Biomedical Engineering Reference
In-Depth Information
FIGURE 18.8 Typical survival curve (depicting cell death) for spores of Bacillus stearothermophilus Fs7954 in
distilled water.
Most microbe populations are not homogeneous. Often a subgroup is more resistant to
the sterilization method chosen. Also, organisms growing in flocs tend to be more resis-
tant to death. These factors are important in processing. Especially in stringent safety
required systems, prudent
investigation of
the potential “hard-to-kill” pollution is
needed.
As we have discussed earlier that survival curve or ratio is not appropriate for
ensuring sterility of the medium, we need to use a more absolute reference to sterility.
Therefore, the probability of one cell surviving in the entire fermentation medium of
concern is a good indicator to use. The probability of the entire population not vanish-
ing during the sterilization process can be calculated based on Eqns (18.14) and
(18.18) ,
P 1 ðtÞ¼1P 0 ðtÞ¼1½1pðtÞ N 0
e k d t Þ N 0
¼ 1ð1
(18.22)
For most applications, we want to ensure that P 1 (t) is very small to ensure that no cells in the
entire population surviving during sterilization. Computationally, this can be challenging as
N 0 can be large in large vessels. In the literature, numerical charts or graphs were frequently
used, but they are not convenient and not compatible with modern convenience of superior
computing powers. Eqn (18.22) can be expanded to give
e k d t Þ N 0
¼ N 0 e k d t N 0 ðN 0 1 Þ
2
P 1 ðtÞ¼1ð1
e 2k d t þ N 0 ðN 0 1 ÞðN 0 2 Þ
6
e 3k d t
(18.23)
e 4k d t þ . þ ð 1 Þ n N 0 !
n ! ðN 0 !
N 0 ðN 0 1 ÞðN 0 2 ÞðN 0 3 Þ
24
e nk d t þ .
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