Micha Peleg

The canning industry’s success in avoiding botulism, according to Teixeira et al. (2006), is due to the application of mathematical models capable of simulating the complex mechanisms of fluid mechanics, thermodynamics, and heat transfer involved in thermal processing of foods." This is to a large extent true.

However, the food industry is still using D and z values to calculate sterility, despite the growing evidence that inactivation of bacterial spores, including those of Clostridium botulinum, does not follow first-order kinetics (e.g., Anderson et al., 1996). The same can be said about thermal inactivation of bacterial cells (van Boekel (2002). To calculate the "D value," food technologists must pass a straight line through curved data or eliminate "undesirable" experimental points, an unacceptable practice in any scientific discipline.

The calculated "F0 value" and process simulations are based on the assumption that the exponential inactivation rate’s temperature dependence follows the log-linear or Arrhenius model. But if either model is taken seriously, the momentary exponential inactivation rate will have to be exactly the same if the food has just reached 115°C or cooled to this temperature after being held at 125°C for 10 minutes!

Since time does not appear in their equations, both models require that the exponential inactivation rate must not depend on the spores’ previous thermal history. Also, why and how could the cascades of biochemical and biophysical processes that destroy bacterial cells and spores be universally coordinated in such a way that they will always produce a single temperature-independent "energy of activation" has never been explained.

More likely, the main reason for the safety of canned foods is not the calculation method’s sophistication or correctness but gross overprocessing that makes the model irrelevant.

The current inactivation models were formulated early in the last century, when there was a premium on linearization. The repeated demonstrations that microbial survival does not follow the standard model have been largely ignored. When the "F0 value" concept was introduced, numerical solution of differential equations was not a viable option. Yet, the prevailing computer programs to calculate thermal processes are still based on the old oversimplified inactivation models. The currently used programs have added numerical integration of the old rate equations, sometimes combined with heat transfer models. The latter is a step forward, but it does not rid the underlying inactivation models of their theoretical flaws.

Today, we have both the mathematical tools and the computational power to handle nonlinear inactivation kinetics (Peleg, 2006), and the predictive ability of the resulting models has been validated experimentally for selected bacterial spores and cells. Microsoft Excel® programs to calculate the efficacy of thermal processes without the unnecessary old assumptions are now available as freeware (www-unix.oit.umass.edu/~aew2000/GrowthAndSurvival.html).

One of the main guidelines regarding microbial inactivation kinetics is "Kinetics of Microbial Inactivation for Alternative Food Processing Technologies" (www.cfsan.fda.gov/~comm/ift-toc.html), a report prepared in 2000 by the Institute of Food Technologists for the Food and Drug Administration. It lists the D and z values of numerous organisms and spores, side by side with their "energy of activation" and a rate constant at a reference temperature, despite the fact that, mathematically, the two corresponding models are mutually exclusive. The site also lists similar parameters for ultra-high pressure and other preservation methods, where, again, there is neither evidence nor reason to expect that the inactivation follows the first-order kinetics.

Those teaching thermal processing should inform their students about the new developments in microbial inactivation kinetics and the shortcomings of the current methods to calculate sterility. It is time to reexamine and revise the theories of thermal processing to guarantee not only the foods’ microbial stability but also their chemical safety, nutritional value, and overall quality.

by Micha Peleg is Professor of Food Engineering, Dept. of Food Science, University of Massachusetts, Amherst, MA 01003 ([email protected]).


Anderson, W.A., McClure, P.J., Baird-Parker, A.C., and Cole, M.B. 1996. The application of a log-logistic model to describe the thermal inactivation of Clostridium botulinum 213B at temperatures below 121.1C. J. Appl. Bacteriol. 80: 283-290.

Peleg, M. 2006. "Advanced Quantitative Microbiology for Food and Biosystems: Models for Predicting Growth and Inactivation."CRC Press, Boca Raton, Fla.

Teixeira, A., Almonacid, S., and Simpson, R. 2006. Keeping botulism out of canned foods. Food Technol. 60(2): 84.

Van Boekel, M.A.J.S. 2003. On the use of the Weibull model to describe thermal inactivation of microbial vegetative cells. Intl. J. Food Microbiol. 72: 159-172.