Parameters of physiological models of glucose–insulin regulation in type 1 diabetes have previously been estimated using data collected over short periods of time and lack the quantification of day-to-day variability.… Click to show full abstract
Parameters of physiological models of glucose–insulin regulation in type 1 diabetes have previously been estimated using data collected over short periods of time and lack the quantification of day-to-day variability. We developed a new hierarchical model to relate subcutaneous insulin delivery and carbohydrate intake to continuous glucose monitoring over 12 weeks while describing day-to-day variability. Sensor glucose data sampled every 10-min, insulin aspart delivery and meal intake were analyzed from eight adults with type 1 diabetes (male/female 5/3, age ${\text{39.9}\,\pm \,\text{9.5}}$ years, BMI $\text{25.4}\,\pm \,\text{4.4 kg/ m}^{2}$, HbA1c ${\text{8.4}\,\pm \,\text{0.6}}$%) who underwent a 12-week home study of closed-loop insulin delivery. A compartment model comprised of five linear differential equations; model parameters were estimated using the Markov chain Monte Carlo approach within a hierarchical Bayesian model framework. Physiologically, plausible a posteriori distributions of model parameters including insulin sensitivity, time-to-peak insulin action, time-to-peak gut absorption, and carbohydrate bioavailability, and good model fit were observed. Day-to-day variability of model parameters was estimated in the range of 38–79% for insulin sensitivity and 27–48% for time-to-peak of insulin action. In conclusion, a linear Bayesian hierarchical approach is feasible to describe a 12-week glucose–insulin relationship using conventional clinical data. The model may facilitate in silico testing to aid the development of closed-loop insulin delivery systems.
