Generation of Non-Isothermal Growth Curves Using a Generalized Logistic (Verhulst) Model in Excel*

NonIsothermGenLogistic.xls
Generates Time, Temperature, Count and Log10(Count) values using an internal Temperature Profile equation with user-adjustable parameters.
Current version: February 4, 2008


This Excel workbook simulates the increasing logarithmic growth of a targeted microorganism during temperature controlled storage in real time. This version of the program simulates the growth of organisms whose isothermal survival curve follows the generalized Verhulst model: dN(t)/dt =k*N^a*(1-N/Na)^b. The temperature dependence of the growth parameters a(Temp), b(Temp) and k(Temp) obey an exponential relationship while Na(Temp) follows a logistic relationship. For more information on the concept, its various applications in calculating the microbial growth during storage at variable temperatures and its implementation with more complicated growth models, contact Micha Peleg at: http://people.umass.edu/~aew2000/ or Maria Corradini at: mariagcorradini@gmail.com

* Excel is a registered trademark of Microsoft Corporation. You can get more information about Excel by visiting Microsoft's web site at: http://www.microsoft.com/

Download the Demonstration Excel Workbook

The demonstration workbook is available in a file format for Windows Excel 97 (or newer) and MacOS Excel 98 through 2004. If you have a modern web browser you should be able to download the binary Excel file directly by clicking on the link below.

Generates Time, Temperature, Count and Log10(Count) values using an internal Temperature Profile equation with user-adjustable parameters.
Excel binary file (504K) for Windows Excel 97 through 2007 and MacOS Excel 98 through 2004:
Click here to download ==> NonIsothermGenLogistic.xls

Note: The first version of the Excel file was dated October 3, 2006. The September 4, 2007 version updated the first reference. The February 4, 2008 version added compatibility with Windows Excel 2007 and made corrections to a few comment notes.

Opening the Excel Workbook File

If you have Microsoft Excel installed on your hard disk, you should be able to open the GeneralNonIsoLogistic.xls file in Excel by double-clicking on its icon. If that doesn't work, open the workbook file by first starting Excel, choosing Open... from the File menu and then selecting the Excel file that was downloaded and saved on your hard disk. If the file does not appear on the list of file names, set the Files of type: pop-up menu to All Files (*.*) then select and open the file. If you were unable to open the file by double-clicking on it, use the alternate method just described to open it and once the file has opened in Excel you should immediately save it by choosing Save from the File menu. This will make it possible to open the file in the future by simply double-clicking on its icon.

When you are shown a dialog box asking about enabling macros, click the Enable Macros button. If you are using a recent version of Excel for Windows, you may need to reduce the security level in Tools>Macro>Security to Medium, then close and reopen the file to enable the macros.

How to Run the Excel Worksheet Model

Clicking the Clear button will erase the two charts from Sheet1. Clicking the Solve button erases the charts before the model is solved so it is not necessary to click Clear before clicking Solve. Read the comment notes attached to cells A1 through A5 for instructions on how to run the worksheet models. To view or print all of a workbook's comment notes together click on the link below.

Worksheet Comment Notes

The Excel file NonIsothermGenLogistic.xls contains two worksheets. Sheet1 contains instructions, user input cells, three embedded charts, and two buttons labeled 'Clear' and 'Solve'. Sheet2 contains the data for the four parameters of the internal temperature profile model along with four embedded charts showing how each parameter changes with Temperature. Cells that have a red triangle marker in their upper right corner have a comment note attached to them.

Click here to see the text of all comment notes from NonIsothermGenLogistic.xls.

If a cell contains the name of one or more cells below it, the note explains how those cells are used. In Windows Excel 97, MacOS Excel 98, or newer the note pops up automatically when you use the mouse to point to a marked cell. To edit or change the size of a note, click on a marked cell to select it, then choose Edit Comment from the Insert menu. Making modifications to any of the formulas in a worksheet or to the Visual Basic macro code may cause the macros to stop working properly.

References

  1. Peleg, M., Corradini, M.G. and Normand, M.D. 2007. The logistic (Verhulst) model for sigmoid microbial growth curves revisited. Food Research Internl. 40:808-818.

  2. Peleg, M. and Penchina, C.M. 2000. Modeling microbial survival during exposure to a lethal agent with varying intensity. Crit. Rev. Food Sci. 40:159-172.

  3. Peleg, M. 2003. Microbial survival curves: Interpretation, mathematical modeling and utilization. Comments on Theoretical Biology 8:357-387.

  4. Peleg, M., Corradini, M.G. and Normand, M.D. 2004 Kinetic models of complex biochemical reactions and biological processes. Chemie Ingenieur Technik 76:413-423.

  5. Peleg, M., Normand, M.D. and Corradini, M.G. 2005. Generating microbial survival curves during thermal processing in real time. Journal of Applied Microbiology 98:406-417.

  6. Corradini, M.G. and Peleg, M. 2005. Estimating non-isothermal bacterial growth in foods from isothermal experimental data. Journal of Applied Microbiology 99:187-200.

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Content last updated: February 4, 2008