**5. Conclusions**

In this work, we propose an extension of the MINMOD model [21] to simulate the circulating glucose evolution during OGTT. We fitted OGTT experimental results performed on rats at different ages after cadmium exposure through their mothers. Using these fitted models, we checked various different hypotheses on the effect of cadmium on the glucose response, by comparing the implementation of these hypotheses in the model to the experimental OGTT results for rats exposed to cadmium.

These simulations indicate that dams' exposure to cadmium negatively affects the slow phase of insulin release in response to glucose in pups at weaning. For the other experimental results at PND26 and PND60, there are no significant differences, ye<sup>t</sup> the modeling approach agrees with the proposed long-lasting effects of cadmium in young animals, long after the indirect exposure via their mothers has ceased.

The results of this study may be extended by the development of a more complex model to better approximate the glucose appearance rate in the context of an OGTT, as well as the mechanism affected by Hypothesis 3.1. For this purpose, the comprehensive modeling of metabolism leading to insulin secretion [33] should be included when relevant experimental data become available. In this paper, we only propose a single fitting parameter set, but probing more complete datasets with more exhaustive and costly methods should be performed in order to further assert our conclusions. Finally, this model has only fitted the experimental glucose response, but not the evolution of insulin plasma concentration over time during OGTT in young rats: combining such more extensive datasets would be important to develop the modeling approach to be used in a more quantitative manner.

**Author Contributions:** Methodology, A.R. and E.F.; Software, A.R.; Formal analysis, A.R. and E.F.; Resources, E.F. and J.-M.M.; Writing—original draft preparation, A.R.; Writing—review and editing, E.F. and J.-M.M.; Supervision, E.F.; Project administration, E.F. and J.-M.M.; and Funding acquisition, E.F. and J.-M.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported in part by a gran<sup>t</sup> from Agence Nationale de la Recherche ANR-13-CESA-008-Cadmidia.

**Conflicts of Interest:** The authors declare no conflict of interest.
