226 DISINFECTION
or, if natural logarithms are used:—N
N(^0) exp( ).kt
These equations have led to the alternative and preferred
descriptions of the response as being exponential or logarith-
mic. Since the number of viable cells decreases throughout
the process, then the rate constant, k, is always negative in
character.
The two curves shown in Figures 2(b) and 2(c) illus-
trate similar, though opposite, deviations in response from
the straight line case. These are described, according to their
shape, as concave or convex, and qualified by the additional
designation upward or downward, to indicate orientation. The
graphs indicate that the rate of disinfection changes gradu-
ally in the early stages, but then assumes a more steady state
of change similar to that in the straight case. In Figure 2(b),
the rate of disinfection is relatively slow at first, but gradu-
ally increases to a steady, limiting value. Various interpre-
tations have been suggested to account for this change;
among them, that the distribution of resistances between the
individual cells exhibits a relative deficiency of cells of low
resistance; or alternatively, that the cells must pass through
one or more intermediate stages before becoming sensitive
to the disinfection process in question. The weakness of such
interpretations is underlined by the fact that changes in the
experimental conditions often result in a change in the shape
of the graphical response. Figure 2(c) illustrates a relatively
fast rate of disinfection initially, which gradually decreases
to a steady, limiting value.
In Figure 2(d) is illustrated the most common deviation
from the straight line response, the sigmoid curve. Responses
of this type are more easily demonstrated in systems employ-
ing a moderate rate of disinfection. As the rate of disinfection
is increased, the limitations of viable counting techniques
make it more and more difficult to monitor the progress of
the process with any precision. This results in the apparent
response becoming indistinguishable from the straight line
case. It is sometimes suggested that the sigmoid response is
the most common situation encountered, but that it is often
unrecognized due to the practical difficulties experienced.
The sigmoid response is usually interpreted as an indication
that the distribution of resistances between the individual
cells is of the log normal type. Complete agreement with this
model distribution is indicated when the sigmoid curve is
symmetrical.
Figure 2(e) illustrates a response of particular interest.
The graph consists of two parts, both of which are linear
but of different slope, with a fairly sharp transition between
the two. This would appear to indicate a fairly rapid rate of
disinfection initially, followed by a fairly sharp transition to
a lower, but steady, rate. Such a sudden transition naturally
engenders interest, if not suspicion. It has been suggested that
this type of response indicates the presence of two distinct
groups of cells, each of which exhibits its own characteristic
distribution of resistances. Experiments with a mixture of
two bacterial cultures of different identity, whether obtained
different species, or consisting of spores and vegetative
cells of the same species, can be shown to yield this type of
response. The first part of the graph corresponds to the usual
response of the more sensitive component, and the second
part to that of the more resistant component. However, at
relatively low temperatures and humidities, exposure of
nominally homogeneous cultures to ethylene oxide gas often
yields this type of response. While it is sometimes suggested
that this indicates the presence of two distinct groups of cells,
as discussed above, it must also be considered that not only
can this phenomenon be demonstrated with cultures appar-
ently homogeneous to other sterilization methods, but also
that this two part response reverts to the exponential type on
increasing the temperature or humidity of the system.
As indicated in the foregoing discussion, consideration
of the shapes of survivor curves may provide useful circum-
stantial evidence on which to base hypotheses relating to
the response of cell populations to disinfection processes.
However, as also indicated in the discussion, the operative
word is “circumstantial.”
Empirical Parameters
While a survivor curve illustrates the response of a cell popu-
lation in terms of variation in number of survivors with time
(or dose) of disinfection treatment, this is essentially a static
time
(Log)
Surviving Fraction
1.0
(a) (b)
(c) (d)
(e)
FIGURE 2
C004_002_r03.indd 226C004_002_r03.indd 226 11/18/2005 10:19:27 AM11/18/2005 10:19:27 AM