## Comment Notes from Excel File: MicrobialGrowthModelBData.xls

#### Current version: February 4, 2008

In worksheet column A:
MicrobialGrowthModelBData.xls [A1] <--This means "MicrobialGrowthModelBData.xls" is in cell A1. The comment note below pops up when you point to cell A1.
MicrobialGrowthModelBData.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*Time^n/(b+Time*n). The temperature dependence of the growth parameter b(Temp) obeys an exponential relationship while a(Temp) and n(Temp) follow a linear relationship. 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 from measured time and temperature data, the user needs to enter Time values (in hours) into worksheet column D starting at cell D2 and Temperature values (in degrees C) corresponding to each Time value into worksheet column E starting at cell E2.

The Growth parameters are: npar1, npar2, apar1, apar2, bpar1 and bpar2 (e.g., for E. coli 1952 they are: npar1=1.7, npar2=0.051, apar1=5.53, apar2=0.0081, bpar1=96869, bpar2=0.19).

This model can be selected to characterize non-isothermal Growth curves with a short lag period, otherwise, the modified logistic model used in MicrobialGrowthModelA.xls 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 column 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, update the calculation cells in column C and the graphical data cells in column 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 useds 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/

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:
YInit [B4]
YInit: The cell below contains an initial guess used to compute the growth function Y. YInit must be greater than 0.

npar1 [B7]
npar1: The cell below contains the independent coefficient in the temperature dependence of the parameter n(Temp) = npar1 + npar2*Temp. npar1 must be greater than 0.

npar2 [B10]
npar2: The cell below contains the rate coefficient in the temperature dependence of the parameter n(Temp) = npar1 + npar2*Temp. npar2 must be greater than 0.

bpar1 [B13]
bpar1: The cell below contains the independent coefficient in the temperature dependence of the growth parameter b(Temp) = bpar1*EXP(-bpar2*Temp). bpar1 must be greater than 0.

bpar2 [B16]
bpar2: The cell below contains the rate coefficient in the temperature dependence of the growth parameter b(Temp) = bpar1 * EXP(-bpar2*Temp). bpar2 must be greater than 0.

apar1 [B19]
apar1: The cell below contains the independent coefficient in the temperature dependence of the parameter a(Temp) = apar1 - apar2*Temp. apar1 must be greater than 0.

apar2 [B22]
apar2: The cell below contains the rate coefficient in the temperature dependence of the parameter a(Temp) = apar1 - apar2*Temp. apar2 must be greater than 0.

In worksheet column C:
nPts [C1]
nPts: The cell below counts the number of Time values (rows) entered by the user in column D which must also equal the number of Temperature values in column E. This determines the number of solution points to be calculated and saved in column F and plotted on both charts.

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.

bSum [C13]
bSum: The cell below contains the sum of the previous and current values of the b 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 parameter value computed from the expression in that cell. bCurr is repeatedly updated by the Solve macro as it calculates.

bPrev [C19]
bPrev: The cell below contains the previous b 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 Temperature (in degrees C) at the current Time step. TempCurr is repeatedly updated by the Solve macro as it calculates. Its value is copied from the current row of the Temp(Time) column into which the user entered measured Temperature values.

TempPrev [C25]
TempPrev: The cell below contains the Temperature (in degrees C) at the previous Time step. TempPrev is repeatedly updated by the Solve macro as it calculates. Its value is copied from the previous row of the Temp(Time) column into which the user entered measured Temperature values.

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 since it is copied from the current row in the Time column into which the user entered measured Time values.

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 since it is copied from the previous row in the Time column into which the user entered measured Time values.

aSum [C34]
aSum: The cell below contains the sum of the previous and current values of the a parameter found in the aPrev and aCurr cells. aSum is repeatedly updated by the Solve macro as it calculates.

aCurr [C37]
aCurr: The cell below contains the current a parameter value computed from the expression in that cell. aCurr is repeatedly updated by the Solve macro as it calculates.

aPrev [C40]
aPrev: The cell below contains the previous a parameter value computed from the expression in that cell. aPrev is repeatedly updated by the Solve macro as it calculates.

nSum [C43]
nSum: The cell below contains the sum of the previous and current values of the n parameter found in the nPrev and nCurr cells. nSum is repeatedly updated by the Solve macro as it calculates.

nCurr [C46]
nCurr: The cell below contains the current n parameter value computed from the expression in that cell. nCurr is repeatedly updated by the Solve macro as it calculates.

nPrev [C49]
nPrev: The cell below contains the previous n parameter value computed from the expression in that cell. nPrev is repeatedly updated by the Solve macro as it calculates.

TempInit [B52]
TempInit: The cell below contains the user-entered Initial Temperature (in degrees C) from cell E2 that will be used to compute the solution. TempInit must be greater than 0.

In worksheet column D:
Time [D1]
Time: The cells below contain user-entered Time values (in hours) which determine the number of solution points and are also 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 user-entered Temperature values (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.

### Generation of Microbial Growth Curves (model B) Using Excel

Content last updated: February 4, 2008