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Related Experiment Videos

Restitution in mapping models with an arbitrary amount of memory.

Soma S Kalb1, Elena G Tolkacheva, David G Schaeffer

  • 1Department of Biomedical Engineering and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708, USA. ss49@duke.edu

Chaos (Woodbury, N.Y.)
|July 23, 2005
PubMed
Summary

Restitution mapping models reveal that dynamic and S1-S2 curves offer limited insight beyond two variables. Constant-basic cycle length (BCL) restitution, however, depends on higher dimensions and can bound cardiac dynamics complexity.

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Area of Science:

  • Cardiac Electrophysiology
  • Computational Biology
  • Nonlinear Dynamics

Background:

  • Restitution, the shortening of action potential duration (APD) with increased heart rate, is linked to fibrillation.
  • Mapping models represent APD as a function of previous diastolic intervals (DIs) and APDs.
  • Previous models with at least three variables are needed to replicate experimental restitution portraits (RPs).

Purpose of the Study:

  • To analyze restitution curves (RCs) within restitution portraits for mapping models with arbitrary memory.
  • To determine the number of variables required for different RCs.
  • To visualize RCs and understand their dimensionality.

Main Methods:

  • Analysis of mapping models with varying degrees of memory (number of previous variables).

Related Experiment Videos

  • Mathematical derivation and graphical visualization of restitution curves.
  • Comparison of dimensionality requirements for dynamic, S1-S2, and constant-BCL restitution.

    • Main Results:

    • Dynamic and S1-S2 RCs are confined to two-dimensional surfaces, limiting their utility in models with >2 variables.
    • Constant-BCL restitution depends on higher-dimensional dynamics.
    • The dimensionality of constant-BCL restitution can provide a lower bound for cardiac dynamics.

    Conclusions:

    • The complexity of cardiac dynamics requires mapping models that account for higher-dimensional features.
    • Constant-BCL restitution is a crucial feature for understanding the dimensionality of cardiac electrophysiological behavior.
    • This analysis refines our understanding of restitution mapping and its implications for fibrillation.