Page 2318, column 1, line 43: "B. coagulans was sporulated on Campden sporulation medium (6)" should read "B. coagulans and B. amyloliquefaciens were sporulated on Campden sporulation medium (6) and nutrient agar, respectively."

In the commercial food industry, demonstration of microbiological safety and thermal process equivalence often involves a mathematical framework that assumes log-linear inactivation kinetics and invokes concepts of decimal reduction time (D T ), z values, and accumulated lethality. However, many microbes, particularly spores, exhibit inactivation kinetics that are not log linear. This has led to alternative modeling approaches, such as the biphasic and Weibull models, that relax strong log-linear assumptions. Using a statistical framework, we developed a novel log-quadratic model, which approximates the biphasic and Weibull models and provides additional physiological interpretability. As a statistical linear model, the log-quadratic model is relatively simple to fit and straightforwardly provides confidence intervals for its fitted values. It allows a D T -like value to be derived, even from data that exhibit obvious "tailing." We also showed how existing models of non-loglinear microbial inactivation, such as the Weibull model, can fit into a statistical linear model framework that dramatically simplifies their solution. We applied the log-quadratic model to thermal inactivation data for the spore-forming bacterium Clostridium botulinum and evaluated its merits compared with those of popular previously described approaches. The log-quadratic model was used as the basis of a secondary model that can capture the dependence of microbial inactivation kinetics on temperature. This model, in turn, was linked to models of spore inactivation of Sapru et al. and Rodriguez et al. that posit different physiological states for spores within a population. We believe that the log-quadratic model provides a useful framework in which to test vitalistic and mechanistic hypotheses of inactivation by thermal and other processes.Thermal processes for the food industry are typically developed and validated through laboratory-based experimentation. A common experimental format involves isothermal inactivation to determine the decimal reduction time (D T ), which is the time required for a 10-fold (1-log 10 or decimal) reduction in the number of microorganisms at a given temperature (T), according to the primary model:where N t is the number of microorganisms (usually per unit of volume or weight) at time t and N 0 is the number of microorganisms at time zero (5). When D T values are determined at different temperatures, the relative lethality of these temperatures can be determined if we assume the secondary model:where T 0 is a reference temperature and z is the temperature difference required for a 10-fold change in the D T of the target microorganism compared with the D T at T 0 (D T0 )(5, 24). The z value concept has been popular in commercial food processing settings (for example, when cans of food are retorted) as it allows dynamic description of inactivation during a nonisothermal process (i.e., when the temperature varies with the processing time) and across space, as heat penetrates the food (10). The thermal equivalence o...