Bull Math Biol. 2003 Sep;65(5):767-93.

A two-current model for the dynamics of cardiac membrane.

Source

Department of Mathematics, Duke University and Center for Nonlinear and Complex Systems, Durham NC 27708, USA.

Abstract

In this paper we introduce and study a model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh-Nagumo model, makes it useful in numerical simulations, especially in two or three spatial dimensions where numerical efficiency is so important. (2) It can be understood analytically without recourse to numerical simulations. This allows us to determine rather completely how the parameters in the model affect its behavior which in turn provides insight into the effects of the many parameters in more realistic models. (3) It naturally gives rise to a one-dimensional map which specifies the action potential duration as a function of the previous diastolic interval. For certain parameter values, this map exhibits a new phenomenon--subcritical alternans--that does not occur for the commonly used exponential map.

PMID:: 12909250; [PubMed - indexed for MEDLINE]

Publication Types, MeSH Terms

Publication Types

Research Support, U.S. Gov't, Non-P.H.S.

MeSH Terms

LinkOut - more resources

Full Text Sources

Other Literature Sources

COS Scholar Universe

Supplemental Content

Save items

Related citations in PubMed

Alternans and the influence of ionic channel modifications: Cardiac three-dimensional simulations and one-dimensional numerical bifurcation analysis. [Chaos. 2007]
Alternans and the influence of ionic channel modifications: Cardiac three-dimensional simulations and one-dimensional numerical bifurcation analysis.
Bauer S, Röder G, Bär M. Chaos. 2007 Mar; 17(1):015104.
Standing waves in the FitzHugh-Nagumo model of cardiac electrical activity. [Phys Rev E Stat Nonlin Soft Ma...]
Standing waves in the FitzHugh-Nagumo model of cardiac electrical activity.
Dauby PC, Desaive T, Croisier H, Kolh P. Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Feb; 73(2 Pt 1):021908. Epub 2006 Feb 16.
Simulation of QRST integral maps with a membrane-based computer heart model employing parallel processing. [IEEE Trans Biomed Eng. 2004]
Simulation of QRST integral maps with a membrane-based computer heart model employing parallel processing.
Trudel MC, Dubé B, Potse M, Gulrajani RM, Leon LJ. IEEE Trans Biomed Eng. 2004 Aug; 51(8):1319-29.
Review [Computer simulations of electrical activity of the heart]. [Usp Fiziol Nauk. 2010]
Review [Computer simulations of electrical activity of the heart].
Aliev RR. Usp Fiziol Nauk. 2010 Jul-Sep; 41(3):44-63.
Review Basic mechanisms of cardiac impulse propagation and associated arrhythmias. [Physiol Rev. 2004]
Review Basic mechanisms of cardiac impulse propagation and associated arrhythmias.
Kléber AG, Rudy Y. Physiol Rev. 2004 Apr; 84(2):431-88.

See reviews... See all...

Cited by 8 PubMed Central articles

Membranes with the same ion channel populations but different excitabilities. [PLoS One. 2012]
Membranes with the same ion channel populations but different excitabilities.
Herrera-Valdez MA. PLoS One. 2012; 7(4):e34636. Epub 2012 Apr 16.
Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans. [Chaos. 2010]
Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans.
Dai S, Schaeffer DG. Chaos. 2010 Jun; 20(2):023131.
Critical scale of propagation influences dynamics of waves in a model of excitable medium. [Nonlinear Biomed Phys. 2009]
Critical scale of propagation influences dynamics of waves in a model of excitable medium.
Starobin JM, Danford CP, Varadarajan V, Starobin AJ, Polotski VN. Nonlinear Biomed Phys. 2009 Jul 9; 3(1):4. Epub 2009 Jul 9.

See all...

Related information

Related Citations
Calculated set of PubMed citations closely related to the selected article(s) retrieved using a word weight algorithm. Related articles are displayed in ranked order from most to least relevant, with the “linked from” citation displayed first.
Cited in PMC
Full-text articles in the PubMed Central Database that cite the current articles.

Recent activity

Clear Turn Off Turn On

A two-current model for the dynamics of cardiac membrane.
A two-current model for the dynamics of cardiac membrane.
Bull Math Biol. 2003 Sep ;65(5):767-93.

PubMed
Tachyphylaxis to capsaicin-induced cough and its reversal by indomethacin, in pa...
Tachyphylaxis to capsaicin-induced cough and its reversal by indomethacin, in patients with the sinobronchial syndrome.
Clin Auton Res. 1992 Dec ;2(6):397-401.

PubMed
Patterns of failure after the multimodality treatment of uterine papillary serou...
Patterns of failure after the multimodality treatment of uterine papillary serous carcinoma.
Int J Radiat Oncol Biol Phys. 2003 Sep 1 ;57(1):208-16.

PubMed
Concurrent chemoradiotherapy treatment of locally advanced pancreatic cancer: ge...
Concurrent chemoradiotherapy treatment of locally advanced pancreatic cancer: gemcitabine versus 5-fluorouracil, a randomized controlled study.
Int J Radiat Oncol Biol Phys. 2003 Sep 1 ;57(1):98-104.

PubMed
Intensity-modulated radiation therapy for head-and-neck cancer: the UCSF experie...
Intensity-modulated radiation therapy for head-and-neck cancer: the UCSF experience focusing on target volume delineation.
Int J Radiat Oncol Biol Phys. 2003 Sep 1 ;57(1):49-60.

PubMed

Your browsing activity is empty.

Activity recording is turned off.

Turn recording back on

PubMed

Result Filters

Display Settings:

Send to: