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Area under lethality curve

Printed From: Dairy Science and Food Technology
Category: Thermal processing
Forum Name: Thermal processing
Forum Description: Effects of heat on food, enzymes and microorganisms
URL: https://www.dairyscience.info/forum/forum_posts.asp?TID=246
Printed Date: 05 Dec 2020 at 3:26pm
Software Version: Web Wiz Forums 12.03 - http://www.webwizforums.com


Topic: Area under lethality curve
Posted By: mstrange
Subject: Area under lethality curve
Date Posted: 01 Dec 2010 at 11:24pm
Hi we are interested in knowing more about ways of getting area undr lethal rate curve. Any help appreciated.Smile



Replies:
Posted By: Admin
Date Posted: 02 Dec 2010 at 11:45pm

This topic is well-described in older textbooks e.g. counting "squares" under the curve and dividing this number by the number of squares in the rectangle obtained by plotting  a lethality value of 1  for 1 minute. Similarly a planimiter can be used to obtain the area under the curve which is divided by the area (determined using the planimiter) of the the rectangle obtained  by plotting  a lethality value of 1  for 1 minute. It is also possible to cut out the areas, weight them and to divide the weight of the smaller area into the weight of the larger one to obtain the F value at the reference temperature.

However, it is very easy to do this calculation using a spreadsheet and numerical integration.
 
I will say  a little more about this when I get some more time. 
 
Additional material added 3-12-2010
 
Area can be calculated using the trapezoidal rule (also known as the trapezoid rule) or Simpson's rule. The http://www.dairyscience.info/newCalculators/lethalcomp.aspx - free F calculator on this site   uses the trapezoidal rule to calculate area under lethality time curve. You can also download http://www.dairyscience.info/feedback/citefo.asp - a spreadsheet to do the calculation .
 
Another option is to use Excel to calculate the trend line, the equation (use the polynomial option, order 2) for the curve and the r-value. If the r value is >0.9 you could consider integrating the equation if your knowledge of calculus is good. http://www.wolframalpha.com/ - WolframAlpha  can be used to check your calculation. 
 


Posted By: Admin
Date Posted: 07 Apr 2011 at 11:23pm
If you are interested in this topic you might find the post at http://dairyscience.info/forum/topic260_post1109.html#1109 - http://dairyscience.info/forum/topic260_post1109.html#1109  of some interest- comparison of Fo values obtained using 3 numerical integration methods (trapezoidal, Simpson's and Romberg rules)
 and 7 data sets.



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