An ionically based mapping model with memory for cardiac restitution.

Journal Article (Journal Article)

Many features of the sequence of action potentials produced by repeated stimulation of a patch of cardiac muscle can be modeled by a 1D mapping, but not the full behavior included in the restitution portrait. Specifically, recent experiments have found that (i) the dynamic and S1-S2 restitution curves are different (rate dependence) and (ii) the approach to steady state, which requires many action potentials (accommodation), occurs along a curve distinct from either restitution curve. Neither behavior can be produced by a 1D mapping. To address these shortcomings, ad hoc 2D mappings, where the second variable is a "memory" variable, have been proposed; these models exhibit qualitative features of the relevant behavior, but a quantitative fit is not possible. In this paper we introduce a new 2D mapping and determine a set of parameters for it that gives a quantitatively accurate description of the full restitution portrait measured from a bullfrog ventricle. The mapping can be derived as an asymptotic limit of an idealized ionic model in which a generalized concentration acts as a memory variable. This ionic basis clarifies how the present model differs from previous models. The ionic basis also provides the foundation for more extensive cardiac modeling: e.g., constructing a PDE model that may be used to study the effect of memory on propagation. The fitting procedure for the mapping is straightforward and can easily be applied to obtain a mathematical model for data from other experiments, including experiments on different species.

Full Text

Duke Authors

Cited Authors

  • Schaeffer, DG; Cain, JW; Gauthier, DJ; Kalb, SS; Oliver, RA; Tolkacheva, EG; Ying, W; Krassowska, W

Published Date

  • February 2007

Published In

Volume / Issue

  • 69 / 2

Start / End Page

  • 459 - 482

PubMed ID

  • 17237915

Pubmed Central ID

  • PMC2206542

Electronic International Standard Serial Number (EISSN)

  • 1522-9602

International Standard Serial Number (ISSN)

  • 0092-8240

Digital Object Identifier (DOI)

  • 10.1007/s11538-006-9116-6


  • eng