These **Excel** workbooks simulate the increasing logarithmic growth ratio 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 model **Y(t) = a/(1+Exp(k*(tc-Time)))-a/(1+Exp(k*tc)**, which is appropriate for **long (and short) lag times**. The temperature dependence of the growth parameters **k(Temp)** and **tc(Temp)** obeys an exponential relationship while **a(Temp)** is fixed. Explanation of the model can be found in Corradini, M.G and Peleg, M. 2005 (see **References** below). 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/

* 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 workbooks are available in a file format for Windows Excel 97 through 2007 and MacOS Excel 98 through 2004. If you have a modern web browser you should be able to download a binary Excel file directly by clicking on one of the links below.

Excel binary file (156K) for Windows Excel 97 through 2007 and MacOS Excel 98 through 2004:

Excel binary file (156K) for Windows Excel 97 through 2007 and MacOS Excel 98 through 2004:

Note: Earlier versions were posted here on the web. The February 21, 2006 versions contained bug fixes, Visual Basic code improvements and pop-up comment note updates. The February 4, 2008 versions add compatibility with Windows Excel 2007 and update several comment notes.

If you have Microsoft Excel installed on your hard drive, you should be able to open either the **MicrobialGrowthModelA.xls** or **MicrobialGrowthModelAData.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 thru A5 for instructions on how to run the worksheet models.** To view or print all of a workbook's comment notes together click on one of the links below.

The Excel files **MicrobialGrowthModelA.xls** or **MicrobialGrowthModelAData.xls** each contain a single worksheet. Sheet1 contains instructions, user input cells, two embedded charts, and two buttons labeled 'Clear' and 'Solve'. **Cells that have a red triangle marker in their upper right corner have a comment note attached to them.**

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

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