Order estimation for a fractional Brownian motion model of glucose control
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 el...
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| Vydané v: | Communications in nonlinear science & numerical simulation Ročník 127; s. 107554 |
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| Hlavní autori: | , , , |
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| Jazyk: | English |
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Elsevier B.V
01.12.2023
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| ISSN: | 1007-5704, 1878-7274 |
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| Abstract | 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.
•We propose a novel order estimation method for fractional stochastic models (FSDE).•We apply the method to a FSDE glucose model fitted from real CGM data.•A scheme for the approximate FSDE integration via finite increments is proposed.•Stochastic correctness of our algorithm in terms of increment covariance is proved.•The accuracy is comparable to other fractional noise integration algorithms. |
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| AbstractList | 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.
•We propose a novel order estimation method for fractional stochastic models (FSDE).•We apply the method to a FSDE glucose model fitted from real CGM data.•A scheme for the approximate FSDE integration via finite increments is proposed.•Stochastic correctness of our algorithm in terms of increment covariance is proved.•The accuracy is comparable to other fractional noise integration algorithms. |
| ArticleNumber | 107554 |
| Author | D’Orsi, Laura Panunzi, Simona Borri, Alessandro De Gaetano, Andrea |
| Author_xml | – sequence: 1 givenname: Simona surname: Panunzi fullname: Panunzi, Simona organization: CNR-IASI Biomathematics Laboratory, National Research Council of Italy, Rome, Italy – sequence: 2 givenname: Alessandro orcidid: 0000-0002-6678-048X surname: Borri fullname: Borri, Alessandro email: alessandro.borri@iasi.cnr.it organization: CNR-IASI Biomathematics Laboratory, National Research Council of Italy, Rome, Italy – sequence: 3 givenname: Laura surname: D’Orsi fullname: D’Orsi, Laura organization: CNR-IASI Biomathematics Laboratory, National Research Council of Italy, Rome, Italy – sequence: 4 givenname: Andrea surname: De Gaetano fullname: De Gaetano, Andrea organization: CNR-IASI Biomathematics Laboratory, National Research Council of Italy, Rome, Italy |
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| Cites_doi | 10.1177/1932296819851790 10.1016/0168-9274(95)00108-5 10.1016/j.diabres.2017.08.005 10.1016/j.aml.2004.05.014 10.1016/j.chaos.2011.12.009 10.3150/13-BEJ568 10.1063/1.529976 10.1137/1010093 10.3892/etm.2021.11097 10.1103/PhysRevE.54.2084 10.1016/j.jtbi.2021.110776 10.1007/s11892-013-0398-4 10.1006/acha.1996.0030 10.1089/dia.2017.0035 10.3150/10-BEJ281 10.1016/j.jmaa.2012.07.062 10.1007/s10955-017-1866-z |
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| Keywords | Stochastic Differential Equations Fractional Brownian motion Estimation Glucose/Insulin |
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