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

This Excel workbook simulates the increasing logarithmic growth of a targeted microorganism during isothermal 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 growth parameters a, b, k and Na should be provided by the user. 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/

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

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.

If you have Microsoft Excel installed on your hard disk, you should be able to open the IsothermGenLogistic.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.

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.

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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Modeling Isothermal and Nonisothermal Microbial Growth Using a Generalized Logistic (Verhulst) Model in Excel