## Comment notes from Excel file: RealTimePasteurization.xls

#### Current version: February 4, 2008

**In worksheet column A:**

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

**RealTimePasteurization.xls:** This **Excel** workbook simulates the diminishing survival ratio of targeted bacterial cells during a heat process intended for their elimination **in real time**. This version of the program simulates the inactivation of organisms whose isothermal survival curve follows the **Weibull** (power law) model with a fixed shape factor (power), **n**, and where the temperature dependence of the survival rate parameter, **b(Temp)**, obeys a log logistic relationship. Explanation of the model can be found in Peleg, M. 2003 (see **References**).

For more information on the concept, its various applications in calculating the efficacy of thermal and non-thermal microbial inactivation processes and biochemical reaction kinetics and its implementation with more complicated survival models, contact Micha Peleg at: http://www-unix.oit.umass.edu/~aew2000/

**Background** [A2]

**Background:** For generating a survival curve with this version of the program, the user needs to generate a temperature profile first by selecting a heating-cooling model and its parameters. The default model included here is for a logistic-Fermi profile having six parameters: **TempInit**, the initial temperature, **TempTarget**, the target temperature, **kHeat**, a heating rate parameter, **TimeHeat**, a heating time "location" parameter, **kCool**, a cooling rate parameter and **TimeCool**, a cooling time "location" parameter. Notice that **TimeCool** >> **TimeHeat** creates a "holding time".

The survival parameters are: **n**, **k** and **TempCrit**. For the *Salmonella*-like organism used here they are: **n**= 0.6, **k**=0.4 C^-1 and **TempCrit**=62 C. The user may set them to other values as needed.

**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 H and delete any existing charts.

Clicking the **Solve** button in column A first calls **Clear** then calls the **Solve** macro to solve the Log Survival equation, update the model and graphical data cells in columns C through H. It will also draw four charts: the Temperature vs Time, the corresponding Log Survival vs Time (log base 10), the Equivalent Time at the Chosen Reference Temperature vs Time and the Weibullian Parameter b 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 program 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 **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., 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.

**Model by:** Professor Micha Peleg

**Program by:** Mark D. Normand, EDP Programmer II

**Both 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-unix.oit.umass.edu/~aew2000/

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

**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 the 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.

**LSAxisMin** [A34]

**LSAxisMin:** The cell below contains the minimum value for the **Log Survival** axis on the LS vs Time chart. **LSAxisMin** must be less than 0 and less than LSAxisMax.

**LSAxisMax** [A36]

**LSAxisMax:** The cell below contains the maximum value for the **Log Survival** axis on the LS vs Time chart. **LSAxisMax** must be less than or equal to 0.

**LSAxisTitle** [A38]

**LSAxisTitle:** The cell below contains the title for the **Log Survival** axis on the LS vs Time chart. **LSAxisTitle** can contain from 0 to 255 characters.

**LSMainTitle** [A40]

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

**LSLineStyle** [A42]

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

**LSLineWeight** [A44]

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

**LSLineColor** [A46]

**LSLineColor:** The cell below contains an index for the LineColor of the LS vs Time curve. **LSLineColor** 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.

**EqTimeAxisMin** [A48]

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

**EqTimeAxisMax** [A50]

**EqTimeAxisMax:** The cell below contains the maximum value for the **EqTime** axis on the EqTime vs Time chart. **EqTimeAxisMax** must be greater than 0 and greater than **EqTimeAxisMin**.

**EqTimeAxisTitle** [A52]

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

**EqTimeMainTitle** [A54]

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

**EqTimeLineStyle** [A56]

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

**EqTimeLineWeight** [A58]

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

**EqTimeLineColor** [A60]

**EqTimeLineColor:** The cell below contains an index for the LineColor of the EqTime vs Time curve. **EqTimeLineColor** 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.

**bAxisMin** [A62]

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

**bAxisMax** [A64]

**bAxisMax:** The cell below contains the maximum value for the **b** axis on the b vs Time chart. **bAxisMax** must be greater than 0 and greater than **bAxisMin**.

**bAxisTitle** [A66]

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

**bMainTitle** [A68]

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

**bLineStyle** [A70]

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

**bLineWeight** [A72]

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

**bLineColor** [A74]

**bLineColor:** The cell below contains an index for the LineColor of the b vs Time curve. **bLineColor** 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 minutes) 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 **delta-t** increment (in minutes) between successive iteration points of the solution and therefore between successive points on the charts. **dt** must be greater than 0.

**TimeFinal** [B7]

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

**LSInit** [B10]

**LSInit:** The cell below contains an **initial guess** used to compute the **Log Survival** function. **LSInit** must be less than 0.

**n** [B13]

**n:** The cell below contains a **shape factor** of the Weibullian description of the isothermal survival curve, Log S(Time) = -b(Temp)*Time^**n**. **n** must be greater than 0.

**k** [B16]

**k:** The cell below contains a **coefficient** in the temperature dependence of the Weibullian rate parameter, b(Temp) = LN(1+EXP(**k***(Temp-**TempCrit**))). **k** must be greater than 0.

**TempCrit** [B19]

**TempCrit:** The cell below contains the **Critical Temperature** (in degrees C) used as a coefficient in the temperature dependence of the Weibullian rate parameter, b(Temp) = LN(1+EXP(**k***(Temp-**TempCrit**))). **TempCrit** must be greater than 0 and greater than or equal to **TempInit**.

**TempInit** [B22]

**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.

**TempTarget** [B25]

**TempTarget:** The cell below contains the **Target Temperature** (in degrees C) of the Temperature profile. **TempTarget** must be greater than 0 and greater than or equal to **TempInit**.

**kHeat** [B28]

**kHeat:** The cell below contains the **Heating Rate** parameter of the temperature profile. **kHeat** must be greater than 0.

**kCool** [B31]

**kCool:** The cell below contains the **Cooling Rate** parameter of the temperature profile. **kCool** must be greater than 0.

**TimeHeat** [B34]

**TimeHeat:** The cell below contains the **Heating Time "Location"** parameter of the temperature profile. **TimeHeat** must be greater than 0.

**TimeCool** [B37]

**TimeCool:** The cell below contains the **Cooling Time "Location"** parameter of the temperature profile. **TimeCool** must be greater than 0.

**TempWater** [B40]

**TempWater:** The cell below contains the **Cooling Water Temperature** (in degrees C). **TempWater** must be < **TempTarget**.

**DeltaTempWater** [B43]

**DeltaTempWater:** The cell below contains the STRONG>Product Temperature (in degrees C) above that of the cooling water. **DeltaTempWater** must be > 0.

**TempIsoRef** [B46]

**TempIsoRef:** The cell below contains the **Isothermal Reference Temperature** (in degrees C). **TempIsoRef** must be > 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 H and plotted.

**EqnRoot** [C4]

**EqnRoot:** The cell below contains the expresson of the **Log Survival** 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 **LSCurr** cell. Computing the **LSCurr** 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**.

**LSCurr** [C7]

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

**LSPrev** [C10]

**LSPrev:** The cell below contains the **Log Survival** solution from the contains **Time** step. Before iteration begins **LSPrev** is set to **LSInit** and thereafter it is repeatedly updated by the **Solve** macro as it calculates.

**bSum** [C13]

**bSum:** The cell below contains the **sum** of the previous and current values of the **b** Weibullian rate parameter found in the **bPrev** and **bCurr** cells. **bSum** is repeatedly updated by the **Solve** macro as it calculates.

**bCurr** [C16]

**bCurr:** The cell below contains the current **b** Weibullian rate parameter value computed from the expression in that cell. **bCurr** is repeatedly updated by the **Solve** macro as it calculates and the value is copied to the appropriate row in the **b(Temp(Time))** column at the end of each iteration.

**bPrev** [C19]

**bPrev:** The cell below contains the previous **b** Weibullian rate parameter value computed from the expression in that cell. **bPrev** 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 minutes) 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 minutes) at the previous solution point. **TimePrev** is repeatedly updated by the **Solve** macro as it calculates.

**bIsotherm** [C34]

**bIsotherm:** The cell below contains the value of the **b** Weibullian rate parameter function at **TempIsoRef**, the **Isothermal Reference Temperature**.

**tIsoCurr** [C37]

**tIsoCurr:** The cell below contains the **Equivalent Isothermal Time** (in minutes) at the current **Time** increment for **TempIsoRef**, the **Isothermal Reference Temperature**. **tIsoCurr** is repeatedly updated by the **Solve** macro as it calculates and the value is copied to the appropriate row in the **EqTime(Time)** column at the end of each iteration.

**tIsoPrev** [C40]

**tIsoPrev:** The cell below contains the **Equivalent Isothermal Time** (in minutes) at the previous **Time** increment for **TempIsoRef**, the **Isothermal Reference Temperature**. **tIsoPrev** 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 minutes), for each step in the solution process and are used as the x-axis values in the Temp vs Time, LS vs Time, EqTime vs Time and b 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:**

**b(Temp(Time))** [F1]

**b(Temp(Time)):** The cells below contain **bCurr**, the **b** Weibullian rate parameter value, for each **Time** step in the solution process and are used as the y-axis values in the b vs Time chart.

**In worksheet column G:**

**LS(Time)** [G1]

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

**In worksheet column H:**

**EqTime(Time)** [H1]

**EqTime(Time):** The cells below contain **tIsoCurr**, the current **Equivalent Isothermal Time** (in minutes), at **TempIsoRef**, the chosen **Isothermal Reference Temperature**, for each **Time** step in the solution process and are used as the y-axis values in the EqTime vs Time chart.

Content last updated: February 4, 2008