Calculo Del Valor D

7/30/2019 Calculo Del Valor D

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Biological Indicator

2010

Process LethalityCalculation and

Workbook


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The biological data derived from a sterilization process is qualitative information, such as

sterile or non-sterile, established by observing either growth or no growth of a biological

challenge. The process is challenged with calibrated bacterial spores with a defined

resistance to the sterilization process. The process is effective if the spore challenge is

killed (no growth). The process is not effective when the spore challenge survives.

When we expose replicate samples to replicate physical conditions we are able to expandour knowledge of the lethality being delivered by the sterilization process. This is

usually expressed as a probabilistic value and is capable of predicting results with a high

level of certainty.

This workbook is intended to provide you with the ability to express biological

measurements in numbers using standard mathematical formulas. These biological

numbers provide the quantative assessment of the sterilization process. When used

properly, the bacterial spore provides the most accurate measure of the effectiveness of

the sterilization process.

The population of the spore challenge is established using standard microbiological platecount procedures and is used in the following mathematical equations. The D-value is

the first assessment of the resistance of a biological challenge to a particular sterilization

process. The D-value is defined as the time in minutes that it takes at a specified set of

conditions to reduce the population of the biological challenge by one log or a factor of

ten. There are two basic approaches to establish the D-value. One approach is referred to

as the survivor curve method and the other is the fraction negative method. In the

survivor curve method, high levels of spores are exposed to successive short time periods

of sterilizing conditions. The data collected is the number of spores that survived the

sterilization conditions. The exposures are performed over increasing durations of clock

time. The surviving spores are recovered using standard microbiological plate count

techniques. The data is plotted on a semi log graph. The X axis is clock time and theY axis is the log scale of the number of spores recovered at each of the exposure times.

The slope of the curve is the D-value. The coefficient of determination (r2) is also

calculated. This coefficient indicates how close the data points are to the calculated

linear regression plot.

The D-value can also be calculated using fraction negative data from units exposed in the

quantal zone. There are two approaches to analyze this data. The first approach is

referred to as the Stumbo, Murphy, Cochran formula. This method calculates a D-value

from each fraction negative data point. When more than one data set is available, the

individual point D-values are summed and divided by the number of data points. This

method is quite useful for determining a process D-value when it may be difficult to

collect more than one fraction negative data set.

The second approach using fraction negative data sets is referred to as the Limited

Holcomb, Spearmen, Karber method. This method not only focuses on the quantal zone

data points, but it looks at the shortest time to all negative units and the longest time to all

positive units. It uses all the quantal zone values and the exposure interval to calculate


3/66

the mean time to sterility. This approach is a little more robust than the Stumbo,

Murphy, Cochran method.

Now that spore populations have been identified and D-values have been established at

specific sets of conditions, the effect of varying temperature conditions can be evaluated.

The temperature coefficient or Z-value is defined as the temperature change required toalter the D-value by one log. This temperature coefficient can be applied to steam, dry

heat and ethylene oxide processes. The Z-value is best calculated using three D-values.

This can be performed graphically as well as calculated. The graphic plot is a semi log

plot with the X axis being the linear temperature scale and the Y axis the log plot ofthe D-values. The slope of the curve is the Z-value. The formula to calculate the slope is

the same log linear regression plot used for the survivor curve. The coefficient of

determination (r2) is also calculated using the same formula as in the survivor curve

method.

The Z-value allows the integration of different lethal rates for different temperatures. A

reference temperature or process set point must be identified. As temperatures increase,spores die faster. The Z-value provides an accurate assessment of lethality over the

normal process temperature variance as seen in come-up time, hold time and come-down

time process phases.

The temperature coefficient is now used to establish an equivalent process lethality (F-

value) at a defined reference temperature. The F-value integrates the varying process

conditions into an expression of equivalent process lethality. The equivalent process

lethality is usually described as equivalent process minutes at the reference temperature.

Complete and accurate temperature profiles are required for this calculation. This

establishes an accurate accumulated lethality value for a known biological challenge and

a dynamic process.

The F equivalent process lethality is now used to establish the equivalent spore log

reductions that are delivered by this equivalent process lethality value. This is

accomplished by dividing the F-value for the process by the process D-value. The result

is the spore log reductions (SLR) provided by the process.

The spore log reduction value is used to establish the sterility assurance level (SAL). The

sterility assurance level is used to assess the microbiological lethality of the process.

This value is the probability of a non-sterile unit (PNSU) occurring in the process.

Sterility assurance level is expressed as 10-x

. X is the log of the microbial challengeeither spores or bioburden, which is labeled N0 minus the SLR value delivered by the

process.


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Calculate the D-value Using the Limited Holcomb, Spearman,

Karber Method

You have collected the following fraction negative data that you will apply to the LimitedHolcomb-Spearman-Karber equations.

The process set at 121.0 C.The initial population N0 = 1.7 x 10

5.

Twenty (20) replicate BIs were used at each exposure.

Calculate the D-value using the data sheet provided.

Exposure Time Number of Units Exposed (n) Number of Units Sterile (r)

8 20 0

9 20 2

10 20 5

11 20 11

12 20 1813 20 20


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The Limited Holcomb, Spearman, Karber Method for

Fraction Negative Data

2507.0010

NLog

TD HSK

rxn

ddTT kHSK

2

THSK = mean time to sterility

Log10 N0 = spore population0.2507 = Eulers constant

Tk

= shortest time to all units sterile

d = time interval between data points

n = number of replicate units per testr = number of units sterile


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CALCULATION OF D-VALUE USING LIMITED-HOLCOMB-

SPEARMAN-KARBER (USP)

Sample Identification #: Exposure conditions:

In the table on the right, fill in the exposure times and # of units killed where: Data

f1= exposure time or dose where all units are positive i Exposure timer

(# units negative)

(at all shorter times or doses, all units are positive) 1

and 2

fk = exposure time or dose where all units are negative

(at all longer times or doses, all units are negative)3

4

Fill in the appropriate data in the blanks below: 5

Time (Tk) for achieving results fk 6

Difference between adjacent times (d) 7

Sample size (n) 8

Sum of the negative replicates ( r) from f1 to fk-1 9

(fk-1 is the time prior to fk) 10

Average spore count per carrier (No) 11

Log No= (round to 4 decimal places) 12

Calculate mean heating time (THSK) for achieving complete kill by the equation: 13

THSK = Tk- d/2 - (d/n * r)

14

( r) from f1 to fk-1(fk-1 is the time prior to fk)

THSK = (round to 4 decimal places)

Calculate D-value (D) by the equation:

D = (THSK)/ (Log No + 0.2507)

D = (round to 4 decimal places)

D-VALUE (rounded to 1 decimal place*)* values 0.0950 are rounded to 1 decimal place.

* values 0.0949 are rounded to 2 decimal places.

Calculation by: Date:
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Sample Identification #: Exposure conditions: 121C



(# units negative)

(at all shorter times or doses, all units are positive) 1 8 0

and 2 9 2


(at all longer times or doses, all units are negative)3 10 5

4 11 11

Fill in the appropriate data in the blanks below: 5 12 18

Time (Tk) for achieving results fk 13 6 13 20

Difference between adjacent times (d) 1 7

Sample size (n) 20 8

Sum of the negative replicates ( r) from f1 to fk-1 36 9


Average spore count per carrier (No) 1.7 x 105 11

Log No= 5.2304 (round to 4 decimal places) 12


THSK = Tk- d/2 - (d/n * r)

14


36

3620

1

2

113 x

7.10)8.1()5.0(13

THSK = 10.7000 (round to 4 decimal places)


D = (THSK)/ (Log No + 0.2507)

9522.14811.5

7000.10

2507.02304.5

7000.10

D = 1.9522 (round to 4 decimal places)

D-VALUE (rounded to 1 decimal place*) 2.0* values 0.0950 are rounded to 1 decimal place.




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Using the Stumbo, Murphy, Cochran Method for Calculating the D-

Value

You have collected fraction negative data; your initial intent was to use the Limited Holcomb-

Spearman-Karber equation, but your data does not include two of the necessary data points. You

do not have a data point that indicated all surviving BIs and you do not have a data point with

all BIs killed. You must use the Stumbo, Murphy, Cochran method. Your process was set tocontrol at 121.0 C.

Calculate the D-value using the formula on the reverse side of this question.

The initial population N0 = 1.7 x 105.

Exposure Time Number of Exposed Units (n) Number of Units Sterile (r)

9 20 2

10 20 5

11 20 11

12 20 18


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The Stumbo, Murphy, Cochran Fraction Negative Data

( )

n

DDDD

n++

=21

110010

1

1

loglog uNN

UD

=

Nui =r

nln

U= exposure time

N0= starting spore population

Nu = most probable number of surviving spores

n = number units exposed

r= number units sterile (negative)


10/66

CALCULATION OF D-VALUE USING

STUMBO-MURPHY-COCHRAN METHOD

Sample Identification #: ________________________ Exposure Conditions: ___________________________

* values 0.0950 are rounded to 1 decimal place.


Calculation by: _________________________________________________________________________ Date: ________________

Reviewed by: __________________________________________________________________________ Date: _______________

Sample size (n) =

Average spore count per carrier (No) = ___________________

Log No =___________________

In the table on the right, fill in the exposure times and # of units

killed starting with the shortest exposure. Round all numbers to 4

decimal laces*.

iExposure

Time (U)

Number

Killed (r)

Calculated

D-value

1

2

3

4

5

6

7

8

9

D-values = ____________average D-value = ______________

D-value = ______________

(round to 1 decimal place*)

Calculation of D1

NU1 = ln (n/r) = _______________

log NU1 = __________________

D1 = U1/(log N0 log NU1) = ___________________

Calculation of D2

NU2 = ln (n/r) = _______________

log NU2 = __________________

D2 = U2/(log N0 log NU2) = ___________________

Calculation of D3

NU3 = ln (n/r) = _______________

log NU3 = __________________

D3 = U3/(log N0 log NU3) = ___________________Calculation of D7

NU7 = ln (n/r) = _______________

log NU7 = __________________

D7 = U7/(log N0 log NU7) = ___________________

Calculation of D5

NU5 = ln (n/r) = _______________

log NU5 = __________________

D5 = U5/(log N0 log NU5) = ___________________

Calculation of D8

NU8 = ln (n/r) = _______________

log NU8 = __________________

D8 = U8/(log N0 log NU8) = ___________________

Calculation of D6

NU6 = ln (n/r) = _______________

log NU6 = __________________

D6 = U6/(log N0 log NU6) = ___________________

Calculation of D4

NU4 = ln (n/r) = _______________

log NU4 = __________________

D4 = U4/(log N0 log NU4) = ___________________

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11/66



Sample Identification #: ________________________ Exposure Conditions: 121C




Reviewed by: __________________________________________________________________________ Date: _______________

Sample size (n) = 20

Average spore count per carrier (No) = 1.7 x 105

Log No = 5.2304



decimal places*.

iExposure

Time (U)

Number

Killed (r)

Calculated

D-value

1 8 0 NA

2 9 2 1.8487

3 10 5 1.9652

4 11 11 2.0169

5 12 18 1.9331

6 13 20 NA

7

8

9D-values = 7.7639

average D-value = 1.9410

D-value = 1.9


Calculation of D1

NU1 = ln (n/r) = 2.3026

log NU1 = 0.3622

D1 = U1/(log N0 log NU1) = 8487.18682.4

9=

Calculation of D2

NU2 = ln (n/r) = 1.3863

log NU2 = 0.1419

D2 = U2/(log N0 log NU2) = 9652.10885.5

10=

Calculation of D3

NU3 = ln (n/r) = 0.5978

log NU3 = -0.2234

D3 = U3/(log N0 log NU3) = 0169.24538.5

11=

Calculation of D7

NU7 = ln (n/r) = _______________

log NU7 = __________________D7 = U7/(log N0 log NU7) = ___________________

Calculation of D5

NU5 = ln (n/r) = _______________

log NU5 = __________________

D5 = U5/(log N0 log NU5) = ___________________

Calculation of D8

NU8 = ln (n/r) = _______________

log NU8 = __________________

D8 = U8/(log N0 log NU8) = ___________________

Calculation of D6

NU6 = ln (n/r) = _______________

log NU6 = __________________

D6 = U6/(log N0 log NU6) = ___________________

Calculation of D4

NU4 = ln (n/r) = 0.1054

log NU4 = -0.9772

D4 = U4/(log N0 log NU4) = 9331.12076.6

12=

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12/66

Calculate the D-value Using the Survivor Curve Method

You are performing a D-value test using the survivor curve method. You collect the followingplate count data at the various exposure times. Your process is set to run at 121.0 C. The initial

population N0 = 2.2 x 105

Calculate the survivor curve D-value using the log linear regression method on the worksheet on

the back of this question.

Calculate the coefficient of determination r2

for the data.

Data Collected

Exposure Time Population Recovered

0.0 minutes 2.2 x 105

1.8 minutes 3.0 x 10

3.6 minutes 2.6 x 103

5.4 minutes 1.0 x 103



13/66

The Survivor Curve D-value using the Log Linear Regression

Method

m = slope of the regression line

[ ][ ] ( )( )[ ][ ] [ ]221010

)()()(log)(log

=

xxn

yxyxnm

n = number of data points

y = recovered spore population

x = exposure time

r2

= coefficient of determination which indicates how close the data points are to the

predicted line

an r2

= 1.000 indicates all data points are on the predicted line

[ ][ ]

( )( )[ ]

n

yy

n

xx

n

yxyx

r

=

2

102

10

2

2

2

10

10

)(log)(log

)()(

)(log)()(log

2


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Calculation of D-value by Log Linear Regression (Survivor Curve)Sample Identification # Round all values to 4 decimal places. Use rounded values in calculations

Recovered

Population =y

Exposure

Time =x log10y x2

x(log10y) (log10y)2

(x)=A (log10y)=B (x2

)= C [x(log10y)]= G (log10y2

)]=E

Assigned Variable A = B = C= G = E=

Calculation of slope (m

) and D-value

Number of data points (n) = ________


)()]()[(

)])([()]()[(2

ACn

BAGnm

=

( )( )[ ] ( )( )[ ]

( )( )[ ] ( )2

=m

( )[ ] ( )[ ]( )[ ] ( )

=m

( )[ ]( )[ ]

=m

m = __________

=

m

valueD1

1

=

11valueD

( )1=valueD

D value = __________ _______________(rounded to one decimal)

Calculation of coefficient of determination (r)

( ) ( )

( ) ( )

=

n

BE

n

AC

n

BAG

r22

2

2

( ) ( )

( ) ( )

=

22

2

2r

( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]

=

2

2r

( )[ ]( )[ ] ( )[ ]

2

2=r

( )( )=2r

r2

= __________

Calculations by: ____________________________ _____________

Date

Reviewed by: ______________________________ _____________

Date


15/66

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Recovered

Population =y

Exposure

Time =x log10y x2

x(log10y) (log10y)2

1.7 x 10 0.0 5.2304 0.0000 0.0000 27.3571

3.0 x 104

2.0 4.4771 4.0000 8.9542 20.0444

1.0 x 10 4.0 3.0000 16.0000 12.0000 9.0000

6.0 x 10 6.0 2.7782 36.0000 16.6692 7.7184

1.1 x 101 8.0 1.0414 64.0000 8.3312 1.0845


)= C [x(log10y)]= G (log10y2

)]=E

Assigned Variable A = 20 B = 16.5271 C= 120.0000 G = 45.9546 E= 65.2044


) and D-value

Number of data points (n) = 5


)()]()[(

)])([()]()[(2

ACn

BAGnm

=

( )( )[ ] ( )( )[ ]

( )( )[ ] ( )22012055271.16209546.455

=m

( )[ ] ( )[ ]( )[ ] ( )400600

5420.3307730.229

=m

( )[ ]( )[ ]200

7690.100=m

m = -0.5038

=

m

valueD1

1

=

5038.0

11valueD

( )9849.11 =valueD

D value = 1.8911 2.0(rounded to one decimal)


( ) ( )

( ) ( )

=

n

BE

n

AC

n

BAG

r22

2

2

( ) ( )

( ) ( )

=

5

5271.16

2044.655

20

120

5

5271.16209546.45

22

2

2r

( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]6290.542044.6580120

1084.669546.452

2

=r

( )[ ]( )[ ] ( )[ ]5754.1040

1538.202

2 =r

( )( )0160.423

1757.4062=r

r2 = 0.9602

Calculations by: ____________________________ _____________Date

Reviewed by: ______________________________ _____________

Date


16/66

Sterilizing Value, Minutes

Example of Plotting the Survivor Curve on Semi Log Graph Paper

1.9 Min


17/66




18/66

Calculate the Z-value Using the Following Data:

D121 = 1.9522

D124 = 1.3127

D127 = 0.8650

ISO 11138 states three D-values between 110 and 130C


19/66

Temperature Coefficient Z-value Using the Log Linear

Regression Method

m = the slope of the regression line

( ) [ ]( ) ( )( ) ( )( )

( ) ( )[ ] ( )[ ]22

1010 loglog

=

xxn

yxyxnm


y = D-value

x = exposure temperature

r2

= coefficient of determination

[ ][ ]

( ) ( )[ ]n

yy

n

xx

n

yxyx

r

=

2102

10

2

2

2

10

10

)(log)(log)()(

)(log)()(log

2


20/66

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Calculation of Z-value by Log Linear RegressionCrop or Lot Number Round all values to 4 decimal places. Use rounded values in calculations.

D value =y

Exposure

Temperature =x

log10y x2 x(log10y) (log10y)2


)= C [x(log10y)]= G (log10y2

)]=E

Assigned

VariableA = B = C= G = E=

Calculation of slope (m) and Z-value

Number of D values (n) = ________


)()]()[(

)])([()]()[(2ACn

BAGnm

=

( )( )[ ] ( )( )[ ]

( )( )[ ] ( )2

=m

( )[ ] ( )[ ]( )[ ] ( )

=m

( )[ ]( )[ ]

=m

m = __________

=

mvalueZ

11

=

11valueZ

( )1=valueZ

Z value = _________ ______________(rounded to one decimal)


( ) ( )

( ) ( )

=

n

BE

n

AC

n

B

AGr

22

2

2

( ) ( )

( ) ( )

=22

2

2r

( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]

=

2

2r

( )[ ]( )[ ] ( )[ ]

2

2=r

( )

( )=

2r

r2

= __________

Calculations by: ____________________________ _____________

Date

Reviewed by: ______________________________ _____________

Date


21/66

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D value =y

Exposure

Temperature =x


1.9522 121 0.2905 14641 35.1505 0.0844

1.3127 124 0.1182 15376 14.6568 0.0140

0.8650 127 -0.0630 16129 -8.0010 0.0040


)= C [x(log10y)]= G (log10y2

)]=E

Assigned

VariableA = 372 B = 0.3457 C= 46146 G = 41.8063 E= 0.1024


Number of D values (n) = 3


)()]()[(

)])([()]()[(2

ACn

BAGnm

=

( )( )[ ] ( )( )[ ]

( )( )[ ] ( )23724614633457.03728063.413

=m

( )[ ] ( )[ ]( )[ ] ( )138384138438

6004.1284189.125

=m

( )[ ]( )[ ]54

1815.3=m

m = -0.0589

=

mvalueZ

11

=

0589.0

11valueZ

( )9779.161 =valueZ

Z value = 16.9779 17.0(rounded to one decimal)


( ) ( )

( ) ( )

=

n

BE

n

AC

n

B

AGr

22

2

2

( ) ( )

( ) ( )

=

3

3457.01024.0

3

37246146

3

3457.03728063.41

22

2

2r

( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]0398.01024.04612846146

8668.428063.412

2

=r

( )[ ]( )[ ] ( )[ ]0626.018

0605.12

2 =r

( )( )1268.1

1247.12=r

r2 = 0.9981

Calculations by: ____________________________ _____________

Date

Reviewed by: ______________________________ _____________

Date


22/66

Example of Plotting the Z-value Curve on Semi Log Graph Paper

16.8C


23/66

Plotting the Z-value Curve on Semi Log Graph Paper


24/66

Process Equivalent Time F

=Z

TT

AZT

Aref

AreftF 10x,

Process Equivalent Lethality ++= AiAAAAref ZTZTZTZTZT FFFFF ,....,,,, 321 tA = process clock time interval, usually 1 minute

Tref= process reference temperature

ZA = actual Z-value for the spore challenge


25/66

Process Equivalent Time

A typical time interval is 1 minute. tA = 1 minute, Tref= 121C, ZA = 8C.

Measure average temperature during 1 minute interval to calculate the iZTiF ,

Time(Min.) Temp. Formula ProcessEquivalent Time

T1 110C

10x110xmin1,1 ==

ZTF

T2 115C

10x110xmin1,2 ==

ZTF

T3 118C

10x110xmin1,3 ==

ZTF

T4 120C

10x110xmin1,4 ==

ZTF

T5 121C

10x110xmin1,5

==

ZT

F

T6 122C

10x110xmin1,6 ==

ZTF

T7 124C

10x110xmin1,7 ==

ZTF

T8 121C

10x110xmin1,8 ==

ZTF

T9 118C

10x110xmin1,9 ==

ZTF

T10 107C

10x110xmin1,10 ==

ZTF

T11 105C10x110xmin1,11 ==

ZTF

ZTF ,

= ZTZT iref FF ,,Process


26/66




Time(Min.)

Temp. Formula ProcessEquivalent

Time

T1 110C3750.1

8

110121

, 10x110xmin11

==ZTF 0.0422

T2 115C7500.0

8

115121

, 10x110xmin12

==ZTF 0.1778

T3 118C3750.0

8

118121

, 10x110xmin13

==ZTF 0.4217

T4 120C1250.08

120121

, 10x110xmin14

==ZTF

0.7499

T5 121C0

8

121121

, 10x110xmin15 ==

ZTF 1.0000

T6 122C1250.08

122121

, 10x110xmin16 ==

ZTF 1.3335

T7 124C3750.0

8

124121

, 10x110xmin17 ==

ZTF 2.3714

T8 121C0

8

121121

, 10x110xmin18 ==

ZTF 1.0000

T9 118C3750.0

8

118121

, 10x110xmin19

==ZTF 0.4217

T10 107C7500.1

8

107121

, 10x110xmin110

==ZTF 0.0178

T11 105C0000.2

8

105121

, 10x110xmin111

==ZTF 0.0100

ZTF , 7.5460



27/66

Calculate the Process Spore Log Reduction Value

SLR =value-DProcess

AZ,

refT

FTimeEquivalentProcess


28/66

Calculate the Process Spore Log Reduction (SLR) Value

The process equivalent time is 58.5 minutes.

The process D-value is 4.5 minutes.

Calculate the spore log reduction.

SLR =value-DProcess

AZ,

refT


SLR = =


29/66

Process Spore Log Reduction (SLR) Value

SLR = 13min5.4min5.58 =

Your process delivers 13 spore log reductions.


30/66

Sterility Assurance Level

( )SLRNlog 01010SAL

=


31/66

Calculate the Sterility Assurance Level

Your process used a spore challenge of 1.5 x 106

therefore, N0 = 1.5 x 106.

Process equivalent lethality is equal to 13 spore log reductions (SLR).

Calculate the sterility assurance level.

Calculation

SAL = 10logNo SLR

N0 =

logN0 =

Process equivalent lethality =

SAL =

SAL =


32/66


Your process used a spore challenge of 1.5 x 106 therefore, N0 = 1.5 x 106.



Calculation

SAL = 10logNo SLR

N0 = 1.5 x 106

logN0 = 6.176

Process equivalent lethality = 13 SLR

SAL = 10(6.176 13)

SAL = 10-6.824


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Plotting the Survivor Curve on Semi Log Graph Paper


34/66

Calculate the D-value Using the Limited Holcomb, Spearman,

Karber Method

You have collected the following fraction negative data that you will apply to the LimitedHolcomb-Spearman-Karber equations.

The process set at 121.0 C.The initial population N0 = 1.7 x 10

5.

Twenty (20) replicate BIs were used at each exposure.

Calculate the D-value using the data sheet provided.

Exposure Time Number of Units Exposed (n) Number of Units Sterile (r)

8 20 0

9 20 2

10 20 5

11 20 11

12 20 1813 20 20


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The Limited Holcomb, Spearman, Karber Method for

Fraction Negative Data

2507.0010

NLog

TD HSK

rxn

ddTT kHSK

2

THSK = mean time to sterility

Log10 N0 = spore population0.2507 = Eulers constant

Tk

= shortest time to all units sterile

d = time interval between data points

n = number of replicate units per testr = number of units sterile


36/66

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Sample Identification #: Exposure conditions:



(# units negative)

(at all shorter times or doses, all units are positive) 1

and 2


(at all longer times or doses, all units are negative)3

4

Fill in the appropriate data in the blanks below: 5

Time (Tk) for achieving results fk 6

Difference between adjacent times (d) 7

Sample size (n) 8

Sum of the negative replicates ( r) from f1 to fk-1 9


Average spore count per carrier (No) 11

Log No= (round to 4 decimal places) 12


THSK = Tk- d/2 - (d/n * r)

14


THSK = (round to 4 decimal places)


D = (THSK)/ (Log No + 0.2507)

D = (round to 4 decimal places)

D-VALUE (rounded to 1 decimal place*)* values 0.0950 are rounded to 1 decimal place.




37/66

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Sample Identification #: Exposure conditions: 121C



(# units negative)

(at all shorter times or doses, all units are positive) 1 8 0

and 2 9 2


(at all longer times or doses, all units are negative)3 10 5

4 11 11

Fill in the appropriate data in the blanks below: 5 12 18

Time (Tk) for achieving results fk 13 6 13 20

Difference between adjacent times (d) 1 7

Sample size (n) 20 8

Sum of the negative replicates ( r) from f1 to fk-1 36 9


Average spore count per carrier (No) 1.7 x 105 11

Log No= 5.2304 (round to 4 decimal places) 12


THSK = Tk- d/2 - (d/n * r)

14


36

3620

1

2

113 x

7.10)8.1()5.0(13

THSK = 10.7000 (round to 4 decimal places)


D = (THSK)/ (Log No + 0.2507)

9522.14811.5

7000.10

2507.02304.5

7000.10

D = 1.9522 (round to 4 decimal places)

D-VALUE (rounded to 1 decimal place*) 2.0* values 0.0950 are rounded to 1 decimal place.




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Using the Stumbo, Murphy, Cochran Method for Calculating the D-

Value

You have collected fraction negative data; your initial intent was to use the Limited Holcomb-

Spearman-Karber equation, but your data does not include two of the necessary data points. You

do not have a data point that indicated all surviving BIs and you do not have a data point with

all BIs killed. You must use the Stumbo, Murphy, Cochran method. Your process was set tocontrol at 121.0 C.

Calculate the D-value using the formula on the reverse side of this question.

The initial population N0 = 1.7 x 105.

Exposure Time Number of Exposed Units (n) Number of Units Sterile (r)

9 20 2

10 20 5

11 20 11

12 20 18


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The Stumbo, Murphy, Cochran Fraction Negative Data

( )

n

DDDD

n++

=21

110010

1

1

loglog uNN

UD

=

Nui =r

nln

U= exposure time

N0= starting spore population

Nu = most probable number of surviving spores

n = number units exposed

r= number units sterile (negative)


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Sample Identification #: ________________________ Exposure Conditions: ___________________________




Reviewed by: __________________________________________________________________________ Date: _______________

Sample size (n) =

Average spore count per carrier (No) = ___________________

Log No =___________________



decimal laces*.

iExposure

Time (U)

Number

Killed (r)

Calculated

D-value

1

2

3

4

5

6

7

8

9

D-values = ____________average D-value = ______________

D-value = ______________


Calculation of D1

NU1 = ln (n/r) = _______________

log NU1 = __________________

D1 = U1/(log N0 log NU1) = ___________________

Calculation of D2

NU2 = ln (n/r) = _______________

log NU2 = __________________

D2 = U2/(log N0 log NU2) = ___________________

Calculation of D3

NU3 = ln (n/r) = _______________

log NU3 = __________________

D3 = U3/(log N0 log NU3) = ___________________Calculation of D7

NU7 = ln (n/r) = _______________

log NU7 = __________________

D7 = U7/(log N0 log NU7) = ___________________

Calculation of D5

NU5 = ln (n/r) = _______________

log NU5 = __________________

D5 = U5/(log N0 log NU5) = ___________________

Calculation of D8

NU8 = ln (n/r) = _______________

log NU8 = __________________

D8 = U8/(log N0 log NU8) = ___________________

Calculation of D6

NU6 = ln (n/r) = _______________

log NU6 = __________________

D6 = U6/(log N0 log NU6) = ___________________

Calculation of D4

NU4 = ln (n/r) = _______________

log NU4 = __________________

D4 = U4/(log N0 log NU4) = ___________________

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Sample Identification #: ________________________ Exposure Conditions: 121C




Reviewed by: __________________________________________________________________________ Date: _______________

Sample size (n) = 20

Average spore count per carrier (No) = 1.7 x 105

Log No = 5.2304



decimal places*.

iExposure

Time (U)

Number

Killed (r)

Calculated

D-value

1 8 0 NA

2 9 2 1.8487

3 10 5 1.9652

4 11 11 2.0169

5 12 18 1.9331

6 13 20 NA

7

8

9D-values = 7.7639

average D-value = 1.9410

D-value = 1.9


Calculation of D1

NU1 = ln (n/r) = 2.3026

log NU1 = 0.3622

D1 = U1/(log N0 log NU1) = 8487.18682.4

9=

Calculation of D2

NU2 = ln (n/r) = 1.3863

log NU2 = 0.1419

D2 = U2/(log N0 log NU2) = 9652.10885.5

10=

Calculation of D3

NU3 = ln (n/r) = 0.5978

log NU3 = -0.2234

D3 = U3/(log N0 log NU3) = 0169.24538.5

11=

Calculation of D7

NU7 = ln (n/r) = _______________

log NU7 = __________________D7 = U7/(log N0 log NU7) = ___________________

Calculation of D5

NU5 = ln (n/r) = _______________

log NU5 = __________________

D5 = U5/(log N0 log NU5) = ___________________

Calculation of D8

NU8 = ln (n/r) = _______________

log NU8 = __________________

D8 = U8/(log N0 log NU8) = ___________________

Calculation of D6

NU6 = ln (n/r) = _______________

log NU6 = __________________

D6 = U6/(log N0 log NU6) = ___________________

Calculation of D4

NU4 = ln (n/r) = 0.1054

log NU4 = -0.9772

D4 = U4/(log N0 log NU4) = 9331.12076.6

12=

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Calculate the D-value Using the Survivor Curve Method

You are performing a D-value test using the survivor curve method. You collect the followingplate count data at the various exposure times. Your process is set to run at 121.0 C. The initial

population N0 = 2.2 x 105

Calculate the survivor curve D-value using the log linear regression method on the worksheet on

the back of this question.

Calculate the coefficient of determination r2

for the data.

Data Collected

Exposure Time Population Recovered

0.0 minutes 2.2 x 105


3.6 minutes 2.6 x 103

5.4 minutes 1.0 x 103



43/66

The Survivor Curve D-value using the Log Linear Regression

Method


[ ][ ] ( )( )[ ][ ] [ ]221010

)()()(log)(log

=

xxn

yxyxnm


y = recovered spore population

x = exposure time

r2

= coefficient of determination which indicates how close the data points are to the

predicted line

an r2

= 1.000 indicates all data points are on the predicted line

[ ][ ]

( )( )[ ]

n

yy

n

xx

n

yxyx

r

=

2

102

10

2

2

2

10

10

)(log)(log

)()(

)(log)()(log

2


44/66

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Recovered

Population =y

Exposure

Time =x log10y x2

x(log10y) (log10y)2


)= C [x(log10y)]= G (log10y2

)]=E

Assigned Variable A = B = C= G = E=


) and D-value

Number of data points (n) = ________


)()]()[(

)])([()]()[(2

ACn

BAGnm

=

( )( )[ ] ( )( )[ ]

( )( )[ ] ( )2

=m

( )[ ] ( )[ ]( )[ ] ( )

=m

( )[ ]( )[ ]

=m

m = __________

=

m

valueD1

1

=

11valueD

( )1=valueD

D value = __________ _______________(rounded to one decimal)


( ) ( )

( ) ( )

=

n

BE

n

AC

n

BAG

r22

2

2

( ) ( )

( ) ( )

=

22

2

2r

( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]

=

2

2r

( )[ ]( )[ ] ( )[ ]

2

2=r

( )( )=2r

r2

= __________

Calculations by: ____________________________ _____________

Date

Reviewed by: ______________________________ _____________

Date


45/66

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Recovered

Population =y

Exposure

Time =x log10y x2

x(log10y) (log10y)2

1.7 x 10 0.0 5.2304 0.0000 0.0000 27.3571

3.0 x 104

2.0 4.4771 4.0000 8.9542 20.0444

1.0 x 10 4.0 3.0000 16.0000 12.0000 9.0000

6.0 x 10 6.0 2.7782 36.0000 16.6692 7.7184

1.1 x 101 8.0 1.0414 64.0000 8.3312 1.0845


)= C [x(log10y)]= G (log10y2

)]=E

Assigned Variable A = 20 B = 16.5271 C= 120.0000 G = 45.9546 E= 65.2044


) and D-value

Number of data points (n) = 5


)()]()[(

)])([()]()[(2

ACn

BAGnm

=

( )( )[ ] ( )( )[ ]

( )( )[ ] ( )22012055271.16209546.455

=m

( )[ ] ( )[ ]( )[ ] ( )400600

5420.3307730.229

=m

( )[ ]( )[ ]200

7690.100=m

m = -0.5038

=

m

valueD1

1

=

5038.0

11valueD

( )9849.11 =valueD

D value = 1.8911 2.0(rounded to one decimal)


( ) ( )

( ) ( )

=

n

BE

n

AC

n

BAG

r22

2

2

( ) ( )

( ) ( )

=

5

5271.16

2044.655

20

120

5

5271.16209546.45

22

2

2r

( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]6290.542044.6580120

1084.669546.452

2

=r

( )[ ]( )[ ] ( )[ ]5754.1040

1538.202

2 =r

( )( )0160.423

1757.4062=r

r2 = 0.9602

Calculations by: ____________________________ _____________Date

Reviewed by: ______________________________ _____________

Date


46/66



1.9 Min


47/66




48/66

Calculate the Z-value Using the Following Data:

D121 = 1.9522

D124 = 1.3127

D127 = 0.8650

ISO 11138 states three D-values between 110 and 130C


49/66

Temperature Coefficient Z-value Using the Log Linear

Regression Method

m = the slope of the regression line

( ) [ ]( ) ( )( ) ( )( )

( ) ( )[ ] ( )[ ]22

1010 loglog

=

xxn

yxyxnm


y = D-value

x = exposure temperature

r2

= coefficient of determination

[ ][ ]

( ) ( )[ ]n

yy

n

xx

n

yxyx

r

=

2102

10

2

2

2

10

10

)(log)(log)()(

)(log)()(log

2


50/66

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D value =y

Exposure

Temperature =x



)= C [x(log10y)]= G (log10y2

)]=E

Assigned

VariableA = B = C= G = E=


Number of D values (n) = ________


)()]()[(

)])([()]()[(2ACn

BAGnm

=

( )( )[ ] ( )( )[ ]

( )( )[ ] ( )2

=m

( )[ ] ( )[ ]( )[ ] ( )

=m

( )[ ]( )[ ]

=m

m = __________

=

mvalueZ

11

=

11valueZ

( )1=valueZ

Z value = _________ ______________(rounded to one decimal)


( ) ( )

( ) ( )

=

n

BE

n

AC

n

B

AGr

22

2

2

( ) ( )

( ) ( )

=22

2

2r

( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]

=

2

2r

( )[ ]( )[ ] ( )[ ]

2

2=r

( )

( )=

2r

r2

= __________

Calculations by: ____________________________ _____________

Date

Reviewed by: ______________________________ _____________

Date


51/66

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D value =y

Exposure

Temperature =x


1.9522 121 0.2905 14641 35.1505 0.0844

1.3127 124 0.1182 15376 14.6568 0.0140

0.8650 127 -0.0630 16129 -8.0010 0.0040


)= C [x(log10y)]= G (log10y2

)]=E

Assigned

VariableA = 372 B = 0.3457 C= 46146 G = 41.8063 E= 0.1024


Number of D values (n) = 3


)()]()[(

)])([()]()[(2

ACn

BAGnm

=

( )( )[ ] ( )( )[ ]

( )( )[ ] ( )23724614633457.03728063.413

=m

( )[ ] ( )[ ]( )[ ] ( )138384138438

6004.1284189.125

=m

( )[ ]( )[ ]54

1815.3=m

m = -0.0589

=

mvalueZ

11

=

0589.0

11valueZ

( )9779.161 =valueZ

Z value = 16.9779 17.0(rounded to one decimal)


( ) ( )

( ) ( )

=

n

BE

n

AC

n

B

AGr

22

2

2

( ) ( )

( ) ( )

=

3

3457.01024.0

3

37246146

3

3457.03728063.41

22

2

2r

( ) ( )[ ][ ]( ) ( )[ ] ( ) ( )[ ]0398.01024.04612846146

8668.428063.412

2

=r

( )[ ]( )[ ] ( )[ ]0626.018

0605.12

2 =r

( )( )1268.1

1247.12=r

r2 = 0.9981

Calculations by: ____________________________ _____________

Date

Reviewed by: ______________________________ _____________

Date


52/66

Example of Plotting the Z-value Curve on Semi Log Graph Paper

16.8C


53/66

Plotting the Z-value Curve on Semi Log Graph Paper


54/66

Process Equivalent Time F

=Z

TT

AZT

Aref

AreftF 10x,

Process Equivalent Lethality ++= AiAAAAref ZTZTZTZTZT FFFFF ,....,,,, 321 tA = process clock time interval, usually 1 minute

Tref= process reference temperature

ZA = actual Z-value for the spore challenge


55/66




Time(Min.) Temp. Formula ProcessEquivalent Time

T1 110C

10x110xmin1,1 ==

ZTF

T2 115C

10x110xmin1,2 ==

ZTF

T3 118C

10x110xmin1,3 ==

ZTF

T4 120C

10x110xmin1,4 ==

ZTF

T5 121C

10x110xmin1,5

==

ZT

F

T6 122C

10x110xmin1,6 ==

ZTF

T7 124C

10x110xmin1,7 ==

ZTF

T8 121C

10x110xmin1,8 ==

ZTF

T9 118C

10x110xmin1,9 ==

ZTF

T10 107C

10x110xmin1,10 ==

ZTF

T11 105C10x110xmin1,11 ==

ZTF

ZTF ,



56/66




Time(Min.)

Temp. Formula ProcessEquivalent

Time

T1 110C3750.1

8

110121

, 10x110xmin11

==ZTF 0.0422

T2 115C7500.0

8

115121

, 10x110xmin12

==ZTF 0.1778

T3 118C3750.0

8

118121

, 10x110xmin13

==ZTF 0.4217

T4 120C1250.08

120121

, 10x110xmin14

==ZTF

0.7499

T5 121C0

8

121121

, 10x110xmin15 ==

ZTF 1.0000

T6 122C1250.08

122121

, 10x110xmin16 ==

ZTF 1.3335

T7 124C3750.0

8

124121

, 10x110xmin17 ==

ZTF 2.3714

T8 121C0

8

121121

, 10x110xmin18 ==

ZTF 1.0000

T9 118C3750.0

8

118121

, 10x110xmin19

==ZTF 0.4217

T10 107C7500.1

8

107121

, 10x110xmin110

==ZTF 0.0178

T11 105C0000.2

8

105121

, 10x110xmin111

==ZTF 0.0100

ZTF , 7.5460



57/66

Calculate the Process Spore Log Reduction Value

SLR =value-DProcess

AZ,

refT



58/66

Calculate the Process Spore Log Reduction (SLR) Value

The process equivalent time is 58.5 minutes.

The process D-value is 4.5 minutes.

Calculate the spore log reduction.

SLR =value-DProcess

AZ,

refT


SLR = =


59/66

Process Spore Log Reduction (SLR) Value

SLR = 13min5.4min5.58 =

Your process delivers 13 spore log reductions.


60/66

Sterility Assurance Level

( )SLRNlog 01010SAL

=


61/66


Your process used a spore challenge of 1.5 x 106

therefore, N0 = 1.5 x 106.



Calculation

SAL = 10logNo SLR

N0 =

logN0 =

Process equivalent lethality =

SAL =

SAL =


62/66


Your process used a spore challenge of 1.5 x 106 therefore, N0 = 1.5 x 106.



Calculation

SAL = 10logNo SLR

N0 = 1.5 x 106

logN0 = 6.176

Process equivalent lethality = 13 SLR

SAL = 10(6.176 13)

SAL = 10-6.824


63/66

Plotting the Survivor Curve on Semi Log Graph Paper


64/66

Biological Indicator

2010

Process LethalityCalculation and

Workbook


65/66

The biological data derived from a sterilization process is qualitative information, such as

sterile or non-sterile, established by observing either growth or no growth of a biological

challenge. The process is challenged with calibrated bacterial spores with a defined

resistance to the sterilization process. The process is effective if the spore challenge is

killed (no growth). The process is not effective when the spore challenge survives.

When we expose replicate samples to replicate physical conditions we are able to expandour knowledge of the lethality being delivered by the sterilization process. This is

usually expressed as a probabilistic value and is capable of predicting results with a high

level of certainty.

This workbook is intended to provide you with the ability to express biological

measurements in numbers using standard mathematical formulas. These biological

numbers provide the quantative assessment of the sterilization process. When used

properly, the bacterial spore provides the most accurate measure of the effectiveness of

the sterilization process.

The population of the spore challenge is established using standard microbiological platecount procedures and is used in the following mathematical equations. The D-value is

the first assessment of the resistance of a biological challenge to a particular sterilization

process. The D-value is defined as the time in minutes that it takes at a specified set of

conditions to reduce the population of the biological challenge by one log or a factor of

ten. There are two basic approaches to establish the D-value. One approach is referred to

as the survivor curve method and the other is the fraction negative method. In the

survivor curve method, high levels of spores are exposed to successive short time periods

of sterilizing conditions. The data collected is the number of spores that survived the

sterilization conditions. The exposures are performed over increasing durations of clock

time. The surviving spores are recovered using standard microbiological plate count

techniques. The data is plotted on a semi log graph. The X axis is clock time and theY axis is the log scale of the number of spores recovered at each of the exposure times.

The slope of the curve is the D-value. The coefficient of determination (r2) is also

calculated. This coefficient indicates how close the data points are to the calculated

linear regression plot.

The D-value can also be calculated using fraction negative data from units exposed in the

quantal zone. There are two approaches to analyze this data. The first approach is

referred to as the Stumbo, Murphy, Cochran formula. This method calculates a D-value

from each fraction negative data point. When more than one data set is available, the

individual point D-values are summed and divided by the number of data points. This

method is quite useful for determining a process D-value when it may be difficult to

collect more than one fraction negative data set.

The second approach using fraction negative data sets is referred to as the Limited

Holcomb, Spearmen, Karber method. This method not only focuses on the quantal zone

data points, but it looks at the shortest time to all negative units and the longest time to all

positive units. It uses all the quantal zone values and the exposure interval to calculate


66/66

the mean time to sterility. This approach is a little more robust than the Stumbo,

Murphy, Cochran method.

Now that spore populations have been identified and D-values have been established at

specific sets of conditions, the effect of varying temperature conditions can be evaluated.

The temperature coefficient or Z-value is defined as the temperature change required toalter the D-value by one log. This temperature coefficient can be applied to steam, dry

heat and ethylene oxide processes. The Z-value is best calculated using three D-values.

This can be performed graphically as well as calculated. The graphic plot is a semi log

plot with the X axis being the linear temperature scale and the Y axis the log plot ofthe D-values. The slope of the curve is the Z-value. The formula to calculate the slope is

the same log linear regression plot used for the survivor curve. The coefficient of

determination (r2) is also calculated using the same formula as in the survivor curve

method.

The Z-value allows the integration of different lethal rates for different temperatures. A

reference temperature or process set point must be identified. As temperatures increase,spores die faster. The Z-value provides an accurate assessment of lethality over the

normal process temperature variance as seen in come-up time, hold time and come-down

time process phases.

The temperature coefficient is now used to establish an equivalent process lethality (F-

value) at a defined reference temperature. The F-value integrates the varying process

conditions into an expression of equivalent process lethality. The equivalent process

lethality is usually described as equivalent process minutes at the reference temperature.

Complete and accurate temperature profiles are required for this calculation. This

establishes an accurate accumulated lethality value for a known biological challenge and

a dynamic process.

The F equivalent process lethality is now used to establish the equivalent spore log

reductions that are delivered by this equivalent process lethality value. This is

accomplished by dividing the F-value for the process by the process D-value. The result

is the spore log reductions (SLR) provided by the process.

The spore log reduction value is used to establish the sterility assurance level (SAL). The

sterility assurance level is used to assess the microbiological lethality of the process.

This value is the probability of a non-sterile unit (PNSU) occurring in the process.

Sterility assurance level is expressed as 10-x

. X is the log of the microbial challengeeither spores or bioburden, which is labeled N0 minus the SLR value delivered by the

process.

Calculo Del Valor D

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