Mathematical Modeling of Nonlinear Dynamics of Blood Hormones

摘要

In this paper, mathematical modeling of nonlinear dynamics of blood hormonesregulatory system, which includes glucose, insulin and glucagon hormones and withthe presence of the secreted insulin due to the pancreatic beta cells, is developedand investigated. This model considers the time evolution of nonlinear dynamics ofthe equations for the blood hormones that represent glucose, glucagon and insulinconcentrations plus insulin and glucagon actions as well as secreted insulin due tothe pancreatic beta cells. Using both theoretical and numerical procedures, wedetermine such quantities by examining some data for the case of one patient atthree different times of the day as well as the case of three patients at the same timeof the day and for different values of the parameters. We find that the nonlineareffects due to the time-dependent interactions between these hormones can benotable and affect the resulting values for each hormone for given instant in time.For the present nonlinear dynamical system, there are parameters whose valuesdiffer for different diabetes patients and their roles to determine the values of theglucose, glucagon and insulin concentrations in the patient’s blood and theresponses that arise due to the insulin and glucagon actions can be notable. We find,in particular, that the cases with relatively moderate or smaller values of theparameters, which represent kinetics of the insulin action, insulin sensitivity, ratefor the glucagon action and the glucagon sensitivity, can lead to moderate or smallervalues of the plasma glucose concentration.