Condition for alternans and its control in a two-dimensional mapping model of paced cardiac dynamics

Tolkacheva, Elena G.; Romeo, Mónica M.; Guerraty, Marie; Gauthier, Daniel J.

doi:10.1103/physreve.69.031904

Cited by 46 publications

(47 citation statements)

References 23 publications

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“…However, this limitation is only apparent. Because the mapping is derived as an asymptotic limit of an ionic model (see the Appendix), given parameter values for the mapping, we can substitute these into (27,31,33) and obtain a system of ODE's with equivalent behavior. This system of ODE's can readily be extended to obtain a PDE model, which can then be used to study electrotonic effects and propagation.…”

Section: Limitations and Future Workmentioning

confidence: 99%

“…Also shown are three dashed lines along which the ratio A/D is constant (specifically, A/D = 1.5, 2, 3), which will facilitate the discussion in Section 3.1. Voltage and concentration vs. time in the ionic model (27), (31) and (33) with the parameter values in Table 2 The restitution curve from the mapping showing 2:1 steady-state behavior (dashed curve) as well as 1:1 behavior (solid curve). Parameters as in Table 1, with D thr = 80 ms.…”

Section: (B) Consequences Of Requiring An Ionic Basis For the Mappingmentioning

confidence: 99%

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An Ionically Based Mapping Model with Memory for Cardiac Restitution

et al. 2007

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Many features of the sequence of action potentials produced by repeated stimulation of a patch of cardiac muscle can be modeled by a 1D mapping, but not the full behavior included in the restitution portrait. Specifically, recent experiments have found that (i) the dynamic and S1-S2 restitution curves are different (rate dependence) and (ii) the approach to steady state, which requires many action potentials (accommodation), occurs along a curve distinct from either restitution curve. Neither behavior can be produced by a 1D mapping. To address these shortcomings, ad hoc 2D mappings, where the second variable is a "memory" variable, have been proposed; these models exhibit qualitative features of the relevant behavior, but a quantitative fit is not possible. In this paper we introduce a new 2D mapping and determine a set of parameters for it that gives a quantitatively accurate description of the full restitution portrait measured from a bullfrog ventricle. The mapping can be derived as an asymptotic limit of an idealized ionic model in which a generalized concentration acts as a memory variable. This ionic basis clarifies how the present model differs from previous models. The ionic basis also provides the foundation for more extensive cardiac modeling: e.g., constructing a PDE model that may be used to study the effect of memory on propagation. The fitting procedure for the mapping is straightforward and can easily be applied to obtain a mathematical model for data from other experiments, including experiments on different species.

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Section: Limitations and Future Workmentioning

confidence: 99%

Section: (B) Consequences Of Requiring An Ionic Basis For the Mappingmentioning

confidence: 99%

An Ionically Based Mapping Model with Memory for Cardiac Restitution

et al. 2007

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“…We remark that assuming such a simple restitution relationship is done primarily for illustrative purposes, whereas it is known that cardiac cells exhibit memory with respect to the pacing history [31][32][33]. That is, A n+1 depends not only upon D n , but also on previous data such as A n and D n-1 .…”

Section: Restitution and Mapping Modelsmentioning

confidence: 99%

“…Whereas such mappings can give a reasonable approximation of the dynamics, cardiac tissue is known to exhibit memory-that is, A n+1 depends not only upon D n , but also upon earlier APD and DI [31][32][33]. Fortunately, the ETDAS method can be applied even if a more sophisticated mapping model with memory is used.…”

Section: Memorymentioning

confidence: 99%

Control of electrical alternans in simulations of paced myocardium using extended time-delay autosynchronization

et al. 2007

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Experimental studies have linked alternans, an abnormal beat-to-beat alternation of cardiac action potential duration (APD), to the genesis of lethal arrhythmias such as ventricular fibrillation. Prior studies have considered various closed-loop feedback control algorithms for perturbing interstimulus intervals in such a way that alternans is suppressed. However, some experimental cases are restricted in that the controller's stimuli must preempt those of the existing waves that are propagating in the tissue and therefore only shortening perturbations to the underlying pacing are allowed. We present results demonstrating that a technique known as Extended Time-Delay Autosynchronization (ETDAS) can effectively control alternans locally while operating within the above constraints. We show that ETDAS, which has already been used to control chaos in physical systems, has numerous advantages over previously proposed alternans control schemes.

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“…Consequently, various dynamical behaviors of such parameters have been proposed to mimic the experimental results [3][4][5][6]. Recently, it was demonstrated theoretically [11] that the introduction of such a parameter is equivalent to the assumption that APD depends on several preceding beats (APDs and/or DIs). It was then shown experimentally that up to three preceding beats [12,13] play a substantial role in the control of the APD.…”

Section: Introductionmentioning

confidence: 99%

The Rate- and Species-Dependence of Short-Term Memory in Cardiac Myocytes

Tolkacheva

2007

J Biol Phys

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Short-term memory is an intrinsic property of paced cardiac myocytes that reflects the influence of pacing history, and not just the immediately preceding diastolic interval (DI), on the action potential duration (APD). Although it is recognized that shortterm memory affects the dynamics of cardiac myocytes in general, and the onset of irregular cardiac rhythm in particular, its has never been adequately quantified or measured directly in experiments or numerical simulations, mainly due to the absence of appropriate techniques. As a result, very little is known about the rate-and species dependent behavior of short-term memory. In this study, we introduce a new approach that allows one to estimate how much short-term memory, M S , is present in the cardiac myocyte at different pacing rates. The new quantification is based on the fact that pacing history affects not only the APD, but the entire dynamics of paced cardiac myocytes, in particular the restitution curve. Using the patch clamp technique and numerical simulations, we measured short-term memory restitution-the dependence of M S on the cycle length-in isolated rabbit and guinea pig ventricular myocytes. In both species, M S is rate-and species-dependent, displaying a biphasic behavior as a function of cycle length. Moreover, our results indicate that there is a significant difference in M S measured between both species at small cycle lengths. Numerical simulations suggest that the kinetics of the rapidly activating delayed rectifier potassium current I Kr is partially responsible for this difference.

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Condition for alternans and its control in a two-dimensional mapping model of paced cardiac dynamics

Cited by 46 publications

References 23 publications

An Ionically Based Mapping Model with Memory for Cardiac Restitution

An Ionically Based Mapping Model with Memory for Cardiac Restitution

Control of electrical alternans in simulations of paced myocardium using extended time-delay autosynchronization

The Rate- and Species-Dependence of Short-Term Memory in Cardiac Myocytes

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