Abstract
Describing dynamic medical systems using machine learning is a challenging topic with a wide range of applications. In this work, the possibility of modeling the blood glucose level of diabetic patients purely on the basis of measured data is described. A combination of the influencing variables insulin and calories are used to find an interpretable model. The absorption speed of external substances in the human body depends strongly on external influences, which is why time-shifts are added for the influencing variables. The focus is put on identifying the best time-shifts that provide robust models with good prediction accuracy that are independent of other unknown external influences. The modeling is based purely on the measured data using Sparse Identification of Nonlinear Dynamics. A differential equation is determined which, starting from an initial value, simulates blood glucose dynamics. By applying the best model to test data, we can show that it is possible to simulate the long-term blood glucose dynamics using differential equations and few, influencing variables.
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References
World Health Organization. Diabetes (2021). https://www.who.int/news-room/fact-sheets/detail/diabetes
Marling, C., Bunescu, R.: The OhioT1DM dataset for blood glucose level prediction: update 2020. CEUR Workshop Proc. 2675, 71–74 (2020)
van Doorn, W.P.T.M., Foreman, Y.D., Schaper, N.C., et al.: Machine learning-based glucose prediction with use of continuous glucose and physical activity monitoring data: the maastricht study. PLoS One (2021)
Kaiser, E., Kutz, J.N., Brunton, S.L.: Sparse identification of nonlinear dynamics for model predictive control in the low-data limit. Proc. R. Soc. A. 474, 20180335 (2018)
American Diabetes Association; Diagnosis and classification of diabetes mellitus. Diab. Care 32(Suppl 1), S62–S67 (2009)
Raol, J.R., Girija, G., Singh, J.: Modelling and parameter estimation of dynamic systems. In: Control, Robotics & Sensors (2004)
Berger, M., Rodbard, D., et al.: Computer simulation of plasma insulin and glucose dynamics after subcutaneous insulin injection. Diab. Care 12, 10 (1989)
Shiang, K.-D., Kandeel, F., et al.: A computational model of the human glucose-insulin regulatory system. J. Biomed. Res. 24, 5 (2010)
Chervoneva, I., Freydin, B., Hipszer, B., Apanasovich, T.V., Joseph, J.I.: Estimation of nonlinear differential equation model for glucose-insulin dynamics in type I diabetic patients using generalized smoothing. Ann. Appl. Stat. 8(2), 886–904 (2014)
Gatewood, L.C., Ackerman, E., Rosevear, J.W., Molnar, G.D.: Modeling blood glucose dynamics. Behav. Sci. 15, 72–87 (1970)
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Joedicke, D., Parra, D., Kronberger, G., Winkler, S.M. (2022). Identifying Differential Equations for the Prediction of Blood Glucose using Sparse Identification of Nonlinear Systems. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2022. EUROCAST 2022. Lecture Notes in Computer Science, vol 13789. Springer, Cham. https://doi.org/10.1007/978-3-031-25312-6_21
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DOI: https://doi.org/10.1007/978-3-031-25312-6_21
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