## Mathematica* 9 files to estimate the kinetic degradation parameters of compounds in stored and thermally processed foods

This webpage offers two versions (A & B) of an interactive Mathematica* 9 program developed with the support of NASA (under Project SA-14-042) to estimate the kinetic degradation parameters of nutrients, pigments and other heat labile compounds in stored and thermally processed foods (e.g., vitamins in processed and stored space-foods).

Both versions of the program are based on the following assumptions:

1. The degradation of the compound in question follows fixed order kinetics, n ~ 1.
2. The process's rate constant temperature dependence follows the exponential model k(T(t)) = kTref exp(c (T(t))-Tref)) where k(T(t)) is the momentary degradation rate at time t and temperature T(t), kTref is the rate constant at a reference temperature Tref and c is a constant having temperature reciprocal units. (It can and has been shown that this simple model can replace the more complicated Arrhenius equation without sacrificing the fit.)
3. The food's past non-isothermal temperature history is available in the form of a digitized time-temperature data file, which can be imported and converted by Mathematica* into an Interpolating Function.

The difference between the two versions is that Version A's settings are for temperature ranges encountered in food storage while those of Version B are for ranges encountered in thermal processing, i.e., during heat pasteurization and sterilization.

The two programs, labeled A and B, are written in Mathematica* 9. They are presented below as Mathematica* notebook (.nb) files, which a user having the installed Mathematica* software can open, view, modify, execute and print. They are also available as Computable Document Format (.cdf) files which can be opened, viewed, printed and interacted with if you have downloaded and installed the free Wolfram CDF Player* application. They are also available as Adobe Portable Document Format (.pdf) files which can be opened, viewed and printed using the free Adobe Acrobat Reader DC+ application.

Version A: You should start by opening the file in Mathematica* and either importing two storage temperature history profiles (time, Temperature) from an external file (e.g., from a tab-separted ASCII text file) or by copying the two {time, Temperature} data lists from another Mathematica* notebook and pasting them into the indicated locations in the version A program's open notebook (.nb) window. You should then evaluate the notebook to run the program which first defines two InterpolatingFunctions, T1 and T2, from the two data sets and plots the two functions together on the same plot. The next step is to use the controls on the displayed Manipulate panel to enter the coordinates of the experimental endpoints with the sliders for tfinal1, Cexper1 and tfinal2, Cexper2. Next enter the values of nassumed and the chosen Tref using their sliders. Move the sliders for kTrefest and cest so as to make the two concentration ratio vs. time curves pass through the two points. The file should then be Saved under a new name that you select. The final values for for kTrefest and cest may be used either as initial guesses for a fit of the parameters k and c or as the values of the two parameters themselves.

Version B: Version B is used in the same manner as described above for Version A except that the (time, Temperature) data apply to heat processing rather than storage.

Micha Peleg and Mark D. Normand
Department of Food Science
University of Massachusetts
Amherst, MA 01003

### Download two Mathematica* 9 notebook (.nb ) files (programs A & B).

The two programs, (A & B) are all written in Mathematica* 9. They are presented below as Mathematica* notebook (.nb) files, which a user having the installed Mathematica* software can open, view, modify, print, interact with and execute. They are also presented as Computable Document Format (.cdf) files which can be opened, viewed, printed and interacted with (but not modified or executed) using the free Wolfram CDF Player* application. They are also presented as Portable Document Format (.pdf) files which can be opened, viewed and printed (but not executed, modified or interacted with) using the free Adobe Acrobat Reader DC+ application.

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You can get more information about Mathematica and the Wolfram CDF Player by visiting the Web site of Wolfram Research at: http://www.wolfram.com/