An ionically based mapping model with memory for cardiac restitution
  Many features of the sequence of action potentials produced by repeated stimulation of a cardiac patch can be modeled by a 1D mapping, but not the full behavior observed in the restitution portrait: in particular, not (i) distinct slopes for dynamic and S1-S2 restitution (rate dependence) and not (ii) long transients in the approach to steady state (accomodation). To address these shortcomings, \emph{ad hoc} 2D mappings, where the second variable is a ``memory'' variable, have been proposed; it seems that these models exhibit some, but not all, of the relevant behavior. In this paper we introduce a new 2D mapping and determine a set of parameters for it that gives a rather accurate description of the full restitution portrait found for one animal. The changes in the mapping, compared to previous models, result from requiring that the mapping can be derived as an asymptotic limit of a simple ionic model. Among other benefits, one can interpret the parameters in the mapping in terms of the ionic model. The ionic model is an extension of a two-current model that adds a third dependent variable, a generalized concentration. The simplicity of the ionic model and the physiological basis for the mapping contribute to the usefulness of these ideas for describing restitution data in a variety of contexts. The fitting procedure is straightforward and can easily be applied to obtain a mathematical model for data from other experiments, including experiments on different species. Uniqueness of the parameter choice is also discussed. 
David G. Schaeffer, John W. Cain, Daniel J. Gauthier, Soma S. Kalb,   Wanda Krassowska, Robert A. Oliver, and Elena G. Tolka...