Many features of the sequence of action potentials produced by repeatedstimulation of a cardiac patch can be modeled by a 1D mapping, but not the fullbehavior observed in the restitution portrait: in particular, not (i) distinctslopes for dynamic and S1-S2 restitution (rate dependence) and not (ii) longtransients in the approach to steady state (accomodation). To address theseshortcomings, emph{ad hoc} 2D mappings, where the second variable is a``memory'' variable, have been proposed; it seems that these models exhibitsome, but not all, of the relevant behavior. In this paper we introduce a new2D mapping and determine a set of parameters for it that gives a ratheraccurate description of the full restitution portrait found for one animal. Thechanges in the mapping, compared to previous models, result from requiring thatthe 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 termsof the ionic model. The ionic model is an extension of a two-current model thatadds a third dependent variable, a generalized concentration. The simplicity ofthe ionic model and the physiological basis for the mapping contribute to theusefulness of these ideas for describing restitution data in a variety ofcontexts. The fitting procedure is straightforward and can easily be applied toobtain a mathematical model for data from other experiments, includingexperiments on different species. Uniqueness of the parameter choice is alsodiscussed.
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