Curvature dependence of propagating velocity for a simplified calcium model

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aut.researcherZhang, Wenjun
dc.contributor.authorZhang, W
dc.date.accessioned2014-02-19T21:29:06Z
dc.date.available2014-02-19T21:29:06Z
dc.date.copyright2014-02-19
dc.date.issued2014-02-19
dc.description.abstractIt is known that curvature relation plays a key role in the propagation of two-dimensional waves in an excitable model. Such a relation is believed to obey the eikonal equation for typical excitable models (e.g., the FitzHugh-Nagumo (FHN) model), which states that the relation between the normal velocity and the local curvature is approximately linear. In this paper, we show that for a simplified model of intracellular calcium dynamics, although its temporal dynamics can be investigated by analogy with the FHN model, the curvature relation does not obey the eikonal equation. Further, the inconsistency with the eikonal equation for the calcium model is because of the dispersion relation between wave speed s and volume-ratio parameter γ in the closed-cell version of the model, not because of the separation of the fast and the slow variables as in the FHN model. Hence this simplified calcium model may be an unexpected excitable system, whose wave propagation properties cannot be always understood by analogy with the FHN model.
dc.identifier.citationarXiv:1402.4554v1 [math.DS]
dc.identifier.urihttps://hdl.handle.net/10292/6862
dc.publisherarXiv.org
dc.relation.urihttp://arxiv.org/abs/1402.4554
dc.rightsarXiv supports and participates in the Open Archives Initiative (OAI). arXiv is a registered OAI-PMH data-provider and provides metadata for all submissions which is updated each night shortly after new submissions are announced. Metadata for arXiv articles may be reused in non-commercial and commercial systems.
dc.rights.accessrightsOpenAccess
dc.subjectCalcium dynamics
dc.subjectEikonal equation
dc.subjectTraveling waves
dc.subjectStability
dc.subjectFitzHugh-Nagumo model
dc.titleCurvature dependence of propagating velocity for a simplified calcium model
dc.typeInternet Publication
pubs.elements-id161643
pubs.organisational-data/AUT
pubs.organisational-data/AUT/Design & Creative Technologies
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