Nonparametric Identification of Glucose-Insulin Process in IDDM Patient with Multi-meal Disturbance

Original Contribution
  • 90 Downloads

Abstract

Modern close loop control for blood glucose level in a diabetic patient necessarily uses an explicit model of the process. A fixed parameter full order or reduced order model does not characterize the inter-patient and intra-patient parameter variability. This paper deals with a frequency domain nonparametric identification of the nonlinear glucose-insulin process in an insulin dependent diabetes mellitus patient that captures the process dynamics in presence of uncertainties and parameter variations. An online frequency domain kernel estimation method has been proposed that uses the input–output data from the 19th order first principle model of the patient in intravenous route. Volterra equations up to second order kernels with extended input vector for a Hammerstein model are solved online by adaptive recursive least square (ARLS) algorithm. The frequency domain kernels are estimated using the harmonic excitation input data sequence from the virtual patient model. A short filter memory length of M = 2 was found sufficient to yield acceptable accuracy with lesser computation time. The nonparametric models are useful for closed loop control, where the frequency domain kernels can be directly used as the transfer function. The validation results show good fit both in frequency and time domain responses with nominal patient as well as with parameter variations.

Keywords

System identification Nonparametric model Glucose-insulin interaction Hammerstein model Frequency domain kernels 

References

  1. 1.
    E.D. Lehmann, The diabetes control and complications trial (DCCT): a role for computers in patient education? J. Diabetes Nutr. Metab. 7(5), 308–316 (1994)Google Scholar
  2. 2.
    D.C. Howey, The treatment of diabetes mellitus. J. Med. Pharmacol. 1–9 (2002)Google Scholar
  3. 3.
    R.S. Parker, F.J. Doyle III, N.A. Peppas, A model-based algorithm for BG control in type 1 diabetic patients. IEEE Trans. Biomed. Eng. 46(2), 148–157 (1999)Google Scholar
  4. 4.
    R.S. Parker, F.J. Doyle III, J.H. Ward, N.A. Peppas, Robust H glucose control in diabetes using a physiological model. Bioeng. Food Nat. Prod. 46(12) (2000)Google Scholar
  5. 5.
    A. Sutradhar, A.S. Chaudhuri, Design and analysis of an optimally convex controller in algebraic framework for a micro-insulin dispenser system. J. AMSE France Adv. Model. Anal. Ser. C 57(1–2), 1–14 (2002)Google Scholar
  6. 6.
    A. Sutradhar, A.S. Chaudhuri, Adaptive LQG/LTR controller for implantable insulin delivery system in type-1 diabetic patient. in Proceedings of 3rd International Conference on System Identification and Control Problems, SICPRO’04, Institute of Control Sciences, Moscow, 28–30 January 2004, pp. 1313–1328Google Scholar
  7. 7.
    R. Hovorka, V. Canonico, L.J. Chassin, U. Haueter, M. Massi-Benedetti, M.O. Federici, T.R. Pieber, H.C. Schaller, L. Schaupp, T. Vering, M.E. Wilinska, Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiol. Meas. 25(4), 905–920 (2004)Google Scholar
  8. 8.
    R.S. Parker, F.J. Doyle III, N.A. Peppas, The intervenous route to blood glucose control. IEEE Eng. Med. Biol. 20(1), 65–71 (2001)Google Scholar
  9. 9.
    P. Kovatchev, M. Breton, C.D. Man, C. Cobelli, In silico preclinical trials: a proof of concept in closed-loop control of diabetes. J. Diabetes Sci. Technol. 3(1), 44–55 (2009)Google Scholar
  10. 10.
    I. Cochin, W. Cadwallender, Analysis and Design of Dynamic Systems, 3rd edn, (Addison-Wesley, 1997)Google Scholar
  11. 11.
    R. Guyton, R.O. Foster, J.S. Soeldner, M.H. Tan, C.B. Kahn, J.L. Koncz, R.E. Gleason, A model of glucose–insulin homeostasis in man that incorporates the heterogeneous fast pool theory of pancreatic insulin release. Diabetes 27, 1027–1042 (1978)Google Scholar
  12. 12.
    T. Sorensen, A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes. Ph.D. thesis, Department of Chemical Engineering, MIT, 1985Google Scholar
  13. 13.
    E.D. Lehmann, T. Deutsch, A physiological model of glucose–insulin interaction in type-1 diabetes mellitus. J. Biomed. Eng. 14, 235–242 (1992)Google Scholar
  14. 14.
    C.D. Man, D.M. Raimondo, R.A. Rizza, C. Cobelli, GIM, simulation software of meal glucose–insulin model. J. Diabetes Sci. Technol. 1(3), 323–330 (2007)Google Scholar
  15. 15.
    A. Sutradhar, A.S. Chaudhuri, Linear state-space model of physiological process in a type-1 diabetic patient with closed loop glucose regulation. J. AMSE France Adv. Model. Anal. Ser. C 66(3), 1–18 (2005)Google Scholar
  16. 16.
    J. Li et al., Modeling the glucose–insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays. J. Theoret. Biol. 242, 722–735 (2006)Google Scholar
  17. 17.
    J.D. Chiu et al., Direct administration of insulin into skeletal muscle reveals that the transport of insulin across the capillary endothelium limits the time course of insulin to activate glucose disposal. Diabetes 57(4), 828–835 (2008)Google Scholar
  18. 18.
    M. Sjostrand et al., Delayed transcapillary delivery of insulin to muscle interstitial fluid after oral glucose load in obese subjects. Diabetes 54(1), 152–157 (2005)Google Scholar
  19. 19.
    B. Aussedat, M. Dupire-Angel, R. Gifford, J.C. Klein, G.S. Wilson, G. Reach, Interstitial glucose concentration and glycemia: implications for continuous subcutaneous glucose monitoring. Am. J. Physiol. Endocrinol. Metab. 278(4), E716–E728 (2000)Google Scholar
  20. 20.
    L. Ljung, System Identification: Theory for the User (Prentice-Hall, Englewood Cliffs, 1987)Google Scholar
  21. 21.
    W. Zhao, H. Chen, Recursive identification for Hammerstein systems with ARX subsystem. IEEE Trans. Automat. Control 51(12), 1966–1974 (2006)Google Scholar
  22. 22.
    A. Sutradhar, A.S. Chaudhuri, On-line identification of ARX model for glucose–insulin interaction in a diabetic patient from input–output data. J. Inst. Eng. India ID-85, 1–7 (2004)Google Scholar
  23. 23.
    A. Bhattacharjee, A. Sengupta, A. Sutradhar, Nonparametric modeling of glucose–insulin process in IDDM patient using Hammerstein–Wiener model. in Proceedings of the 11th International Conference on Control, Automation, Robotics and Vision ICARCV 2010, Singapore, 7–10 December 2010Google Scholar
  24. 24.
    T. Westwick, R.E. Kearney, Identification of Nonlinear Physiological Systems (Wiley-Interscience, 2003)Google Scholar
  25. 25.
    G. Budura, C. Botoca, Efficient implementation and performance evaluation of the second order Volterra Filter based on the MMD approximation. WSEAS Trans. Circuits Syst. 7(3), 139–149 (2008)Google Scholar
  26. 26.
    K. Sam Shanmugam, M.T. Jong, Identification of nonlinear systems in frequency domain. IEEE Trans. Aerosp. Electron. Syst. AES-11(6) (1975)Google Scholar
  27. 27.
    G. Bicken, G.F. Carey, R.O. Stearman, Frequency domain Kernel estimation for 2nd-order Volterra models using random multi-tone excitation. VLSI Des. 15(4), 701–713 (2002)Google Scholar
  28. 28.
    A. Bhattacharjee, A. Sutradhar, Frequency domain Hammerstein model of glucose–insulin process in IDDM patient. in Proceedings of the International Conference on Systems in Medicine and Biology (ICSMB 2010), IIT Kharagpur (2010)Google Scholar
  29. 29.
    S.D. Patek, Linear quadratic gaussian-based closed-loop control of type 1 diabetes. J. Diabetes Sci. Technol. 1(6) (2007)Google Scholar

Copyright information

© The Institution of Engineers (India) 2013

Authors and Affiliations

  1. 1.Department of Electrical EngineeringBengal Engineering & Science UniversityShibpur, HowrahIndia
  2. 2.Centre for Healthcare Science and TechnologyBengal Engineering & Science UniversityShibpur, HowrahIndia

Personalised recommendations