Modeling Between-Subject Variability in Subcutaneous Absorption of a Fast-Acting Insulin Analogue by a Nonlinear Mixed Effects Approach

Developing the UVA/Padova Type 1 Diabetes Simulator: Modeling, Validation, Refinements, and Utility

Arguably, diabetes mellitus is one of the best quantified human conditions. In the past 50 years, the metabolic monitoring technologies progressed from occasional assessment of average glycemia via HbA1c, through episodic blood glucose readings, to continuous glucose monitoring (CGM) producing data points every few minutes. The high-temporal resolution of CGM data enabled increasingly intensive treatments, from decision support assisting insulin injection or oral medication, to automated closed-loop control, known as the "artificial pancreas." Throughout this progress, mathematical models and computer simulation of the human metabolic system became indispensable for the technological progress of diabetes treatment, enabling every step, from assessment of insulin sensitivity via the now classic Minimal Model of Glucose Kinetics, to in silico trials replacing animal experiments, to automated insulin delivery algorithms. In this review, we follow these developments, beginning with the Minimal Model, which evolved through the years to become large and comprehensive and trigger a paradigm change in the design of diabetes optimization strategies: in 2007, we introduced a sophisticated model of glucose-insulin dynamics and a computer simulator equipped with a "population" of N = 300 in silico "subjects" with type 1 diabetes. In January 2008, in an unprecedented decision, the Food and Drug Administration (FDA) accepted this simulator as a substitute to animal trials for the pre-clinical testing of insulin treatment strategies. This opened the field for rapid and cost-effective development and pre-clinical testing of new treatment approaches, which continues today. Meanwhile, animal experiments for the purpose of designing new insulin treatment algorithms have been abandoned.

Nonlinear Mixed Effects Modeling of Glucagon Kinetics in Healthy Subjects

OBJECTIVE

To date, the lack of a model of glucagon kinetics precluded the possibility of estimating and studying glucagon secretion in vivo, e.g., using deconvolution, as done for other hormones like insulin and C-peptide. Here, we used a nonlinear mixed effects technique to develop a robust population model of glucagon kinetics, able to describe both the typical population kinetics (TPK) and the between-subject variability (BSV), and relate this last to easily measurable subject characteristics.

METHODS

Thirty-four models of increasing complexity (variably including covariates and correlations among random effects) were identified on glucagon profiles obtained from 53 healthy subjects, who received a constant infusion of somatostatin to suppress endogenous glucagon production, followed by a continuous infusion of glucagon (65 ng/kg/min). Model selection was performed based on its ability to fit the data, provide precise parameter estimates, and parsimony criteria.

RESULTS

A two-compartment model was the most parsimonious. The model was able to accurately describe both the TPK and the BSV of model parameters as function of body mass and body surface area. Parameters were precisely estimated, with central volume of distribution V1 = 5.46 L and peripheral volume of distribution V2 = 5.51 L. The introduction of covariates resulted in a significant shrinkage of the unexplained BSV and considerably improved the model fit.

CONCLUSION

We developed a robust population model of glucagon kinetics.

SIGNIFICANCE

This model provides a deeper understanding of glucagon kinetics and is usable to estimate glucagon secretion in vivo by deconvolution of plasma glucagon concentration data.

Hybrid Closed-Loop Control with Ultrarapid Lispro Compared with Standard Insulin Aspart and Faster Insulin Aspart: An In Silico Study

OBJECTIVE

There is room for improvement in the performance of closed-loop regulation algorithms during the prandial period. This in silico study evaluated the efficiency and safety of ultrarapid lispro insulin using the Diabeloop DBLG1® algorithm.

METHODS

We modeled the insulin profile of URLi according to literature data and integrated it to the model used within a simulation platform built from a 60 patients' virtual cohort. We then ran the DBLG1® algorithm in silico with various meal intakes using modeled URLi, Aspart and Faster Aspart. The primary endpoints were glucose metrics (time in 70-180 mg/dL range and time below range).

RESULTS

When insulin time constant values were tuned, time in 70-180 mg/dL range was 69.4 [61.1-75.6] (Aspart) vs 74.7 [65.5-81.5] (URLi). Glucose coefficient of variation was reduced from 34.1 [29.7-37.8] to 28.4 [25.7-34.6]. Time below 70 mg/dL and 54 mg/dL were significantly reduced with URLi, whether or not DBLG1 was specifically tuned to this insulin. Metrics with Faster Aspart were intermediate and did not significantly differ from URLi.

CONCLUSIONS

This simulation study performed on a virtual T1D population suggests that the use of URLi within an unmodified closed-loop DBLG1 regulation algorithm is safe and, with DBLG1 being tuned to this specific insulin type, improved the regulation performances as compared with Aspart. This fact supports the use of such an insulin in clinical investigations.

Modeling Between-Subject Variability in Subcutaneous Absorption of a Long-Acting Insulin Glargine 100 U/mL by a Nonlinear Mixed Effects Approach

Subcutaneous insulin absorption is well-known to vary significantly both between and within subjects (BSV and WSV, respectively). This variability considerably obstacles the establishing of a reproducible and effective insulin therapy. Some models exist to describe the subcutaneous kinetics of both fast and long-acting insulin analogues; however, none of them account for the BSV. The aim of this study is to develop a nonlinear mixed effects model able to describe the BSV observed in the subcutaneous absorption of a long-acting insulin glargine 100 U/mL. Four stochastic models of the BSV were added to a previously validated model of subcutaneous absorption of insulin glargine 100 U/mL. These were assessed on a database of 47 subjects with type 1 diabetes. The best model was selected based on residual analysis, precision of the estimates and parsimony criteria. The selected model provided good fit of individual data, precise population parameter estimates and allowed quantifying the BSV of the insulin glargine 100 U/mL pharmacokinetics. Future model development will include the description of the WSV of long- acting insulin absorption.