title: Estimation of secondary effect parameters in glycaemic dynamics using accumulating data from a virtual type 1 diabetic patient.
abstract: Some individuals with type 1 diabetes mellitus find self-managed glycaemic control difficult due to the confounding influence of secondary effects. Stress and sleep deprivation temporarily lower insulin sensitivity (SI), often resulting in hyperglycaemia, while aerobic exercise depletes glucose, leading to hypoglycaemia if treatment is unchanged. This study tests the estimation of these factors and circadian rhythms of SI in noisy data. Sparse, irregular and noisy virtual blood glucose data, mimicking the glycaemic dynamics of an individual with type 1 diabetes, was created via adapted pharmacokinetic-pharmacodynamic models of glucose and insulin that included the impact of the secondary effects. A Gauss-Newton algorithm was used to recover the original model parameters for SI, stress, fatigue and exercise. During longer identification periods, compensation was made for drift in SI. Monte Carlo analyses were undertaken to validate the methods. The coefficient of variation (CV) in all parameters decreased as the data accumulated in proportion to the 1/n rule (R(2) > 99.9%). Relatively small biases from the original parameter values occurred (<1%). Long term drift trends in SI were captured and did not obscure estimation of the secondary effects (biases < 1%, CV approximately equivalent to drift free outcomes). Adherence to the 1/n trend indicates a robust identification method and the ability of accumulating data to override the effect of measurement error. Compensation for SI drift allows viable observation of secondary effects and SI rhythms over longer time periods. Collectively, these outcomes indicate that quality results for identified parameters could be obtained during in vivo studies.
authors.affiliation: Centre for Bioengineering, Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand . Electronic address: erin.mansell@pg.canterbury.ac.nz.
authors.forename: Erin J
authors.initials: EJ
authors.lastname: Mansell
authors.affiliation: Centre for Bioengineering, Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand . Electronic address: paul.docherty@canterbury.ac.nz.
authors.forename: Paul D
authors.initials: PD
authors.lastname: Docherty
authors.affiliation: Centre for Bioengineering, Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand.
authors.forename: Liam M
authors.initials: LM
authors.lastname: Fisk
authors.affiliation: Centre for Bioengineering, Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8140, New Zealand.
authors.forename: J Geoffrey
authors.initials: JG
authors.lastname: Chase
mesh_terms: D001786:Blood Glucose / Q000378:metabolism*; D003922:Diabetes Mellitus, Type 1 / Q000378:metabolism*; D006801:Humans; D008962:Models, Theoretical
chemical_list: D001786:Blood Glucose
keywords: Gauss–Newton; Glycaemic control; Monte Carlo; Parameter identification; Stress; Type 1 diabetes