A Nonlinear State Space Model for the Blood Glucose Metabolism of a Diabetic (Ein nichtlineares Zustandsraummodell für den Blutglukosemetabolismus eines Diabetikers)
The blood glucose metabolism of a diabetic is a complex nonlinear process closely linked to a number of internal factors which are not easily accessible to measurement. Based on accessible information – such as occasional blood glucose measurements and information about food intake and physical exercise – the system appears highly stochastic and the quantity of main interest, the blood glucose concentration, is very difficult to model and to predict. In this paper we describe a stochastic nonlinear state space model for modeling the blood glucose concentration of a diabetic patient. The model structure is based on physiological prior knowledge and the main nonlinearities are modeled using artificial neural networks. Offline training of the model is performed using a newly developed Monte-Carlo generalized EM (expectation maximization) algorithm. Online prediction is performed using particle filters. Our experimental results show that our approach provides better prediction results than a number of competing approaches.