Structural identifiability and indistinguishability analyses of glucose-insulin models

In this thesis, the structural identifiability analyses of established and novel glucose-insulin models was performed, to determine whether the models are globally structurally identifiable with the observations available. Structural identifiability analysis is an essential step in the modelling process and a key prerequisite to experimental design and parameter estimation. Analyses were performed assuming observations of both glucose and insulin concentrations on two versions of the well-cited Minimal Model (MM), the Original Minimal Model (OMM) and Extended Minimal Model (EMM) for the modelling of the responses to an Intravenous Glucose Tolerance Test (IVGTT); a Euglycemic Hyperinsulinemic Clamp model and two novel modified versions of the MM, a Closed-Loop Minimal Model (CLMM) and a Double-Pole in Closed-Loop Minimal Model (DPCLMM), when the models describe a complete course of glucose-insulin dynamics during an IVGTT. The CLMM proved to be unidentifiable so a reparameterisation procedure was performed on this model, yielding a globally structurally identifiable reparameterised model. Parameter estimation using these models was also performed for sets of IVGTT and glucose clamp data. The results of the parameter estimation demonstrated that global structural identifiability does not as always guarantee numerical identifiability, or vice versa. A structural indistinguishability analysis was also performed to compare the MM and the CLMM, given the same observations, where it was shown that both models are distinguishable over both pre- and post- insulin switching phases. This is the first time that all such analyses have been performed on these specific model structures. The generic and numerical results obtained demonstrate issues that may arise in practice when attempting to calculate insulin sensitivity when using such models.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Structural identifiability and indistinguishability analyses of the minimal model and a euglycemic hyperinsulinemic clamp model for glucose–insulin dynamics

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 Hyper-insulinemic 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