Variational Bayesian inference method in stochastic modelling of subcutaneous glucose concentration

Diabetes is a lifelong condition in which the body cannot control blood glucose. Patients living with diabetes must learn to control blood glucose levels to avoid life- threatening situations. Researchers have been working on establishing an effective dynamic model to describe and predict blood glucose concentration levels for more than half a century. Many models have been developed to reflect the complex neuro- hormonal control system, but one of the major challenges remains is how to determine large amounts of parameters in these models while only the glucose concentration time series is provided. We used a top-down data driven approach to establish a stochastic nonlinear model with minimal order and minimal number of parameters tailored for each patient to describe and predict the response of blood glucose concentration to food intake. Various degrees of nonlinearities are considered for three groups of people (the control group, Type I diabetes and Type II diabetes group). Variational Bayesian method is applied to select the best model and infer the needed parameters. The parameters describe the dynamics and characteristics of the underlying physiological processes. Since the mechanisms of the glucose absorption are different for Type I, Type II diabetes and non-diabetic people, different distributions of parameters and noises for these groups are expected. The results from fifteen profiles with 72 hour continuous glucose time series shows that the glucose concentration change during 2 hours after food intake can be modelled by second order linear or nonlinear system for all three groups. The value of the parameters and intensities of the noises vary from peak to peak for a single profile. The analysis of variance for parameters and noise intensities shows significant differences between the control group and both diabetes group. Further comparison with existing models is going to be investigated in the near future