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Nonlinear dynamics of two-dimensional cardiac action potential duration mapping model with memory
M Kesmia1, S Boughaba1, S Jacquir2
1Département de Mathématiques, Université de Constantine I, Constantine, Algeria.
Journal of Mathematical Biology
|January 3, 2019
Summary
This study analyzes a 2D cardiac action potential duration (APD) model with memory, revealing new dynamics like bistabilities and novel synchronization rhythms. The findings enhance understanding of APD alternans and chaotic dynamics in cardiac electrophysiology.
Area of Science:
- Computational Biology
- Nonlinear Dynamics
- Cardiac Electrophysiology
Background:
- Action potential duration (APD) restitution, relating APD to diastolic interval (DI), is crucial for predicting cardiac arrhythmias.
- APD alternans, characterized by alternating short and long APDs with corresponding long and short DIs, are linked to arrhythmogenesis.
- Previous models have not fully captured the complex dynamics, including memory effects, influencing APD behavior.
Purpose of the Study:
- To analyze the nonlinear dynamics of a 2D mapping model of cardiac action potential duration (APD) with memory, derived from a 1D map.
- To investigate bifurcations and emergent phenomena, such as bistabilities and novel synchronization patterns, under varying stimulation periods.
- To characterize the chaotic dynamics of the 2D-map APD model using fractal analysis and Lyapunov exponents.
Main Methods:
- Development and analysis of a two-dimensional mapping model incorporating memory effects for cardiac action potential duration (APD).
- Systematic variation of stimulation period and model parameters to observe bifurcations and dynamic transitions.
- Application of nonlinear dynamics tools, including fractal dimension calculation, Lyapunov exponents, and Kolmogorov entropy, to characterize chaotic behavior.
Main Results:
- The 2D-map APD model with memory exhibits previously undescribed bistabilities and novel synchronization rhythms as stimulation frequency increases.
- Bifurcations were observed and characterized, providing new insights into the parameter space of APD dynamics.
- The model accurately reflects chaotic dynamics, with a highlighted fractal structure of the strange attractor and quantified chaotic properties.
Conclusions:
- The 2D-map APD model with memory offers a more comprehensive framework for understanding cardiac electrophysiological dynamics.
- The identified bistabilities and synchronization patterns contribute to a deeper understanding of APD alternans and arrhythmia mechanisms.
- Characterization of chaos in this model paves the way for future research in controlling cardiac chaos and refining APD dynamics studies.
Keywords:
BifurcationCardiac action potential durationChaosFixed pointFractal structureMemoryPeriodic dynamicsStrange attractorMore Related Videos
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