Prof. Dr. habil. Levente Kovács, Dr. György Eigner, Dr. Dániel András Drexler

Main directions of the research

  • Nonlinear model-based robust control algorithm and LPV (Linear Parameter Varying) methodology
  • Virtual patients identification with the Levenberg-Marquardt algorithm
  • The framework is not sensitive to different meal intake profiles
  • Hypoglycemia is efficiently avoided

A detailed description of the research

Diabetes is predicted by the World Health Organization (WHO) to be the “disease of the future” especially in developing countries. The diabetic population (being an estimated 171 million people in 2000) is predicted to be doubled by 2030 [1],[2].

The quest for an artificial pancreas can be structured in three different tasks [14]: continuous glucose sensor for measurements, insulin pump for infusion and control algorithm problem.

To design appropriate control, an adequate model is necessary. From the many models that appeared in the literature [4] and the wide palette of control strategies [3], it becomes evident that modeling of the glucose-insulin system and controlling its behavior are two tightly connected questions that cannot be separated. The model predicted control proved to be an efficient solution for individualized treatment of type 1 diabetes [3], but due to insulin sensitivity and patient variability, hard constraints are also beneficial [5].

Hence, we have focused on one of the most complex models, the Sorensen-model [6] and developed a nonlinear model-based robust control algorithm being more exact in comparison with linear model-based methods (as it avoids linearization and works directly with the nonlinear model itself) [7]. The nonlinear model-based approach was realized using LPV (Linear Parameter Varying) methodology capturing the validity of the Sorensen-model inside a polytopic region and building up the LPV model as a linear combination of the linearized models derived in each polytopic point [7].

Regarding diabetes, the Hungarian artificial pancreas research topic was briefly summarized. The developed nonlinear model-based LPV robust controller was created on the most complex Sorensen-model and our first quasi in-silico results were tested and compared on real data of 30 type 1 diabetes patient.

The developed framework kept the blood glucose level more than 90% of the time inside the 70-120 mg/dL interval (without any recalibration of the algorithm) proving its robustness. Hypoglycemia (not caused by physical activity) is efficiently avoided. The research proved that there is real hope in developing a general (robust) framework, which could keep by hard constraints blood glucose level inside a defined interval; moreover, it is not sensitive to different meal intake profiles. Hence, it could efficiently support individualized control (ex. model predictive control – MPC) protocols that appeared in the literature [3].

Based on the obtained results, we went further and started to investigate the model-free property of the controller: if the originally used modified Sorensen-model [8] is changed to another model, how should the controller react without redesigning it. We have used the well-known model of Hovorka [9] and created a whole new set of virtual patients. This model represents the core of the in-silico simulator of the University of Cambridge version 2.2 (SimEdu). Using the results, which were collected from the insulin pump centers of the Hungarian Artificial Pancreas Working Group (HAP) [10], these two T1DM models were used to generate the virtual patients. The identification was carried out using the Levenberg-Marquardt algorithm [11] and the Optimization toolbox of MATLAB. The running time has been greatly reduced by providing a fair estimation of the Jacobian matrix without the use of loops.

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[2] Wild S., Roglic G., Green A., Sicree R., King H.: Global Prevalence of Diabetes – Estimates for the year 2000 and projections for 2030, 2004, Diabetes Care, Vol. 27 (5), pp. 1047-1053.
[3] Cobelli C., Dalla Man C., Sparacino G., Magni L., de Nicolao G., Kovatchev B.: Diabetes: Models, Signals, and Control (Methodological Review), IEEE Reviews in Biomedical Engineering, 2009, Vol. 2, pp. 54–96.
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[5] R. Femat, E. Ruiz-Velazquez, and G. Quiroz, “Weighting Restriction for Intravenous Insulin Delivery on T1DM Patient via H∞ Control”, IEEE Transactions on Automation Science and Engineering, vol. 6 (2), pp. 239-247, 2009.
[6] J.T. Sorensen, A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes, PhD Thesis, Dept. of Chemical Eng. Massachusetts Institute of Technology, Cambridge, 1985.
[7] L. Kovács, B. Benyó, J. Bokor, and Z. Benyó, “Induced L2-norm Minimization of Glucose-Insulin System for Type I Diabetic Patients”, Computer Methods and Programs in Biomedicine, vol. 102 (2), pp. 105-118, 2011.
[8] R. S. Parker, F. J. Doyle III, J. H. Ward. and N. A. Peppas,
“Robust H∞ Glucose Control in Diabetes Using a Physiological Model”, AIChE Journal, vol. 46, no. 12, pp. 2537-2549, 2000.
[9] M. E. Wilinska, L. J. Chassin, C. L. Acerini, J. M. Allen, D. B.
Dunger and R. Hovorka, “Simulation environment to evaluate closed-loop insulin delivery systems in type 1 diabetes”, J Diabetes Sci Technol, vol. 4, no. 1, pp. 132–144, 2010.
[10] Kovács L., Barkai L.: Magyar Mesterséges Pancreas Workshop, Diabetologia Hungarica,2010, Vol. XXVIII (4), pp. 336-337.
[11] J. Nocedal and S. J. Wright, Numerical Optimization, Springer,
Heidelberg; 2006.