Comparison of Glucose Insulin Model for Artificial Pancreas: Comparison of glucose-insulin model

Muhammad  Umer Saleem; Muhammad  Farman; M. A.  Meraj; M.F.  Tabassum

Authors

Muhammad Umer Saleem Division of Science and Technology, University of Education, Lahore, Pakistan
Muhammad Farman Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan
M. A. Meraj Department of Mathematics, COMSATS Institute of Information & technology, Sahiwal Campus, Pakistan
M.F. Tabassum Department of Mathematics, University of Management and Technology, Lahore, Pakistan

Keywords:

Ordinary differential equation models, Artificial pancreas, Observability, Controllability, Linear control

Abstract

The controllability and observability of a glucose-insulin system are checked for Bergman’s minimal model, Sandhya model, Hovorka model, Sturis Tolic model and their modified form for a type 1 diabetic patient. These models are to simulate the glucose-insulin system for the treatment of type 1 diabetes mellitus. Models take the only insulin as input and glucose as an output. A control system can only be used in the form of closed-loop control to stabilize the system. It would enable diabetic patients to control their disease. Currently, no fully automated artificial pancreas is available. Comparison of controllability and observability are measured for this purpose. These models can be used to simulate a glucose-insulin system for the treatment of type 1 diabetes. This may play an important role in the development of the fully automatic artificial pancreas and stabilize the control loop system for the Glucose Insulin pump.

References

Guyton, A. C. & J. E. Hall, Text Book of Medical Physiology, Elsevier Saunders, St. Louis (2005).

Li, J, & Y. Kuang, A review on delay differential equation models in diabetes modeling, the insulin therapies and the intracellular activities of cells case, Mathematics, and Computer in simulation, 5: 1-24 (2011).

Saleem, M.U, M. Farman, M. O. Ahmad, & M. Rizwan, Control of an Artificial Human Pancreas, Chinese Journal of Physics, 55(6) 2273-2280 (2017).

Coron, J. M. Control and nonlinearity, American Mathematical society, 136 (2007).

Hautus, M.L.J. Controllability and observability conditions for linear autonomous systems, Akad. Wet. Proc., A72 443-448 (1969).

Tolic, M., E. Mosekilde, & J. Sturis. Modeling the Insulin Glucose Feedback System, The Significance of Pulsatile Insulin Secretion, Denmark, Academic press, 348-354 (2005).

Li, J., Y. Kuang, & A. Makroglou, Mathematical models and software tools for the glucose-insulin regulatory system and diabetes, Applied numerical mathematics 56: 219-224 (2005).

Jensen, E.F. Modeling and simulation of Glucose Insulin Metabolism, Technical University of Denmark, Denmark, (2007).

Sandhya, S, & D. Kumar, Mathematical model for glucose-insulin regulatory system of diabetes mellitus, Advances in Applied Mathematical Biosciences, 2(1), 39-46 (2011).

Turksoy, K.L., Quinn, E. Littlejohn, & A. Cinar. Multivariable adaptive identification and control for artificial pancreas systems, IEEE Transactions on Bio-medical Engineering, 61, 883–891(2014).

Schmidt S. & B. Vladimir. The Contribution of Glucagon in an Artificial Pancreas for People with Type 1 Diabetes 2015 American Control Conference Palmer House Hilton. 1-3 (2015).

Farman, M., M.U. Saleem., M.F. Tabassum., A. Ahmad, & M.O. Ahmad, A Linear Control of Composite model for Glucose Insulin Glucagon, Ain Shamas Engineering Journal, 10: 867-872 (2019).

Saleem, M.U., M. Farman., M. Rizwan., M.O. Ahmad, & A. Ahmad, Controllability and Observability of Glucose Insulin Glucagon systems in Human, Chines journal of Physics , 56(5) 1909-1916 (2018).

Farman, M., M.U. Saleem, & M.A. Meraj, Control of Glucose Insulin Regulatory System for Type 1 Diabetes, Science International, 28(1): 15-18 (2016).

Gonzalez, A., H. Voos, & M. Dorauach, Glucose-Insulin system based on Minimal Model: a Realistic Approach, University of Luxembourg, L-1359 (2015).

Farman, M., M.U. Saleem., M.O. Ahmad., M.F. Tabassum, & M.A. Meraj, Exploring Mathematical Models for the Treatment of Type-I Diabetes, Science International, 28(2) 795-798 (2016).

Hovorka, R. A nonlinear model predictive control of glucose concentration in subjects of type one diabetes, Physiological measurement, 19: 905–920 (2004).

Saleem, M.U., M. Farman, & M.A. Meraj A linear Control of Hovorka model, Science International, 28(1) 15-18 (2016).

Tolic, M., E. Mosekilde, & J. Sturis, Modeling the Insulin Glucose Feedback System, The Significance of Pulsatile Insulin Secretion, Journal theoretical Biology, 207: 361-375 (2000).

Saleem, M.U., M. Farman., A. Ahmad, M. Naeem, & M.O. Ahmad, Stability Analysis and Control of Fractional Order Diabetes Mellitus Model for Artificial Pancreas, Punjab University journal of mathematics, 51(4)85-101 (2019).

Comparison of Glucose Insulin Model for Artificial Pancreas