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Cardiac Alternans Arising From an Unfolded Border-Collision Bifurcation

[+] Author Affiliations
Xiaopeng Zhao, David G. Schaeffer, Carolyn M. Berger, Wanda Krassowska, Daniel J. Gauthier

Duke University, Durham, NC

Paper No. DETC2007-35304, pp. 223-232; 10 pages
doi:10.1115/DETC2007-35304
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

Following an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly and remains at a constant value before returning to the resting value, a phenomenon known as an action potential. When the pacing rate of a periodic train of stimuli is increased above a critical value, the action potential undergoes a period-doubling bifurcation, where the resulting alternation of the action potential duration is known as alternans in the medical literature. In principle, a period-doubling bifurcation may occur through either a smooth or a nonsmooth mechanism. Previous experiments reveal that the bifurcation to alternans exhibits hybrid smooth/nonsmooth behaviors, which is due to large variations in the system’s properties over a small interval of bifurcation parameter. To reproduce the experimentally observed hybrid behaviors, we have developed a model of alternans that exhibits an unfolded border-collision bifurcation. Excellent agreement between simulation of the model and experimental data suggests that features of the unfolded border-collision model should be included in modeling cardiac alternans.

Copyright © 2007 by ASME

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