Improving the precision of model parameters using model based signal enhancement and the linear minimal model following an IVGTT in the healthy man

• Published in: Applied mathematics and computation Vol. 196; no. 1; pp. 185 - 192
• Main Authors: Fernandez, Margarita, Acosta, Dionisio, Quiroz, Adolfo
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.02.2008; Elsevier
• Subjects: Algebra; Calculus of variations and optimal control; Exact sciences and technology; Glucose; Insulin; Intravenous glucose tolerance test; Mathematical analysis; Mathematics; Minimal model; Non-parametric testing; Number theory; Numerical analysis; Numerical analysis. Scientific computation; Sciences and techniques of general use; Sensitivity index; Signal processing; Non-parametric testing; Minimal model; Intravenous glucose tolerance test; Signal processing; Glucose; Insulin; Sensitivity index; Data analysis; Approximation; Fitting; Linear model; Numerical analysis; Applied mathematics; Singular value decomposition
• DOI: 10.1016/j.amc.2007.05.044
• ISSN: 0096-3003

The problem of signal enhancement has been addressed by several authors in the past and continues to be of particular interest in many applications. In this respect, the present authors have been exploring the effect of the model based signal enhancement (MBSE) approach to recover the signal of blood glucose dynamics from noise contaminated measurements collected from seven healthy patients after an intravenous glucose tolerance test (IVGTT). These observations correspond to a system with an impulse–response behaviour for which it is often hypothesized that a sum of exponential signals can be used for modeling the data. The exponential model order has been derived from the singular value decomposition analysis of these data set. A linear version of the classic minimal model, known as the linear minimal model (LMM), has been used to model the patient’s behaviour. After fitting the LMM first to the experimental data and then to the MBSE signal obtained from the exponential modelling approximation, the effect on the precision of the LMM parameters has been statistically assessed. A non-parametric test has been devised to evaluate the significance of the differences between the precision obtained when no MBSE is applied and the precision after MBSE is performed. The results obtained suggest that the precision of the LMM parameters can be improved by more than 50% ( p-value < 0.01) for all the model parameters. In particular, the insulin sensitivity S I and glucose effectiveness S G parameters that are useful diagnostic indices in Type 2 Diabetes Mellitus are improved by 50% and 62% respectively.