Online Frequency Domain Volterra Model of Glucose-Insulin Process in Type-1 Diabetics

A. Bhattacharjee^1, and A. Sutradhar¹

¹Department of Electrical Engineering, Bengal Engineering and Science University, Shibpur, Howrah, India

Cite this paper:
A. Bhattacharjee and A. Sutradhar. Online Frequency Domain Volterra Model of Glucose-Insulin Process in Type-1 Diabetics. Journal of Biomedical Engineering and Technology. 2014; 2(2):13-20. doi: 10.12691/jbet-2-2-2

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 an online frequency domain kernel estimation method for modeling a nonlinear dynamic system of multivariable glucose-insulin process in a type-1 diabetic patient that captures the process dynamics in presence of uncertainties and parameter variations. The present work proposes a frequency domain kernel estimation of a Volterra model using the harmonic excitation input by taking FFT on the input data sequence from the glucose-insulin process of the patient. Volterra equations up to second order kernels with extended input vector for Volterra model are solved online by adaptive recursive least square (ARLS) algorithm. Twice the length of the extended input vector for the glucose-insulin process is considered for finding the frequency domain kernels that can be directly used as the Volterra transfer function and are useful for closed loop internal model control. The input-output data taken from the 19th order first principle model of the patient in intravenous route, have been used to identify the system with a short filter memory length of M=2 and the validation results have shown good fit both in frequency and time domain responses with nominal patient as well as with intrapatient parameter variations.

Keywords:
System identification nonparametric model glucose-insulin interaction Volterra model frequency domain kernels Volterra transfer function

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	D. C. Howey. “The Treatment of Diabetes Mellitus”; Journal of Medical Pharmacology, pp. 1-9, Feb 2002.
[2]	R. S. Parker, F. J. Doyle III, and N. A. Peppas. “A Model-based Algorithm for BG Control in Type 1 Diabetic Patients”; IEEE. Trans. on Biomedical Engg. Vol. 46, No.2, Feb 1999, pp. 148-157.
[3]	R. S. Parker, F. J. Doyle III, J. H. Ward and N. A. Peppas. “Robust H∞ Glucose Control in Diabetes Using a Physiological Model”, Bioengineering, Food, and Natural Products, Vol. 46, No. 12, December 2000.
[4]	A. Sutradhar and A. S. Chaudhuri; “Design and Analysis of an Optimally Convex Controller in Algebraic Framework for a Micro-insulin Dispenser System”, Journal of AMSE, France, Advances in Modeling & Analysis, Series C, Vol. 57 No. 1-2, 2002, pp. 1-14.
[5]	A. Sutradhar and A. S. Chaudhuri; “Adaptive LQG/LTR Controller for Implantable Insulin Delivery System in Type-1 Diabetic Patient”; Proceedings of 3rd International Conference on System Identification and Control Problems, SICPRO’04, held at Institute of Control Sciences, Moscow, 28-30 January, 2004. pp. 1313-1328.
[6]	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, and M. E. Wilinska, "Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes," Physiological measurement, vol. 25, no. 4, Aug. 2004, pp. 905-920.
[7]	I. Cochin and W. Cadwallender. Analysis and Design of Dynamic Systems, 3e, Addison-Wesley, ©1997.
[8]	B. P. Kovatchev, M. Breton, C. D. Man, and C. Cobelli; “In Silico Preclinical Trials: A Proof of Concept in closed-loop control of diabetes”; Journal of Diabetes Science and Technology, Volume 3, Issue 1, January 2009, pp. 44-55.
[9]	J. R. Guyton, R.O. Foster, J.S. Soeldner, M.H. Tan, C.B. Kahn, JL. Koncz, and R.E. Gleason, “A model of glucose-insulin homeostasis in man that incorporates the heterogeneous fast pool theory of pancreatic insulin release," Diabetes, vol. 27, 1978, pp. 1027-1042.
[10]	J. 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, 1985.
[11]	E. D. Lehmann and T. Deutsch. “A Physiological Model of Glucose-insulin Interaction in Type-1 Diabetes Mellitus”; Jl. of Biomedical Engineering, Vol. 14, May 1992, pp. 235-242.
[12]	C. D. Man, D. M. Raimondo, R. A. Rizza, and C. Cobelli; “GIM, Simulation Software of Meal Glucose–Insulin Model”; Journal of Diabetes Science and Technology, Volume 1, Issue 3, May 2007, pp. 323-330.
[13]	A. Sutradhar and A. S. Chaudhuri; “Linear State-Space Model of Physiological Process in a Type-1 Diabetic Patient with Closed Loop Glucose Regulation”; Journal of AMSE, France, Advances in Modeling & Analysis, Series C, Vol. 66 No. 3, 2005, pp. 1-18.
[14]	J. Li et. al. “Modeling the glucose–insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays”; Journal of Theoretical Biology 242, 2006 Elsevier; pp. 722-735.
[15]	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, April 2008 vol. 57 no. 4, pp. 828-835.
[16]	M. Sjostrand et. al. “Delayed Transcapillary Delivery of Insulin to Muscle Interstitial Fluid After Oral Glucose Load in Obese Subjects”: Diabetes, January 2005 vol. 54 no. 1, pp.152-157.
[17]	B. Aussedat, M. Dupire-Angel, R. Gifford, J. C. Klein, G. S. Wilson, and G. Reach; “Interstitial glucose concentration and glycemia: implications for continuous subcutaneous glucose monitoring” American Journal of physiology Endocrinology and metabolism, April 1, 2000 vol. 278 no. 4 pp. E716-E728.
[18]	R. S. Parker, F. J. Doyle III, and N. A. Peppas.”The intervenous route to blood glucose control”; IEEE Engineering in Medicine and Biology, Jan/Feb 2001; pp. 65-71.
[19]	L. Ljung, System identification: Theory for the user, Prentice-Hall (Englewood Cliffs, NJ), 1987
[20]	W. Zhao and H. Chen, Recursive identification for Hammerstein systems with ARX subsystem, IEEE Trans. Automat. Contr., 51(12), 2006, 1966-1974.
[21]	A. Sutradhar and A. S. Chaudhuri; “On-line Identification of ARX model for Glucose-Insulin Interaction in a Diabetic Patient from Input-Output Data”; Journal of Institution of Engineers (India), Vol. ID-85, May 2004. pp. 1-7.
[22]	A. Bhattacharjee, A. Sengupta and A. Sutradhar, “Nonparametric Modeling of Glucose-Insulin Process in IDDM Patient using Hammerstein-Wiener Model”; Proceedings of the 11th International Conference on Control, Automation, Robotics and Vision (ICARCV 2010), Singapore, 07-10 December 2010.
[23]	D. T. Westwick and R. E. Kearney; “Identification of Nonlinear Physiological Systems”; -Wiley-Interscience, ©2003.
[24]	G. Budura, C. Botoca, ‘Efficient Implementation and Performance Evaluation of the Second Order Volterra Filter Based on the MMD Approximation’, WSEAS Transactions on Circuits and Systems, Issue 3, Volume 7, March 2008; pp. 139-149.
[25]	K. Sam Shanmugam, Mark T. Jong, “Identification of Nonlinear Systems in Frequency Domain” IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-11, No.6 November 1975.
[26]	G. Bicken, G. F. Carey and R.O. Stearman; “Frequency Domain Kernel Estimation for 2nd-order Volterra Models using Random Multi-tone Excitation”, VLSI Design; Taylor & Francis, Vol. 15(4), 2002, pp. 701-713.
[27]	A. Bhattacharjee and A. Sutradhar, “Frequency Domain Hammerstein Model of Glucose-Insulin Process in IDDM Patient”; Proceedings of the International Conference on Systems in Medicine and Biology (ICSMB 2010), IIT Kharagpur, 2010.
[28]	A. Bhattacharjee and A. Sutradhar, “Nonparametric Identification of Glucose-Insulin Process in IDDM Patient with Multi-meal Disturbance”; Journal of the Institution of Engineers (India): Series B, Vol. 93, No.4, pp. 237-246, Springer, Feb 2013.