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

The synchronization phenomenon that occurs in the Langerhans islets among pancreatic β 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 β 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 β cells to switch from silent phase to active, the latter is based on how to deal with in phase synchronization between active β cells. The coupling signal is triggered in discrete events caused by the crossing of a threshold of an active β 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 β cells with different behaviors