Modeling microbial survival during exposure to a lethal agent with varying intensity.

Traditionally, the efficacy of preservation and disinfection processes has been assessed on the basis of the assumption that microbial mortality follows a first-order kinetic. However, as departures from this assumed kinetics are quite common, various other models, based on higher-order kinetics or population balance, have also been proposed. The database for either type of models is a set of survival curves of the targeted organism or spores determined under constant conditions, that is, constant temperature, chemical agent concentration, etc. Hence, to calculate the outcome of an actual industrial process, where conditions are changing, as in heating and cooling during a thermal treatment or when the agent dissipates as in chlorination or hydrogen peroxide application, one has to integrate the momentary effects of the lethal agent. This involves mathematical models based on assumed mortality kinetics, and simulated or measured history, for example, temperature-time or concentration-time relationships at the "coldest" point. It is shown that the survival curve under conditions where the agent intensity increases, decreases, or oscillates can be constructed without assuming any mortality kinetics and without the use of the traditional D and Z values, which require linear approximation, and without thermal death times, which require extrapolation. The actual survival curves can be compiled from the isothermal survival curves provided that growth and damage repair do not occur over the pertinent time scale and that the mortality rate is a function of only the momentary agent intensity and of the organism's or spore's survival fraction (but not of the rate at which this fraction has been reached). The calculation is greatly facilitated if both the "isothermal" survival curves and the time-dependent agent intensity can be expressed algebraically. The differential equation derived from these considerations can be solved numerically to produce the required survival curve under the changing conditions. The concept is demonstrated with simulated survival curves during heating at different rates, heating and cooling cycles, oscillating temperature, and exposure to a dissipating chemical agent. The simulated thermal processes are based on published data of Clostridium botulinum spores, whose semilogarithmic survival curves have upward concavity and on a hypothetical "Listeria-like" organism whose semilogarithmic curves have downward concavity.