A Mathematica* 9 file for Shelf Life Determination by Two Criteria from Digitized Temperature Data

This web page offers a program developed as part of a project on vitamin loss kinetics in space foods supported by NASA under project SA - 14 - 042.

This program allows the user to estimate the times, tc1 & tc2, at which the degradation curves of two nutrients will cross their respective threshold concentration ratios Concc1 & Concc2, given that the storage temperature profile is entered as a digitized time-temperature data file. The assumptions are that in the pertinent temperature range the degradation of the two nutrients follows fixed order kinetics, n≥0 [1], and that the temperature-dependence of the corresponding rate constant k(T) follows the exponential model [1, 2], i.e., t(T(t)) = kTref*exp(c*(T(t) - Tref)). Thus, the other entered values are the assumed kinetic orders, n1 & n2, the reference temperatures, Tref1 & Tref2, the rate constants at the corresponding reference temperatures, kTref1 & kTref2, the constants, c1 & c2, and the threshold concentration ratios, Concc1 & Concc2.

To assure a numerical solution with the FindRoot function, the reader can move the t01 & t02 sliders close to the intersection points which will be used as initial guesses of the sought times.

The storage time tmax and temperature range, Tmin & Tmax, can also be set with sliders.

The Manipulate panel display includes the temperature data in the form of an interpolated function plot (top), the calculated numerical values of the two threshold crossing times, tc1 & tc2, (middle) and plots of the two degradation curves with their corresponding threshold levels shown as dashed lines (bottom). The intersection points are plotted as colored dots and the chosen initial guesses in slightly paler colors of the same hue.

For comparison, the program can also be used for isothermal storage by clicking on the isothermal checkbox and then setting the temperature with the T slider below the checkbox.

WARNING: Note that not all possible entry combinations necessarily have a solution within the specified time range.

References

[1] Peleg, M., Normand, M. D. and Kim, A. D. 2014. Estimating Nutrients' Thermal Degradation Kinetic Parameters with the Endpoints Method. Food Research International 66:313-324.

[2] Peleg M., Normand, M. D. and Corradini, M. G. 2012. The Arrhenius equation revisited. Critical Reviews in Food Science and Nutrition 52:830-851.

The program is written in Mathematica* 9. It is presented below as a Mathematica* notebook (.nb) file, which a user having the installed Mathematica* software can open, view, modify, print and interact with. It is also presented as a Computable Document Format (.cdf) file which can be opened, viewed, printed and interacted with (but not modified) using the free Wolfram CDF Player* application. It is also presented as a Portable Document Format (.pdf) file which can be opened, viewed and printed (but not modified or interacted with) using the free Adobe Acrobat Reader DC† application.

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

Use this page to download a Mathematica* 9 file either as a Mathematica* notebook (.nb), Computable Document Format (.cdf) and Portable Document Format (.pdf) file. If you have Mathematica* version 9 or newer and the Wolfram CDF Player* already installed then you can view the files immediately in a window of your web browser. (If you clicked on the .cdf file's link then you will be able to operate the controls of the included Manipulate panel in the browser window's display. If you clicked on the .nb file's link then the Manipulate panel will not be visible or useable until the file is saved and opened in Mathematica*.) In either case you should save the file by clicking on the window of downloaded text and choosing "Save Page As..." from your browser's File menu. If you have installed Mathematica* you will be able to open, view, modify, print and interact with the saved .nb or .cdf file in its proper format. If you have only installed the Wolfram CDF Player* then you should download only the .cdf file which may be opened, viewed and printed but not modified. However, you will be able to interacte with and operate the controls of the Manipulate panel in either a browser window or in the Wolfram CDF Player. If you only want to open, view and print the file and you have the Adobe Acrobat Reader program installed then you should download the .pdf file.

Download a Mathematica* 9 notebook (.nb) file.

A notebook (.nb) file may be opened, viewed, printed, modified and interacted with if you have Mathematica* 9 or newer.

A 451K .nb file: To download, click here => ShelfLifeDeterminationByTwoCriteriaFromDigitizedTemperatureData.nb


Download a Mathematica* 9 Computable Document Format (.cdf) file.

A Computable Document Format (.cdf) file may be opened, viewed, interacted with and printed (but not modified) using the free Wolfram CDF Player* application.

A 455K .cdf file: To download, click here => ShelfLifeDeterminationByTwoCriteriaFromDigitizedTemperatureData.cdf


Download an Adobe Acrobat Portable Document Format (.pdf) file.

A Portable Document Format (.pdf) file may be opened, viewed and printed (but not modified or interacted with) using the free Adobe Acrobat Reader DC† application.

A 684K .pdf file: To download, click here => ShelfLifeDeterminationByTwoCriteriaFromDigitizedTemperatureData.pdf


* Mathematica® and Wolfram CDF Player® are registered trademarks of Wolfram Research, Inc.
You can get more information about Mathematica by visiting the web site of Wolfram Research at: http://www.wolfram.com/

† Adobe Acrobat Reader DC® is registered trademark of Adobe Systems, Inc.
You can get more information about Adobe Acrobat Reader by visiting the web site of Adobe Systems at: http://www.adobe.com/


[Return to ] Prof. Micha Peleg

[Return to ] Mark D. Normand

[Return to ] UMass Department of Food Science

[Return to ] University of Massachusetts at Amherst

Content last updated: June 29, 2015