Modeling and predicting non-isothermal microbial growth using general purpose software

Published experimental isothermal growth curves of Clostridium perfringens cells in ground ham were fitted with a modified three-parameter version of the logistic equation as a primary model and the temperature dependence of the three parameters by ad hoc empirical secondary models. These were used to predict the organism's non-isothermal growth curves under three different cooling regimes. The assumption has been that the organism's instantaneous (or momentary) non-isothermal growth rate is the isothermal rate at the given temperature at a time that corresponds to its instantaneous population size. This could be translated into a differential rate model equation, whose coefficients are constructed from terms that reflect the changing growth parameters with temperature and hence with time. The continuous rate equation, however, can be solved incrementally by a numerical procedure that can be implemented in similar purpose software like Microsoft Excel®. In all three cases, there was good agreement between the growth curves predicted by the model and those found experimentally. This demonstrated that the procedure can be used to generate growth curves under complicated thermal histories that may include regular and irregular temperature oscillations.