Math @ Duke

Publications [#244129] of David G. Schaeffer
Papers Published
 Mitchell, CC; Schaeffer, DG, A twocurrent model for the dynamics of cardiac membrane.,
Bulletin of Mathematical Biology, vol. 65 no. 5
(2003),
pp. 767793, ISSN 00928240 [12909250], [doi]
(last updated on 2019/03/21)
Abstract: 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 FitzHughNagumo 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 onedimensional map which specifies the action potential duration as a function of the previous diastolic interval. For certain parameter values, this map exhibits a new phenomenonsubcritical alternansthat does not occur for the commonly used exponential map.


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