CSIRO Division of Food and Nutritional Sciences, Building E6B, Macquarie University, P.O. Box 52, North Ryde, NSW 1670, Australia.
Appl Environ Microbiol. 2009 Nov;75(22):6998-7005. doi: 10.1128/AEM.01067-09. Epub 2009 Sep 18.
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-log-linear 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.
在商业食品行业中，微生物安全性和热加工等效性的证明通常涉及一个数学框架，该框架假设对数线性失活动力学，并引用十进制减少时间 (D(T))、Z 值和累积致死率的概念。然而，许多微生物，特别是孢子，表现出的失活动力学不是对数线性的。这导致了替代的建模方法，如双相和 Weibull 模型，它们放宽了对数线性的强假设。我们使用统计框架开发了一种新的对数二次模型，该模型近似于双相和 Weibull 模型，并提供了额外的生理可解释性。作为一种统计线性模型，对数二次模型相对简单，可以拟合，并为其拟合值提供置信区间。它允许从明显“滞后”的数据中得出类似于 D(T)的值。我们还展示了如何将非对数线性微生物失活动力学的现有模型，如 Weibull 模型，拟合到统计线性模型框架中，从而大大简化其解决方案。我们将对数二次模型应用于产孢细菌肉毒梭菌的热失活动力学数据，并将其与先前描述的流行方法进行了比较，评估了其优点。对数二次模型被用作二次模型的基础，该模型可以捕捉微生物失活动力学对温度的依赖性。反过来，这个模型又与 Sapru 等人和 Rodriguez 等人的孢子失活动力学模型联系起来，这些模型假设在一个群体中孢子有不同的生理状态。我们相信，对数二次模型为通过热和其他过程进行失活动力学的活力论和机械论假设提供了一个有用的框架。
