Memory Models for the Electrical Properties of Local Cardiac Systems

Otani, Niels F.; Gilmour, Robert F.

doi:10.1006/jtbi.1997.0447

Cited by 85 publications

(93 citation statements)

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“…As shown in Otani et al 1997, evolution similar to (17b) could also be obtained from an ionic model: specifically, a model in which charge accumulates in the cell during the action potential and is pumped out during the diastolic interval.…”

Section: Comparison With Previous Mathematical Modelsmentioning

confidence: 81%

“…In an effort to model rate dependence, various authors (Chialvo et al, 1990;Otani and Gilmour, 1997;Fox et al, 2002a) have introduced ad hoc 2D mapping models, one variable being A n and the other a "memory" variable. It was shown in Kalb et al 2004 that, although these models exhibit the right qualitative behavior, no single set of parameter values can match all the data in the restitution portrait, such as in Figure 2(a).…”

Section: Mapping Modelsmentioning

confidence: 99%

“…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%

“…The equations (27), (31) and (33) define the three-variable idealized ionic model. Figure 7 shows two time traces of the voltage and concentration at a basic cycle length B = 650 ms.…”

Section: A2 the Ionic Model Including Concentrationmentioning

confidence: 99%

“…Note that the restitution function in (4) contains two parameters, α and A max , that do not appear in the ionic model (27), (31) The parameter values in Table 2, with substitution into (37, 38), yield the parameters for the mapping that are given in Table 1, to within round-off errors.…”

Section: A3 Approximation Of the Ionic Model By A 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: Comparison With Previous Mathematical Modelsmentioning

confidence: 81%

Section: Mapping Modelsmentioning

confidence: 99%

Section: Limitations and Future Workmentioning

confidence: 99%

“…The equations (27), (31) and (33) define the three-variable idealized ionic model. Figure 7 shows two time traces of the voltage and concentration at a basic cycle length B = 650 ms.…”

Section: A2 the Ionic Model Including Concentrationmentioning

confidence: 99%

Section: A3 Approximation Of the Ionic Model By A Mappingmentioning

confidence: 99%

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