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Applied and Environmental Microbiology, November 2009, p. 6998-7005, Vol. 75, No. 22
0099-2240/09/$08.00+0     doi:10.1128/AEM.01067-09
Copyright © 2009, American Society for Microbiology. All Rights Reserved.

Development of a Log-Quadratic Model To Describe Microbial Inactivation, Illustrated by Thermal Inactivation of Clostridium botulinum

G. Stone,¹ B. Chapman,^2* and D. Lovell³

CSIRO Division of Mathematical and Information Sciences, Building E6B, Macquarie University, North Ryde, NSW 2113, Australia,¹ CSIRO Division of Food and Nutritional Sciences, P.O. Box 52, North Ryde, NSW 1670, Australia,² CSIRO Division of Mathematical and Information Sciences, Building 108, North Road, Australian National University Campus, Acton, ACT 2601, Australia³

Received 9 May 2009/ Accepted 10 September 2009

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.

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* Corresponding author. Mailing address: CSIRO Division of Food and Nutritional Sciences, P.O. Box 52, North Ryde, NSW 1670, Australia. Phone: (612) 9490-8470. Fax: (612) 9490-8499. E-mail: belinda.chapman{at}csiro.au

Published ahead of print on 18 September 2009.

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Applied and Environmental Microbiology, November 2009, p. 6998-7005, Vol. 75, No. 22
0099-2240/09/$08.00+0     doi:10.1128/AEM.01067-09
Copyright © 2009, American Society for Microbiology. All Rights Reserved.