On 1 Apr 2002 03:54:54 -0800, rgregoryclark at yahoo.com (Robert Clark)
wrote:
>Thanks for the response.
Thank *you* for the data and for contacting me.
-- Davin
I will, below, attempt to calculate the z-values for Bacillus sp. ATCC
27380 and Bacillus xerothermodurands.
>Morphology of Extremely Heat Resistant Spores from Bacillus
>sp. ATCC 27380 by Scanning and Transmission Electron
>Microscopy
>Youvan, Watanabe, Holmquist
>Life Sciences and Space Research, vol. 15, 1976, p. 65-72.
>ABSTRACT
>Bacillus sp. ATCC 27380 is a recently discovered aerobic
>mesophile, isolated from surface soil, that produces spores with
>extreme resistance to dry heat: the length of time to 90% kill is
>139 hr. at 125 C and 13-17 hr. at 138 C.
We have two sets of two D-value data-points from which to make our
calculations. Two points are the minimum for a z-value calculation.
We can easily see right-off-the-bat that 139hr and 13-17hr is about a
one log reduction (in time 13 x 10 = 130, 17 x 10 = 170, actual is 139
so it is in the same log) per 13 degrees C (from 138 - 125 = 13).
Unfortunately, we will not be able to also get a r, or r^2 correlation
coefficient with only two points. However, for illustration, I will
calculate as if we have more than two points. I will convert hours
into minutes because of the short D-values at higher temperatures.
Later we may need to convert minutes into seconds, but for now let's
just "think" in minutes.
D-values:
1) 125C = 139hr D-value converted into minutes, we get 139hr x
60min/hr= 8340 minutes.
2) 138C = 13hr, which is 13hr x 60min/hr = 780 minutes.
3) 138C = 17hr, which is 17hr x 60min/hr = 1020 minutes.
[and , 4) 150C = 2.5hr = 150 minutes. I am not going to use the ATCC
note D-value that claimed (Why is it not in the paper cited?) 150C =
2.5hr (150 minutes, log base-10 = 2.1761) D-value. Note that is is
the same for B. zerothermodurans. But, if ATCC 27380, with n =3,
gives a z-value = 14.30C and an r = -0.09968 and r^2 = 0.9936 (if 138C
= 13hr is used), then, if 138C = 17hr, I get a z-value = 14.33, r =
-1.000 and r^2 = 1.000 (which is the highest correlation possible).]
The z-value is the negative reciprocal of the slope of the thermal
death time curve, where the D-values are expressed as log-base 10
values. So, we convert our D-values in minutes into log base 10
values times (still minutes).
1) 8340min becomes 3.9212min for 125C
2) 780 becomes 2.8921 for 138C
3) 1020 becomes 3.0086 for 138C
[4) 150 becomes 2.1761 for 150C]
Plotting this in a linear regression (least squares method), we get:
1) and 2) data gives a y-intercept of 13.8164, and a slope of -0.0792,
and the negative reciprocal is a z-value of 12.6 degrees C. So, if we
want to lower the minutes of heat exposure by one log, we need to
increase the temperature by 12.6C.
1) and 3) data gives a y-intercept of 12.6962, and a slope of -0.0702,
and the negative reciprocal is a z-value of 14.25 degrees C. So, if
we want to lower the minutes of heat exposure by one log, we need to
increase the temperature by 14.25C.
[Data can be entered starting with the highest D-value and proceeding
to the lowest, since psychologically, we want increasing temperature
and a falling (negative) slope of the line.]
Say we want to know how the temperature we will need reduce the spores
down to <1 CFU, given a reasonable procesing time. If we take the
data from 1) and 3) -- the worst data case -- and go up in temperature
starting from 138C, here is what happens:
138C + 14.25 = 152.25C. At 152.25C we will go from 3.0086 (1020
minutes to kill one log) to 2.0086 (is about a 102 minute D-value).
>From 152.25 + 14.25 = 166.5C will give about 10 minute D-value.
Continuing, 166.5 + 14.25 = 180.75C gives a 1 minute D-value and
180.75C + 14.25 = 195C gives a 1/10 minutes (6 seconds) D-value,
finally with one more z-value added on, we get 209.25C with a 1/100
minute (0.6 second) D-value.
138C = 1020 minutes (D-value)
152.25C = 102 minutes
166.5C = 10.2 minutes
180.75C = 1.02 minute
195C = 0.1 minute (6 seconds)
209.25C = 0.01 minutes (0.6 seconds)
223.5C = 0.001 minutes (0.06 seconds)
etc. . .
The reason I have stopped here is because in the Brown et al paper,
they say the second stage of the medical waste destruction chamber has
a 2 second residence time at 1000C. Later I will use a 10-D rather
than a 12-D sterility assurance concept.
>Organism: Bacillus xerothermodurans (Bond and Favero)
>Bacillus xerothermodurans sp. nov., a Species Forming
>Endospores Extremely Resistant to Dry Heat.
>Bond and Favero
>International Journal of Systematic Bacteriology, vol. 27, no. 2,
>April 1977, p. 157-169
>. . . dry heat (D_125C = 139 hours, D_130C = 54 h,
>D_135C = 24 h, D_145C = 8 h, D_150C = 2.5 h; where D = time
>at temperature effecting 90% reduction in viable count);
1) 125C = 139hr D-value converted into minutes, we get 139hr x
60min/hr= 8340 minutes.
2) 130C = 54hr, which is 54hr x 60min/hr = 3240 minutes.
3) 135C = 24hr, which is 24hr x 60min/hr = 1440 minutes.
4) 145C = 8hr, which is 8hr x 60min/hr = 480 minutes.
5) 150C = 2.5hr, which is 2.5hr x 60min/hr = 150 minutes.
Log Conversion:
1) 125C = 3.9212 D-value time in minutes
2) 130C = 3.5106
3) 135C = 3.1584
4) 145C = 2.6812
5) 150C = 2.1761
L.R.:
y-intercept = 12.0762
Slope = -0.0656
r = -0.9934
r^2 = 0.9869
z-value = 15.25 degrees C.
So, comparing the two Bacillus spores, we need (only) a z-value of one
more degree C per a one D-value change for B. zerothermodurans than
for the ATCC 27380 Bacillus sp. (15.25C vs. 14.25C respectively).
150C = 150 minutes (D-value)
165.25C = 15 minutes
180.5C = 1.5 minutes
195.75C = 0.15 minute (9 seconds)
211C = 0.015 minute (0.9 seconds)
226.25C = 0.0015 minutes (0.09 seconds)
241.5C = 0.00015 minutes (0.009 seconds)
etc. . .
--------------
So, for ATCC 27380, if we start with an absolute count of 10^10 spores
(10-D sterility assurance concept for food canning), we would expect
at 223.5C, 10 logs of spores x (times) the D-value of 0.06 seconds =
0.6 seconds to kill down to the <1 CFU level.
And, for B. zerothermodurans, if we start with an absolute count of
10^10 spores, we would expect at 226.25C, 10 logs of spores x (times)
the D-value of 0.09 seconds = 0.9 seconds to kill down to the <1 CFU
level.
We, need a higher temperature (or more time, or in the above example .
. . both) for B. zerothermodurans to get the same count as ATCC 27380.
[We do this with "naked" spores on a flat surface such as an aluminum
self-adhesive tape. The entire tape is removed from the oven and
cultured in a special liquid spore-recovery broth. We usually use two
spore count levels, 10^5 and 10^6 CFU.
Using the count level target of "<1 CFU", on repeating this
experiment, I would expect at least one sterility test would be
positive in ten-thousand runs, because this is like a "most probable
number" method, the standard is actually 3 positives/10,000 at 10^6.
In practice we use a sterility assurance level that gives us . . . 3
or fewer positives in 10,000 tests with a 6-log inoculum of spores.
10^6 using 10^4 = 10^10.
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How to calculate these linear predictive models:
The temperature required to decrease the spores by one log (which is a
90% reduction) is called the "z-value" and is used in heat processing
of food. For instance, if 125C has a D-value (kills one log, 90%) in
139hr (8340 minutes) and 138C has a D-value of 17 hours (1020
minutes), after converting the D-value times into log base-10, then
the "z-value" is the negative reciprocal of the slope of the linear
regression line formed by these two points which is 14.25 degrees C.
1. Clear summation registers.
2. Type-in the highest log base-10 of the D-value: 3.9212
minutes, press enter.
3. Type-in the temperature for that D-value: 125C, press
summation
4. Type-in the lowest log base-10 D-value: 3.0086 minutes, press
enter.
5. Type-in the temperature for that D-value: 138C, press
summation.
6. Press L.R. to get y-intercept. 12.6962
7. Press exchange x<>y.
8. Slope is displayed: -0.0702
9. Press 1/x to display the reciprocal of the slope: - 14.2450
10. The negative of this is: 14.25 degrees C. This is what we can
call a z-value in degrees C.
11. This is the temperature needed to lower the D-value by one log
(log of the minutes).
The above is for the HP11C calculator.
The z-value is common to heat processing. It finds the temperature
required to lower the exposure time by one D-value (here, the D-value
are expressed in logs base 10.) We however, measure our D-values in
time i.e., hours, minutes, or seconds.
This is useful since you can now "tailor make" a heat process and be
close to what you want from the start. Then, you perform a
validation, because, sometimes the real-world does not match the
mathematical idealized formulas.
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