Assessment of four model forms for predicting thermal inactivation kinetics of Escherichia coli in liquid as affected by combined exposure time, liquid temperature and pH

Abstract

The design of a continuous sterilizer is generally predicated on mathematical models that have been developed from bench-scale thermal inactivation studies. However, there exists a lack of a rigorous mathematical and quantitative understanding of the kinetics of thermal inactivation of microbial contaminants in liquids for process design and simulation. Of particular interest are models that can be reliably used to predict the combined effect of exposure time (f), liquid temperature (7) and pH. Analyses of extensive bench-scale data (n = 208) from within the University of Adelaide's Food Technology Research Group for Escherichia coli have been used to assess the adequacy of four appropriate kinetic model forms for the rate coefficient for thermal inactivation (k) as effected by combined Tand pH. E. coli represents a class of bacterial contaminants common to a range of liquids. The models considered were: the classical log–linear, Davey linear-Arrhenius (D-LA), square-root (or Belehradek) and a cubic-order polynomial (noP). The square-root model has not previously been applied to thermal inactivation data (but almost exclusively to bacterial growth in both the lag phase and growth phase). Each model for k was used together with a first-order chemical reaction for predicting the number of viable survivors. In this way the combined effect of t, T and pH could be simulated. The criteria adopted for model assessment included: the accuracy of prediction against observed data; relative complexity; ease of synthesis and use; and potential for physiological interpretation of model coefficients. Percentage variance accounted for (%V), together with analyses of residuals, is used as a stringent test of accuracy of prediction against observed data. The square-root and D-LA models, respectively, explained 98.0 and 96.00%V in the thermal inactivation rate coefficient. The percentage variance accounted for in these data by the classical log–linear form was 90.5%V and that for the noP 99.0%V The D-LA model was shown to best satisfy the overall criteria for model selection. For these data it has four terms, namely, T, T2 , pH and pH2. Importantly, it is of a practical form that could be readily integrated with equations describing the liquid rheology and fluid hydrodynamics in a continuous sterilizer. However, a major shortcoming with the D-LA model for the rate coefficient is that it fails to satisfactorily predict numbers of survivors at combinations of, greater exposure times (t > 25 s), exposure temperatures (62 °C) and low values of liquid pH (4.5), where the observed survivor curve exhibits tailing. Extrapolation of the D-LA model cannot therefore be reliably carried out together with a first-order chemical reaction. A more adequate model for prediction of the combined effect of t, T and pH on the rate coefficient for thermal inactivation is needed. This must involve accurate prediction of the occurrence of tailing in numbers of viable survivors.