Journal article
A two-current model for the dynamics of cardiac membrane
Bulletin of mathematical biology, Vol.60(4), pp.753-807
09/2003
DOI: 10.1006/bulm.1998.0041
Abstract
We introduce a simple mathematical model of regulation of division of labor in insect societies based on fixed-response thresholds. Individuals with different thresholds respond differently to task-associated stimuli. Low-threshold individuals become involved at a lower level of stimulus than high-threshold individuals. We show that this simple model can account for experimental observations of Wilson (1984), extend the model to more complicated situations, explore its properties, and study under what conditions it can account for temporal polyethism.
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.
Details
- Title: Subtitle
- A two-current model for the dynamics of cardiac membrane
- Creators
- Colleen Mitchell - Duke UniversityDavid Schaeffer - Duke UniversityJean-Louis Deneubourg - Université Libre de Bruxelles
- Resource Type
- Journal article
- Publication Details
- Bulletin of mathematical biology, Vol.60(4), pp.753-807
- Publisher
- Springer-Verlag
- DOI
- 10.1006/bulm.1998.0041
- ISSN
- 0092-8240
- eISSN
- 1522-9602
- Language
- English
- Date published
- 09/2003
- Academic Unit
- Mathematics
- Record Identifier
- 9984240865402771
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