A model of glucose clearance to improve the description of glucose homeostasis
Roberto Bizzotto (1), Andrea Natali (2), Amalia Gastaldelli (3), Elza Muscelli (2), Attila Brehm (4), Michael Roden (5,6,7), Ele Ferrannini (2), Andrea Mari (1)
(1) Institute of Biomedical Engineering, National Research Council, Padova, Italy; (2) Department of Internal Medicine, University of Pisa School of Medicine, Pisa, Italy; (3) Institute of Clinical Physiology, National Research Council, Pisa, Italy; (4) Medical Department, Hanusch Hospital, Vienna, Austria; (5) Department of Endocrinology and Diabetology, Medical Faculty, Heinrich-Heine University, Düsseldorf, Germany; (6) Institute for Clinical Diabetology, German Diabetes Center, Düsseldorf, Germany; (7) German Center of Diabetes Research, Partner Düsseldorf, Germany
Objectives: Glucose homeostasis models have been developed as tools for the clinical development of glucose-lowering drugs . The description of the known dependence of glucose clearance (GCL) on glycaemia  was however not included in these models and never quantitatively analysed. This work aims at modelling GCL in a wide range of clinical settings and individual phenotypes.
Methods: Data were obtained from a three-step hyperglycaemic clamp (N=8) , a two-step euglycaemic hyperinsulinaemic clamp (N=8) , paired oral glucose test (OGTT) and euglycaemic hyperinsulinaemic clamp in the same volunteers (N=8), a mixed-meal test (N=91) , and paired mixed-meal test and hyperinsulinaemic hyperglycaemic clamp in the same volunteers (N=8) . The participants involved in the tests had normal or impaired glucose tolerance or type 2 diabetes. A model (A) was developed based on a circulatory model of glucose kinetics  and a model for GCL based on basic notions of glucose transport. Glucose utilization was modelled as a Michaelis-Menten function of glucose concentration with constant Km and insulin-controlled Vmax. Vmax was expressed as a Hill function of insulin at the site of action. Population and individual model parameters were estimated on glucose tracer data with Monolix 4.3.2. A prototypical glucose homeostasis model (B) was then set up by adding a b-cell  and an insulin kinetics  submodel. Model B was used to simulate an OGTT and a constant insulin infusion (310 pmol min-1 m-2), including or excluding the glucose effect on GCL from model A.
Results: Estimation of model A parameters provided a good fit of the data. Individual parameter estimates were similarly distributed in the different tests. GCL suppression with high glycaemia was in qualitative agreement with the literature. In the typical subject, glucose clearance at an insulin concentration of 500 pmol/l was reduced from 227 to 148 ml min-1m-2 when glucose was raised from 5 to 10 mmol/l. Including vs. excluding the glucose effect on GCL produced an increase in maximum glucose during OGTT of 0.6 mmol/l and a decrease in steady state glycaemia after insulin infusion of 1.0 mmol/l.
Conclusions: In contrast to classical models that ignore the effects of glucose on GCL, our model reproduces specific and relevant features observed with concomitant hyperinsulinaemia and hyperglycaemia. This model is expected to improve the representation of glucose homeostasis, and to produce more reliable predictions of drug effects.
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