The topology of defibrillation

Keener, James P.

doi:10.1016/j.jtbi.2003.11.033

Cited by 17 publications

(20 citation statements)

References 40 publications

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“…Despite the lack of mathematical formalism, the similarities between limit cycle oscillators and spatially distributed excitable systems have been investigated by analytical, graphical, and topological methods (14)(15)(16)(17)(18). For example, reentry in a 1D ring of excitable elements is analogous to a limit cycle oscillation if the conduction speed is constant ensuring an unvarying period (15).…”

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confidence: 99%

Termination of spiral waves during cardiac fibrillation via shock-induced phase resetting

Gray

Chattipakorn

2005

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

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Multiple unstable spiral waves rotating around phase singularities (PSs) in the heart, i.e., ventricular fibrillation (VF), is the leading cause of death in the industrialized world. Spiral waves are ubiquitous in nature and have been extensively studied by physiologists, mathematicians, chemists, and biologists, with particular emphasis on their movement and stability. Spiral waves are not easy to terminate because of the difficulty of ''breaking'' the continuous spatial progression of phase around the PSs. The only means to stop VF (i.e., cardiac defibrillation) is to deliver a strong electric shock to the heart. Here, we use the similarities between spiral wave dynamics and limit cycle oscillators to characterize the spatio-temporal dynamics of VF and defibrillation via phase-resetting curves. During VF, only PSs, including their formation and termination, were associated with large phase changes. At low shock strengths, phase-resetting curves exhibited characteristics of weak (type 1) resetting. As shock strength increased, the number of postshock PSs decreased to zero coincident with a transition to strong (type 0) resetting. Our results indicate that shock-induced spiral wave termination in the heart is caused by altering the phase around the PSs, such that, depending on the preshock phase, sites are either excited by membrane depolarization (phase advanced) or exhibit slowed membrane repolarization (phase delay). Strong shocks that defibrillate break the continuity of phase around PSs by forcing the state of all sites to the fast portion of state space, thus quickly leading to a ''homogeneity of state,'' subsequent global repolarization and spiral wave termination.defibrillation ͉ phase resetting curve M any systems in nature exhibit incredibly varied spatiotemporal patterns such as traveling waves, spiral waves, and Turing patterns (1-7). Spiral waves rotate around phase singularities (PSs) and often do not remain stationary and can even break up into a state of defect-mediated turbulence (7,8). During ventricular fibrillation (VF), PS pairs of opposite chirality are mutually annihilated if the phase gradient between them is sufficiently large to halt propagation (9). The probability of all PSs extinguishing at the same time, and thus resulting in spontaneous termination of VF, varies with the size of the heart (10). In humans, VF almost never terminates spontaneously, and electrical defibrillators are necessary to stop VF and restore the normal rhythm.Normally, the human heart beats about once per second; a pacemaker region periodically generates an electrical wave that propagates rapidly through the heart, triggering nearly synchronous contraction. Like many oscillators, this pacemaker region can be reset by an advance or a delay that depends on the time and strength of the stimulus (11, 12). Typically, periodic systems are characterized as limit cycle oscillators (similar to the minute hand moving around a clock) and the stimulus-induced perturbations are described by using phase-resetting curves (PRC...

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confidence: 99%

Termination of spiral waves during cardiac fibrillation via shock-induced phase resetting

Gray

Chattipakorn

2005

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

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“…It is worth mentioning that the control and stabilization of spatio-temporal fronts in biological system, and in particular the FHN system, has been successfully approached in the literature -see [25,57-59] and references therein-. Most of these works made use of electric fields of moderate intensity, computed through given feed-back control logics to attain the desired objective.…”

Section: Resultsmentioning

confidence: 99%

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques

et al. 2012

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BackgroundSystems biology allows the analysis of biological systems behavior under different conditions through in silico experimentation. The possibility of perturbing biological systems in different manners calls for the design of perturbations to achieve particular goals. Examples would include, the design of a chemical stimulation to maximize the amplitude of a given cellular signal or to achieve a desired pattern in pattern formation systems, etc. Such design problems can be mathematically formulated as dynamic optimization problems which are particularly challenging when the system is described by partial differential equations.This work addresses the numerical solution of such dynamic optimization problems for spatially distributed biological systems. The usual nonlinear and large scale nature of the mathematical models related to this class of systems and the presence of constraints on the optimization problems, impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques.ResultsHere, the use of a control vector parameterization approach combined with efficient and robust hybrid global optimization methods and a reduced order model methodology is proposed. The capabilities of this strategy are illustrated considering the solution of a two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model.ConclusionsIn the process of chemotaxis the objective was to efficiently compute the time-varying optimal concentration of chemotractant in one of the spatial boundaries in order to achieve predefined cell distribution profiles. Results are in agreement with those previously published in the literature. The FitzHugh-Nagumo problem is also efficiently solved and it illustrates very well how dynamic optimization may be used to force a system to evolve from an undesired to a desired pattern with a reduced number of actuators. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.

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“…In the VF phase, singularities represent sites in which the activation state cannot be determined; they are surrounded by a continuum of activation states ranging from fully activated to fully recovered 19 . These phase singularities represent the sources and spatiotemporal organization of fibrillation 20–22 . Valderrabano et al 19 .…”

Section: Discussionmentioning

confidence: 99%

“…19 These phase singularities represent the sources and spatiotemporal organization of fibrillation. [20][21][22] Valderrabano et al 19 emphasized that phase singularities, the "key players" in the maintenance of VF, align with anatomic structures: in the epicardium, they form along the course of epicardial arteries whereas in the endocardium they form along ridges of endocardial trabeculae. Once in a particular structure, they tend to meander in it.…”

Section: Group A/p L/l S/i A/p L/l S/i A/p L/l S/imentioning

confidence: 99%

Selecting the Transthoracic Defibrillation Shock Directional Vector Based on VF Amplitude Improves Shock Success

Brooks

Zhang

Dendi

et al. 2009

Cardiovasc electrophysiol

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The topology of defibrillation

Cited by 17 publications

References 40 publications

Termination of spiral waves during cardiac fibrillation via shock-induced phase resetting

Termination of spiral waves during cardiac fibrillation via shock-induced phase resetting

Dynamic optimization of distributed biological systems using robust and efficient numerical techniques

Selecting the Transthoracic Defibrillation Shock Directional Vector Based on VF Amplitude Improves Shock Success

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