title: On the computational complexity of the bidomain and the monodomain models of electrophysiology.
abstract: The bidomain model, coupled with accurate models of cell membrane kinetics, is generally believed to provide a reasonable basis for numerical simulations of cardiac electrophysiology. Because of changes occurring in very short time intervals and over small spatial domains, discretized versions of these models must be solved on fine computational grids, and small time-steps must be applied. This leads to huge computational challenges that have been addressed by several authors. One popular way of reducing the CPU demands is to approximate the bidomain model by the monodomain model, and thus reducing a two by two set of partial differential equations to one scalar partial differential equation; both of which are coupled to a set of ordinary differential equations modeling the cell membrane kinetics. A reduction in CPU time of two orders of magnitude has been reported. It is the purpose of the present paper to provide arguments that such a reduction is not present when order-optimal numerical methods are applied. Theoretical considerations and numerical experiments indicate that the reduction factor of the CPU requirements from bidomain to monodomain computations, using order-optimal methods, typically is about 10 for simple cell models and less than two for more complex cell models.
authors.affiliation: Simula Research Laboratory and Department of Informatics, University of Oslo, Oslo, Norway. sundnes@simula.no
authors.forename: Joakim
authors.initials: J
authors.lastname: Sundnes
authors.forename: Bjørn Fredrik
authors.initials: BF
authors.lastname: Nielsen
authors.forename: Kent Andre
authors.initials: KA
authors.lastname: Mardal
authors.forename: Xing
authors.initials: X
authors.lastname: Cai
authors.forename: Glenn Terje
authors.initials: GT
authors.lastname: Lines
authors.forename: Aslak
authors.initials: A
authors.lastname: Tveito
mesh_terms: D000818:Animals; D002462:Cell Membrane / Q000502:physiology; D003198:Computer Simulation; D004594:Electrophysiology / Q000379:methods; D006321:Heart / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular