The study of HPP inactivation of microbial cells and spores has produced survival curves that were modelled by mathematical functions aiming to describe adequately and accurately the inactivation kinetics (207).Although these models have been previously mainly used in thermal inactivation they have been adapted for HPP inactivation. Therefore, this subject will be interchangeably approached giving priority to HPP inactivation kinetics of S. aureus when information is available. By applying accurate inactivation kinetics, both the bactericidal effect of HPP and the implementation of safe processing conditions become possible (135,206,208), while a thorough knowledge of inactivation kinetics would ideally assure a decisive application of HPP (187).
Kinetic models are mainly used to mathematically quantify microbial inactivation data achieved in HPP experiments (usually isothermal), using different processing parameters such as pressure, temperature and/or time (110).When microorganisms are exposed to HPP, or to other lethal food processing technologies, the concentration of survivors decreases with increasing processing parameters (209). Most often, the inactivation of microorganisms follows first-order kinetics (also known as the log-linear model), which means that, over time, all cells would have the same sensitivity and probability of dying over pressure treatments (135,209–
Chapter 1
211). In a simple explanation, for cells treated with HPP, the logarithm of the surviving cells is plotted against time, producing a straight line (209). From this model one can calculate the D value, which is the time, usually in minutes, needed to decrease the number of microorganisms' cells by a factor of 10 (usually indicates as one log or decimal reduction of the number of microorganisms) and it is used as a measure of the microorganism resistance to HPP (209). From the temperature dependence of D value the “z-value”, which is the temperature interval at which D value will decrease or increase by a factor of 10, can be determined (212). However, although first-order kinetics adequately describes many cases of thermal and HPP microorganisms’ inactivation, the many exceptions to this model rendered it to be an exception rather than the rule. Consequently, over the last 25 years, nonlinear models for inactivation data appeared as a preferable alternative (187,207,210,211,213–215).
The use of nonlinear models is the result of important deviations from linearity due to the display of curves with a shoulder (downward concavity), tailing (upward concavity) and sigmoid shape (it begins with an upward concavity and finishes with a downward concavity or vice versa) (216). The shoulder phenomenon is the period in the beginning of the survival curve in which no measurable inactivation takes place after pressure application (217). The tailing phenomenon can be described as the stabilization at the end of a survival curve after an initial linear decrease due to the existence of a pressure resistant population in a culture, by the effects of experimental conditions, or cell-age distribution (110,218). When in rare cases both phenomena occur, survival curves with sigmoid profiles appear (187).
In fact, the complexity of effects of HPP treatments in microbial cells makes HPP inactivation difficult to follow first-order kinetics. Nowadays, it is accepted that nonlinear inactivation kinetics models explain the majority of pressure inactivation curves (207). The most commonly used nonlinear models in HPP inactivation kinetics include the Weibull (219), modified Gompertz (220), log-logistic (221), and the Baranyi (222) models. The use of these models assumes the existence of differences in the survival time due to differences in individual cells (209) and yields several independent parameters that allow the characterization of shapes as well as the response of the cells in relation to time (207). Even though first-order kinetics is not always followed, there are numerous studies where D and z values are calculated by using first-order kinetics models (211). This is true for many published papers concerning S. aureus inactivation by HPP (Table 1.4) and so, in this section only papers which refer and/or compare other models will be approached.
Chapter 1
logistic models and computed their mean square error (MSE; smaller values of MSE indicate a better fit of the model to the data) values were computed. For the condition 21.5 °C/600 MPa the log-logistic model (MSE=0.3) allowed a more accurate description of the inactivation of S.
aureus, followed by the Weibull model (MSE = 0.7). For the condition 50 °C/500 MPa both the
log-logistic model and the Weibull model allowed an adequate description of the inactivation of
S. aureus with a MSE value of 0.2. For both conditions, the linear model presented higher MSE
values (1.7 for 21.5 °C/600 MPa and 2.4 for 50 °C/500 MPa), showing that this model should not be used to describe S. aureus inactivation under these conditions. Cebrián et al. (2010) (187) studied HPP inactivation kinetics of eight S. aureus strains under different conditions (pressures between 350 and 600 MPa and holding times up to 60min) and fitted the Baranyi model to the inactivation curves, since the study aimed to analyze different phases of inactivation (shoulders, log-linear phase of inactivation and tails). The Baranyi model allowed the authors to describe accurately these phases and consequently to separately correlate each phenomenon with the mechanisms of inactivation. In the study of Tassou et al. (2007) (192), HPP inactivation kinetics of a HPP resistant strain of S. aureus was examined in different matrices (phosphate buffer and ham model system). Although the log-linear model was applied to determine D and z values, the Baranyi's model was fitted to the ratio log10(N/N0) for the estimation of the death rate constant,
the standard error of fit and the correlation coefficients. The authors observed an apparent first- order kinetic behavior for both matrices, but the inactivation data was better described by the Baranyi's model. Guan et al. (2006) (178) studied HPP inactivation kinetics in S. aureus (ATCC 12600) at different process temperatures in UHT whole milk. By examining the survival curves they observed that the linear model was unsuitable to describe the obtained survival curves and so they fitted the data to three nonlinear models (Weibull, log-logistic and modified Gompertz) and computed their MSE. The modified Gompertz model was more appropriate to describe the inactivation of S. aureus at processing temperatures of 4 and 21° C, while the Weibull model was more appropriate at 45 °C. The Weibull model was also successfully applied to describe the survival curves of S. aureus (strain 485) in carrot juice and in peptone water (216). In the study of Viazis et al. (2008) (181), HPP inactivation kinetics was assessed in two S. aureus strains (ATCC 6538 and ATCC 25923) in human milk and in peptone water. For the strain ATCC 6538 first-order inactivation kinetics was observed. However, due to tailing phenomenon observed for the strain ATCC 25923, the investigators fitted the data to the Weibull model, thus demonstrating a much higher fit compared with the linear model initially applied. Yao et al. (2015) (206) also achieved a good fit of data to the Weibull model for HPP inactivation kinetics in S. aureus (CGMCC 1.1861, ATCC 6538) independently of the initial inoculum levels and of the matrix (saline solution or meat slurry). Furthermore, the analysis of the shape factors (n) values (a Weibull model
Chapter 1
parameter), indicated that the survival curves of S. aureus fitted with Weibull model were concave upward or tailing (n < 1).
Hence, although first-order kinetics has been applied to many HPP inactivation kinetics of
S. aureus, this model, is not always the most adequate. Data should always be fitted to adequate
and accurate models, so that safer processing conditions can be estimated and assured, thus preventing risks by food sub-processing or unnecessary food over-processing, which leads to undesirable food quality losses.