## Comment Notes from Excel File: MicrobialGrowthModelA.xls

#### Current version: February 4, 2008

**In worksheet column A:**

**MicrobialGrowthModelA.xls** [A1] <--This means "MicrobialGrowthModelA.xls" is in cell A1. The comment note below pops up when you point to cell A1.

**MicrobialGrowthModelA.xls:** This **Excel** workbook simulates 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)**. 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**).

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 the authors.

**Background** [A2]

**Background:** For generating a growth curve with this version of the program, the user needs to generate a **temperature profile** first by selecting a temperature model and its parameters. The default model included here has four parameters: **TempInit**, the initial temperature, **kHeat**, the heating rate, **Tpar1**, the amplitude of the fluctuation and **Tpar2**, the frequency of the fluctuation.

The growth parameters are: **a**, **kpar1**, **kpar2**, **tcpar1** and **tcpar2** (e.g., for *Pseudomonas spp*, they are: a=5.86, kpar1=0.017, kpar2=0.125, tcpar1=159.2, tcpar2=0.17).

This model should be selected to characterize non-isothermal growth curves with a **long lag period**, otherwise, the model in **MicrobialGrowthModelB.xls**, Y(t)=a*t^n/(b+t^n), is recommeded.

**How to run** [A3]

**How to run:** This workbook needs to run some macros. Therefore, you must click the **Enable Macros** button when opening the workbook.

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.

Make any desired changes to the chart settings in column A.

Enter an initial value for each model variable in column B. The pop-up comment note that appears when the **name** cell above a variable's cell is pointed to with the mouse lists any restrictions on the legal range of values for that variable.

Once legal values have been entered for each variable, you may click the **Clear** button in column A to have the **Clear** macro initialize the calculation cells in column C, clear the graphical data columns D through F and delete any existing charts.

Clicking the **Solve** button in column A first calls **Clear** then calls the **Solve** macro. The macro will solve the growth equation and update the model and graphical data cells in columns C through F. It will also draw two charts: the Temperature vs Time and growth equation Y vs Time.

**Modifications** [A4]

**Modifications:** If you wish to see or modify the macros, they are accessed from the **Tools**>**Macro**>**Visual Basic Editor** menu item. Checking the legality of user entries is done by the **Init** function which calls the **NumOK** and **TextOK** functions. All numeric cells in columns B and C are assigned names by the **Init** function. Those names are then used in the formulas in column C to refer to a cell in place of normal **Excel** cell references (such as B4 or R4C2). Unless absolutely necessary, changing the Visual Basic code should be avoided because an error can produce incorrect values or cause the program to stop working. This workbook runs properly in Windows **Excel 97**, **2000**, **XP**, **2003** and **2007** and in **Excel 2001** for the Mac.

**Speed:** With all versions of **Excel** the speed of the computations can be greatly improved (by 20 times or more) by changing Application.ScreenUpdating from True to False in the **Solve** macro. In that case, however, you will not be able to watch the charts being drawn. They will only appear after the final **OK** button is clicked.

**Mac Problems:** If you are using a pre-OS X version of MacOS running **Excel 98** and receive a Run-time error saying "Method 'MaxChange' of object '_Application' failed" you need to comment out the line .MaxChange=0.000001 in the **Clear** subroutine by inserting a single-quote (') as the first character on the line. This is due to a bug in **Excel 98**. You should then enter 0.000001 manually in the Maximum change: edit box of **Tools**>**Preferences...**>**Calculation**.

Continuous ScreenUpdating is **off** by default in **Excel X** and **Excel 2004** for MacOS X and we don't know how to reenable it. Therefore, you cannot watch the data and charts update in real time in **Excel X** and **2004**. However, they will appear once the solution computations have finished and the final **OK** button is clicked. The change described above under **Speed** should be made with Mac **Excel X** and **2004**.

**References** [A5]

**References:**

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.

**Model by:** Professor Micha Peleg and Maria G. Corradini, Ph.D.

**Program by:** Mark D. Normand, EDP Programmer II and Maria G. Corradini, Ph.D.

**Peleg & Normand located at:**

UMass Department of Food Science

Chenoweth Lab.

Amherst, MA 01003

Tel. (Peleg): 413-545-5852

Tel. (Normand): 413-545-2365

Fax: 413-545-1262

Email & Web (Peleg), see: http://www.umass.edu/~aew2000/

Email & Web (Normand), see: http://www.umass.edu/~adva000/

Email (Corradini): mariagcorradini@gmail.com

**Last modified:** February 4, 2008

**Chart Settings:** [A13]

**Chart Settings:** The following cells allow the user to set the values of certain attributes of the charts on this worksheet. In some cases restrictions are placed on the values that may be entered.

**TimeAxisMin** [A14]

**TimeAxisMin:** The cell below contains the minimum value for the **Time** axis on the charts. **TimeAxisMin** must be greater than or equal to 0.

**TimeAxisMax** [A16]

TimeAxisMax: The cell below contains the maximum value for the **Time** axis on the charts. **TimeAxisMax** must be greater than 0 and greater than **TimeAxisMin**.

**TimeAxisTitle** [A18]

**TimeAxisTitle:** The cell below contains a title for the **Time** axis on the charts. **TimeAxisTitle** can contain from 0 to 255 characters.

**TempAxisMin** [A20]

**TempAxisMin:** The cell below contains the minimum value for the **Temperature** axis on the Temp vs Time chart. **TempAxisMin** must be greater than or equal to 0.

**TempAxisMax** [A22]

**TempAxisMax:** The cell below contains the maximum value for the **Temperature** axis on the Temp vs Time chart. **TempAxisMax** must be greater than 0 and greater than **TempAxisMin**.

**TempAxisTitle** [A24]

**TempAxisTitle:** The cell below contains the title for the **Temperature** axis on the Temp vs Time chart. **TempAxisTitle** can contain from 0 to 255 characters.

**TempMainTitle** [A26]

**TempMainTitle:** The cell below contains the main title for the Temp vs Time chart. **TempMainTitle** can contain from 0 to 255 characters.

**TempLineStyle** [A28]

**TempLineStyle:** The cell below contains an index for the LineStyle of the Temp vs Time curve. **TempLineStyle** may be either 1=Continuous, 2=Dash, 3=Dot, 4=DashDot or 5=DashDotDot.

**TempLineWeight** [A30]

**TempLineWeight:** The cell below contains an index for the LineWeight of the Temp vs Time curve. **TempLineWeight** may be either 1=Thin, 2=Medium or 3=Heavy.

**TempLineColor** [A32]

**TempLineColor:** The cell below contains an index for the LineColor of the Temp vs Time curve. **TempLineColor** may be either 1=Black, 2=White (Not allowed), 3=Red, 4=Bright Green, 5=Blue, 6=Yellow, 7=Pink, 8=Turquoise, 9=Dark Red, 10=Green, 11=Dark Blue, 12=Dark Yellow, 13=Violet, 14=Teal, 15=25% Gray or 16=50% Gray.

**YAxisMin** [A34]

**YAxisMin:** The cell below contains the minimum value for the **Y** (Growth) axis on the Y vs Time chart. **YAxisMin** must be greater than or equal to 0.

**YAxisMax** [A36]

**YAxisMax:** The cell below contains the maximum value for the **Y** (Growth) axis on the Y vs Time chart. **YAxisMax** must be greater than 0. and greater than **YAxisMin**.

**YAxisTitle** [A38]

**YAxisTitle:** The cell below contains the title for the **Y** (Growth) axis on the Y vs Time chart. **YAxisTitle** can contain from 0 to 255 characters.

**YMainTitle** [A40]

**YMainTitle:** The cell below contains the main title for the Y vs Time chart. **YMainTitle** can contain from 0 to 255 characters.

**YLineStyle** [A42]

**YLineStyle:** The cell below contains an index for the LineStyle of the Y vs Time curve. **YLineStyle** may be either 1=Continuous, 2=Dash, 3=Dot, 4=DashDot or 5=DashDotDot.

**YLineWeight** [A44]

**YLineWeight:** The cell below contains an index for the LineWeight of the Y vs Time curve. **YLineWeight** may be either 1=Thin, 2=Medium or 3=Heavy.

**YLineColor** [A46]

**YLineColor:** The cell below contains an index for the LineColor of the Y vs Time curve. **YLineColor** may be either 1=Black, 2=White (Not allowed), 3=Red, 4=Bright Green, 5=Blue, 6=Yellow, 7=Pink, 8=Turquoise, 9=Dark Red, 10=Green, 11=Dark Blue, 12=Dark Yellow, 13=Violet, 14=Teal, 15=25% Gray or 16=50% Gray.

**In worksheet column B:**

**TimeInit** [B1]

**TimeInit:** The cell below contains the **Initial Time** (in hours) at the start of the solution. **TimeInit** must be greater than or equal to 0.

**dt** [B4]

**dt:** The cell below contains the **Time** step or **dt:** increment (in hours) between successive iteration points of the solution and therefore between successive points on the charts. **dt** must be greater than 0 and less than or equal to 0.5.

**TimeFinal** [B7]

**TimeFinal:** The cell below contains the **Final Time** (in hours) at which a solution will be calculated. **TimeFinal** must be greater than or equal to 0 and greater than or equal to **TimeInit**.

**YInit** [B10]

**YInit:** The cell below contains an **initial guess** used to compute the **Y** growth function. **YInit** must be greater than 0.

**a** [B13]

**a:** The cell below contains the **asymptotic level** coefficient of the model that describes the growth curve Y(t) = **a**/(1+Exp(**k***(**tc**-Time)))-**a**/(1+Exp(**k*****tc**)). **a** must be greater than 0.

**kpar1** [B16]

**kpar1:** The cell below contains the **independent** coefficient in the temperature dependence of the parameter k(Temp) = **kpar1** * EXP(**kpar2** * Temp). **kpar1** must be greater than 0.

**kpar2** [B19]

**kpar2:** The cell below contains the **rate** coefficient in the temperature dependence of the parameter k(Temp) = **kpar1** * EXP(**kpar2** * Temp). **kpar2** must be greater than 0.

**tcpar1** [B22]

**tcpar1:** The cell below contains the **independent** coefficient in the temperature dependence of the parameter tc(Temp) = **tcpar1** * EXP(-**tcpar2** * Temp). **tcpar1** must be greater than 0.

**tcpar2** [B25]

**tcpar2:** The cell below contains the **rate** coefficient in the temperature dependence of the parameter tc(Temp) = **tcpar1** * EXP(-**tcpar2** * Temp). **tcpar2** must be greater than 0.

**kHeat** [B28]

**kHeat:** The cell below contains the **heating rate** parameter of the temperature profile. **kHeat** must be greater than -1000.

**TempInit** [B31]

**TempInit:** The cell below contains the **Initial Temperature** (in degrees C) of the temperature profile at the start of the solution. **TempInit** must be greater than 0.

**Tpar1** [B34]

**Tpar1:** The cell below contains the **amplitude** parameter (in degrees C) of the fluctuation in the temperature profile. **Tpar1** must be greater than 0.

**Tpar2** [B37]

**Tpar2:** The cell below contains the **frequency** parameter of the fluctuation in the temperature profile. **Tpar2** must be greater than 0.

**In worksheet column C:**

**nPts** [C1]

**nPts:** The cell below contains the **number of solution points** (rows) to be generated, stored in columns D through F and plotted.

**EqnRoot** [C4]

**EqnRoot:** The cell below contains the expression of the **growth equation** and displays the root of that equation at the current **Time** step. At each **Time** step the **Solve** macro uses **Excel**'s iterative **Goal Seek** command to drive the **EqnRoot** value to zero by changing the value in the **YCurr** cell. Computing the **YCurr** values is the main goal of this workbook. How close **EqnRoot** comes to zero is controlled by the value assigned in the **Clear** macro to **Application.MaxChange**.

**YCurr** [C7]

**YCurr:** The cell below contains the **growth solution** from the current **Time** step. Before iteration begins **YCurr** is set to **YInit** and thereafter **YCurr** is repeatedly updated by the **Solve** macro as it calculates and its value is copied to the appropriate row in the **Y(Time)** column at the end of each iteration. Computing the **YCurr** values is the main goal of this workbook.

**YPrev** [C10]

**YPrev:** The cell below contains the **growth solution** from the previous **Time** step. Before iteration begins **YPrev** is set to **YInit** and thereafter it is repeatedly updated by the **Solve** macro as it calculates.

**kSum** [C13]

**kSum:** The cell below contains the **sum** of the previous and current values of the **k** parameter found in the **kPrev** and **kCurr** cells. **kSum** is repeatedly updated by the **Solve** macro as it calculates.

**kCurr** [C16]

**kCurr:** The cell below contains the current **k** parameter value computed from the expression in that cell. **kCurr** is repeatedly updated by the **Solve** macro as it calculates.

**kPrev** [C19]

**kPrev:** The cell below contains the previous **k** parameter value computed from the expression in that cell. **kPrev** is repeatedly updated by the **Solve** macro as it calculates.

**TempCurr** [C22]

**TempCurr:** The cell below contains the current **Temperature** (in degrees C) computed from the temperature profile expression in that cell. **TempCurr** is repeatedly updated by the **Solve** macro as it calculates and the value is copied to the appropriate row in the **Temp(Time)** column at the end of each iteration.

**TempPrev** [C25]

**TempPrev:** The cell below contains the previous **Temperature** (in degrees C) computed from the temperature profile expression in that cell. **TempPrev** is repeatedly updated by the **Solve** macro as it calculates.

**TimeCurr** [C28]

**TimeCurr:** The cell below contains the **Time** (in hours) at the current solution point. **TimeCurr** is repeatedly updated by the **Solve** macro as it calculates and the value is copied to the appropriate row in the **Time** column at the end of each iteration.

**TimePrev** [C31]

**TimePrev:** The cell below contains the **Time** (in hours) at the previous solution point. **TimePrev** is repeatedly updated by the **Solve** macro as it calculates.

**tcSum** [C34]

**tcSum:** The cell below contains the **sum** of the previous and current values of the **tc** parameter found in the **tcPrev** and **tcCurr** cells. **tcSum** is repeatedly updated by the **Solve** macro as it calculates.

**tcCurr** [C37]

**tcCurr:** The cell below contains the current **tc** parameter value computed from the expression in that cell. **tcCurr** is repeatedly updated by the **Solve** macro as it calculates.

**tcPrev** [C40]

**tcPrev:** The cell below contains the previous **tc** parameter value computed from the expression in that cell by referencing the **Temperature** value in the **TempPrev** cell. **tcPrev** is repeatedly updated by the **Solve** macro as it calculates.

**In worksheet column D:**

**Time** [D1]

**Time:** The cells below contain **TimeCurr**, the current **Time** (in hours), for each step in the solution process and are used as the x-axis values in the Temp vs Time and Y vs Time charts.

**In worksheet column E:**

**Temp(Time)** [E1]

**Temp(Time):** The cells below contain **TempCurr**, the current **Temperature** (in degrees C), for each **Time** step in the solution process and are used as the y-axis values in the Temp vs Time chart.

**In worksheet column F:**

**Y(Time)** [F1]

**Y(Time):** The cells below contain **YCurr**, the current **Y** growth value, for each **Time** step in the solution process and are used as the y-axis values in the Y vs Time chart. Computing the **Y** growth values is the main goal of this workbook.

Content last updated: February 4, 2008