Calibration of a microdialysis sensor and recursive glucose level estimation in ICU patients using Kalman and particle filtering

Abstract This paper deals with the estimation of glucose levels in ICU patients by the application of statistical filter theory to the data provided by a commercial continuous glucose monitoring system using a microdialysis sensor. Kalman and particle filtering are applied to simple models of the glucose dynamics. The particle filter enables the joint filtering and calibration of the sensor. The results show that the proposed filters lead to significant reduction in the estimation error with computational cost well within the capabilities of modern digital equipment. Additionally, the filters can be used for the automatic recognition of sensor faults. These results show that suitable filters can help in the construction of an artificial pancreas.

[1]  Giovanni Sparacino,et al.  Online Denoising Method to Handle Intraindividual Variability of Signal-to-Noise Ratio in Continuous Glucose Monitoring , 2011, IEEE Transactions on Biomedical Engineering.

[2]  Adrien-Marie Legendre,et al.  Nouvelles méthodes pour la détermination des orbites des comètes , 1970 .

[3]  E. Daskalaki,et al.  Real-time adaptive models for the personalized prediction of glycemic profile in type 1 diabetes patients. , 2012, Diabetes technology & therapeutics.

[4]  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.

[5]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[6]  H. Sorenson,et al.  Recursive bayesian estimation using gaussian sums , 1971 .

[7]  Bert Pluymers,et al.  The application of Model Predictive Control to normalize glycemia of critically ill patients , 2007, 2007 European Control Conference (ECC).

[8]  M Schetz,et al.  Intensive insulin therapy in critically ill patients. , 2001, The New England journal of medicine.

[9]  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.

[10]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[11]  Giovanni Sparacino,et al.  Enhanced accuracy of continuous glucose monitoring by online extended kalman filtering. , 2010, Diabetes technology & therapeutics.

[12]  Zeinab Mahmoudi,et al.  A multistep algorithm for processing and calibration of microdialysis continuous glucose monitoring data. , 2013, Diabetes technology & therapeutics.

[13]  Georgios D. Mitsis,et al.  Data-Driven and Minimal-Type Compartmental Insulin-Glucose Models: Theory and Applications , 2014 .

[14]  Georgios D. Mitsis,et al.  Data-driven Modeling for Diabetes , 2014 .

[15]  Stavroula G. Mougiakakou,et al.  An Actor-Critic based controller for glucose regulation in type 1 diabetes , 2013, Comput. Methods Programs Biomed..

[16]  Arnaud Doucet,et al.  A survey of convergence results on particle filtering methods for practitioners , 2002, IEEE Trans. Signal Process..

[17]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[18]  George P. Papavassilopoulos,et al.  Improved auxiliary and Unscented Particle Filter variants , 2013, 52nd IEEE Conference on Decision and Control.

[19]  T. Bayes.  An essay towards solving a problem in the doctrine of chances , 2003 .

[20]  Harold W. Sorenson,et al.  Parameter estimation: Principles and problems , 1980 .

[21]  Greet Van den Berghe,et al.  Role of intravenous insulin therapy in critically ill patients. , 2004 .

[22]  R. Bergman.  Toward Physiological Understanding of Glucose Tolerance: Minimal-Model Approach , 1989, Diabetes.

[23]  Mihalis G. Markakis,et al.  Computational study of an augmented minimal model for glycaemia control , 2008, 2008 30th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[24]  Nando de Freitas,et al.  The Unscented Particle Filter , 2000, NIPS.

[25]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[26]  Simon J. Godsill,et al.  An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo , 2007, Proceedings of the IEEE.

[27]  S. Wild,et al.  Global prevalence of diabetes: estimates for the year 2000 and projections for 2030. , 2004, Diabetes care.

[28]  V.Z. Marmarelis,et al.  Nonlinear modeling of glucose metabolism: comparison of parametric vs. nonparametric methods , 2007, 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[29]  Giovanni Sparacino,et al.  Continuous glucose monitoring time series and hypo/hyperglycemia prevention: requirements, methods, open problems. , 2008, Current diabetes reviews.

[30]  Robert B. Ash,et al.  Basic probability theory , 1970 .

[31]  Xiao-Li Hu,et al.  A Basic Convergence Result for Particle Filtering , 2008, IEEE Transactions on Signal Processing.

[32]  Herman Bruyninckx,et al.  Kalman filters for non-linear systems: a comparison of performance , 2004 .

[33]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[34]  P. Billingsley,et al.  Probability and Measure , 1980 .

[35]  Claudio Cobelli,et al.  Artificial Pancreas: Model Predictive Control Design from Clinical Experience , 2013, Journal of diabetes science and technology.

[36]  George P. Papavassilopoulos,et al.  Kalman Filtering for a Generalized Class of Nonlinear Systems and a New Gaussian Quadrature Technique , 2012, IEEE Transactions on Automatic Control.

[37]  G. P. Papavassilopoulos,et al.  Development and numerical investigation of new non-linear Kalman filter variants , 2011 .

[38]  B Wayne Bequette,et al.  Continuous Glucose Monitoring: Real-Time Algorithms for Calibration, Filtering, and Alarms , 2010, Journal of diabetes science and technology.

[39]  Kristine L. Bell,et al.  A Tutorial on Particle Filters for Online Nonlinear/NonGaussian Bayesian Tracking , 2007 .

[40]  Carolo Friederico Gauss.  Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium , 2014 .

[41]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[42]  Mihalis G. Markakis,et al.  Nonlinear Modeling of the Dynamic Effects of Infused Insulin on Glucose: Comparison of Compartmental With Volterra Models , 2009, IEEE Transactions on Biomedical Engineering.

[43]  G. V. Berghe,et al.  Intensive insulin therapy in critically ill patients. , 2001, The New England journal of medicine.

[44]  George P. Papavassilopoulos,et al.  Computationally Efficient Kalman Filtering for a Class of Nonlinear Systems , 2011, IEEE Transactions on Automatic Control.