Asymptotic approximation of an ionic model for cardiac restitution

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.