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

Abstract

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.

Fig 1

Thermal profiles (A, B and C) analysed as a case study (-). Expected survivor curve for each profile (—).

Fig 2

Frequency bar plot illustrating the OED calculated for the three profiles analyzed (A, B and C). The colour of the bar indicates the total number of sampling points.

Fig 3

Scaled local sensitivity functions of profile A (A), B (B) and C (C) with respect to the D-value (-) and the z-value (—).

Fig 4

Inverse of the determinant of the FIM calculated for each thermal profile (A, B and C) as a function of the number of sampling points for an OED (red dot) and for a uniform design (blue dot).

Fig 5

Comparison of the standard deviation estimated for the D and z-values for different experimental designs for the three thermal profiles analysed as case study (A, B and C).