Subcutaneous neural inverse optimal control for an Artificial Pancreas

Type 1 Diabetes mellitus (T1DM) is a chronic disease that occurs when the body cannot produce insulin. Since insulin was discovered in 1920, the way to keep T1DM patients blood glucose at normal levels has been insulin injections, via subcutaneous or intravenous paths. The efforts for an external infusion therapy have resulted in the so-called Artificial Pancreas. Such device attempts to integrate continuous insulin infusion, continuous glucose monitoring and an automatic control algorithm, which calculates the required insulin infusion. Considering all the problems related to T1DM, in this paper a neural model which captures the nonlinear behavior of the complex glucose-insulin dynamics is proposed; based on this model, a control algorithm is developed using the neural inverse optimal control via control lyapunov function (CLF) technique. Simulation results illustrate the applicability of the propounded scheme.

[1]  E.N. Sanchez,et al.  Electric load demand prediction using neural network trained by Kalman filtering , 2004, 2004 IEEE International Joint Conference on Neural Networks (IEEE Cat. No.04CH37541).

[2]  Cesar C. Palerm,et al.  Physiologic insulin delivery with insulin feedback: A control systems perspective , 2011, Comput. Methods Programs Biomed..

[3]  Alexander G. Loukianov,et al.  Discrete-Time Inverse Optimal Control for Nonlinear Systems , 2013 .

[4]  S. Haykin Kalman Filtering and Neural Networks , 2001 .

[5]  Claudio Cobelli,et al.  GIM, Simulation Software of Meal Glucose—Insulin Model , 2007, Journal of diabetes science and technology.

[6]  Edgar N. Sánchez,et al.  Blood glucose Level Neural Model for Type 1 Diabetes Mellitus Patients , 2011, Int. J. Neural Syst..

[7]  R. Hovorka Continuous glucose monitoring and closed‐loop systems , 2006, Diabetic medicine : a journal of the British Diabetic Association.

[8]  C. Cobelli,et al.  In Silico Preclinical Trials: A Proof of Concept in Closed-Loop Control of Type 1 Diabetes , 2009, Journal of diabetes science and technology.

[9]  Alexander G. Loukianov,et al.  Real-Time Discrete Neural Block Control Using Sliding Modes for Electric Induction Motors , 2010, IEEE Transactions on Control Systems Technology.

[10]  Eyal Dassau,et al.  Practical Approach to Design and Implementation of a Control Algorithm in an Artificial Pancreatic Beta Cell , 2009 .

[11]  S. Genuth,et al.  The effect of intensive treatment of diabetes on the development and progression of long-term complications in insulin-dependent diabetes mellitus. , 1993, The New England journal of medicine.

[12]  Alexander G. Loukianov,et al.  Discrete-Time Adaptive Backstepping Nonlinear Control via High-Order Neural Networks , 2007, IEEE Transactions on Neural Networks.

[13]  Ying Wang,et al.  A Chaotic Prediction Method to Time Series Data , 2010 .

[14]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[15]  Frank L. Lewis,et al.  Neural Network Control Of Robot Manipulators And Non-Linear Systems , 1998 .

[16]  Howard Zisser,et al.  Closed-Loop Control and Advisory Mode Evaluation of an Artificial Pancreatic β Cell: Use of Proportional-Integral-Derivative Equivalent Model-Based Controllers , 2008, Journal of diabetes science and technology.

[17]  Tomoki Ohsawa,et al.  Discrete Hamilton-Jacobi theory and discrete optimal control , 2010, 49th IEEE Conference on Decision and Control (CDC).

[18]  Giovanni Sparacino,et al.  Glucose Concentration can be Predicted Ahead in Time From Continuous Glucose Monitoring Sensor Time-Series , 2007, IEEE Transactions on Biomedical Engineering.

[19]  Marios M. Polycarpou,et al.  High-order neural network structures for identification of dynamical systems , 1995, IEEE Trans. Neural Networks.

[20]  Roman Hovorka Management of diabetes using adaptive control , 2005 .

[21]  Ana Gabriela Gallardo-Hernández,et al.  A Discrete-Time Recurrent Neurofuzzy Network for Black-Box Modeling of insulin Dynamics in Diabetic Type-1 Patients , 2010, Int. J. Neural Syst..

[22]  R. Freeman,et al.  Robust Nonlinear Control Design: State-Space and Lyapunov Techniques , 1996 .

[23]  Jay S Skyler,et al.  Continuous subcutaneous insulin infusion--an historical perspective. , 2010, Diabetes technology & therapeutics.

[24]  Ali Cinar,et al.  Adaptive control strategy for regulation of blood glucose levels in patients with type 1 diabetes , 2009 .

[25]  R. Hovorka,et al.  Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. , 2004, Physiological measurement.

[26]  A. El-Jabali Neural network modeling and control of type 1 diabetes mellitus , 2005, Bioprocess and biosystems engineering.

[27]  C. Byrnes,et al.  Design of discrete-time nonlinear control systems via smooth feedback , 1994, IEEE Trans. Autom. Control..

[28]  Victor M. Becerra,et al.  Optimal control , 2008, Scholarpedia.

[29]  M. Nørgaard,et al.  Advances in Derivative-Free State Estimation for Nonlinear Systems , 1998 .

[30]  Frank L. Lewis,et al.  Discrete-Time Nonlinear HJB Solution Using Approximate Dynamic Programming: Convergence Proof , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[31]  John Thomas Sorensen,et al.  A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes , 1985 .

[32]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systemsy , 1995 .

[33]  Marco Forgione,et al.  Run-to-Run Tuning of Model Predictive Control for Type 1 Diabetes Subjects: In Silico Trial , 2009, Journal of diabetes science and technology.

[34]  Ricardo Femat,et al.  Weighting Restriction for Intravenous Insulin Delivery on T1DM Patient via $H_{\infty}$ Control , 2009, IEEE Transactions on Automation Science and Engineering.

[35]  B De Moor,et al.  An adaptive input–output modeling approach for predicting the glycemia of critically ill patients , 2006, Physiological measurement.

[36]  Edgar N. Sánchez,et al.  Inverse optimal neural control of blood glucose level for type 1 diabetes mellitus patients , 2012, J. Frankl. Inst..

[37]  D. Dunger,et al.  Closed-loop insulin delivery for treatment of type 1 diabetes , 2011, BMC medicine.

[38]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[39]  Randy A. Freeman,et al.  Robust Nonlinear Control Design , 1996 .

[40]  L. Cao Practical method for determining the minimum embedding dimension of a scalar time series , 1997 .

[41]  Eyal Dassau,et al.  Safety Constraints in an Artificial Pancreatic β Cell: An Implementation of Model Predictive Control with Insulin on Board , 2009, Journal of diabetes science and technology.

[42]  Y. Z. Ider,et al.  Quantitative estimation of insulin sensitivity. , 1979, The American journal of physiology.

[43]  Eyal Dassau,et al.  Closed-Loop Control of Artificial Pancreatic $\beta$ -Cell in Type 1 Diabetes Mellitus Using Model Predictive Iterative Learning Control , 2010, IEEE Transactions on Biomedical Engineering.

[44]  A H Clemens,et al.  Development and evaluation of a glucose analyzer for a glucose controlled insulin infusion system ((Biostator). , 1978, Clinical chemistry.

[45]  Claudio Cobelli,et al.  Meal Simulation Model of the Glucose-Insulin System , 2007, IEEE Transactions on Biomedical Engineering.

[46]  J. Grizzle,et al.  The Extended Kalman Filter as a Local Asymptotic Observer for Nonlinear Discrete-Time Systems , 1992, 1992 American Control Conference.

[47]  Guanrong Chen,et al.  Discrete-Time Output Trajectory Tracking by Recurrent High-Order Neural Network Control , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[48]  T. Deutsch,et al.  A Physiological Model Of Glucose-insulin Interaction , 1991, Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society Volume 13: 1991.