title: Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart.
abstract: Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model.
authors.affiliation: Simula Research Laboratory, Center for Biomedical Computing, P.O. Box 134, Lysaker 1325, Norway.
authors.forename: Aslak
authors.initials: A
authors.lastname: Tveito
authors.forename: Ola
authors.initials: O
authors.lastname: Skavhaug
authors.forename: Glenn T
authors.initials: GT
authors.lastname: Lines
authors.forename: Robert
authors.initials: R
authors.lastname: Artebrant
mesh_terms: D000465:Algorithms; D001145:Arrhythmias, Cardiac / Q000503:physiopathology; D016275:Atrial Function; D019295:Computational Biology / Q000379:methods*; D006321:Heart / Q000502:physiology* / Q000503:physiopathology; D006329:Heart Conduction System / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular; D011667:Pulmonary Veins / Q000502:physiology; D012984:Software