@MASTERSTHESIS\{IMM2002-0874,
    author       = "C. W. Torn{\o}e",
    title        = "Grey-box {PK}/{PD} modelling of insulin",
    year         = "2002",
    keywords     = "insulin, grey-box {PK}/{PD} modelling, stochastic differential  equations, maximum likelihood estimation, extended Kalman filter, euglycaemic clamp study, {IVGTT,} and {OGTT}",
    school       = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/874-full.html",
    abstract     = "Grey-box {PK}/{PD} modelling is presented as a new and promising way of modelling the pharmacokinetics and pharmacodynamics of the in vivo system of insulin and glucose and to estimate model and derived {PK}/{PD} parameters. The concept behind grey-box modelling consists of using a priori physical knowledge along with information from data in the estimation of model parameters.

The grey-box {PK}/{PD} modelling principle is applied to two different insulin studies.

The {PK}/{PD} properties of two types of insulin are investigated in an euglycaemic clamp study where a single bolus of insulin is injection subcutaneously. The effect of insulin on the glucose disappearance is investigated by artificially maintaining a blood glucose concentration close to the normal fasting level. The infused glucose needed to maintain the clamped blood glucose concentration can therefore be used as a measure for the glucose utilization. The {PK} and {PD} parameters are successfully estimated simultaneously thereby describing the uptake, distribution, and effect of two different types of insulin.

The glucose tolerance tests are used for assessing the glucose tolerance of possible diabetic patients. The intravenous glucose tolerance test (IVGTT) is modelled using Bergman's `Minimal Model' from where metabolic indices are estimated and compared for normal glucose tolerant and impaired glucose tolerant subjects. The grey-box estimates of the system noise parameters using {CTSM} indicate that the minimal model of glucose kinetics is too simple and should preferably be revised. The estimated metabolic indices from the {IVGTT} are compared with previously published results using MinMod and further compared with those from an oral glucose tolerance test (OGTT). The derived {OGTT} models are inaccurate and not suitable for predicting the indices from an {IVGTT}."
}