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Objectives: Extension of a disease model describing the regulation of the glucose-insulin system after an intravenous glucose tolerance test (IVGTT) to the oral glucose tolerance test (OGTT).

Background: Since the 1960s, several attempts have been made to describe the glucose-insulin system with mathematical models [e.g. 1-3]. Such models have been used for the characterization of disease states (primarily with respect to diabetes mellitus) as well as for drug development. Most of the models published so far focus on either glucose or insulin while treating the other variable as known input. As feedback mechanisms play a crucial role in the glucose-insulin system, simultaneous modeling of both variables should be preferred [4]. A project aiming at developing an integrated mechanism-based model that can describe and simulate glucose and insulin concentration-time profiles following different types of glucose provocation experiments in healthy volunteers and in type II diabetic patients is currently under development at the University of Uppsala and Roche Basel. This work is part of the overall project.

Methods: The 9-compartment model describing the time courses of glucose and insulin following i.v. glucose administration developed by Silber et al. [5] was used as a starting point. This model was developed based on physiological knowledge of the glucose-insulin system. In brief, it consisted of two-compartment disposition submodels for glucose and labeled glucose with endogenous production and insulin-dependent and insulin-independent elimination. The insulin submodel was a one-compartment disposition model with endogenous production, distinguishing between a fast primary and a slow secondary release phase, and linear elimination. Feedback loops were incorporated for the regulation of the production of endogenous glucose and insulin, both depending on blood glucose concentrations, and for the regulation of glucose elimination depending on insulin concentrations. The delay of action of these regulations was mediated through effect compartments.

Concentration versus time data was modeled simultaneously by non-linear mixed effect modeling using NONMEM (version VI beta). Drug free data collected after OGTT and insulin modified IVGTT from 42 patients was used. For the OGTT, patients were required to drink a solution of 75 g dextrose in 300 ml of juice within 5 minutes. Six blood samples for the determination of plasma glucose and insulin were collected pre-dose and until 240 minutes after the glucose load. An IVGTT was performed in the same subjects on the following day. A total of 300 mg glucose per kg body weight of a glucose solution enriched with 13 ± 5 % of stable labeled glucose ([6,6-²H₂] glucose) was infused intravenously within 30 seconds. An i.v. infusion of 0.05 U of insulin per kg body weight was given over a period of 5 minutes starting 20 minutes after the glucose load. Thirty-four blood samples were collected pre-dose and until 240 minutes post-dose for the measurement of insulin, stable-labeled glucose and total glucose concentrations.

Results and Discussion: The absorption phase of glucose following the OGTT was adequately described by extending the IVGTT model with a flexible absorption model using transit compartments [6] and a first-order absorption. A similar delay model was used to account for the insulin secretion observed after the OGTT.

The main deviating parameters between IVGTT and OGTT were the first-phase insulin secretion and the insulin-dependent glucose elimination which were both higher after the OGTT. First-phase insulin secretion after i.v. glucose administration hardly occurred in patients at all, whereas following oral glucose administration, it was significant. This result was in line with previous findings in the literature, stating that glucose administration via the gastrointestinal tract has a potentiating effect on insulin secretion [7]. This potentiating effect of oral glucose administration is known to be related to the release of the insulin secretagogue GLP-1 (glucagon-like peptide-1) from the gastrointestinal tissues [8,9]. After the OGTT, the estimated insulin-dependent clearance of glucose was found to be 2-3 fold higher compared to the IVGTT. Higher insulin-dependent glucose disposal after an OGTT compared to an IVGTT has already been observed in previous works [10,11]. This may be due to gastrointestinal factors or first-pass effects enhancing insulin sensitivity in the liver or the muscle tissue that remain to be identified.

Diagnostic plots showed that the model described the data very well. All parameters were well estimated (CV < 25%), residual errors were approximately 5% CV for glucose and labeled glucose, and 29% for insulin. The model was also found to adequately simulate glucose and insulin concentration-time profiles in diabetic patients following intravenous and oral glucose tolerance tests.

Conclusions: The disease model developed previously on IVGTT data was successfully extended to OGTT data. The next step will be to further expand this model to describe other types of glucose excursions such as meal tests. This present model extends to previous modeling of the glucose insulin system as it provides the first integrated model for insulin and glucose following an OGTT, and it simultaneously addresses more than one type of provocation.

The ability of this model to distinguish between endogenous glucose production and administered glucose on the one hand, and between insulin-dependent and insulin-independent glucose elimination on the other hand, especially after an OGTT, could be very useful in drug development in the future. In particular, it might be a valuable tool for proof of concept, i.e. support for hypothesized mechanisms of action. In addition, this model could provide good estimates of inter- and intra-patient variability within a type II-diabetic population. Moreover, it might be used to quantify drug effects and to optimize the design of future clinical trials.

References:
[1] Bergman RN, Ider YZ, Bowden CR, Cobelli C. Quantitative estimation of insulin sensitivity. Am J Physiol. 1979; Jun;236(6):E667-77.
[2] Avogaro A, Bristow JD, Bier DM, Cobelli C, Toffolo G. Stable-label intravenous glucose tolerance test minimal model. Diabetes. 1989 Aug; 38(8):1048-55.
[3] Vicini P, Caumo A, Cobelli C. The hot IVGTT two-compartment minimal model: indexes of glucose effectiveness and insulin sensitivity. Am J Physiol. 1997 Nov;273(5 Pt 1):E1024-32.
[4] De Gaetano A, Arino O. Mathematical modelling of the intravenous glucose tolerance test. J Math Biol. 2000 Feb; 40(2):136-68.
[5] Silber et al. A Disease Model for the Regulation of the Glucose-Insulin System. Poster at PAGE 2004 (further poster on the topic will be presented at PAGE 2005).
[6] Savic et al. Evaluation of a transit compartment model versus a lag time model for describing drug absorption delay. Oral presentation at PAGE 2004.
[7] Creutzfeldt W. The incretin concept today. Diabetologia 1979 Feb; 16(2):75-85.
[8] Drucker DJ. Glucagon-like peptides. Diabetes 1998 Feb;  47(2):159-69.
[9] Holst JJ, Gromada J, Nauck MA. The pathogenesis of NIDDM involves a defective expression of the GIP receptor. Diabetologia 1997 Aug; 40(8):984-6.
[10] Caumo A, Bergman RN, Cobelli C. Insulin sensitivity from meal tolerance tests in normal subjects: a minimal model index. J Clin Endocrinol Metab. 2000 Nov;85(11):4396-402.
[11] Thomaseth K, Pavan A, Pacini G, Kautzy-Willer A, Avogaro A. Mathematical Models of Glucose and Free Fatty Acids Kinetics During Glucose Tolerance Tests. Presentation at WMC 2003, International Conference on Health Sciences Simulation, Orlando, Florida, Jan 19-23, 2003.