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:

- The degradation of the compound in question follows fixed order kinetics, n ~ 1.
- The process's rate constant temperature dependence follows the exponential model
*k*(*T*(*t*)) =*k*_{Tref}exp(*c*(*T*(*t*))-*T*_{ref})) where*k*(*T*(*t*)) is the momentary degradation rate at time*t*and temperature*T*(*t*),*k*_{Tref}is the rate constant at a reference temperature*T*_{ref}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.) - 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 *t*_{final1}, *C*_{exper1} and *t*_{final2}, *C*_{exper2}. Next enter the values of *n*_{assumed} and the chosen *T*_{ref} using their sliders. Move the sliders for *k*_{Trefest} and *c*_{est} 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 *k*_{Trefest} and *c*_{est} 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.

Use this page to download two Mathematica* 9 .nb (notebook) files (programs A & B). If you have Mathematica* version 9 or newer already installed then you can view the files immediately in a window of your web browser. However, once a notebook file is visible you should save it by clicking on the window of downloaded text and then choosing "Save Page As..." from your browser's File menu. If you have installed Mathematica* you will then be able to open, view, modify, execute and print the saved .nb files in Mathematica*. If you want to see an interactive but non-editable version of either file and you have the Wolfram CDF Player* installed, click on its .cdf link. If you want to see a static (non-interactive) version of either file and you have Adobe Acrobat Reader+ installed, click on its .pdf link.

A .nb file (446K) containing program A. **To download, click here =>** DegradationParametersEstimationFromInterpolatedTemperatureDataA(Storage).nb

A .cdf file (446K) containing program A. **To download, click here =>** DegradationParametersEstimationFromInterpolatedTemperatureDataA(Storage).cdf

A .pdf file (279K) containing program A. **To download, click here =>** DegradationParametersEstimationFromInterpolatedTemperatureDataA(Storage).pdf

A .nb file (381K) containing program B. **To download, click here =>** DegradationParametersEstimationFromInterpolatedTemperatureB(HeatProcessing).nb

A .cdf file (381K) containing program B. **To download, click here =>** DegradationParametersEstimationFromInterpolatedTemperatureB(HeatProcessing).cdf

A .pdf file (258K) containing program B. **To download, click here =>** DegradationParametersEstimationFromInterpolatedTemperatureB(HeatProcessing).pdf

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+ Adobe Acrobat Reader DC® is registered trademark of Adobe Systems, Inc.

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