Design Principles of a Low Voltage Cardiac Defibrillator Based on the Effect of Feedback Resonant Drift

Biktashev, V. N.; Holden, AV

doi:10.1006/jtbi.1994.1132

Cited by 87 publications

(61 citation statements)

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“…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.…”

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confidence: 99%

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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mentioning

confidence: 99%

Nonlinear-dynamical arrhythmia control in humans

Christini

Steín²,

Markowitz³

et al. 2001

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

114

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“…Importantly, it was found that response functions (RFs) are closely related to the symmetries of the RDE (2) in two spatial dimensions [7,27], which allows one to compute them numerically for given diffusion matrix P and reaction kinetics F(u) [30,61]. Before studying the RDE in a rotating frame of reference, it is necessary to reconcile sign conventions for the angular frequency, since we will be using an extension of the DXSPIRAL program of Biktasheva et al [61] to compute RFs.…”

Section: Response Functionsmentioning

confidence: 99%

“…Thereafter, he applied the Fredholm alternative theorem to obtain necessary conditions on the filament motion, which are the desired equations of motion. The introduction of critical adjoint eigenmodes of the system, which are also known as "response functions" (RFs) [26], formed the basis of many subsequent analytical results on pattern evolution in excitable systems [8,22,25,[27][28][29][30][31][32][33][34][35]. Strikingly, the RFs were observed to be strongly localized near the spiral wave's rotation center, which can be rightfully called "particle-wave dualism of spiral waves" [31].…”

Section: Introductionmentioning

confidence: 99%

Effective dynamics of twisted and curved scroll waves using virtual filaments

Dierckx

Verschelde

2013

Phys. Rev. E

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Scroll waves are three-dimensional excitation patterns that rotate around a central filament curve; they occur in many physical, biological, and chemical systems. We explicitly derive the equations of motion for scroll wave filaments in reaction-diffusion systems with isotropic diffusion up to third order in the filament's twist and curvature. The net drift components define at every instance of time a virtual filament which lies close to the instantaneous filament. Importantly, virtual filaments obey simpler, time-independent laws of motion which we analytically derive here and illustrate with numerical examples. Stability analysis of scroll waves is performed using virtual filaments, showing that filament curvature and twist add as quadratic terms to the nominal filament tension. Applications to oscillating chemical reactions and cardiac tissue are discussed.

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“…There are growing experimental and theoretical efforts to develop low amplitude defibrillation methods in both fields of nonlinear science and cardiac physiology [18][19][20][21]. A socalled local and low-amplitude pacing control scheme has become a promising method for defibrillation in cardiac tissue [22,23].…”

Section: Introductionmentioning

confidence: 99%

Motion of spiral waves induced by local pacing

Chen

Wei

et al. 2008

Open Physics

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Abstract:The motion of spiral waves in excitable media driven by a weak pacing around the spiral tip is investigated numerically as well as theoretically. We presented a Bifurcations diagram containing four types of the spiral motion induced by different frequencies of pacing: rigidly rotating, inward-petal meandering, resonant drift, and outward-petal meandering spiral. Simulation shows that the spiral resonantly drifts when the frequency of pacing is close to that of the spiral rotation. We also find that the speed and direction of the drift can be efficiently controlled by means of the strength and phase of the local pacing, which is consistent with analytical results based on the framework of the weak deformation approximation.

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Design Principles of a Low Voltage Cardiac Defibrillator Based on the Effect of Feedback Resonant Drift

Cited by 87 publications

References 0 publications

Nonlinear-dynamical arrhythmia control in humans

Nonlinear-dynamical arrhythmia control in humans

Effective dynamics of twisted and curved scroll waves using virtual filaments

Motion of spiral waves induced by local pacing

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