Nonlinear Dynamics

, Volume 51, Issue 1–2, pp 189–198 | Cite as

Asymptotic approximation of an ionic model for cardiac restitution

Original Paper


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.


Cardiac dynamics Ionic model Mapping model Asymptotic analysis 


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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • David G. Schaeffer
    • 1
    • 2
  • Wenjun Ying
    • 3
  • Xiaopeng Zhao
    • 2
    • 3
  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Center for Nonlinear and Complex SystemsDuke UniversityDurhamUSA
  3. 3.Department of Biomedical EngineeringDuke UniversityDurhamUSA

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