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