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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
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.
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).
- 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.