Mathematical modelling for the microbiological risk assessment of food following mild preservation treatments

Resumen

This thesis uses mathematical modelling to describe the effect that different preservation treatments have on the microbial load of a food product, as well as on its quality. The work performed can be divided into three major parts. The first one (chapters I-III) deals with the development of a mathematical model for the description of microbial inactivation during thermal processes taking into account the stress adaptation that bacteria may develop during the mild stages of the treatment. This phenomenon has already been reported by other authors in previous works, and several mathematical models have been proposed to describe it. However, they have limitations. For instance, the application of some of them is limited to thermal profiles of a specific shape, and their model parameters are sometimes hard to interpret. The model has been built as an extension of the classical log-linear model, so that model parameters previously estimated using isothermal experiments can be reused. The bacterial stress adaptation is modelled using a variable (which can be interpreted as the concentration of an ideal substance) that represents the degree of adaptation of the microbial cells to the thermal stress. It has been validated using non-isothermal inactivation data obtained for Escherichia coli (Chapter I) and Listeria monocytogenes (Chapter II), demonstrating its ability to describe the stress adaptation of different bacterial taxa. Moreover, the model has also been able to succesfully predict the non-isothermal inactivation of L. monocytogenes in milk, proving its applicability to describe the microbial inactivation in a food product. One of the advantages of the proposed model with respect to the previous ones is the ease to understand the evolution of the stress adaptation through the treatment. Therefore, it can be used to compare the response of two different bacterial strains to a thermal treatment, providing further insight about situations in which the stress adaptation may become relevant. Chapter III closes the first block with a study where the response during thermal treatments allowing for stress adaptation of two different strains of E. coli is compared. Based on this analysis, it is concluded that one strain is more resistant if the heating rate is fast, not allowing the development of an adaptation. However, if the heating phase is long, the other strain might become more critical for food safety due to a higher adaptation to heat stress. The second part (chapters IV-VI) applies mathematical models already existing in predictive microbiology for both assessing the microbial safety of thermal and non-thermal treatments and estimating the shelf-life of a food product. In order to increase the reproducibility of the mathematical calculations, as well as to ease the access to mathematical modelling for scientists without any programming background, the software package bioinactivation has been developed. This application, described in Chapter IV, includes several function for the modelling of microbial inactivation, including the calculation of predictions and the model fitting of non-isothermal experiments. It is able to predict the microbial response using prediction intervals, taking into consideration the uncertainty and variability of the microbial response to the preservation treatment. The required functions have been wrapped in an R package (bioinactivation core), and a user-friendly web application to selected functions has been developed (bioinactivation SE). Both formats have been made available to the scientific community for free. They have been applied in Chapters V and VI to practical case studies. In Chapter V, the shelf life of a vegetable-based product according to microbial safety and food quality criteria is estimated. From a food safety point of view, the ability of L. monocytogenes to proliferate during storage is modelled, whereas for food quality the evolution of several sensorial and physicochemical attributes is described. In Chapter VI predictive modelling is applied to evaluate the feasibility of two emerging technologies as an alternative to thermal treatments. Namely, the application of High Hydrostatic Pressure for the inactivation of L. monocytogenes in a smoothie, and the combination of thermal treatments and a natural antimicrobial (D-limonene) for the inactivation of Salmonella Senftenberg were studied. The third part (chapter VII) applies Optimal Experiment Design (OED) to find the most informative time points for the characterization of the resistance of a bacterial population in a non-isothermal treatment. This methodology is based on the optimization of a measurement of the Fisher Information matrix and has been previously applied for the identification of dynamic mathematical models in food microbiology, as well as in other fields. In our case, it has been adapted to the mathematical models used in predictive microbiology for the description of microbial inactivation during non-isothermal treatments. Moreover, a penalty term has been added in order to penalize infeasible experiment designs (with a time between samples too short). The higher precision of the experimental design generated following this procedure with respect to an experimental design uniformly distributed in time has been demonstrated using data for non-isothermal inactivation of L. monocytogenes. In conclusion, mathematical modelling has been applied to better describe the impact of preservation processes on the microbial concentration. This has been made by means of new mathematical alternatives to describe adaptation to mild heat treatments, use of user-friendly software that estimates precisely confidence intervals and improved experimental design. The combination of these approaches improves the accuracy of the estimations of the microbial response to the preservation treatment, taking into consideration its variability and uncertainty. The methodologies and tools developed and/or applied in this thesis can be beneficial for improving microbial food safety in a wide variety of food formulations and preservation technologies, with important health, nutritional or economic implications.