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Here, we will review the authors\u2019 work, by putting it into a concise historical background. We will discuss first the parametric portrait provided by the oral minimal models\u2014building on the classical intravenous glucose tolerance test minimal models\u2014to measure otherwise non-accessible key parameters like insulin sensitivity and beta-cell responsivity from a physiological oral test, the mixed meal or the oral glucose tolerance tests, and what can be gained by adding a tracer to the oral glucose dose. These models were used in various pathophysiological studies, which we will briefly review. A deeper understanding of insulin sensitivity can be gained by measuring insulin action in the skeletal muscle. This requires the use of isotopic tracers: both the classical multiple-tracer dilution and the positron emission tomography techniques are discussed, which quantitate the effect of insulin on the individual steps of glucose metabolism, that is, bidirectional transport plasma-interstitium, and phosphorylation. Finally, we will present a cellular model of insulin secretion that, using a multiscale modeling approach, highlights the relations between minimal model indices and subcellular secretory events. In terms of maximal models, we will move from a parametric to a flux portrait of the system by discussing the triple tracer meal protocol implemented with the tracer-to-tracee clamp technique. This allows to arrive at quasi-model independent measurement of glucose rate of appearance (Ra), endogenous glucose production (EGP), and glucose rate of disappearance (Rd). Both the fast absorbing simple carbs and the slow absorbing complex carbs are discussed. This rich data base has allowed us to build the UVA\/Padova Type 1 diabetes and the Padova Type 2 diabetes large scale simulators. In particular, the UVA\/Padova Type 1 simulator proved to be a very useful tool to safely and effectively test in silico closed-loop control algorithms for an artificial pancreas (AP). This was the first and unique simulator of the glucose system accepted by the U.S. Food and Drug Administration as a substitute to animal trials for in silico testing AP algorithms. Recent uses of the simulator have looked at glucose sensors for non-adjunctive use and new insulin molecules.<\/jats:p>","DOI":"10.1177\/19322968211015268","type":"journal-article","created":{"date-parts":[[2021,5,25]],"date-time":"2021-05-25T06:42:20Z","timestamp":1621924940000},"page":"1270-1298","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":16,"title":["Minimal and Maximal Models to Quantitate Glucose Metabolism: Tools to Measure, to Simulate and to Run in Silico Clinical Trials"],"prefix":"10.1177","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0169-6682","authenticated-orcid":false,"given":"Claudio","family":"Cobelli","sequence":"first","affiliation":[{"name":"Department of Woman and Child\u2019s Health University of Padova, Padova, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4908-0596","authenticated-orcid":false,"given":"Chiara","family":"Dalla Man","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Padova, Padova, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2021,5,25]]},"reference":[{"key":"bibr1-19322968211015268","doi-asserted-by":"publisher","DOI":"10.1109\/RBME.2009.2036073"},{"key":"bibr2-19322968211015268","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2014.2310514"},{"key":"bibr3-19322968211015268","volume-title":"The Dynamic State of Body Constituents","author":"Schoenheimer R.","year":"1942"},{"key":"bibr4-19322968211015268","doi-asserted-by":"publisher","DOI":"10.2337\/diab.26.11.1016"},{"key":"bibr5-19322968211015268","doi-asserted-by":"publisher","DOI":"10.1063\/1.1697874"},{"key":"bibr6-19322968211015268","volume-title":"Basic Principles of the Tra\u00e7er Method","author":"Sheppard CW.","year":"1962"},{"key":"bibr7-19322968211015268","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(62)86855-6"},{"key":"bibr8-19322968211015268","doi-asserted-by":"publisher","DOI":"10.1038\/1841648b0"},{"key":"bibr9-19322968211015268","doi-asserted-by":"publisher","DOI":"10.1063\/1.1722264"},{"key":"bibr10-19322968211015268","volume-title":"Compartmental Analysis in Biology and Medicine","author":"Jacquez JA.","year":"1972"},{"key":"bibr11-19322968211015268","doi-asserted-by":"publisher","DOI":"10.1152\/ajpregu.1980.239.1.R7"},{"key":"bibr12-19322968211015268","doi-asserted-by":"publisher","DOI":"10.1152\/ajpregu.1984.246.5.R665"},{"key":"bibr13-19322968211015268","doi-asserted-by":"crossref","first-page":"R259","DOI":"10.1152\/ajpcell.1984.246.3.C259","volume":"246","author":"Cobelli C","year":"1984","journal-title":"Am J Physiol"},{"key":"bibr14-19322968211015268","volume-title":"The Mathematical Modeling of Endocrine-Metabolic Systems. 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