title: A bilayer model of human atria: mathematical background, construction, and assessment.
abstract: OBJECTIVE
  Atrial numerical modelling has generally represented the organ as either a surface or tissue with thickness. While surface models have significant computational advantages over tissue models, they cannot fully capture propagation patterns seen in vivo, such as dissociation of activity between endo- and epicardium. We introduce an intermediate representation, a bilayer model of the human atria, which is capable of recreating recorded activation patterns.
  
  
  RESULTS
  We simultaneously solved two surface monodomain problems by formalizing an optimization method to set a coupling term between them. Two different asymptotically equivalent numerical implementations of the model are presented. We then built a geometrically and electrophysiologically detailed model of the human atria based on CT data, including two layers of fibre directions, major muscle bundles, and discrete atrial coupling. We adjusted parameters to recreate clinically measured activation times. Activation was compared with a monolayer model. Activation was fit to the physiological range measured over the entire atria. The crista terminalis and pectinate muscles were important for local right atrial activation, but did not significantly affect total activation time. Propagation in the bilayer model was similar to that of a monolayer, but with noticeable difference, due to three-dimensional propagation where fibre direction changed abruptly across the wall, resulting in a slight dissociation of activity.
  
  
  CONCLUSIONS
  Atrial structure plays the dominant role in determining activation. A bilayer model is able to take into account transmural heterogeneities, while maintaining the low computational load associated with surface models.
authors.affiliation: IMB, University of Bordeaux, 351 Cours de la Liberation, Talence 33405, France Carmen, Inria Bordeaux Sud-Ouest, 200 Avenue de la Vieille Tour, Talence 33405, France Electrophysiology and Heart Modeling Institute LIRYC, PTIB-Campus Xavier Arnozan, Avenue du Haut Lévêque, Pessac 33600, France simon.labarthe@u-bordeaux2.fr.
authors.forename: Simon
authors.initials: S
authors.lastname: Labarthe
authors.affiliation: Carmen, Inria Bordeaux Sud-Ouest, 200 Avenue de la Vieille Tour, Talence 33405, France Electrophysiology and Heart Modeling Institute LIRYC, PTIB-Campus Xavier Arnozan, Avenue du Haut Lévêque, Pessac 33600, France Hôpital Haut-Lévèque CHU Bordeaux, University Bordeaux Segalen, Avenue de Magellan, Pessac 33604, France.
authors.forename: Jason
authors.initials: J
authors.lastname: Bayer
authors.affiliation: IMB, University of Bordeaux, 351 Cours de la Liberation, Talence 33405, France Carmen, Inria Bordeaux Sud-Ouest, 200 Avenue de la Vieille Tour, Talence 33405, France Electrophysiology and Heart Modeling Institute LIRYC, PTIB-Campus Xavier Arnozan, Avenue du Haut Lévêque, Pessac 33600, France.
authors.forename: Yves
authors.initials: Y
authors.lastname: Coudière
authors.affiliation: IMB, University of Bordeaux, 351 Cours de la Liberation, Talence 33405, France Carmen, Inria Bordeaux Sud-Ouest, 200 Avenue de la Vieille Tour, Talence 33405, France Electrophysiology and Heart Modeling Institute LIRYC, PTIB-Campus Xavier Arnozan, Avenue du Haut Lévêque, Pessac 33600, France.
authors.forename: Jacques
authors.initials: J
authors.lastname: Henry
authors.affiliation: Electrophysiology and Heart Modeling Institute LIRYC, PTIB-Campus Xavier Arnozan, Avenue du Haut Lévêque, Pessac 33600, France Hôpital Haut-Lévèque CHU Bordeaux, University Bordeaux Segalen, Avenue de Magellan, Pessac 33604, France.
authors.forename: Hubert
authors.initials: H
authors.lastname: Cochet
authors.affiliation: Electrophysiology and Heart Modeling Institute LIRYC, PTIB-Campus Xavier Arnozan, Avenue du Haut Lévêque, Pessac 33600, France Hôpital Haut-Lévèque CHU Bordeaux, University Bordeaux Segalen, Avenue de Magellan, Pessac 33604, France.
authors.forename: Pierre
authors.initials: P
authors.lastname: Jaïs
authors.affiliation: IMB, University of Bordeaux, 351 Cours de la Liberation, Talence 33405, France Carmen, Inria Bordeaux Sud-Ouest, 200 Avenue de la Vieille Tour, Talence 33405, France Electrophysiology and Heart Modeling Institute LIRYC, PTIB-Campus Xavier Arnozan, Avenue du Haut Lévêque, Pessac 33600, France.
authors.forename: Edward
authors.initials: E
authors.lastname: Vigmond
mesh_terms: D000200:Action Potentials; D001145:Arrhythmias, Cardiac / Q000000981:diagnostic imaging / Q000503:physiopathology*; D016279:Atrial Function, Left; D016280:Atrial Function, Right; D064752:Atrial Remodeling; D003198:Computer Simulation; D006325:Heart Atria / Q000000981:diagnostic imaging / Q000503:physiopathology*; D006801:Humans; D007700:Kinetics; D008955:Models, Cardiovascular; D009716:Numerical Analysis, Computer-Assisted; D014057:Tomography, X-Ray Computed
keywords: Atrial numerical modelling