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Abstract
BackgroundDue 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.ResultsA 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) SI index, insulin sensitivity is directly represented by the free parameter KxgI 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%) KxgI from the SDM, 20 out of 40 having identifiable SI from the MM. KxgI correlates well with the inverse of the HOMA-IR index, while SI correlates only when excluding five subjects with extreme SI values. With the exception of these five subjects, the SDM and MM derived indices correlate very well (r = 0.93).ConclusionThe 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.
Highlights
Due to the increasing importance of identifying insulin resistance, a need exists to have a reliable mathematical model representing the glucose/insulin control system
The best model under the Akaike Information Criterion (AIC) criterion was model A, which performed significantly better than either model B or C, which in turn performed significantly better than model D
Coefficients of variation for all parameters in all subjects were found to be smaller than 52%, except: for parameter τg, which in 5 subjects was estimated to about zero, producing a large CV, and which otherwise exhibited a large CV in 13 other subjects; for parameter γ, in those 3 subjects for whom it was estimated at a value less than 1 as well as for another single subject; and for parameter Kxi in 2 subjects
Summary
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. Due to its relatively simple structure and to its great clinical importance, the glucose/insulin system has been the object of repeated mathematical modeling attempts [1223,23-30]. The model formulation, while applicable to the standard IVGTT, should logically and extend to model other often envisaged experimental procedures, like repeated glucose boli, or infusions. A simple, discrete Single Delay Model ("the discrete SDM") of both feedback control arms of the glucose-insulin system during an IVGTT has already been validated as far as its formal properties are concerned [31,32]
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