Analysis of Stochastic Noise of Blood-Glucose Dynamics. Issue 1 (July 2017) - Benyó, Balázs; Paláncz, Béla; Szlávecz, Ákos; Stewart, Kent; Homlok, József; Pretty, Christopher G.; Chase, J. Geoffrey
Abstract: Introduction of the stochastic noise in the modelling of blood-glucose dynamics becoming more and more acceptable because of the high complexity of the physiological processes. The representation of the stochastic noise term in the phenomenological as well as in data-driven models until now limited to stationary Gaussian process. In this paper the statistical nature of the stochastic blood-glucose system model noise is investigated to prove or disprove this general assumption. To ensure the generalization of the noise term a Wiener process ( W ( t )) with time depending diffusion coefficient (σ( t ) W ( t )) was considered. This stochastic term was embedded into the phenomenological ICING ( Intensive Control Insulin-Nutrition-Glucose ) model and then σ( t ) was identified by using clinical measurements from nine patients. The mean value, the standard deviation, as well as the covariance of the slide distributions of the stochastic glucose trajectories generated by the Ito type process were investigated. We have found that this stochastic term is Gaussian process but not stationary. Our final goal is to find general representation of the stochastic noise term by a parametric time series processes.