Statistical Inference for Optimisation of Drug Delivery from Stents

Abstract

The current study employs state-of-the-art optimisation methods for estimation of unknown parameters in a mathematical model of highly non-linear partial differential equations describing drug delivery from a drug-eluding stent. A classical optimisation scheme entails enormous run times due to the need to numerically solve the computationally expensive equations a large number of times to obtain the objective (black-box) function. We address this issue by employing an efficient global optimisation scheme, i.e. Bayesian optimisation (BO). This scheme aims to find the optimum of the black-box function by using an emulator of the original objective function to select the next query point (while balancing exploration and exploitation), and sequentially refining the emulator. Additionally, the proposed optimisation scheme is adapted to scenarios where there are hidden constraints in parameter space by incorporating a classifier that learns the infeasible parameter domains. We demonstrate that given a fixed number of expensive mathematical model evaluations, the proposed BO scheme outperforms state-of-the-art classical optimisation methods in terms of accuracy. present study focuses on applying state-of-the-art optimisation methods, namely BO in a drug-eluting stent application.