Bulletin of Mathematical Biology

, Volume 65, Issue 5, pp 767–793 | Cite as

A two-current model for the dynamics of cardiac membrane

  • Colleen C. Mitchell
  • David G. Schaeffer


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 alternans—that does not occur for the commonly used exponential map.


Bifurcation Diagram Action Potential Duration Solution Branch Balt Cardiac Action Potential 


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Copyright information

© Society for Mathematical Biology 2003

Authors and Affiliations

  • Colleen C. Mitchell
    • 1
  • David G. Schaeffer
    • 1
  1. 1.Department of MathematicsDuke University and Center for Nonlinear and Complex SystemsDurhamUSA

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