@MASTERSTHESIS\{IMM2013-06551,
    author       = "A. H. Hansen",
    title        = "PK/{PD} modelling of subcutaneous glucose dynamics",
    year         = "2013",
    school       = "Technical University of Denmark, {DTU} Compute, {E-}mail: compute@compute.dtu.dk",
    address      = "Matematiktorvet, Building 303{-B,} {DK-}2800 Kgs. Lyngby, Denmark",
    type         = "",
    note         = "{DTU} supervisor: Henrik Madsen, hmad@dtu.dk, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "This thesis describes the development and improvement of a physiological system consisting of stochastic differential equations on state-space form that models glucose-insulin dynamics in a Type 1 Diabetes patient. The study is a part of the DiaCon collaboration. The system aims at predicting one patient’s glucose dynamics while resting, without any exogenous inputs positively exciting the response. Traditionally, ordinary differential equations are used in {PK}/{PD} modelling. The incorporation of stochastic differential equations allows a separation of noise into measurement noise, arising from data collection, and system noise such as random biological variation and model deficiencies.
The model parameters are found by maximum likelihood estimation using the tool {CTSM-R}. The Extended Kalman Filter is used to calculate the likelihood function in order to estimate the optimum parameter set, \^. Having estimated a parameter set, physiological and statistical validations are considered for further improvement.
The {CTSM-R} tool allows stochastic modelling of continuous time series giving a unique tool to improve existing models. When approaching the system, focus has been on grey-box modelling. Progression is tracked using statistical methods.
This thesis revealed an error in the {CTSM-R} tool, in the calculation of the initial covariance matrix. This error is now corrected. Specific focus is devoted to maximum a posteriori probability to ensure physiological reliable estimates. Moreover, a combination with autoregressive processes has shown to improve predictions, also when adding multiple output sensors.
The final system of non-linear stochastic differential equations has successfully been used to model glucose-insulin dynamics accurately."
}