Secondary growth models from predictive microbiology can describe how the growth rate of microbial populations varies with environmental conditions. Because these models are built based on time and resource consuming experiments, model-based Optimal Experimental Design (OED) can be of interest to reduce the experimental load. In this study, we identify optimal experimental designs for two common models (full Ratkowsky and Cardinal Parameters Model (CPM)) for a different number of experiments (10-30). Calculations are also done fixing one or more model parameters, observing that this decision strongly affects the layout of the OED. Using in silico experiments, we conclude that OEDs are more informative than conventional (equidistant) designs with the same number of experiments. However, OEDs cluster the experiments near the growth limits (Xmin and Xmax) resulting in impractical designs with aggregated experimental runs ~10 times longer than conventional designs. To mitigate this, we propose a novel optimality criterion (i.e., the objective function) that accounts for the aggregated time. The novel criterion provides a reduction in parameter uncertainty with respect to the conventional design, without an increase in the experimental load. These results underline that an OED is only based on information theory (Fisher information), so the results can be impractical when actual experimental limitations are considered. The study also emphasizes that most OED schemes identify where to measure, but do not give an indication on how many experiments should be made. In this sense, numerical simulations can estimate the parameter uncertainty that would be obtained for a particular experimental design (OED or not). These results and methodologies (available in Open Code) can guide the design of future experiments for the development of secondary growth models.
Keywords: Parameter estimation; Penalty criterion; Predictive microbiology; Simulations.
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