**Theoretical Modeling of Oral Glucose Tolerance Tests Guides the Interpretation of the Impact of Perinatal Cadmium Exposure on the Offspring's Glucose Homeostasis**

#### **Alexandre Rocca 1,2,\*, Eric Fanchon 2,\* and Jean-Marc Moulis 3**


Received: 23 February 2020; Accepted: 6 April 2020; Published: 15 April 2020

**Abstract:** Oral glucose tolerance tests, in which the concentration of glucose is monitored in the circulation over 2 h after ingesting a bolus, probe diabetic or pre-diabetic conditions. The resulting glucose curves inform about glucose turnover, insulin production and sensitivity, and other parameters. However, extracting the relevant parameters from a single complex curve is not straightforward. We propose a simple modeling method recapitulating the most salient features of the role of insulin-secreting pancreatic *β*-cells and insulin sensitive tissues. This method implements four ordinary differential equations with ten parameters describing the time-dependence of glucose concentration, its removal rate, and the circulating and stored insulin concentrations. From the initial parameter set adjusted to a reference condition, fitting is done by minimizing a weighted least-square residual. In doing so, the sensitivity of *β*-cells to glucose was identified as the most likely impacted function at weaning for the progeny of rats that were lightly exposed to cadmium in the perigestational period. Later in life, after young rats received non-contaminated carbohydrate enriched food, differences are more subtle, but modeling agrees with long-lasting perturbation of glucose homeostasis.

**Keywords:** OGTT; minimal model; cadmium; glucose response mechanism
