Reducing risk of closed loop control of blood glucose in artificial pancreas using fractional calculus.

Healthcare costs in the US are among the highest in the world. Chronic diseases such as diabetes significantly contribute to these extensive costs. Despite technological advances to improve sensing and actuation devices, we still lack a coherent theory that facilitates the design and optimization of efficient and robust medical cyber-physical systems for managing chronic diseases. In this paper, we propose a mathematical model for capturing the complex dynamics of blood glucose time series (e.g., time dependent and fractal behavior) observed in real world measurements via fractional calculus concepts. Building upon our time dependent fractal model, we propose a novel model predictive controller for an artificial pancreas that regulates insulin injection. We verify the accuracy of our controller by comparing it to conventional non-fractal models using real world measurements and show how the nonlinear optimal controller based on fractal calculus concepts is superior to non-fractal controllers in terms of average risk index and prediction accuracy.