulation during an action potential, alternans of APD results in an alternans of refractoriness, the magnitude of which may vary across different regions of the heart. Several studies have shown that the resulting spatial dispersion of refractoriness facilitates the development of local conduction block [2][3][4][5], which may in turn cause the normally planar wave of electrical excitation in cardiac tissue to break and form spiral waves [6]. If the spiral waves also encounter regions of disparate refractoriness, they may disintegrate into multiple wavelets, which may account for the onset of the lethal heart rhythm disorder ventricular fibrillation [7][8][9].Given that APD alternans may be mechanistically linked to the onset of reentrant arrhythmias, its elimination might be an effective antiarrhythmic strategy. Initial work in that direction showed that closed-loop feedback methods could be used to suppress a type of alternans (known as atrioventricular-nodal conduction alternans) with period-doubling dynamics that are related to those of APD alternans [10][11][12][13]. More recently, it was shown that a related control method could terminate APD alternans in isolated frog hearts [14,15]. The latter studies showed clearly that perturbations to the electrical stimulus interval could be used to eliminate APD alternans in a system that does not have spatiotemporally varying repolarization and wavepropagation dynamics (the frog sections were small enough that there were no apparent spatial variations in dynamics). NIH Public Access

show abstract

Defibrillation via the Elimination of Spiral Turbulence in a Model for Ventricular Fibrillation

Cited by 107 publications

References 16 publications

Driven Heisenberg magnets: Nonequilibrium criticality, spatiotemporal chaos and control

Driven Heisenberg magnets: Nonequilibrium criticality, spatiotemporal chaos and control

The effect of mechanical deformation on spiral turbulence

Control of Electrical Alternans in Canine Cardiac Purkinje Fibers

Contact Info

Product

Resources

About