Identification of individualised empirical models of carbohydrate and insulin effects on T1DM blood glucose dynamics

One of the main limiting factors in improving glucose control for type 1 diabetes mellitus (T1DM) subjects is the lack of a precise description of meal and insulin intake effects on blood glucose. Knowing the magnitude and duration of such effects would be useful not only for patients and physicians, but also for the development of a controller targeting glycaemia regulation. Therefore, in this paper we focus on estimating low-complexity yet physiologically sound and individualised multi-input single-output (MISO) models of the glucose metabolism in T1DM able to reflect the basic dynamical features of the glucose–insulin metabolic system in response to a meal intake or an insulin injection. The models are continuous-time second-order transfer functions relating the amount of carbohydrate of a meal and the insulin units of the accordingly administered dose (inputs) to plasma glucose evolution (output) and consist of few parameters clinically relevant to be estimated. The estimation strategy is continuous-time data-driven system identification and exploits a database in which meals and insulin boluses are separated in time, allowing the unique identification of the model parameters.

[1]  K N Frayn,et al.  Glycaemic index methodology , 2005, Nutrition Research Reviews.

[2]  Michael D. Skillen,et al.  A diabetes management system empowering patients to reach optimised glucose control: From monitor to advisor , 2010, 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology.

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

[4]  Y. Jang,et al.  Standards of Medical Care in Diabetes-2010 by the American Diabetes Association: Prevention and Management of Cardiovascular Disease , 2010 .

[5]  J. B. Jørgensen,et al.  Robust model identification applied to type 1 diabetes , 2010, Proceedings of the 2010 American Control Conference.

[6]  M. Horowitz,et al.  Gastric emptying in diabetes: clinical significance and treatment , 2002, Diabetic medicine : a journal of the British Diabetic Association.

[7]  L. Magni,et al.  Diabetes: Models, Signals, and Control , 2010, IEEE Reviews in Biomedical Engineering.

[8]  Rolf Johansson,et al.  Stochastic theory of continuous-time state-space identification , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[9]  Malgorzata E. Wilinska,et al.  Insulin kinetics in type-1 diabetes: continuous and bolus delivery of rapid acting insulin , 2005, IEEE Transactions on Biomedical Engineering.

[10]  C. C. Palerm,et al.  Effect of input excitation on the quality of empirical dynamic models for type 1 diabetes , 2009 .

[11]  S. Colagiuri,et al.  The Diabetes Control and Complications Trial , 1983, Henry Ford Hospital medical journal.

[12]  Giuseppe De Nicolao,et al.  Modeling and Control of Diabetes: Towards the Artificial Pancreas , 2011 .

[13]  Alessandro Chiuso,et al.  On the Asymptotic Properties of Closed-Loop CCA-Type Subspace Algorithms: Equivalence Results and Role of the Future Horizon , 2010, IEEE Transactions on Automatic Control.

[14]  Peter Young,et al.  Parameter estimation for continuous-time models - A survey , 1979, Autom..

[15]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[16]  L. Magni,et al.  Model Predictive Control of Type 1 Diabetes: An in Silico Trial , 2007, Journal of diabetes science and technology.

[17]  V. Basevi.  Standards of Medical Care in Diabetes—2010 , 2010, Diabetes Care.

[18]  Rolf Johansson,et al.  Diabetes mellitus modeling and short-term prediction based on blood glucose measurements. , 2009, Mathematical biosciences.

[19]  Alessandro Chiuso,et al.  Consistency analysis of some closed-loop subspace identification methods , 2005, Autom..

[20]  Rolf Johansson,et al.  Direct continuous time system identification of MISO transfer function models applied to type 1 diabetes , 2011, IEEE Conference on Decision and Control and European Control Conference.

[21]  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.

[22]  Michel Verhaegen,et al.  Stochastic theory of continuous-time state-space identification , 1999, IEEE Trans. Signal Process..

[23]  Odile Leroy.  Final publishable summary report , 2012 .

[24]  Claudio Cobelli,et al.  A System Model of Oral Glucose Absorption: Validation on Gold Standard Data , 2006, IEEE Transactions on Biomedical Engineering.

[25]  Rolf Johansson,et al.  Impulsive Predictive Control of T1DM Glycemia: An In-Silico Study , 2012 .

[26]  A Kapur.  Insulin kinetics. , 1997, The Journal of the Association of Physicians of India.

[27]  Rolf Johansson,et al.  Identification of continuous-time models , 1994, IEEE Trans. Signal Process..

[28]  D L DeMets,et al.  Glycosylated hemoglobin predicts the incidence and progression of diabetic retinopathy. , 1988, JAMA.

[29]  Fredrik Ståhl,et al.  Diabetes Mellitus Glucose Prediction by Linear and Bayesian Ensemble Modeling , 2012 .

[30]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[31]  D. Nathan,et al.  Long-term complications of diabetes mellitus. , 1993, The New England journal of medicine.

[32]  Torben Knudsen.  Consistency analysis of subspace identification methods based on a linear regression approach , 2001, Autom..

[33]  Karl Johan Åström,et al.  Zeros of sampled systems , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[34]  Boris Kovatchev,et al.  Analysis, Modeling, and Simulation of the Accuracy of Continuous Glucose Sensors , 2008, Journal of diabetes science and technology.

[35]  C. Cobelli,et al.  Artificial Pancreas: Past, Present, Future , 2011, Diabetes.

[36]  R. Bergman,et al.  Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose. , 1981, The Journal of clinical investigation.

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

[38]  Dale E. Seborg,et al.  Control-Relevant Models for Glucose Control Using A Priori Patient Characteristics , 2012, IEEE Transactions on Biomedical Engineering.

[39]  Marco Lovera,et al.  Continuous-time subspace identification in closed-loop , 2010 .

[40]  Niels Kjølstad Poulsen,et al.  Overnight Control of Blood Glucose in People with Type 1 Diabetes , 2012 .

[41]  Rolf Johansson,et al.  Subspace-Based Model Identification of Diabetic Blood Glucose Dynamics , 2009 .

[42]  Luigi del Re,et al.  Estimating Interval Process Models for Type 1 Diabetes for Robust Control Design , 2011 .

[43]  Henrik Madsen,et al.  Effects of everyday life events on glucose, insulin, and glucagon dynamics in continuous subcutaneous insulin infusion-treated type 1 diabetes: collection of clinical data for glucose modeling. , 2012, Diabetes technology & therapeutics.

[44]  Eyal Dassau,et al.  Modeling the Effects of Subcutaneous Insulin Administration and Carbohydrate Consumption on Blood Glucose , 2010, Journal of diabetes science and technology.

[45]  J. Assal,et al.  [Long-term complications in diabetes mellitus]. , 1989, Acta medica portuguesa.

[46]  B. Zinman,et al.  Intensive diabetes treatment and cardiovascular disease in patients with type 1 diabetes. , 2005, The New England journal of medicine.

[47]  Rolf Johansson.  Continuous-Time Model Identification and State Estimation Using Non-Uniformly Sampled Data , 2009 .

[48]  R. Hovorka,et al.  Absorption patterns of meals containing complex carbohydrates in type 1 diabetes , 2013, Diabetologia.

[49]  Alessandro Chiuso,et al.  The role of vector autoregressive modeling in predictor-based subspace identification , 2007, Autom..