A Novel Insulin/Glucose Model after a Mixed-Meal Test in Patients with Type 1 Diabetes on Insulin Pump Therapy

Abstract

Current closed-loop insulin delivery methods stem from sophisticated models of the glucose-insulin (G/I) system, mostly based on complex studies employing glucose tracer technology. We tested the performance of a new minimal model (GLUKINSLOOP 2.0) of the G/I system to characterize the glucose and insulin dynamics during multiple mixed meal tests (MMT) of different sizes in patients with type 1 diabetes (T1D) on insulin pump therapy (continuous subcutaneous insulin infusion, CSII). The GLUKINSLOOP 2.0 identified the G/I system, provided a close fit of the G/I time-courses and showed acceptable reproducibility of the G/I system parameters in repeated studies of identical and double-sized MMTs. This model can provide a fairly good and reproducible description of the G/I system in T1D patients on CSII, and it may be applied to create a bank of "virtual" patients. Our results might be relevant at improving the architecture of upcoming closed-loop CSII systems.

Figure 1. Time courses of plasma insulin and glucose levels during the 292 Kcal and 600 Kcal MMTs.

Panels A,B: mean (±SEM) plasma insulin and glucose concentrations at each time point during the 292 Kcal MMT (MMT1) in the 10 study participants. Panels C,D: MMT2, n = 3, MMT = 292 Kcal. Panels E-F: MMT2, n = 3, MMT = 600 Kcal.

Figure 2. The GLUKINSLOOP 2.0 model.

In this schematic representation of the model continuous arrows indicate transformations and dashed ones indicate regulations. Arrows pointing towards grey dots indicate degradation. A more detailed figure and an accompanying thorough explanation of the model are provided in the Supplementary Material (Figure S1).

Figure 3. Mean weighted residuals of the model fit to experimental insulin and glucose time courses during MMT1 and MMT2.

The weighted residuals are a quantitative point-by-point assessment of the goodness-of-fit of the model to the experimental data: a theoretically perfect fit should generate weighted residuals with mean 0 and SD of 1, reflecting the distribution of errors during the experimental sampling. Panels A,B: mean ± SD of weighted residuals at each time point during the 292 Kcal MMT (MMT1) in all 10 study participants. Panels C,D: MMT2, n = 3, MMT = 292 Kcal. Panels E,F: MMT2, n = 3, MMT = 600 Kcal.

Figure 4. The Oral Glucose Input function.

Panels (A–C) show the output of the OGI function layered by different MMTs. The OGI function, i.e. the predicted glucose rate of appearance in the bloodstream at each time point after the MMT ingestion, is provided as mean ± SEM of the individual OGI values for the study patients undergoing the MMT1 and MMT2 and is expressed as mg/Kg/min (see Figure S12 for the same panels expressed as μmol/min). Curves’ shapes and peaks are consistent with literature’s analogous functions. Detailed description of the function can be found in Supplementary Material.