Parameter estimation of a meal glucose–insulin model for TIDM patients from therapy historical data

Abstract

The effect of meal on blood glucose concentration is a key issue in diabetes mellitus because its estimation could be very useful in therapy decisions. In the case of type 1 diabetes mellitus (T1DM), the therapy based on automatic insulin delivery requires a closed-loop control system to maintain euglycaemia even in the postprandial state. Thus, the mathematical modelling of glucose metabolism is relevant to predict the metabolic state of a patient. Moreover, the eating habits are characteristic of each person, so it is of interest that the mathematical models of meal intake allow to personalise the glycaemic state of the patient using therapy historical data, that is, daily measurements of glucose and records of carbohydrate intake and insulin supply. Thus, here, a model of glucose metabolism that includes the effects of meal is analysed in order to establish criteria for data-based personalisation. The analysis includes the sensitivity and identifiability of the parameters, and the parameter estimation problem was resolved via two algorithms: particle swarm optimisation and evonorm. The results show that the mathematical model can be a useful tool to estimate the glycaemic status of a patient and personalise it according to her/his historical data.

WITHDRAWN: Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

“…This particular model was published in [7] where authors aimed a very well glucoregulatory system description without involving a large number of mathematical equations, see [20,21]. The initial proposed model consists of three differential equations and eight parameters that describe the variation of blood glucose concentration, blood insulin concentration, and amount of glucose in the intestine.…”

Postprandial Glucose Control in Type 1 Diabetes: Importance of the Gastric Emptying Rate

“…A further step has been taken with closed-loop automated insulin delivery systems (CLS), in which insulin infusion is regulated by an algorithm based on CGM systems. Compared with conventional insulin pump therapy, CLS have been shown to improve overall glucose control although PP glucose excursions still remain a challenge [81,82,83], suggesting that other factors contribute to PP glucose profile.…”

Ultimate Bounds for a Diabetes Mathematical Model Considering Glucose Homeostasis

“…The mathematical model proposed in [15] is used as a baseline to study the T1DM and a T2DM. A previous version of this model was published in [16], where the authors aimed to create a very good glucoregulatory system description without involving a large number of mathematical equations; see [20,21]. That model consists of three ODEs with eight parameters describing the dynamic concentrations of blood insulin, blood glucose concentration, and glucose in the intestine.…”