title: Predicting Plasma Glucose From Interstitial Glucose Observations Using Bayesian Methods.
abstract: One way of constructing a control algorithm for an artificial pancreas is to identify a model capable of predicting plasma glucose (PG) from interstitial glucose (IG) observations. Stochastic differential equations (SDEs) make it possible to account both for the unknown influence of the continuous glucose monitor (CGM) and for unknown physiological influences. Combined with prior knowledge about the measurement devices, this approach can be used to obtain a robust predictive model. A stochastic-differential-equation-based gray box (SDE-GB) model is formulated on the basis of an identifiable physiological model of the glucoregulatory system for type 1 diabetes mellitus (T1DM) patients. A Bayesian method is used to estimate robust parameters from clinical data. The models are then used to predict PG from IG observations from 2 separate study occasions on the same patient. First, all statistically significant diffusion terms of the model are identified using likelihood ratio tests, yielding inclusion of [Formula: see text], [Formula: see text], and [Formula: see text]. Second, estimates using maximum likelihood are obtained, but prediction capability is poor. Finally a Bayesian method is implemented. Using this method the identified models are able to predict PG using only IG observations. These predictions are assessed visually. We are also able to validate these estimates on a separate data set from the same patient. This study shows that SDE-GBs and a Bayesian method can be used to identify a reliable model for prediction of PG using IG observations obtained with a CGM. The model could eventually be used in an artificial pancreas.
authors.affiliation: DTU Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark alexanderhhansen@gmail.com.
authors.forename: Alexander Hildenbrand
authors.initials: AH
authors.lastname: Hansen
authors.affiliation: DTU Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark.
authors.forename: Anne Katrine
authors.initials: AK
authors.lastname: Duun-Henriksen
authors.affiliation: DTU Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark.
authors.forename: Rune
authors.initials: R
authors.lastname: Juhl
authors.affiliation: Department of Endocrinology, Hvidovre University Hospital, Hvidovre, Denmark.
authors.forename: Signe
authors.initials: S
authors.lastname: Schmidt
authors.affiliation: Department of Endocrinology, Hvidovre University Hospital, Hvidovre, Denmark.
authors.forename: Kirsten
authors.initials: K
authors.lastname: Nørgaard
authors.affiliation: DTU Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark.
authors.forename: John Bagterp
authors.initials: JB
authors.lastname: Jørgensen
authors.affiliation: DTU Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark.
authors.forename: Henrik
authors.initials: H
authors.lastname: Madsen
keywords: Bayesian methods; PG-IG dynamics; plasma glucose dynamics; stochastic differential equations; stochastic gray-box modeling; type 1 diabetes mellitus