Modeling Day-to-Day Variability of Glucose-Insulin Regulation Over 12-Week Home Use of Closed-Loop Insulin Delivery

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 39.9 ± 9.5 years, BMI 25.4 ± 4.4kg/m2, HbA1c 8.4 ± 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.