Structural identifiability and indistinguishability analyses of the Minimal Model and a Euglycemic Hyperinsulinemic Clamp model for glucose–insulin dynamics

Abstract Many mathematical models have been developed to describe glucose–insulin kinetics as a means of analysing the effective control of diabetes. This paper concentrates on the structural identifiability analysis of certain well-established mathematical models that have been developed to charact...

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Bibliographic Details
Published in:	Computer methods and programs in biomedicine Vol. 104; no. 2; pp. 120 - 134
Main Authors:	Chin, S.V, Chappell, M.J
Format:	Journal Article
Language:	English
Published:	Ireland Elsevier Ireland Ltd 01-11-2011
Subjects:	Blood Glucose - metabolism Clamp Glucose Clamp Technique Humans Hyperinsulinism - blood Insulin - blood Internal Medicine Intravenous glucose tolerance test (IVGTT) Minimal Model Models, Theoretical Other Parameter estimation Structural identifiability Structural indistinguishability Intravenous glucose tolerance test (IVGTT) Clamp Parameter estimation Structural identifiability Structural indistinguishability Minimal Model
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Summary:	Abstract Many mathematical models have been developed to describe glucose–insulin kinetics as a means of analysing the effective control of diabetes. This paper concentrates on the structural identifiability analysis of certain well-established mathematical models that have been developed to characterise glucose–insulin kinetics under different experimental scenarios. Such analysis is a pre-requisite to experiment design and parameter estimation and is applied for the first time to these models with the specific structures considered. The analysis is applied to a basic (original) form of the Minimal Model (MM) using the Taylor Series approach and a now well-accepted extended form of the MM by application of the Taylor Series approach and a form of the Similarity Transformation approach. Due to the established inappropriate nature of the MM with regard to glucose clamping experiments an alternative model describing the glucose–insulin dynamics during a Euglycemic Hyperinsulinemic Clamp (EIC) experiment was considered. Structural identifiability analysis of the EIC model is also performed using the Taylor Series approach and shows that, with glucose infusion as input alone, the model is structurally globally identifiable. Additional analysis demonstrates that the two different model forms are structurally distinguishable for observation of both glucose and insulin.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0169-2607 1872-7565
DOI:	10.1016/j.cmpb.2010.08.012