title: Nonlinear dynamics of paced cardiac cells.
abstract: When a cardiac cell is rapidly paced it can exhibit a beat-to-beat alternation in the action potential duration (APD) and the intracellular calcium transient. This dynamical instability at the cellular level has been shown to correlate with the genesis of cardiac arrhythmias and has motivated the application of nonlinear dynamics in cardiology. In this article, we review mathematical approaches to describe the underlying mechanisms for alternans using beat-to-beat iterated maps. We explain the development and properties of these maps, and show that they provide a fruitful framework to understand dynamical instabilities of voltage and calcium in paced cardiac cells.
authors.affiliation: Division of Cardiology, David Geffen School of Medicine at UCLA, University of California-Los Angeles, Los Angeles, CA 90095, USA.
authors.forename: Yohannes
authors.initials: Y
authors.lastname: Shiferaw
authors.forename: Zhilin
authors.initials: Z
authors.lastname: Qu
authors.forename: Alan
authors.initials: A
authors.lastname: Garfinkel
authors.forename: Alain
authors.initials: A
authors.lastname: Karma
authors.forename: James N
authors.initials: JN
authors.lastname: Weiss
mesh_terms: D000200:Action Potentials; D002118:Calcium / Q000378:metabolism; D005936:Glucans / Q000378:metabolism; D006321:Heart / Q000502:physiology*; D009206:Myocardium / Q000166:cytology* / Q000378:metabolism
chemical_list: D005936:Glucans; C439358:alternan; D002118:Calcium