Document Detail

A condition for setting off ectopic waves in computational models of excitable cells.
MedLine Citation:
PMID:  18539188     Owner:  NLM     Status:  MEDLINE    
The purpose of this paper is to study the stability of steady state solutions of the Monodomain model equipped with Luo-Rudy I kinetics. It is well established that re-entrant arrhythmias can be created in computational models of excitable cells. Such arrhythmias can be initiated by applying an external stimulus that interacts with a partially refractory region, and spawn breaking waves that can eventually generate extremely complex wave patterns commonly referred to as fibrillation. An ectopic wave is one possible stimulus that may initiate fibrillation. Physiologically, it is well known that ectopic waves exist, but the mechanism for initiating ectopic waves in a large collection of cells is poorly understood. In the present paper we consider computational models of collections of excitable cells in one and two spatial dimensions. The cells are modeled by Luo-Rudy I kinetics, and we assume that the spatial dynamics is governed by the Monodomain model. The mathematical analysis is carried out for a reduced model that is known to provide good approximations of the initial phase of solutions of the Luo-Rudy I model. A further simplification is also introduced to motivate and explain the results for the more complicated models. In the analysis the cells are divided into two regions; one region (N) consists of normal cells as model by the standard Luo-Rudy I model, and another region (A) where the cells are automatic in the sense that they would act as pacemaker cells if they where isolated from their surroundings. We let delta denote the spatial diffusion and a denote a characteristic length of the automatic region. It has previously been shown that reducing diffusion or increasing the automatic region enhances ectopic activity. Here we derive a condition for the transition from stable resting state to ectopic wave spread. Under suitable assumptions on the model we provide mathematical and computational arguments indicating that there is a constant eta such that a steady state solution of this system is stable whenever delta approximately > etaa(2), and unstable whenever delta approximately < etaa(2).
Aslak Tveito; Glenn T Lines
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Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't     Date:  2008-04-22
Journal Detail:
Title:  Mathematical biosciences     Volume:  213     ISSN:  0025-5564     ISO Abbreviation:  Math Biosci     Publication Date:  2008 Jun 
Date Detail:
Created Date:  2008-06-09     Completed Date:  2008-09-02     Revised Date:  2009-11-11    
Medline Journal Info:
Nlm Unique ID:  0103146     Medline TA:  Math Biosci     Country:  United States    
Other Details:
Languages:  eng     Pagination:  141-50     Citation Subset:  IM    
Center for Biomedical Computing, Simula Research Laboratory, P.O. Box 134, 1325 Lysaker, Norway.
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MeSH Terms
Action Potentials
Atrial Fibrillation / etiology*,  physiopathology
Cell Communication
Electric Conductivity*
Electric Stimulation
Electrophysiologic Techniques, Cardiac
Heart Conduction System / physiopathology
Membrane Potentials
Models, Cardiovascular*
Myocytes, Cardiac* / chemistry,  metabolism
Numerical Analysis, Computer-Assisted*
Systems Biology / methods

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine

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