Asymptotic approximation of an ionic model for cardiac restitution

Abstract

Cardiac restitution has been described both in terms of ionic models-systems of ODE's-and in terms of mapping models. While the former provide a more fundamental description, the latter are more flexible in trying to fit experimental data. Recently we proposed a two-dimensional mapping that accurately reproduces restitution behavior of a paced cardiac patch, including rate dependence and accommodation. By contrast, with previous models only a qualitative, not a quantitative, fit had been possible. In this paper, a theoretical foundation for the new mapping is established by deriving it as an asymptotic limit of an idealized ionic model.

A predictive method allowing the use of a single ionic model in numerical cardiac electrophysiology

“…It also helps the charge balance through time. This model improves predictions where rate dependence and accommodation are involved (see [29,30] for details). Besides this, a relevant change is brought to the source term g (u, v) upon what the solution features the overshoot after the depolarisation as illustrated in Figure 1.…”

“…The difference between the previous works in this domain ( [5,16] for ODE models and [22,29,30] for mapping models) is that here, the results of the analysis not only portrays a general behaviour of the solution features (i.e. give some dependences on some parameters of the model, but not all possibly influent parameters), but can reliably predict a desired solution with explicit dependences on all model parameters and all the physiological constants.…”

“…Several modified versions of the MS model are brought in the literature (see for example [10,17,29,30]). The following outlines the subtleties of the different versions of the reaction terms.…”

“…It can be used to control the excitability and mimic a natural pacemaker activity. Schaeffer and et al [29,30] brought an extension to the original MS model. The new model has three variables, where the third variable is concentration-like and acts as a memory variable.…”

“…Past this value the rest of the phase II happens as with the original MS model. In [30], the following set of parameters is proposed: (2.7) with the associated time scale τ close (u) of equation (2.9). In instances where the overshoot following depolarisation is not needed, one can set τ close (u) ≡ τ sclose and recovers the original MS model if a = 0.…”