Stochastic Simulation and Parameter Estimation of the ICING Model*

This paper develops a novel gray-box form of the ICING (Intensive Control Insulin-Nutrition-Glucose) model (Lin et al. (2011)) used both for glycemic control of Intensive Care patients and implementation of virtual trials. The computations of the system trajectories and their statistical features like mean value, standard deviation, and slice distribution were carried out using a stochastic Runge-Kutta method in the presence of Wiener-type diffusion process term. Parameter estimation of the resulting stochastic model is achieved via maximum likelihood technique. The global optimization problem was solved using genetic algorithms, simulated annealing and Nelder-Mead procedures. The parameter estimation has been carried out at different system noise levels, and the optimal parameters corresponding to the maximum of the likelihood function were selected. While the gray-box model yielded improvement, it was not significant according to the likelihood ratio test in the case of the examined model parameters. Further investigations including estimation of more parameters simultaneously, adding diffusion terms to more equations, would be necessary to yield a definitive improvement on this deterministic baseline model. The Mathematica code used is transparent and can be easily applied to develop other similar stochastic system models.