Reconciliation of the D/z model and the arrhenius model: the effect of temperature on thermal inactivation of microorganisms

Authors: Huang, Lihan

Submitted to: Journal of Food Science
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 5/22/2019
Publication Date: 10/1/2019
Citation: Huang, L. 2019. Reconciliation of the D/z model and the arrhenius model: the effect of temperature on thermal inactivation of microorganisms. Journal of Food Science. 295:499-504. https://doi.org/10.1016/j.foodchem.2019.05.150.
DOI: https://doi.org/10.1016/j.foodchem.2019.05.150

Interpretive Summary: Thermal processing is one of the most effective methods for food preservation. The process of pasteurization and sterilization is based on kinetic analysis of microorganisms exposed to different heating temperatures. However, two of the most fundamental kinetic models using in thermal processing appear to conflict with each other. The study adopted a new mathematical approach to reconcile the difference in the century-old kinetic models. It provides a unified theoretical foundation for kinetic analysis of microorganisms during thermal processing.

Technical Abstract: In thermal processing, the inactivation of microorganisms (vegetative cells and spores) generally follows the 1st-order kinetics. The effect of temperature (T in °C) on microbial inactivation can be either described by the Arrhenius model for the rate of inactivation (k) or by the Bigelow’s D/z model for the decimal reduction time (D). Although both models can be used with equal accuracy, it appears rather difficult to genuinely reconcile these two models due to the difference in the model structures and nonlinearity between the reciprocal of temperature in Kelvin (1/TK) and T. Therefore, the objective of this research is to develop a mathematical approach to reconcile these two models. Based on the thermal resistance of microorganisms, the temperatures used for inactivation are divided into two groups. The first group is for vegetative cells or viruses, ranging from 50 to 100 deg C. The second group for bacterial spores, ranging from 90 to 140 deg C. Results of data analysis show that the nonlinear curve of 1/TK vs T can be almost perfectly approximated by two lines with one in each group between 50 and 140 deg C. Linear regression is used to correlate 1/TK with T through the expression of 1/TK = a + b T for each group to determine the values of a and b. With this expression, the analysis shows that the Arrhenius model and the D/z model are perfectly interchangeable for each group. The difference between these two models are therefore practically reconciled.