Modeling the Combined Effect of Pressure and Mild Heat on the Inactivation Kinetics of Escherichia coli, Listeria innocua, and Staphylococcus aureus in Black Tiger Shrimp ( Penaeus monodon)

This paper evaluates the applicability of the Weibull model to describe thermal inactivation of microbial vegetative cells as an alternative for the classical Bigelow model of first-order kinetics; spores are excluded in this article because of the complications arising due to the activation of dormant spores. The Weibull model takes biological variation, with respect to thermal inactivation, into account and is basically a statistical model of distribution of inactivation times. The model used has two parameters, the scale parameter alpha (time) and the dimensionless shape parameter beta. The model conveniently accounts for the frequently observed nonlinearity of semilogarithmic survivor curves, and the classical first-order approach is a special case of the Weibull model. The shape parameter accounts for upward concavity of a survival curve (beta 1). Although the Weibull model is of an empirical nature, a link can be made with physiological effects. Beta 1 indicates that the remaining cells become increasingly damaged. Fifty-five case studies taken from the literature were analyzed to study the temperature dependence of the two parameters. The logarithm of the scale parameter alpha depended linearly on temperature, analogous to the classical D value. However, the temperature dependence of the shape parameter beta was not so clear. In only seven cases, the shape parameter seemed to depend on temperature, in a linear way. In all other cases, no statistically significant (linear) relation with temperature could be found. In 39 cases, the shape parameter beta was larger than 1, and in 14 cases, smaller than 1. Only in two cases was the shape parameter beta = 1 over the temperature range studied, indicating that the classical first-order kinetics approach is the exception rather than the rule. The conclusion is that the Weibull model can be used to model nonlinear survival curves, and may be helpful to pinpoint relevant physiological effects caused by heating. Most importantly, process calculations show that large discrepancies can be found between the classical first-order approach and the Weibull model. This case study suggests that the Weibull model performs much better than the classical inactivation model and can be of much value in modelling thermal inactivation more realistically, and therefore, in improving food safety and quality.

Two complementary measures are proposed as simple indices of the performance of models in predictive food microbiology. The indices assess the level of confidence one can have in the predictions of the model and whether the model displays any bias which could lead to 'fail-dangerous' predictions. The use of the indices is demonstrated using data collated from independent and published literature. This analysis supports previous reports that evaluation of predictive models by comparison to published microbial growth rate data may be inappropriate because of limitations in that data. The indices may fail to reveal some forms of systematic deviation between observed and predicted behaviour. It is concluded, however, that the indices provide an objective and readily interpreted summary of model performance and may serve as a first step towards the development of an objective and useful definition of the term 'validated model' in predictive food microbiology.