A conservation principle and its effect on the formulation of Na-Ca
exchanger current in cardiac cells.
A. Varghese, und G. Sell. J. Theor. Biol., 189 (1):
33--40(November 1997)
Zusammenfassung
In this paper we show the presence of a latent conservation principle
in the formulation of ionic currents in cardiac cells and examine
its effect on a formulation of the sodium-calcium exchange current
appearing in the Noble model of the sinoatrial node cell in the mammalian
heart see Noble et al. (1989) or Winslow et al. (1991). Our objective
is to show that this formulation, if not corrected, will result in
a serious instability in this cardiac cell model. In particular,
under certain initial conditions, the solutions of the model equations
will blow-up in finite time. We also propose a correction to the
model equation for the sodium-calcium exchange current, and we show
that the modified model agrees favorably with the original model.
These phenomena also occur in the other cardiac cell models, such
as those modeling the Purkinje fiber, the atrial cell and the ventricular
cell. The changes proposed in this paper can be applied directly
to these models as well.
%0 Journal Article
%1 Varg_1997_33
%A Varghese, A.
%A Sell, G. R.
%D 1997
%J J. Theor. Biol.
%K 9398501 Animals, Cardiovascular, Cell Exchanger, Gov't, Ion Mammals, Membrane, Models, Node, Non-P.H.S., Pumps, Research Sinoatrial Sodium-Calcium Support, U.S.
%N 1
%P 33--40
%T A conservation principle and its effect on the formulation of Na-Ca
exchanger current in cardiac cells.
%U http://dx.doi.org/10.1006/jtbi.1997.0487
%V 189
%X In this paper we show the presence of a latent conservation principle
in the formulation of ionic currents in cardiac cells and examine
its effect on a formulation of the sodium-calcium exchange current
appearing in the Noble model of the sinoatrial node cell in the mammalian
heart see Noble et al. (1989) or Winslow et al. (1991). Our objective
is to show that this formulation, if not corrected, will result in
a serious instability in this cardiac cell model. In particular,
under certain initial conditions, the solutions of the model equations
will blow-up in finite time. We also propose a correction to the
model equation for the sodium-calcium exchange current, and we show
that the modified model agrees favorably with the original model.
These phenomena also occur in the other cardiac cell models, such
as those modeling the Purkinje fiber, the atrial cell and the ventricular
cell. The changes proposed in this paper can be applied directly
to these models as well.
@article{Varg_1997_33,
abstract = {In this paper we show the presence of a latent conservation principle
in the formulation of ionic currents in cardiac cells and examine
its effect on a formulation of the sodium-calcium exchange current
appearing in the Noble model of the sinoatrial node cell in the mammalian
heart [see Noble et al. (1989) or Winslow et al. (1991)]. Our objective
is to show that this formulation, if not corrected, will result in
a serious instability in this cardiac cell model. In particular,
under certain initial conditions, the solutions of the model equations
will blow-up in finite time. We also propose a correction to the
model equation for the sodium-calcium exchange current, and we show
that the modified model agrees favorably with the original model.
These phenomena also occur in the other cardiac cell models, such
as those modeling the Purkinje fiber, the atrial cell and the ventricular
cell. The changes proposed in this paper can be applied directly
to these models as well.},
added-at = {2009-06-03T11:20:58.000+0200},
author = {Varghese, A. and Sell, G. R.},
biburl = {https://www.bibsonomy.org/bibtex/21902d6f9a11c7e4e8b87d97961c52031/hake},
description = {The whole bibliography file I use.},
file = {Varg_1997_33.pdf:Varg_1997_33.pdf:PDF},
interhash = {57a7bbffce00a224f036bc0ff71eed51},
intrahash = {1902d6f9a11c7e4e8b87d97961c52031},
journal = {J. Theor. Biol.},
key = 154,
keywords = {9398501 Animals, Cardiovascular, Cell Exchanger, Gov't, Ion Mammals, Membrane, Models, Node, Non-P.H.S., Pumps, Research Sinoatrial Sodium-Calcium Support, U.S.},
month = Nov,
number = 1,
pages = {33--40},
pii = {S0022519397904872},
pmid = {9398501},
timestamp = {2009-06-03T11:21:35.000+0200},
title = {A conservation principle and its effect on the formulation of Na-Ca
exchanger current in cardiac cells.},
url = {http://dx.doi.org/10.1006/jtbi.1997.0487},
volume = 189,
year = 1997
}