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Model predictive control of blood glucose in critically ill patients using Gaussian processes

Modellprädiktive Regelung des Blutzuckerspiegels bei Intensivpatienten mittels Gaußschen Prozessen
  • Carl-Friedrich Benner

    Carl-Friedrich Benner received the B.Sc. and M.Sc. degree in mechanical engineering from ETH Zürich, Switzerland. Since 2018 he has been working as a Ph.D. candidate at the Chair for Medical Information Technology, RWTH Aachen University.

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    , Nikolai Weber

    Nikolai Weber received the B.Sc. and M.Sc. degree in electrical engineering from RWTH Aachen University, Germany. Part of the results presented here were his master thesis at the Chair for Medical Information Technology. Since 2021 he has been working as a Ph.D. candidate at the Institute of Automatic Control, RWTH Aachen University.

    , Steffen Leonhardt

    Steffen Leonhardt received the M.S. degree in computer engineering from the University at Buffalo, NY, USA, the Ph.D. in electrical engineering from the Technical University of Darmstadt, Darmstadt, Germany, the M.D. degree in medicine from J.W. Goethe University, Frankfurt, Germany, and the Dr.h.c. (Honorary) degree from Czech Technical University in Prague, Czech Republic. In 2003, he was appointed a Full Professor and the Head of the Chair for Medical Information Technology at RWTH Aachen University, Aachen, Germany.

    and Marian Walter

    Marian Walter received his Dipl.-Ing. degree in electrical engineering and the Ph.D. in electrical engineering from the Technical University of Darmstadt, Darmstadt, Germany. Since 2004 he has been working as a Senior Engineer at the Chair for Medical Information Technology, RWTH Aachen University.

Abstract

Stress-induced hyperglycemia and high glycemic variability are common in intensive care patients. Several clinical studies show the benefits of tight blood glucose control, including lower mortality. This article presents an algorithm for blood glucose control in the intensive care unit. An Unscented Kalman Filter is developed to estimate the glucose metabolism state and time-varying insulin sensitivity from blood glucose measurements. Gaussian Processes are used to predict future insulin sensitivity changes based on previous measurements. A model predictive controller is designed to estimate optimal insulin infusion based on current state, predicted insulin sensitivity and planned nutrition. The developed control algorithm allows individualized blood glucose control with reduced glycemic variability and reduced risk of hypoglycemia in the intensive care unit.

Zusammenfassung

Stressbedingte Hyperglykämie und hohe glykämische Variabilität treten häufig bei Intensivpatienten auf. Einige klinische Studien zeigen, dass eine engmaschige Blutzuckerregelung sich positiv auf die Genesung auswirkt und zu einer geringeren Sterblichkeit führt. In diesem Artikel wird ein Algorithmus für die Blutzuckerkontrolle auf der Intensivstation vorgestellt. Es wird ein Unscented Kalman-Filter entwickelt, um den Zustand des Glukosestoffwechsels und die zeitlich variierende Insulinsensitivität anhand von Blutzuckermessungen zu schätzen. Mit Hilfe von Gaußschen Prozessen werden künftige Änderungen der Insulinsensitivität auf Grundlage früherer Messungen vorhergesagt. Ein modellprädiktiver Regler wird entwickelt, um die optimale Insulininfusion auf der Grundlage des aktuellen Zustands, der vorhergesagten Insulinsensitivität und der geplanten Ernährung zu ermitteln. Der entwickelte Regelalgorithmus ermöglicht eine individualisierte Blutzuckerkontrolle mit geringerer glykämischer Variabilität und reduziertem Hypoglykämierisiko auf der Intensivstation.


Corresponding author: Carl-Friedrich Benner, Chair for Medical Information Technology, RWTH Aachen University, Pauwelsstr. 20, 52074 Aachen, Germany, E-mail:

About the authors

Carl-Friedrich Benner

Carl-Friedrich Benner received the B.Sc. and M.Sc. degree in mechanical engineering from ETH Zürich, Switzerland. Since 2018 he has been working as a Ph.D. candidate at the Chair for Medical Information Technology, RWTH Aachen University.

Nikolai Weber

Nikolai Weber received the B.Sc. and M.Sc. degree in electrical engineering from RWTH Aachen University, Germany. Part of the results presented here were his master thesis at the Chair for Medical Information Technology. Since 2021 he has been working as a Ph.D. candidate at the Institute of Automatic Control, RWTH Aachen University.

Steffen Leonhardt

Steffen Leonhardt received the M.S. degree in computer engineering from the University at Buffalo, NY, USA, the Ph.D. in electrical engineering from the Technical University of Darmstadt, Darmstadt, Germany, the M.D. degree in medicine from J.W. Goethe University, Frankfurt, Germany, and the Dr.h.c. (Honorary) degree from Czech Technical University in Prague, Czech Republic. In 2003, he was appointed a Full Professor and the Head of the Chair for Medical Information Technology at RWTH Aachen University, Aachen, Germany.

Marian Walter

Marian Walter received his Dipl.-Ing. degree in electrical engineering and the Ph.D. in electrical engineering from the Technical University of Darmstadt, Darmstadt, Germany. Since 2004 he has been working as a Senior Engineer at the Chair for Medical Information Technology, RWTH Aachen University.

  1. Research ethics: Not applicable.

  2. Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: The authors state no conflict of interest.

  4. Research funding: The research was partly funded by the “Bundesministerium für Wirtschaft und Technology”, Grant No. 16KN074236.

  5. Data availability: Not applicable.

References

[1] S. E. Inzucchi, “Management of hyperglycemia in the hospital,” New Engl. J. Med., vol. 355, no. 18, pp. 1903–1911, 2006. https://doi.org/10.1056/nejmcp060094.Search in Google Scholar PubMed

[2] K. Stoudt and S. Chawla, “Don’t sugar coat it: glycemic control in the intensive care unit,” J. Intensive Care Med., vol. 34, nos. 11–12, pp. 889–896, 2019. https://doi.org/10.1177/0885066618801748.Search in Google Scholar PubMed PubMed Central

[3] C.-W. Hsu, “Glycemic control in critically ill patients,” World J. Crit. Care Med., vol. 1, no. 1, pp. 31–39, 2012. https://doi.org/10.5492/wjccm.v1.i1.31.Search in Google Scholar PubMed PubMed Central

[4] G. Van Den Berghe, et al.., “Intensive insulin therapy in critically ill patients,” N. Engl. J. Med., vol. 345, no. 19, pp. 1359–1367, 2001. https://doi.org/10.1056/nejmoa011300.Search in Google Scholar

[5] P. Singer, et al.., “ESPEN guideline on clinical nutrition in the intensive care unit,” Clin. Nutr., vol. 38, no. 1, pp. 48–79, 2019. https://doi.org/10.1016/j.clnu.2018.08.037.Search in Google Scholar PubMed

[6] S. Finfer, et al.., “Intensive versus conventional glucose control in critically ill patients,” New Engl. J. Med., vol. 360, no. 13, pp. 1283–1297, 2009. https://doi.org/10.1056/nejmoa0810625.Search in Google Scholar PubMed

[7] J. C. Preiser, O. Lheureux, A. Thooft, S. Brimioulle, J. Goldstein, and J. L. Vincent, “Near-continuous glucose monitoring makes glycemic control safer in ICU patients,” Crit. Care Med., vol. 46, no. 8, pp. 1224–1229, 2018. https://doi.org/10.1097/ccm.0000000000003157.Search in Google Scholar

[8] C. Cobelli, C. Dalla Man, G. Sparacino, L. Magni, G. De Nicolao, and B. Kovatchev, “Diabetes: models, signals, and control,” IEEE Rev. Biomed. Eng., vol. 2, pp. 54–96, 2009. https://doi.org/10.1109/rbme.2009.2036073.Search in Google Scholar PubMed PubMed Central

[9] J. Lin, et al.., “A physiological Intensive Control Insulin-Nutrition-Glucose (ICING) model validated in critically ill patients,” Comput. Methods Programs Biomed., vol. 102, no. 2, pp. 192–205, 2011. https://doi.org/10.1016/j.cmpb.2010.12.008.Search in Google Scholar PubMed

[10] T. Van Herpe, et al.., “A minimal model for glycemia control in critically ill patients,” in Annual International Conference of the IEEE Engineering in Medicine and Biology – Proceedings, 2006, pp. 5432–5435.10.1109/IEMBS.2006.260613Search in Google Scholar PubMed

[11] J. G. Chase, et al.., “Implementation and evaluation of the SPRINT protocol for tight glycaemic control in critically ill patients: a clinical practice change,” Crit. Care, vol. 12, no. 2, pp. 1–15, 2008. https://doi.org/10.1186/cc6868.Search in Google Scholar PubMed PubMed Central

[12] R. N. Bergman, L. S. Phillips, and C. Cobelli, “Physiologic evaluation of factors controlling glucose tolerance in man. Measurement of insulin sensitivity and β-cell glucose sensitivity from the response to intravenous glucose,” J. Clin. Invest., vol. 68, no. 6, pp. 1456–1467, 1981. https://doi.org/10.1172/jci110398.Search in Google Scholar PubMed PubMed Central

[13] K. Lunze, et al.., “Analysis and modelling of glucose metabolism in diabetic Göttingen minipigs,” Biomed. Signal Process. Control, vol. 13, no. 1, pp. 132–141, 2014. https://doi.org/10.1016/j.bspc.2014.04.003.Search in Google Scholar

[14] L. Ortmann, et al.., “Gaussian process-based model predictive control of blood glucose for patients with type 1 diabetes mellitus,” in 2017 Asian Control Conference, ASCC 2017, 2018, pp. 1092–1097.10.1109/ASCC.2017.8287323Search in Google Scholar

[15] C.-F. Benner, L. Pan, S. Leonhardt, and M. Walter, “Robust control of blood glucose in the intensive care unit,” in Abstracts of the 55th Annual Meeting of the German Society of Biomedical Engineering, vol. 66, Biomedical Engineering/Biomedizinische Technik, 2021, p. 133.Search in Google Scholar

[16] C.-F. Benner, S. Leonhardt, and M. Walter, “Blood glucose control in critically ill patients,” in Abstracts of the 2022 Joint Annual Conference of the Austrian (ÖGBMT), German (VDE DGBMT) and Swiss (SSBE) Societies for Biomedical Engineering, vol. 67, 2022, p. 81.10.1515/bmt-2022-2001Search in Google Scholar

[17] R. Hovorka, et al.., “Blood glucose control by a model predictive control algorithm with variable sampling rate versus a routine glucose management protocol in cardiac surgery patients: a randomized controlled trial,” J. Clin. Endocrinol. Metab., vol. 92, no. 8, pp. 2960–2964, 2007. https://doi.org/10.1210/jc.2007-0434.Search in Google Scholar PubMed

[18] S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, vol. 8, Chichester, England, John Wiley and Sons, 2001.Search in Google Scholar

[19] S. Särkkä, “On unscented Kalman filtering for state estimation of continuous-time nonlinear systems,” IEEE Trans. Autom. Control, vol. 52, no. 9, pp. 1631–1641, 2007. https://doi.org/10.1109/tac.2007.904453.Search in Google Scholar

[20] S. J. Julier, “The scaled unscented transformation,” Proc. Am. Control Conf., vol. 6, no. 2, pp. 4555–4559, 2002. https://doi.org/10.1109/acc.2002.1025369.Search in Google Scholar

[21] B. J. Misgeld, P. G. Tenbrock, K. Lunze, J. W. Dietrich, and S. Leonhardt, “Estimation of insulin sensitivity in diabetic Göttingen Minipigs,” Control Eng. Pract., vol. 55, pp. 80–90, 2016. https://doi.org/10.1016/j.conengprac.2016.06.004.Search in Google Scholar

[22] C. K. Williams and C. E. Rasmussen, Gaussian Processes for Machine Learning, Cambridge, MA, MIT Press, 2006.Search in Google Scholar

[23] D. K. Duvenaud, Automatic Model Construction with Gaussian Processes, 2014, p. 144. Available at: https://Github.Com/Duvenaud/Phd-Thesis.Search in Google Scholar

[24] C. E. Rasmussen and H. Nickisch, “Gaussian processes for machine learning (GPML) toolbox,” J. Mach. Learn. Res., vol. 11, no. 100, pp. 3011–3015, 2010.Search in Google Scholar

[25] J. B. Rawlings and D. Q. Mayne, Model Predictive Control: Theory and Design, Madison, Wisconsin, USA, Nob Hill Publishing, LLC, 2016.Search in Google Scholar

[26] F. Allgöwer, R. Findeisen, and Z. K. Nagy, “Nonlinear model predictive control: from theory to application,” J. Chin. Inst. Chem. Eng., vol. 35, no. 3, pp. 299–315, 2004.Search in Google Scholar

[27] M. P. Borrelli, F. Borrelli, A. Bemporad, and M. Morari, Predictive Control for Linear and Hybrid Systems, Cambridge, England, Cambridge University Press, 2017.10.1017/9781139061759Search in Google Scholar

[28] J. A. Andersson, J. Gillis, G. Horn, J. B. Rawlings, and M. Diehl, “CasADi: a software framework for nonlinear optimization and optimal control,” Math. Program. Comput., vol. 11, no. 1, pp. 1–36, 2019. https://doi.org/10.1007/s12532-018-0139-4.Search in Google Scholar

[29] A. Wächter and L. T. Biegler, “On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming,” Math. Program., vol. 106, no. 1, pp. 25–57, 2006. https://doi.org/10.1007/s10107-004-0559-y.Search in Google Scholar

Received: 2023-11-21
Accepted: 2024-03-27
Published Online: 2024-05-07
Published in Print: 2024-05-27

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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