Systems of pancreatic beta-cells and glucose regulation.

We present mathematical models for systems of beta-cells in pancreatic islets. The first topic begins with the effects of noise and coupling strength on bursting action potentials of beta-cells. From the discussion, the regular bursts are produced by a proper amount of noise and coupling strength. Furthermore, the bursting duration and period depend on the cluster size of beta-cells. We also observe the real size of islets mostly consisting of beta-cells and obtain the size distribution of islets. In addition, we derive either log-normal or Weibull distributions of the islet sizes based on recent observation on islet growth. Islets of Langerhans are composed of several endocrine cells which interact with each other. Considering asymmetric and inhibitory interactions of these endocrine cells, we introduce a simple islet model consisting of alpha-, beta-, and delta-cells. Finally, a whole feedback model for glucose regulation is constructed, connecting the microscopic bursting mechanism and the macroscopic blood glucose regulation of the body. We analyzed these models via numerical simulations based on in vivo and in vitro experimental data.