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A condition for setting off ectopic waves in computational models of excitable cells
1Center for Biomedical Computing, Simula Research Laboratory, P.O. Box 134, 1325 Lysaker, Norway. aslak@simula.no
Mathematical Biosciences
|June 10, 2008
Summary
This study investigates ectopic wave spread in computational models of excitable cells, finding that stability depends on spatial diffusion and automatic region size. Reduced diffusion or larger automatic regions enhance ectopic activity, potentially leading to arrhythmias.
Area of Science:
- Computational Biology
- Cardiac Electrophysiology
- Mathematical Modeling
Background:
- Re-entrant arrhythmias and fibrillation are complex wave patterns in excitable cells, often initiated by external stimuli like ectopic waves.
- The precise mechanisms underlying ectopic wave initiation in large cell collections remain poorly understood.
- Existing models utilize the Monodomain model for spatial dynamics and Luo-Rudy I kinetics for cell behavior.
Purpose of the Study:
- To analyze the stability of steady-state solutions in the Monodomain model with Luo-Rudy I kinetics.
- To investigate the conditions under which ectopic wave spread occurs from automatic cell regions.
- To establish a mathematical criterion for the transition from a stable resting state to ectopic wave propagation.
Main Methods:
- Computational modeling of excitable cell collections in one and two spatial dimensions.
- Mathematical analysis using a reduced model approximating Luo-Rudy I kinetics.
- Division of cells into normal (N) and automatic (A) regions, with analysis of spatial diffusion (delta) and automatic region size (a).
Main Results:
- A condition for the transition from stable resting state to ectopic wave spread was derived.
- Mathematical and computational evidence indicates a critical constant (eta) where stability changes.
- Steady-state solutions are stable when delta > eta*a^2 and unstable when delta < eta*a^2.
Conclusions:
- The stability of cardiac tissue models is critically dependent on the interplay between spatial diffusion and the extent of automatic regions.
- Reduced diffusion or increased automaticity promotes ectopic activity, highlighting potential mechanisms for arrhythmia initiation.
- The derived condition provides a quantitative framework for understanding and predicting ectopic wave behavior in cardiac models.
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