A systematic stochastic design strategy achieving an optimal tradeoff between peak BGL and probability of hypoglycaemic events for individuals having type 1 diabetes mellitus

Abstract

This paper has two key contributions. The first contribution is a systematic procedure for fitting an envelope of models which captures a range of possible blood glucose level (BGL) responses for a particular individual having Type 1 diabetes. An important aspect of the procedure is that it requires minimal testing on the individual. Moreover, the testing can be carried out by the individual at home. The developed envelope of models, termed ‘Metabolic Digital Twin Envelope’ (MDTE) takes into account the quantification of possible errors including those arising from utilising a simplified model (commonly called “bias” errors) and those arising from unmodelled disturbances and noise (commonly called “variance” errors). The second, and most important, contribution is a methodology that allows convex optimisation to be used to develop an insulin injection policy which minimises mean square peak BGL whilst ensuring that there is a strict lower bound on the probability of hyperglycaemic events. The optimisation methodology is posed as a stochastic design strategy based on using the probabilistic models for each individual afforded by the MDTE.