the handbook of food engineering practice crc press chapter 10 ...

The study of the temperature dependence of microbial growth has lately been an area
of increased activity. The described kinetic principles are applied to compile the neccessary
data for modeling growth behavior, in a multidisciplinary field coded predictive
microbiology (Buchanan,1993; McClure et al., 1994; McMeekin et al., 1993). For a
temperature range below the optimum growth temperature either of the two simple
equations, Arrhenius and square root, sufficiently model the dependence for all practical
purposes (Labuza et al., 1991). The two-parameter empirical square root model, proposed
by Ratkowsky et al.(1982) has the form
k = b (T-T min ) (39)
where k is growth rate, b is slope of the regression line of k vs temperature, and T min is
the hypothetical growth temperature where the regression line cuts the T axis at k =0.
The relation between Q 10 and this expression is
⎛T-T min +10⎞ 2
Q 10 = ⎝ T-T min ⎠
(40)
Equations with more parameters, to model growth (and lag phase)
dependence through the whole biokinetic range, were also introduced, either based on the
square root model ( Ratkowsky et al., 1983) or the Arrhenius equation (Mohr and Krawiek,
1980 ; Scoolfield et al., 1981, Adair et al., 1989). They were reviewed and experimentally
evaluated by Zwietering et al. ( 1991).
Traditionally the mathematical models relating the numbers of microorganisms to
temperature have been divide into two main groups (Whiting and Buchanan, 1994): Those
describing propagation or growth primarily refer to the lower temperature range, and those
describing thermal destruction at lethal temperature range. Recently, a combined approach
utilizing a single mathematical formula to describe both the propagation and destruction
rate constant over the entire temperature range, from growth (k(T)>0) to lethality was
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