WOLFRAM|DEMONSTRATIONS PROJECT

Extracting Microbial Inactivation Parameters from Final Survival Ratios

​
microbe type
a
b
c
d
plot of estimation mode
three final points
m
1
: 2, 3  1
m
2
: 1, 3  2
m
3
: 1, 2  3
mean of
m
1
​,
m
2
​,
m
3
a: Salmonella cells
Recording truly isothermal microbial survival curves, especially at high lethal temperatures, is extremely difficult if not impossible. When a microbe’s thermal inactivation kinetics is known to follow a three-parameter model, the three parameters can be estimated directly from the final survival ratios after three dynamic heat treatments, which also eliminates the need to determine the entire survival curves. The method is demonstrated with simulated non-isothermal survival data of two bacterial vegetative cells and two bacterial endospores using the Weibull log-logistic (WeLL) model with a constant shape factor.
The WeLL model’s three parameters are the temperature,
T
c
, marking the inactivation onset,
k
, the slope of the rate parameter rise at temperatures well above
T
c
, and
n
, the shape factor of the isothermal inactivation times' Weibullian distribution, assumed to be practically temperature independent in the pertinent temperature range. These three survival parameters are calculated numerically by solving three simultaneous survival equations, which are the solutions of the three differential rate equations that correspond to the temperature profiles in these procedures.