A WAY FOR PREDICTING AND MANAGING THE GLYCAEMIC INSTABILITY OF THE DIABETIC PATIENT

Farida Benmakrouha, Christiane Hespel, Mikhail V. Foursov, Jean-Pierre Hespel

2009

Abstract

We study the Bounded-Input-Bounded-Output (BIBO) stability of the system modeling the behavior “insulin delivery/glycaemia” of the diabetic patient, under continuous insulin infusion, continuous glucose monitoring, in order to point out that the patient is entering in a period of stable/unstable equilibrium. The model is a bilinear dynamical system predicting for an interval of 15 minutes, with an average error of 15%. In case of stable equilibrium, the prediction will be valid for a longer time interval, when in case of unstable equilibrium, it will leads one to reduce the time intervals. The BIBO stability is studied by computing the generating series G of the model. This series, generalization of the transfer fuction, is a tool for analyzing the stability of bilinear systems. It is a rational power series in noncommutative variables and by evaluating it, a formal expression of the output in form of iterated integrals is provided. Three cases arise: firstly, the output can be explicitly computed; secondly, the output can be bounded/unbounded if the input is bounded; thirdly, no conclusion seems available about the BIBO stability by using G. We propose a stabilizing constant input h by studying the univariate series Gh.

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Paper Citation


in Harvard Style

Benmakrouha F., Hespel C., Foursov M. and Hespel J. (2009). A WAY FOR PREDICTING AND MANAGING THE GLYCAEMIC INSTABILITY OF THE DIABETIC PATIENT . In Proceedings of the International Conference on Biomedical Electronics and Devices - Volume 1: BIODEVICES, (BIOSTEC 2009) ISBN 978-989-8111- 64-7, pages 335-338. DOI: 10.5220/0001121003350338


in Bibtex Style

@conference{biodevices09,
author={Farida Benmakrouha and Christiane Hespel and Mikhail V. Foursov and Jean-Pierre Hespel},
title={A WAY FOR PREDICTING AND MANAGING THE GLYCAEMIC INSTABILITY OF THE DIABETIC PATIENT},
booktitle={Proceedings of the International Conference on Biomedical Electronics and Devices - Volume 1: BIODEVICES, (BIOSTEC 2009)},
year={2009},
pages={335-338},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001121003350338},
isbn={978-989-8111- 64-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Biomedical Electronics and Devices - Volume 1: BIODEVICES, (BIOSTEC 2009)
TI - A WAY FOR PREDICTING AND MANAGING THE GLYCAEMIC INSTABILITY OF THE DIABETIC PATIENT
SN - 978-989-8111- 64-7
AU - Benmakrouha F.
AU - Hespel C.
AU - Foursov M.
AU - Hespel J.
PY - 2009
SP - 335
EP - 338
DO - 10.5220/0001121003350338