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A stochastic optimization based stochastic optimal control framework for artifical pancreas (NYU Courant SURE 2019)

This repository features my joint research project with Xinyu Li on a stochastic optimization based stochastic optimal control framework for artifical pancreas in my junior year at NYU Courant Institute (advised by Prof. Jonathan Goodman, through NYU Courant Summer Undergraduate Research Experience program). In this project, we formulated a model of the insulin-glucose metabolism to characterize the dynamics of insulin and glucose levels, as well as the impact of meal intake and insulin injection on them, in a hypothetical type 1 diabetes patient. To prepare the system for real-world applications, we denoised the measurements using Kalman filter, and determined the optimal insulin injection amount for the patient by modern stochastic optimization algorithms from deep learning.

References:

  • Kalman filter: Ribeiro, Maria Isabel. "Kalman and extended kalman filters: Concept, derivation and properties." Institute for Systems and Robotics 43.46 (2004): 3736-3741.
  • The minimal model for the insulin-glucose metabolism:
    • Ni, Ta-Chen, Marilyn Ader, and Richard N. Bergman. "Reassessment of glucose effectiveness and insulin sensitivity from minimal model analysis: a theoretical evaluation of the single-compartment glucose distribution assumption." Diabetes 46.11 (1997): 1813-1821.
    • Cobelli, C. L. A. U. D. I. O., et al. "Estimation of insulin sensitivity and glucose clearance from minimal model: new insights from labeled IVGTT." American Journal of Physiology-Endocrinology And Metabolism 250.5 (1986): E591-E598.
    • Natalucci, Silvia, et al. "Insulin sensitivity and glucose effectiveness estimated by the minimal model technique in spontaneously hypertensive and normal rats." Experimental Physiology 85.6 (2000): 777-781.
    • Ludwig, Tomas, and Ivan Ottinger. "Identification of T1DM minimal model using non-consistent data from IVGTT." Journal of Electrical Systems and Information Technology 1.2 (2014): 144-149.
    • Winkel, Brian. "2017-Gupta, Richa and Deepak Kumar-Numerical Model for Glucose Metabolism for Various Types of Food and Effect of Physical Activities on Type 1 Diabetic Patient." (2020).
    • Ludwig, T., et al. "TYPE 1 DIABETES MELLITUS MODEL: SIMULATION STUDY."
    • Calm, Remei, et al. "Prediction of glucose excursions under uncertain parameters and food intake in intensive insulin therapy for type 1 diabetes mellitus." 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 2007.
    • Nyman, Elin, Gunnar Cedersund, and Peter Strålfors. "Insulin signaling–mathematical modeling comes of age." Trends in Endocrinology & Metabolism 23.3 (2012): 107-115.
  • Stochastic optimization:
    • Duchi, John, Elad Hazan, and Yoram Singer. "Adaptive subgradient methods for online learning and stochastic optimization." Journal of machine learning research 12.7 (2011).
    • Kingma, Diederik P., and Jimmy Ba. "Adam: A method for stochastic optimization." arXiv preprint arXiv:1412.6980 (2014).
    • Hinton, Geoffrey, Nitish Srivastava, and Kevin Swersky. "Neural networks for machine learning lecture 6a overview of mini-batch gradient descent." Cited on 14.8 (2012): 2.