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Modelling the Maximum Specific Microbial Growth Rate: Data, Models and Predictions

Publication date: 2018-04-12

Author:

Akkermans, Simen
Van Impe, Jan

Abstract:

In predictive microbiology, mathematical models are built to describe microbial responses as a function of the intrinsic and extrinsic properties of food products with the aim of improving microbial food safety and quality. One of the most common types of models that are studied in this field are the so called secondary models for growth. These models are used to describe the effect of environmental conditions on the maximum specific microbial growth rate. However, several problems can be distinguished when building such models. The four problems dealt with in this thesis are (i) the high experimental workload, (ii) the effect of measurement uncertainty on the modelling results, (iii) the difficulty of correctly calculating the model prediction uncertainty and (iv) the lack of an adequate model structure for the combined effect of environmental conditions on the microbial growth rate. The first part of this thesis presents a general introduction to the research and a detailed background on the modelling cycle for predictive microbiology. The second part focusses on improving the modelling cycle from experimental data collection to the calculation of the model prediction accuracy. The first research chapter deals with determining the most efficient experimental designs for identifying parameters of secondary models. The objective here was to achieve the most accurate overall model predictions. The inscribed central composite design was selected as the most efficient design of experiments technique, but it was overshadowed by the much more efficient D-optimal design. The two next chapters investigate how the uncertainty on the experimental measurements should be taken into account when building secondary models. The one-step parameter estimation method was found to be more suitable than the two-step method for correctly taking the variation of the dependent variable into account. Moreover, a weighted total least squares parameter estimation was proposed for taking errors on the measurement of the independent variables into account. The last chapter of this part studied the use of different uncertainty propagation methods for calculating the model prediction uncertainty. The sigma point method was found to deliver a robust calculation that entails a limited computational workload and is relatively easy to implement. The third part of this thesis discusses a novel model structure that was developed for modelling the combined effect of environmental conditions on the microbial growth rate. This gamma-interaction model is proposed as an alternative to the commonly used gamma model in the first chapter of this part. It is also compared with two additional model structures with a higher complexity than the gamma model. This comparison was based on an experimental case study on the effect of temperature and pH on the growth rate of Escherichia coli. The gamma-interaction model was preferred on the basis that it was the most accurate, compatible with an efficient modelling method and easy to implement and interpret. The second chapter of this part continues the comparison between the gamma and gamma-interaction model by including the effect of water activity in the model for temperature and pH. One of the main findings of this chapter is that a cross-validation study demonstrates that the gamma-interaction model delivered more accurate predictions due to the additional model complexity and parameters. The final part of this thesis summarises the conclusions and provides an outlook to future research.