Clinical time series data analysis using mathematical models and DBNs

Much knowledge of human physiology is formalised as systems of differential equations. For example, standard models of pharmacokinetics and pharmacodynamics use systems of differential equations to describe a drug's movement through the body and its effects. Here, we propose a method for automatically incorporating this existing knowledge into a Dynamic Bayesian Network (DBN) framework. A benefit of recasting a differential equation model as a DBN is that the DBN can be used to individualise the model parameters dynamically, based on real-time evidence. Our approach provides principled handling of data and model uncertainty, and facilitates integration of multiple strands of temporal evidence. We demonstrate our approach with an abstract example and evaluate it in a real-world medical problem, tracking the interaction of insulin and glucose in critically ill patients. We show that it is better able to reason with the data, which is sporadic and has measurement uncertainties.