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

Abstract

Despite the great progress made in insulin preparation and titration, many patients with diabetes are still experiencing dangerous fluctuations in their blood glucose levels. This is mainly due to the large between- and within-subject variability, which considerably hampers insulin therapy, leading to defective dosing and timing of the administration process. In this work, we present a nonlinear mixed effects model describing the between-subject variability observed in the subcutaneous absorption of fast-acting insulin. A set of 14 different models was identified on a large and frequently-sampled database of lispro pharmacokinetic data, collected from 116 subjects with type 1 diabetes. The tested models were compared, and the best one was selected on the basis of the ability to fit the data, the precision of the estimated parameters, and parsimony criteria. The selected model was able to accurately describe the typical trend of plasma insulin kinetics, as well as the between-subject variability present in the absorption process, which was found to be related to the subject’s body mass index. The model provided a deeper understanding of the insulin absorption process and can be incorporated into simulation platforms to test and develop new open- and closed-loop treatment strategies, allowing a step forward toward personalized insulin therapy.

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

“…One recent study identified a fast-acting insulin absorption by applying a two-stage method consisting of first estimating the model parameters in each subject of the population and, then, assessing the mean vector and the covariance matrix providing a measure of the population variability. 16 Covariates, that is, dependencies of model parameters on subject characteristics such as the body mass index, the height or the age of the patient, as well as correlation between model parameters are also estimated. The approach used is the nonlinear mixed effects (NLME) modeling.…”

The Minimally-Invasive Oral Glucose Minimal Model: Estimation of Gastric Retention, Glucose Rate of Appearance, and Insulin Sensitivity From Type 1 Diabetes Data Collected in Real-Life Conditions

“…The MI-OMM model couples the R-OMM described in Eqs. 1-3, with the descriptions of subcutaneous absorption of fast-acting insulin analogues [22], [23] (Section II-C.1), and plasma-interstitium glucose kinetics [24], [25] (Section II-C.2) (Fig 2 , panel B). The incorporation of these modules extended the usability of the R-OMM to non-hospitalized experimental settings, since it allowed describing CGM data as function of subcutaneous insulin infusion rate and the ingested amount of carbohydrates while keeping the model ability to provide parameters and variables with a clear physiological meaning.…”

“…1) Subcutaneous insulin absorption and plasma insulin kinetic model: The subcutaneous insulin absorption model [22], [23], coupled with a single-compartment model of insulin kinetics in plasma [26], is described by the following differential equations:…”

“…Measurements noise on SMBG data, w(t), was assumed to be independent, Gaussian with constant CV=2%. To facilitate the a posteriori identifiability, model parameters were estimated using a Bayesian Maximum A Posteriori estimator [29], with the a priori probability density function assumed to be log-normally distributed, with known mean µp and covariance matrix Σp of the log-transformed parameters, derived from the literature [13], [16], [23], [30]. In summary, the objective function to minimize was:…”

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

“…In particular, the critically important process of SC glucose transport was described by the so-called “triangular model,” as presented in Figure 1b. 68 With this technology, any meal and insulin delivery scenario could be pilot-tested very efficiently—a 24-hour period of closed-loop control is simulated in under 2 seconds. We need to emphasize, however, that good in silico performance of a control algorithm does not guarantee in vivo performance—it only helps test extreme situations and the stability of the algorithm and rule out inefficient scenarios.…”