Integral-based parameter identification for long-term dynamic verification of a glucose-insulin system model

Hyperglycaemia in critically ill patients increases the risk of further complications and mortality. This paper introduces a model capable of capturing the essential glucose and insulin kinetics in patients from retrospective data gathered in an intensive care unit (ICU). The model uses two time-varying patient specific parameters for glucose effectiveness and insulin sensitivity. The model is mathematically reformulated in terms of integrals to enable a novel method for identification of patient specific parameters. The method was tested on long-term blood glucose recordings from 17 ICU patients, producing 4% average error, which is within the sensor error. One-hour forward predictions of blood glucose data proved acceptable with an error of 2-11%. All identified parameter values were within reported physiological ranges. The parameter identification method is more accurate and significantly faster computationally than commonly used non-linear, non-convex methods. These results verify the model's ability to capture long-term observed glucose-insulin dynamics in hyperglycemic ICU patients, as well as the fitting method developed. Applications of the model and parameter identification method for automated control of blood glucose and medical decision support are discussed.