Modelling the heat stress and the recovery of bacterial spores

After heat treatment, the temperature incubation and the medium composition, (pH and sodium chloride content) influence the capacity of injured spores to repair heat damage. The concept of heat resistance D- (decimal reduction time) and z-values (temperature increase which results in a ten fold reduction of the D value) is not sufficient and the ratio of spore recovery after incubation should be considered in calculations used in thermal processing of food. This paper aims to derive a model describing the recovery of injured spores as a function of both the heat treatment intensity and the environmental conditions. According to data from numerous investigators, when spores are incubated in unfavorable conditions, the ratio of cell recovery and the apparent D-value are reduced. Moreover the ratio of the apparent D-value and the estimated in optimal incubation D-value is constant and independent of the heat treatment conditions. Beyond these observations it is shown that the ratio of cell recovery with respect to the heat treatment F-value (exposure time, in minutes, at 121.1°C which results in the same destruction ratio that the considered heat treatment does) is linear and can be quantified by using two factors independent of the heat treatment: the γ-factor reflects the degree of precariousness due to the heat stress while the ε-factor reflects more intrinsically the incubation conditions without previous heat treatment. The γ-factor varies as a function of the incubation temperature according to an Arrhenius law.