Journal of Applied Mathematics & Bioinformatics

Mathematical Modeling of Nonlinear Dynamics of Blood Hormones

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• Abstract

   

  In this paper, mathematical modeling of nonlinear dynamics of blood hormones regulatory system, which includes glucose, insulin and glucagon hormones and with the presence of the secreted insulin due to the pancreatic beta cells, is developed and investigated. This model considers the time evolution of nonlinear dynamics of the equations for the blood hormones that represent glucose, glucagon and insulin concentrations plus insulin and glucagon actions as well as secreted insulin due to the pancreatic beta cells. Using both theoretical and numerical procedures, we determine such quantities by examining some data for the case of one patient at three different times of the day as well as the case of three patients at the same time of the day and for different values of the parameters. We find that the nonlinear effects due to the time-dependent interactions between these hormones can be notable and affect the resulting values for each hormone for given instant in time. For the present nonlinear dynamical system, there are parameters whose values differ for different diabetes patients and their roles to determine the values of the glucose, glucagon and insulin concentrations in the patient’s blood and the responses 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 the parameters, which represent kinetics of the insulin action, insulin sensitivity, rate for the glucagon action and the glucagon sensitivity, can lead to moderate or smaller values of the plasma glucose concentration.

   

  Keywords: Blood glucose, Glucose dynamics, Blood hormones.