Limitations of the Log-Logistic Model for the Analysis of Sigmoidal Microbial Inactivation Data for High-Pressure Processing (HPP)

Abstract

This study identified limitations of the log-logistic model to evaluate microbial inactivation kinetics by high-pressure processing (HPP) including the need to assign a numerical value to “approximate” the undefined expression log10t = 0 and the misinterpretation of its parameters due to a derivation flaw. Peer-reviewed HPP microbial inactivation data were adjusted to a sigmoidal equation (SIG), the original “vitalistic” log-logistic models (VIT-1, VIT-6), and two functions that did not follow the original derivation procedure (LOG-1, LOG-6). Their goodness of fit was determined utilizing the coefficient of determination (R2) and Akaike information criteria (AIC). The shape of the survival curve greatly influenced the performance of log-logistic models. VIT and LOG models performed equally when the kinetic curve showed a sigmoidal shape, and the numerical values of their parameter estimates were identical regardless of the log10 (t = 0) approximation. Conversely, most concave curves yielded inaccurate parameter estimates for all models. LOG-1 and VIT-1 performed best when log10t = 0 was −1 or −2, whereas LOG-6 and VIT-6 yielded best results for values of −3 to −9. SIG ranked last for most datasets but occasionally performed best (Akaike weight factor wAICi = 0.40–1.00) when microbial survival counts showed clear sigmoidal shapes. VIT models consistently displayed R2 ≥ 0.98, and their parameters can be interpreted within a “biological” context using the corrected derivation shown for LOG models. However, concave curves are more frequently observed for HPP microbial inactivation, and fitting the experimental data to log-logistic models deems unnecessary.