ABSTRACT
For thermal resistance studies, the bacteriologist’s defini-
tion of death is simple and practical, i.e., “a bacterium is
dead when it has lost its ability to reproduce.”[4,23]
The z-value, lately referred as thermal resistance constant
and denoted by z(T),[10] is a characteristic of a micro-
organism and expresses the change in death rate with respect
to a change in lethal temperature. Numerically it is equal to
the number of degrees (in F or C) required to change by one logarithmic cycle (tenfold factor) the value of the decimal
reduction time (D-value). Graphically, it can be determined
by plotting the logarithm of D-value as a function of the
lethal temperature, which since 1950 is frequently referred to
as the TDT curve, instead of using the traditional TDT
plot.[7,22,24-32] The difference between both graphs is trivial
since F-values are multiples of D-values.[4] Sometimes the
graph is also called the thermal resistance[3,8,9,33,34] or ther-
mal destruction (TD) curve.[4,35-37]
Over the temperature range of concern in food steriliza-
tion technology, TDT curves approximate straight lines[4]
(Fig. 1). Mathematically, z-value is equal to the negative
reciprocal of the slope of the death rate curve and may be
expressed as follows:
log DT1 log DT2 T1 T2 ¼
z ð1Þ
Eq. 1 is used when z-value is calculated from
D-values[22,31,38-44] and it is sometimes denoted by the zD symbol. Also, the z-value can be determined from TDT
(F-value) data[8,18,42,45-47] and in this case the symbol zF is
sometimes used. Thus, the slope of the TDT curve may be
expressed as follows:
log FT1 log FT2 T1 T2 ¼
z ð1aÞ
Eq. 1 is frequently rewritten in the following form[6,10]:
log DT
¼ ðT T refÞ
z ð2Þ
or rearranged as[6,8,48,49]:
DT ¼ DT ref 10ðT refTÞ=z ð3Þ
Based on Eq. 1a, we obtain the equation of the TDT
curve[6,8,48]:
TDT ¼ FT ¼ FT ref 10ðT refTÞ=z ð3aÞ
The decimal reduction time term, using the abbreviation
DRT instead of the symbol D used nowadays, was first
introduced in 1943 by Katzin, Sandholzer, and Strong[50] in
their quantitative determinations of microbial death rate by
heat. At the same time, Ball[51] followed by Stumbo[19,20]
used the symbol Z (Zeta) to represent the “slope value of
the logarithmic survivor curve” and defined it as “the
number of minutes required for the survivor curve to tra-
verse one logarithmic cycle.” To avoid confusion of the
symbol Z with the z value, which represent the slope of
the TDT curve, researchers in the field agreed to use the
symbol D instead of Z.[22] The decimal reduction time
(D-value) concept came into general use after 1950.[2,4,6]
The D-value is defined as “the time required to inacti-
vate 90% of the spores or vegetative cells of a given
organism when exposed to a constant lethal temperature
in a given medium.”[8,10,52] The expanded definition as
“the time required for the concentration of any component,
including micro-organisms, to change by a factor of ten at a
fixed temperature”[48] allows its application to chemical
factors following also first-order reaction kinetics.[6]
Numerically, it is equal to the number of minutes required
for the survivor or chemical concentration curve to cross a
1-log cycle. In the case of microbial inactivation, it can be
determined graphically by plotting the number of surviving
microorganisms as a function of the time of heating at a
constant lethal temperature using what is typically called a
survivor curve[8,9] (Fig. 2). Mathematically, it is equal to
the negative reciprocal of the slope of the survivor curve
and can be calculated as follows:
log Nt1 log Nt2 t1 t2 ¼
DT ð4Þ
Eq. 4 can be rearranged into the survivor curve equation to
describe changes in microbial population as a function of
heating time:
log Nt
N0 ¼ t
DT ð5Þ
As suggested by Pflug,[53,54] Eq. 5 is the empirical model
expressing the F-value as multiple of D-values as follows:
FzT ref ¼ DT ref ðlog N0 log NtÞ ð5aÞ
Eq. 5a is widely used by food microbiologist to determine
the time required in a thermal process to achieve a desired
“safe” final concentration of spores established from pub-
lic health (“commercial sterility”) or “economic spoilage”
considerations.[6,48,55] Unfortunately, most authors do not
use the superscript z to emphasize the type of micro-
organism considered in this determination.
