Memory and complex dynamics in cardiac Purkinje fibers

Gilmour, Robert F.; Otani, Niels F.; Watanabe, Mari

doi:10.1152/ajpheart.1997.272.4.h1826

Cited by 77 publications

(100 citation statements)

References 19 publications

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“…In contrast to (17), for the mapping (2-5), the steady-state value of C is given by (13), so the derivative dC ss /dD ss is negative for all values of the DI. Thus, S 12 < S dyn…”

Section: Comparison With Previous Mathematical Modelsmentioning

confidence: 94%

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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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“…In contrast to (17), for the mapping (2-5), the steady-state value of C is given by (13), so the derivative dC ss /dD ss is negative for all values of the DI. Thus, S 12 < S dyn…”

Section: Comparison With Previous Mathematical Modelsmentioning

confidence: 94%

“…The concentration is determined by a balance between I(t), the current which leads to the build-up of charge in the cell, and constant linear pumping, which removes charge from the cell 13 :…”

Section: A2 the Ionic Model Including Concentrationmentioning

confidence: 99%

An Ionically Based Mapping Model with Memory for Cardiac Restitution

et al. 2007

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“…• Purkinje fibers undergo much less contraction than other heart tissue, but alternans is still observed in these fibers [see for example Gilmour et al (1997)]. …”

Section: Introductionmentioning

confidence: 99%

A two-current model for the dynamics of cardiac membrane

Mitchell

Schaeffer

2003

Bulletin of Mathematical Biology

298

318

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In this paper we introduce and study a model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh-Nagumo model, makes it useful in numerical simulations, especially in two or three spatial dimensions where numerical efficiency is so important. (2) It can be understood analytically without recourse to numerical simulations. This allows us to determine rather completely how the parameters in the model affect its behavior which in turn provides insight into the effects of the many parameters in more realistic models. (3) It naturally gives rise to a one-dimensional map which specifies the action potential duration as a function of the previous diastolic interval. For certain parameter values, this map exhibits a new phenomenon-subcritical alternansthat does not occur for the commonly used exponential map.

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“…This protocol is referred to as the dynamic protocol. 12,13 We quantified restitution relationship using a previously developed feedback-based protocol 14 that permits explicit control of DIs that can be changed sequentially in time. Motivation for using a feedback-based protocol was that although in restitution hypothesis the functional relationship is used to predict change in DI and APD for beats in sequence, the functional relationship is not quantified during sequential changes in DI in currently utilized protocols.…”

mentioning

confidence: 99%

“…In order to address some of these limitations, a second approach has been recently proposed. 12,13 In the newer scheme, tissue is also paced for several tens of beats (S1); however, instead of generating DI-APD pairs by using S2 stimulus, they are measured at the end of S1 stimulus train. Then the sequence of S1 stimuli is repeated by progressively shortening S1-S1 intervals.…”

mentioning

confidence: 99%

Restitution of Action Potential Duration During Sequential Changes in Diastolic Intervals Shows Multimodal Behavior

Patwardhan

2004

Circulation Research

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Abstract-Restitution of action potential duration (APD) is thought to be critical in activation instability. Although restitution is used to predict APD during sequential changes in diastolic interval (DI), currently used protocols to determine restitution do not use sequential changes in DI. We explored restitution using a new pacing protocol to change DI sequentially and independently of APD. Transmembrane potentials were recorded from right ventricular endocardial tissue isolated from six dogs. We used three patterns of DIs: oscillatory, to demonstrate differences in APDs depending on previous activation history; random, to minimize effects of previous activation history, each DI preceding an APD had an equal probability of being short or long; and linear, to compare restitution relationship obtained during sequential changes in DI with those obtained using currently used protocols; DIs mimicked those that resulted using currently used protocols, except that they changed in sequence. During oscillatory DIs, restitution showed bimodal trajectory similar to hysteresis. Decrease in APD during decreasing DIs was faster than increase in APD during increasing DIs. When effects of previous activation history were minimized, we observed that for a given DI there were multiple values of APD. Restitution relationship obtained during sequential changes in DI was shallower than those obtained using currently used protocols. Our results show that the new pacing protocol may permit direct evaluation of effects of memory on APD. Sequential and explicit control of DI suggests that use of a unimodal relationship to predict APD when DIs change in sequence may not be appropriate. Key Words: action potential duration Ⅲ electrical restitution Ⅲ arrhythmia Ⅲ fibrillation C ardiac electrical restitution is considered to importantly influence whether an electrical disturbance degenerates into a reentrant activation. 1 Specifically, it is hypothesized that the slope of action potential duration (APD) restitution function, which relates diastolic interval (DI) and following APD, can predict stability of electrical activation. 2-9 The hypothesized mechanism is that a slope equal to or greater than 1 can lead to alternans of APD and block propagation. Activation block, in turn, facilitates reentry, leading to arrhythmia. Conversely, for slopes less than 1, disturbances in APD get smaller, returning to a stable activation. Consistent with this view, in a few animal studies, drugs that decrease the slope of restitution have been shown to have antiarrhythmic properties. 10,11 Therefore, it has been suggested that investigation of restitution relationship may prove helpful during development of treatments for arrhythmia or in evaluation of efficacy of antiarrhythmia drugs. 2 The APD restitution function is widely quantified using one of two pacing schemes. In one scheme, tissue is paced for several tens of beats at constant cycle length (S1) followed by a stimulus (S2) delivered at progressively shorter or longer intervals. The APD resultin...

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Memory and complex dynamics in cardiac Purkinje fibers

Cited by 77 publications

References 19 publications

An Ionically Based Mapping Model with Memory for Cardiac Restitution

An Ionically Based Mapping Model with Memory for Cardiac Restitution

A two-current model for the dynamics of cardiac membrane

Restitution of Action Potential Duration During Sequential Changes in Diastolic Intervals Shows Multimodal Behavior

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