Introducing optimal experimental design in predictive modeling: A motivating example

Predictive microbiology emerges more and more as a rational quantitative framework for predicting and understanding microbial evolution in food products. During the mathematical modeling of microbial growth and/or inactivation, great, but not always efficient, effort is spent on the determination of the model parameters from experimental data. In order to optimize experimental conditions with respect to parameter estimation, experimental design has been extensively studied since the 1980s in the field of bioreactor engineering. The so-called methodology of optimal experimental design established in this research area enabled the reliable estimation of model parameters from data collected in well-designed fed-batch reactor experiments. In this paper, we introduce the optimal experimental design methodology for parameter estimation in the field of predictive microbiology. This study points out that optimal design of dynamic input signals is necessary to maximize the information content contained within the resulting experimental data. It is shown that from few dynamic experiments, more pertinent information can be extracted than from the classical static experiments. By introducing optimal experimental design into the field of predictive microbiology, a new promising frame for maximization of the information content of experimental data with respect to parameter estimation is provided. As a case study, the design of an optimal temperature profile for estimation of the parameters Dref and z of an Arrhenius-type model for the maximum inactivation rate kmax as a function of the temperature, T, was considered. Microbial inactivation by heating is described using the model of Geeraerd et al. (1999). The need for dynamic temperature profiles in experiments aimed at the simultaneous estimation of the model parameters from measurements of the microbial population density is clearly illustrated by analytical elaboration of the mathematical expressions involved on the one hand, and by numerical simulations on the other.