W

temperature

Fig. 16.7. One strategy for determining the combined effect of temperature and water activity on the specific growth rate parameter would be to determine the "response surface", that is, to determine the specific growth rate parameter at various different combinations of temperature and water activity. An equation, involving two independent variables, can then be fitted to this surface. Such a strategy was recently used by Hamidi-Esfahani et al. (2004). The disadvantage is the number of experiments required. This example involves all possible combinations of 8 temperatures and 7 water activities, that is, a total of 56 different experiments.

temperature water activity

Fig. 16.7. One strategy for determining the combined effect of temperature and water activity on the specific growth rate parameter would be to determine the "response surface", that is, to determine the specific growth rate parameter at various different combinations of temperature and water activity. An equation, involving two independent variables, can then be fitted to this surface. Such a strategy was recently used by Hamidi-Esfahani et al. (2004). The disadvantage is the number of experiments required. This example involves all possible combinations of 8 temperatures and 7 water activities, that is, a total of 56 different experiments.

where the subscript "T" in fT denotes that this is the fractional specific growth rate based on variations in temperature. Similarly, in the case of water activity effects, using Eq. (7.18) gives:

If equations are written for all of the environmental variables that are taken into account in the model, then the overall fractional specific growth rate can be calculated on the basis of the geometric mean of the individual fractional specific growth rates (Sargantanis et al. 1993). In the case in which only temperature and water activity are taken into account, the equation for the combined effect on the specific growth rate would be:

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