A kernel-based method to determine optimal sampling times for the simultaneous estimation of the parameters of rival mathematical models

When several models are proposed for one and the same process, experimental design techniques are available to design optimal discriminatory experiments. However, because the experimental design techniques are model-based, it is important that the required model predictions are not too uncertain. This uncertainty is determined by the quality of the already available data, since low-quality data will result in poorly estimated parameters, which on their turn result in uncertain model predictions. Therefore, model discrimination may become more efficient and effective if this uncertainty is reduced first. This can be achieved by performing dedicated experiments, designed to increase the accuracy of the parameter estimates. However, performing such an additional experiment for each rival model may undermine the overall goal of optimal experimental design, which is to minimize the experimental effort. In this article, a kernel-based method is presented to determine optimal sampling times to simultaneously estimate the parameters of rival models in a single experiment. The method is applied in a case study where nine rival models are defined to describe the kinetics of an enzymatic reaction (glucokinase). The results clearly show that the presented method performs well, and that a compromise experiment is found which is sufficiently informative to improve the overall accuracy of the parameters of all rival models, thus allowing subsequent design of an optimal discriminatory experiment.