22 March 2011

Are food-borne pathogen survival times really exponentially distributed?

From Scientific American, an excerpt from Modernist Cuisine: The Art and Science of Cooking on the complex origins of food safety rules.

This is the six-volume, six-hundred-dollar magnum opus of Nathan Myhrvold (former chief technology officer at Microsoft, and chefs Chris Young and Maxime Bilet; you can read more about it at the Wall Street Journal.

In particular I noticed the following:
If a 1D reduction requires 18 minutes at 54.4 degrees C / 130 degrees F , then a 5D reduction would take five times as long, or 90 minutes, and a 6.5D reduction would take 6.5 times as long, or 117 minutes.

A "nD" reduction is one that kills all but 10-n of the foodborne pathogens.

What struck me here is that the distribution of the pathogen lifetimes, assuming these numbers are actually correct, is exponential. And, therefore, memoryless -- if you're a bacterium under these conditions, your chances of dying in the first eighteen minutes are ninety percent, and if you're still alive at ninety minutes, your chances of dying in the next eighteen minutes are still ninety percent. This surprised me. The decay of radioactive atoms can be described in this way -- but are bacteria really so simple?

The excerpt as a whole is quite interesting -- apparently a lot more than just science is going into recommendations of how long food should be cooked.

(Myhrvold has a bachelor's degree in math and a PhD in mathematical economics, among other degrees; Young has a bachelor's degree in math and was working on a doctoral degree before he left for the culinary world. So perhaps it is fair of me to think that they would get this right.)

2 comments:

jonathan said...

Well here you're making the (I think mild) assumption that the bacteria on the food would live longer than the cooking time to start with.
wiki says that some bacteria have lifetimes of about 9.8 minutes

http://en.wikipedia.org/wiki/Bacteria#Growth_and_reproduction

The heat could be messing with the frequency of birthsas well as the frequency of death

CarlBrannen said...

You might enjoy one of my dad's papers on the subject (which is still cited): http://www.jstor.org/pss/3574133 or http://www.springerlink.com/content/v8132mm25x57560t/