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.
%0 Journal Article
%1 Sund_2006_1088
%A Sundnes, Joakim
%A Nielsen, Bj�rn Fredrik
%A Mardal, Kent Andre
%A Cai, Xing
%A Lines, Glenn Terje
%A Tveito, Aslak
%D 2006
%J Ann. Biomed. Eng.
%K Animals; Cardiovascular Cell Computer Electrophysiology; Heart; Humans; Membrane; Models, Simulation;
%N 7
%P 1088--1097
%R 10.1007/s10439-006-9082-z
%T On the computational complexity of the bidomain and the monodomain
models of electrophysiology.
%U http://dx.doi.org/10.1007/s10439-006-9082-z
%V 34
%X 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.
@article{Sund_2006_1088,
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.},
added-at = {2009-06-03T11:20:58.000+0200},
author = {Sundnes, Joakim and Nielsen, Bj�rn Fredrik and Mardal, Kent Andre and Cai, Xing and Lines, Glenn Terje and Tveito, Aslak},
biburl = {https://www.bibsonomy.org/bibtex/266bb26ae082e78ddbbbd1f40b904a427/hake},
description = {The whole bibliography file I use.},
doi = {10.1007/s10439-006-9082-z},
interhash = {241c0ac588f8668507a93a5a8d2973c6},
intrahash = {66bb26ae082e78ddbbbd1f40b904a427},
journal = {Ann. Biomed. Eng.},
keywords = {Animals; Cardiovascular Cell Computer Electrophysiology; Heart; Humans; Membrane; Models, Simulation;},
month = Jul,
number = 7,
pages = {1088--1097},
pmid = {16773461},
timestamp = {2009-06-03T11:21:33.000+0200},
title = {On the computational complexity of the bidomain and the monodomain
models of electrophysiology.},
url = {http://dx.doi.org/10.1007/s10439-006-9082-z},
volume = 34,
year = 2006
}