title: A data driven nonlinear stochastic model for blood glucose dynamics.
abstract: The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.
authors.affiliation: School of Engineering, University of Warwick, UK.
authors.forename: Yan
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Department of Primary Care Health Sciences, Oxford University, UK.
authors.forename: Tim A
authors.initials: TA
authors.lastname: Holt
authors.affiliation: School of Engineering, University of Warwick, UK. Electronic address: n.khovanova@warwick.ac.uk.
authors.forename: Natalia
authors.initials: N
authors.lastname: Khovanova
mesh_terms: D000328:Adult; D000368:Aged; D001786:Blood Glucose / Q000032:analysis*; D016022:Case-Control Studies; D003922:Diabetes Mellitus, Type 1 / Q000097:blood; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D017711:Nonlinear Dynamics; D013269:Stochastic Processes
chemical_list: D001786:Blood Glucose
keywords: Blood-glucose dynamics; Data-driven models; Diabetes mellitus; Nonlinear systems; Stochastic systems; System identification