Optimization and control in glucose metabolism based on the oral minimal model

Abstract

In the mathematical models to describe physiological phenomena, optimization problem and control tactics are important. Because optimal parameters to represent status of subjects should be estimated and biological variables beyond the normal range should be recovered by using of the pertinent control or interventions. For this objective, the model is required to be validated based on clinical data and the optimal algorithm for each subject is able to be designed. The oral minimal model is the mathematical system to understand glycemic control in vivo, which can be helpful to evaluate the beta-cell function and insulin sensitivity. In this study, 10 healthy subjects with normal glucose tolerance and 14 patients with type 2 diabetes mellitus participated. In the results, firstly, blood glucose concentration level, C-peptide level, and Insulin response can be predicted by using of the oral minimal model. Secondly, insulin sensitivity and disposition indices are lower in type 2 diabetes group than normal group. Thirdly, the oral minimal model indices are well correlated with pre-existing clinical indices. Therefore the oral minimal model could be applied to the Korean. Furthermore, a proportional-integral-derivative (PID) controller and optimal control using dynamic programming can be used to establish algorithms to control blood glucose level in type 2 diabetes mellitus. PID controller showed capability to lower glucose level efficiently and the level of the glucose was continuously lowered without fluctuation. An optimal control scheme with two simplified additional insulin loading profiles also could lower blood glucose level efficiently, and the barrier term in the cost function could prevent too low blood glucose level. Among 14 T2DM patients, immediate injections of two insulin loadings were recommended in most cases for effective control of the glucose level. Based on this model and tactics, it is expected that latent interactions in glucose metabolism are clarified, and the models and efficient control algorithms for the artificial pancreas could be developed.