Influence of non-linearity to the Optimal Experimental Design demonstrated by a biological system

Abstract

A precise estimation of parameters is essential to generate mathematical models with a highly predictive power. A framework that attempts to reduce parameter uncertainties caused by measurement errors is known as Optimal Experimental Design (OED). The Fisher Information Matrix (FIM), which is commonly used to define a cost function for OED, provides at the best only a lower bound of parameter uncertainties for models that are non-linear in their parameters. In this work, the Sigma Point method is used instead, because it enables a more reliable approximation of the parameter statistics accompanied by a manageable computational effort. Moreover, it is shown that Sigma Points can also be used to define design criteria for OED that incorporate the influence of parameter uncertainties on the simulated model states, i.e. mean square error of prediction. To reduce the computational effort of OED further, the Kriging Interpolation approach is applied leading to an easily evaluable surrogate cost function. The advantages of the Sigma Point method combined with the Kriging Interpolation in the framework of OED are demonstrated for the example of a biological two-substrate uptake model.