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

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

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.

References

  1. A. M. Albisser, B. S. Leibel, T. G. E. e. a. An artificial endocrine pancreas. Diabetes, 23:389-396.
  2. Albisser, A. M. Intelligent instrumentation in diabetes management. CRC Crit. Rev. Biomed. Eng., 17:1-24.
  3. C. Hespel, J. P. Hespel, E. M. G. J. G. F. B. (2000). Algebraic identification: Application to insulin infusion. ISGIID'2000 Evian.
  4. E. Renard, G. Costalat, H. C. J. B. (2006). Artificial beta-cell: clinical experience toward an implantable closed-loop insulin delivery system. Diabetes Metabolism, pages 497-502.
  5. F. Benmakrouha, C. H. (2007). Generating formal power series and stability of bilinear systems. 8th Hellenic European Conference on Computer Mathematics and its Applications (HERCMA 2007).
  6. Fliess, M. (1981). Fonctionnelles causales non linéaires et indéterminées non commutatives. Bull . Soc . Math. France, 109:3-40.
  7. Hoang, N. M. (1990). Contribution au développement d'outils informatiques pour résoudre des problèmes d'automatique non linéaire. Master's thesis, Université de LilleI.
  8. J. L. Selam, P. Micossi, F. L. D. e. a. (1992). Clinical trial of programmable implantable insulin pump for type i diabetes. Diabetes Care, 15:877-885.
  9. J. Sjoberg, Q. Zhang, L. L. e. a. (1995). Nonlinear black-box modeling in system identification: a unified overview. Automatica, 31:1691-1724.
  10. M. V. Foursov, C. H. (2002). On formal invertibility of the input/output behavior of dynamical systems. preprint IRISA, 1439.
  11. M. V. Foursov, C. H. (2003). On algebraic modeling and regulation of the behavior of diabetics. Innovative Technologies for Insulin Delivery and Glucose Sensing.
  12. M. V. Foursov, C. Hespel, D. B. J. H. (2004). Nouvelle méthode de modélisation algébrique et de régulation de la glycémie. Infu-Systèmes 21, 3:22-24.
  13. Renard, E. (2003). Closed-loop system with implantable pump and iv sensor. proceedings of the symposium ”Looking to the future”, pages 78-79.
  14. Schutzenberger, M. P. (1961). On the definition of a family of automata. Inform. Contr., 4:245-270.
Download


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