Articolo in rivista, 2023, ENG, 10.1016/j.cnsns.2023.107554

Order estimation for a fractional Brownian motion model of glucose control

Simona Panunzi; Alessandro Borri; Laura D'Orsi; Andrea De Gaetano

CNR-IASI Biomathematics Laboratory, National Research Council of Italy, Rome, Italy; CNR-IASI Research Unit, National Research Council of Italy, L'Aquila, Italy; CNR-IRIB, Institute of Biomedical Research and Innovation, National Research Council of Italy, Palermo, Italy; Department of Biomatics, Óbuda University, Budapest, Hungary

When a subject is at rest and meals have not been eaten for a relatively long time (e.g. during the night), presumably near-constant, zero-order glucose production occurs in the liver. Glucose elimination from the bloodstream may be proportional to glycemia, with an apparently first-order, linear elimination rate. Besides glycemia itself, unobserved factors (insulinemia, other hormones) may exert second and higher order effects. Random events (sleep pattern variations, hormonal cycles) may also affect glycemia. The time-course of transcutaneously, continuously measured glycemia (CGM) thus reflects the superposition of different orders of control, together with random system error. The problem may be formalized as a fractional random walk, or fractional Brownian motion. In the present work, the order of this fractional stochastic process is estimated on night-time CGM data from one subject.

Communications in nonlinear science & numerical simulation 127

Keywords

Glucose/Insulin, Stochastic Differential Equations, Fractional Brownian motion, Estimation

CNR authors

D Orsi Laura, De Gaetano Andrea, Panunzi Simona, Borri Alessandro

CNR institutes

IASI – Istituto di analisi dei sistemi ed informatica "Antonio Ruberti", IRIB – Istituto per la Ricerca e l'Innovazione Biomedica