Optimal experimental design for discriminating between microbial growth models as function of suboptimal temperature: From in silico to in vivo

Guidelines for the design of (optimal) isothermal inactivation experiments

Kinetic models are nowadays a basic tool to ensure food safety. Most models used in predictive microbiology have model parameters, whose precision is crucial to provide meaningful predictions. Kinetic parameters are usually estimated based on experimental data, where the experimental design can have a great impact on the precision of the estimates. In this sense, Optimal Experiment Design (OED) applies tools from optimization and information theory to identify the most informative experiment under a set of constrains (e.g. mathematical model, number of samples, etc). In this work, we develop a methodology for the design of optimal isothermal inactivation experiments. We consider the two dimensions of the design space (time and temperature), as well as a temperature-dependent maximum duration of the experiment. Functions for its application have been included in the bioOED R package. We identify design patterns that remain optimum regardless of the number of sampling points for three inactivation models (Bigelow, Mafart and Peleg) and three model microorganisms (Escherichia coli, Salmonella Senftenberg and Bacillus coagulans). Samples at extreme temperatures and close to the maximum duration of the experiment are the most informative. Moreover, the Mafart and Peleg models require some samples at intermediate time points due to the non-linearity of the survivor curve. The impact of the reference temperature on the precision of the parameter estimates is also analysed. Based on numerical simulations we recommend fixing it to the mean of the maximum and minimum temperatures used for the experiments. The article ends with a discussion presenting guidelines for the design of isothermal inactivation experiments. They combine these optimum results based on information theory with several practical limitations related to isothermal inactivation experiments. The application of these guidelines would reduce the experimental burden required to characterize thermal inactivation.

On the use of in-silico simulations to support experimental design: A case study in microbial inactivation of foods

The mathematical models used in predictive microbiology contain parameters that must be estimated based on experimental data. Due to experimental uncertainty and variability, they cannot be known exactly and must be reported with a measure of uncertainty (usually a standard deviation). In order to increase precision (i.e. reduce the standard deviation), it is usual to add extra sampling points. However, recent studies have shown that precision can also be increased without adding extra sampling points by using Optimal Experiment Design, which applies optimization and information theory to identify the most informative experiment under a set of constraints. Nevertheless, to date, there has been scarce contributions to know a priori whether an experimental design is likely to provide the desired precision in the parameter estimates. In this article, two complementary methodologies to predict the parameter precision for a given experimental design are proposed. Both approaches are based on in silico simulations, so they can be performed before any experimental work. The first one applies Monte Carlo simulations to estimate the standard deviation of the model parameters, whereas the second one applies the properties of the Fisher Information Matrix to estimate the volume of the confidence ellipsoids. The application of these methods to a case study of dynamic microbial inactivation, showing how they can be used to compare experimental designs and assess their precision, is illustrated. The results show that, as expected, the optimal experimental design is more accurate than the uniform design with the same number of data points. Furthermore, it is demonstrated that, for some heating profiles, the uniform design does not ensure that a higher number of sampling points increases precision. Therefore, optimal experimental designs are highly recommended in predictive microbiology.