Practical application of dynamic temperature profiles to estimate the parameters of the square root model

Abstract

Optimal experimental design for parameter estimation (OED/PE) is a promising method to improve parameter estimation accuracy and minimise experimental effort in the field of predictive microbiology. In this paper, the OED/PE methodology was applied on two practical examples: the growth of Bacillus cereus and Enterobacter cloacae in liquid whole egg product. Both strains were recovered from samples of a commercial product. The goal of the modelling exercise was to quantify the influence of temperature on bacterial growth. The Baranyi-model for bacterial growth combined with the Ratkowsky square root model to describe temperature dependence was used. Using this model, a temperature step profile was calculated based on the optimal D-criterion. The model was then fitted against the experimental bacterial growth curve measured under the dynamic temperature conditions. This process was repeated until the parameters could be estimated with sufficient accuracy, apparent by the model prediction errors. For B. cereus, prior information could be extracted from the literature, allowing calculating a dynamic temperature profile directly. Two-step profiles were sufficient to obtain a good estimation for the model parameters. No prior information could be found for E. cloacae. Therefore, a limited series of static experiments had to be conducted to obtain usable prior model parameters estimates. Only one dynamic experiment was then needed to achieve a good estimation.