Mathematical modeling of glucose and insulin dynamics in adolescent girls to quantify measures of insulin sensitivity

Abstract

The regulation of plasma glucose is a key component of human metabolism and is largely regulated by insulin that facilitates glucose uptake by tissues. When tissues become more resistant to insulin, glucose concentrations remain elevated longer and more insulin is required to elicit the same physiologic response. Insulin resistance (IR) is a crucial element of the pathology of the metabolic syndrome, which includes increased risk of stroke, heart disease, type 2 diabetes mellitus, and nonalcoholic fatty liver disease (NAFLD). Decreased insulin sensitivity (SI) is associated with pubertal changes, is more prevalent in teenage girls, and obesity is known to further decrease SI. The Oral Minimal Model (OMM) is a differential-equations based model that describes glucose-insulin dynamics during an oral glucose tolerance test (OGTT) to quantify SI . However, the OMM framework was developed for adult data and practical identifiability issues create challenges with applying the models to diverse metabolic phenotypes. This research focuses on extending the OMM framework to describe OGTT data from a group of adolescent girls with obesity. Initial application of OMM in this cohort established OGTT protocol duration dependence of estimates of SI . To better understand which features of the data facilitate robust model parameter identification, we conducted a local sensitivity analysis of the OMM. We found that the model was least sensitive to changes in a subset of parameters and, therefore, these parameters could be difficult to estimate reliably. This finding was confirmed in an uncertainty quantification of OMM whereby we used a Markov Chain Monte Carlo approach to obtain the precision on key parameter estimates. The addition of glucose tracers in the OGTT enables estimation of the rate of appearance of exogenous glucose (Ra_exo), a key input of OMM-type models developed for separately assessing total and hepatic SI. Published methods for approximating Ra_exo had a significant impact on estimates of both total and hepatic SI. To overcome this limitation, we developed an Ra_exo model-independent method to estimate hepatic SI in this population. These methodologies may inform the analysis and adaptation of physiological models for other applications.