A discrete Single Delay Model for the Intra-Venous Glucose Tolerance Test

Abstract

Background

Due to the increasing importance of identifying insulin resistance, a need exists to have a reliable mathematical model representing the glucose/insulin control system. Such a model should be simple enough to allow precise estimation of insulin sensitivity on a single patient, yet exhibit stable dynamics and reproduce accepted physiological behavior.

Results

A new, discrete Single Delay Model (SDM) of the glucose/insulin system is proposed, applicable to Intra-Venous Glucose Tolerance Tests (IVGTTs) as well as to multiple injection and infusion schemes, which is fitted to both glucose and insulin observations simultaneously. The SDM is stable around baseline equilibrium values and has positive bounded solutions at all times. Applying a similar definition as for the Minimal Model (MM) S _I index, insulin sensitivity is directly represented by the free parameter K _xgI of the SDM.

In order to assess the reliability of Insulin Sensitivity determinations, both SDM and MM have been fitted to 40 IVGTTs from healthy volunteers. Precision of all parameter estimates is better with the SDM: 40 out of 40 subjects showed identifiable (CV < 52%) K _xgI from the SDM, 20 out of 40 having identifiable S _I from the MM. K _xgI correlates well with the inverse of the HOMA-IR index, while S _I correlates only when excluding five subjects with extreme S _I values. With the exception of these five subjects, the SDM and MM derived indices correlate very well (r = 0.93).

Conclusion

The SDM is theoretically sound and practically robust, and can routinely be considered for the determination of insulin sensitivity from the IVGTT. Free software for estimating the SDM parameters is available.