Abstract
Predictive models in food microbiology can quantitatively describe the microbial ecology of foods and they are valuable tools for estimating the fate of microorganisms as a consequence of food processing or handling procedures. Such models are useful when time is critical or in the absence of rapid methods for determining the microbiological safety of foods. Bayesian methods have been implemented into food microbiology models, especially in the last decade, to obtain predictions close to real-life scenarios. This thesis looks further into the application of Bayesian inference to food predictive models, focusing on two case studies with one specific aim: to obtain more realistic predictions and separate the uncertainty and variability associated with the estimation of kinetic parameters.
As a part of this PhD thesis, two hierarchical Bayesian models were developed, an inactivation model and a growth model, each for a specific purpose.
First, a hierarchical Bayesian model for predicting the thermal inactivation parameters of strains belonging to Listeria species was developed. For this purpose, the D-values in aqueous media for different strains of Listeria monocytogenes and L. innocua were obtained from the scientific literature through meta-analysis. These values were used to estimate the D-, zT-, and zpH-values for L. monocytogenes across a range of temperatures (55 to 70 °C) and pH values (3 to 8 units) using Bayesian inference. A total of 476 D-values were procured from 27 different studies involving 76 strains (71 strains of L. monocytogenes and five strains of L. innocua). Different variability hypotheses, such as variability between different strains or studies, were introduced onto the inactivation parameters using four mixed-linear hierarchical Bayesian models. The models were subsequently compared based on their prediction efficiency and by estimating the Bayes-R2 and WAIC values. The best model out of the four – the hierarchical model that considered random effects due to both strain and study on the thermal inactivation parameters (TP-Strain-Study-HAM) - was used to estimate the posterior distributions for the D-, zT-, and zpH-values. The results obtained indicate that the separate estimation of variability due to strains and studies is essential. The variability introduced in D- and z-values due to variability between studies was higher than that of variability between strains. The parameters estimated using the model for different strains of Listeria species will be applicable for processing aqueous foods such as milk and liquid products such as sauces and gravies across a temperature range of 55 to 70 °C and pH values of 3 to 8 units.
Second, a hierarchical Bayesian model for predicting the growth parameters of different strains of Shiga toxin-producing Escherichia coli (STEC) during post-slaughter chilling of raw beef coupons was developed. The model development involved data procurement via case specific experiments followed by model development using the experimental data.
For obtaining experimental data, three STEC strains (virulent E. coli O157: H7, O26, and O103) were individually inoculated onto the surface of beef coupons obtained within 1-2 h of slaughter. The inoculated beef coupons were subsequently subjected to one of the three commercially applied post-slaughter boning cooling profiles in New Zealand – hot (27 to 5 °C in 15 h), warm (37 to 5 °C in 24 h), and cold boning (37 to 5 °C in 48 h), under laboratory conditions that simulated the temperature change. The increase in the number of bacteria over time with the decrease in temperature was estimated using standard diluting, plating, and incubation methods. Growth of the bacteria and an increase in their number occurred during all of the three boning cooling profiles. For comparison purposes, preliminary growth parameters (Growth rate, lag phase duration, and maximum population density) were estimated for each cooling profile using the Baranyi and Roberts primary growth model, assuming the bacterial numbers were obtained at constant temperatures. The bacterial numbers, irrespective of the serotype, increased from an initial inoculum of 4 log10CFU/g to attain a maximum population density (MPD) of ~10.1 log10CFU/g, ~ 10 log10CFU/g, or ~ 7 log10CFU/g within 10 h for warm, cold or hot boning temperature profiles, respectively, which emphasizes the significance of estimating accurate numbers of STEC during processing. The growth rates (GR) were the highest for cold (0.78 log10CFU/g/h for O157: H7, 1.14 log10CFU/g/h for O103, and 1.16 log10CFU/g/h for O26) and warm (0.69 log10CFU/g/h for O157: H7, 1.13 log10CFU/g/h for O103, and 1.19 log10CFU/g/h for O26) boning cooling profiles while comparatively lower for the hot boning cooling profile (0.39 log10CFU/g/h for O157: H7, 0.51 log10CFU/h for O103, and 0.43 log10CFU/h for O26). There was little practical difference between the GRs of E. coli O103 and O26, while the GR for O157 was comparatively lower than the other two serotypes. The predictions estimated using the current industry-standard model, the Refrigeration index (RI) model, either over (Cold boning cooling profile) or underestimated (warm and hot boning cooling profiles) the growth of E. coli depending upon the boning profile. Given the complex and dynamic nature of the data, the primary model used was not the best choice for fitting the data. Better models are required to account for the variability in STEC growth between different cooling profiles and serotypes to obtain more realistic and accurate predictions of STEC growth during post-slaughter beef chilling conditions.
Using the growth data obtained for STEC (O26, O103, and O157: H7) under the dynamic boning chilling profiles, a one-step/global dynamic hierarchical Bayesian model which combined the primary and secondary models was constructed. The Huang growth model was used as the primary model. The Euler method of stepwise integration was employed as a secondary model to account for the dynamic change in temperature over time and to integrate the growth of bacteria over discretized temperature categories. Hamiltonian Monte Carlo (HMC) simulations were used to predict bacterial growth parameters (Growth rate, lag phase duration, and maximum population density) using different dynamically changing temperature profiles. The model predictions showed that the global dynamic Bayesian model produced more accurate and realistic predictions of STEC growth during post-slaughter cooling profiles than the deterministic RI method. However, inconsistencies were observed between the categorical growth rates and maximum population densities depending upon the initial inoculation levels. This observation has previously received little attention during the development of models. It may be a function of individual cell heterogeneity or differences between bacterial populations when present in high or low numbers. Thus, the model developed in the thesis requires further improvement in order to account for these inconsistencies and improve prediction accuracy. When developed, an improved model could be used as a new safety tool by the New Zealand meat industry to ensure the safety of exported beef.
This thesis shows the application of Bayesian inference to practical food microbiology problems to obtain realistic predictions for bacterial growth and inactivation under different environmental conditions. Further, the use of Bayesian inference allowed for the separation and estimation of uncertainty (such as measurement errors and replicate errors) and variability (such as heterogeneity between strains and variability between food matrices). The models can also be extended for application to other vegetative bacteria under similar food matrices.