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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 427050, 7 pages
http://dx.doi.org/10.1155/2013/427050
Research Article

Discrete Coupling and Synchronization in the Insulin Release in the Mathematical Model of the Cells

1Instituto de Investigación en Comunicación Óptica, Departamento de Físico Matemáticas, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, 78000 San Luis Potosí, SLP, Mexico
2División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica A.C., Camino a la Presa San José 2055, Colonia Lomas 4a Sección, 78216 San Luis Potosí, SLP, Mexico

Received 19 October 2012; Revised 19 December 2012; Accepted 26 December 2012

Academic Editor: Gualberto Solís-Perales

Copyright © 2013 L. J. Ontañón-García and E. Campos-Cantón. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The synchronization phenomenon that occurs in the Langerhans islets among pancreatic cells is an interesting topic because these cells are responsible for the release of insulin in the blood stream. The aim of this work is to generate in-phase bursting electrical activity (BEA) in cells with different behaviors such as active, inactive, and continuous spiking cells based on mathematical models using a discrete time coupling. The approach considers two steps, the former is a mechanism on how to force cells to switch from silent phase to active, the latter is based on how to deal with in phase synchronization between active cells. The coupling signal is triggered in discrete events caused by the crossing of a threshold of an active cell which is given or defined by a Poincaré plane. The coupling on the inactive cells is applied to the state in which are the concentrations of agents which regulate the BEA. Based on numerical simulations, synchronization in the insulin release is obtained from cells with different behaviors.