A cyber-physical system approach to artificial pancreas design

Healthcare costs in the US are among the highest in the world. Widespread chronic diseases such as diabetes constitute a significant cause of rising healthcare costs. Despite the increased need for smart healthcare systems that monitor patients´ body balance, there is no coherent theory that facilitates the design and optimization of efficient and robust cyber physical systems. In this paper, we propose a mathematical model for capturing the dynamics of blood glucose characteristics (e.g., time dependent fractal behavior) observed in real world measurements via fractional calculus concepts. Building on our time dependent fractal model, we propose a novel mathematical model as well as hardware architecture for an artificial pancreas that relies on solving a constrained multi-fractal optimal control problem for regulating insulin injection. We verify the accuracy of our mathematical model by comparing it to conventional nonfractal models using real world measurements and showing that the nonlinear optimal controller based on fractal calculus concepts is superior to nonfractal controllers. We also verified the feasibility of in silico realization of the proposed optimal control algorithm by prototyping on FPGA platform.