Dynamic modelling of blood glucose concentration in people with type 1 diabetes

Abstract

The behaviour of blood glucose concentration (BGC) in free living conditions is not well understood in people with type 1 diabetes; in particular, the effect of different types of activity experienced in everyday life has not been fully investigated. Better understanding of the effect of major disturbances to BGC can improve treatment regimes and delay or prevent complications associated with diabetes. The current research investigates approaches to modelling BGC, based on blood glucose, physical activity, food and insulin data collected from a Diabetes UK study. Exploratory analysis of the study data found that BGC is non-stationary and exhibits strong autocorrelation, which varies among and within individuals. Analysis of BGC in the frequency domain also highlights indistinct low-frequency periodicities. However, BGC measurements alone are not enough to predict BGC over several hours using autoregressive models. Dynamic linear models are used to model BGC empirically using inputs from measured physical activity, and estimates of glucose and insulin absorption after food intake and injections, respectively, derived from physiological models in the literature. Dynamic linear models are used for parameter learning and predicting BGC over several hours: the models show some capability for predicting BGC for up to one hour, in particular highlighting periods of low and high BGC, but parameter estimates do not comply with established physiological knowledge. A new semi-empirical compartmental model is developed to impose a structure that incorporates well established physiology. A set of differential equations are converted into a probabilistic Bayesian framework, suitable for simultaneous, model-wide parameter estimation and prediction. A simulation study is conducted to determine the feasibility of using Markov chain Monte Carlo methods as a means for parameter estimation, and test performance in the predictive space. The methods show an ability to estimate a subset of the parameters simultaneously with good coverage, robustness to parameter misspecification, and insensitivity to specification of prior distributions. The current research represents a new paradigm for analysing mathematical models of BGC, and highlights important practical and theoretical issues not previously addressed in the quest for an artificial pancreas as treatment for type 1 diabetes.

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Identifiers

ORCID for Sujit K. Sahu: orcid.org/0000-0003-2315-3598

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