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

• Published in: Food and bioprocess technology 2016-05, Vol.9 (5), p.904-916
• Main Authors: Serment-Moreno, Vinicio, Torres, J. Antonio, Fuentes, Claudio, Ríos-Alejandro, José Guadalupe, Barbosa-Cánovas, Gustavo, Welti-Chanes, Jorge
• Format: Article
• Language: English
• Subjects: Agriculture; Biotechnology; Chemistry; Chemistry and Materials Science; Chemistry/Food Science; Deactivation; Derivation; Food Science; Goodness of fit; Inactivation; Mathematical models; Microorganisms; Original Paper; Parameter estimation; Pasteurization; Survival
• ISSN: 1935-5130; 1935-5149
• DOI: 10.1007/s11947-016-1677-2

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 log 10 t  = 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 ( R 2 ) 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 log 10 ( t  = 0) approximation. Conversely, most concave curves yielded inaccurate parameter estimates for all models. LOG-1 and VIT-1 performed best when log 10 t  = 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 w AIC i  = 0.40–1.00) when microbial survival counts showed clear sigmoidal shapes. VIT models consistently displayed R 2  ≥ 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.