title: Existence of excitation waves for a collection of cardiomyocytes electrically coupled to fibroblasts.
abstract: We consider mathematical models of a collection of cardiomyocytes (myocardial tissue) coupled to a varying number of fibroblasts. Our aim is to understand how conductivity (δ) and fibroblast density (η) affect the stability of the collection. We provide mathematical and computational arguments indicating that there is a region of instability in the η-δ space. Mathematical arguments, based on a simplified model of the coupled myocyte-fibroblast system, show that for certain parameter choices, a stationary solution cannot exist. Numerical experiments (1D,2D) are based on a recently developed model of electro-chemical coupling between a human atrial myocyte and a number of associated atrial fibroblasts. The numerical experiments demonstrate that there is a region of instability of the form observed in the simplified model analysis.
authors.affiliation: Simula Research Laboratory, Center for Biomedical Computing, Lysaker 1325, Norway. aslak@simula.no
authors.forename: Aslak
authors.initials: A
authors.lastname: Tveito
authors.forename: Glenn
authors.initials: G
authors.lastname: Lines
authors.forename: Robert
authors.initials: R
authors.lastname: Artebrant
authors.forename: Ola
authors.initials: O
authors.lastname: Skavhaug
authors.forename: Mary M
authors.initials: MM
authors.lastname: Maleckar
mesh_terms: D000465:Algorithms; D001145:Arrhythmias, Cardiac / Q000209:etiology / Q000503:physiopathology; D002450:Cell Communication / Q000502:physiology; D002452:Cell Count; D003198:Computer Simulation; D004553:Electric Conductivity; D055724:Electrophysiological Phenomena / Q000502:physiology*; D005347:Fibroblasts / Q000502:physiology*; D006801:Humans; D008564:Membrane Potentials / Q000502:physiology; D008955:Models, Cardiovascular; D009200:Myocardial Contraction / Q000502:physiology*; D032383:Myocytes, Cardiac / Q000502:physiology*