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Figure 2. The efficiency with the different optimizations compared to the standard design. 100 % effeciency indicates no improvement compared to the standard design.

Optimal design of the intravenous glucose tolerance test (IVGTT) in type 2 diabetic patients

Background and Objective Intravenous glucose provocations are very informative for studying the glucose-insulin system. The standard frequently sampled IVGTT design contains approximately 30 blood samples of glucose, insulin and sometimes also labeled glucose during 4 hours following an intravenous bolus dose of glucose. In the insulin modified IVGTT, a 5-minute insulin infusion is given at 20 minutes.

Optimal experimental design is a model based methodology that can be used to increase the efficiency of clinical trials by optimizing the sampling schedule or other design parameters, e.g. dose. As a suitable model for describing the IVGTT is available it was used for optimization of study design with respect to precision of parameter estimates.

The objective of this study was to evaluate the possibilities of an improved study design of the insulin modified IVGTT in type 2 diabetic patients.

Figure 1. Model of glucose and insulin regulation in type 2 diabetic patients developed by Silber et al.1 The model contains sub-models for glucose, insulin and labeled glucose (not shown) as well as control mechanisms for glucose uptake and insulin secretion.

ResultsThe results show that the design of the insulin modified IVGTT can be substantially improved by the use of an optimal design compared to the standard design, see table 1 and figure 2. Despite the comparably low number of samples included the predicted uncertainty of parameter estimates was low in all tested cases.

The single largest improvement of the design was given when the insulin dose was modified, giving an increased efficiency of 304% compared to the standard design. With that design it is possible to reduce the number of individuals in a study to 1/3 compared to when the basic design is used. Optimizing on the insulin infusion resulted in only minor improvements. When hot glucose was excluded the efficiency of the standard design was only 21% compared to the standard design, indicating that hot glucose contains much information. Optimizing on sampling times resulted in modest improvement of efficiency indicating that already 10 samples provide an informative design and that ”the room for improvement” is limited. When both glucose and insulin doses were optimized simulatenously this resulted in high doses of both despite the boundaries on glucose concentration.

MethodsA previously published model developed for glucose and insulin regulation in type 2 diabetic patients was implemented in the optimal design software PopED1,2 (see figure 1). The standard experimental design was a 0.3 g/kg intravenous glucose dose at time 0 followed by an insulin infusion of 50 mU/kg at 20 minutes. In order to decrease run times the number of samples was reduced to 10 (0, 2, 10, 15, 30, 45, 70, 100, 150, 240 minutes).

Several aspects of the study design of the insulin modified IVGTT were evaluated including; (1) glucose dose, (2) insulin dose (start and stop time and total insulin dose), (3) combination of glucose and insulin dose, (4) sampling times of a reduced sampling schedule, and (5) exclusion of labeled glucose. Constraints were incorporated to avoid prolonged hyper- and/or hypoglycemia. The lower constraint was set to a glucose concentration of 54mg/dL during the entire experiment and the upper constraint was set to 360 mg/dL after 30 minutes (approximately twice the baseline glucose concentration). The constraints on glucose concentrations were incorporated in order to restrict the search space with the lower boundary restricting the maximum insulin dose and the upper boundary the maximum glucose dose allowed.

Efficiency was calculated as a measure of the improvement with an optimal design compared to the basic design according to equation 1. The determinant of the Fisher Information Matrix (FIM) of the optimal design was compared to the FIM of the basic design correcting for the number of parameters in the model.

Npar

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ConclusionWe conclude that improvement can be made to the design of the insulin modified IVGTT. Also when the number of samples is reduced parameters are predicted to be estimated with a high certainty. This illustrates how complex provocation experiments can be improved by sequential modeling and optimal design.

Authors:

Hanna E Silber*,

Joakim Nyberg,

Andrew Hooker,

Mats O Karlsson

Institution:

Department of Pharmaceutical Biosciences,

Division of Pharmacokinetics and Drug Therapy,

Uppsala University, Uppsala, Sweden

*hanna.silber@farmbio.uu.se

References:

1. Silber H E, Jauslin P M, Frey N, Gieschke R, Simonsson U S H, and Karlsson M O. An integrated model for glucose and insulin regulation in healthy volunteers and type 2 diabetic patients following intravenous glucose provocations. J Clin Pharmacol 2007; 47: 1159-71.

2. Foracchia M, Hooker A, Vicini P, and Ruggeri A. POPED, a software for optimal experiment design in population kinetics. Comput Methods Programs Biomed 2004; 74: 29-46.

Optimization Standard design Optimal design

Insulin dose 50 mU/kg 264 mU/kg

Insulin start of infusion 20 min 43.3 min

Insulin infusion length 5 min 9.1 min

Insulin dose, start and stop start time=20 min stop time=25 mindose = 50 mU/kg

start time=33.6 min stop time=47.5 mindose = 259.7 mU/kg

Glucose dose 0.3 mg/kg 0.81 mg/kg

Glucose + insulin dose glucose=0.3 mg/kg,insulin=50 mU/kg

glucose=5.4 mg/kg,insulin=442.4 mU/kg

Sampling times 0, 2, 10, 15, 30, 45, 70,100, 150, 240 minutes

2.1, 19.9, 19.9, 24, 43.2, 48, 81.6, 112.1, 240, 240 minutes.

Table 1. Results of optimization