Gap junctions and excitation patterns in continuum models of  islets

Pranay Goel; James Sneyd

doi:10.3934/dcdsb.2012.17.1969

Article Contents

2012, Volume 17, Issue 6: 1969-1990. Doi: 10.3934/dcdsb.2012.17.1969

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Gap junctions and excitation patterns in continuum models of islets

Pranay Goel^1, and
James Sneyd^2,

1.
Indian Institute of Science Education and Research, Pune, Maharashtra 411021
2.
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland

Received: October 2011

Revised: March 2012

Published: September 2012

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Abstract

We extend the development of homogenized models for excitable tissues coupled through "doughball" gap junctions. The analysis admits nonlinear Fickian fluxes in rather general ways and includes, in particular, calcium-gated conductance. The theory is motivated by an attempt to understand wave propagation and failure observed in the pancreatic islets of Langerhans. We reexamine, numerically, the role that gap junctional strength is generally thought to play in pattern formation in continuum models of islets.

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Mathematics Subject Classification: Primary: 74Q10, 35B27; Secondary: 92B25.

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