Estimating the Heat Resistance Parameters of Bacterial Spores from their Survival Ratios at the End of UHT and other Heat Treatments

Abstract

Accurate determination of bacterial cells or the isothermal survival curves of spores at Ultra High Temperatures (UHT) is hindered by the difficulty in withdrawing samples during the short process and the significant role that the come up and cooling times might play. The problem would be avoided if the survival parameters could be derived directly from the final survival ratios of the non-isothermal treatments but with known temperature profiles. Non-linear inactivation can be described by models that have at least three survival parameters. In the simplified version of the Weibullian -log logistic model they are n, representing the curvature of the isothermal semilogarithmic survival curves, T(c), a marker of the temperature where the inactivation accelerates and k, the slope of the rate parameter at temperatures well above T(c). In principle, these three unknown parameters can be calculated by solving, simultaneously, three rate equations constructed for three different temperature profiles that have produced three corresponding final survival ratios, which are determined experimentally. Since the three equations are constructed from the numerical solutions of three differential equations, this might not always be a practical option. However, the solution would be greatly facilitated if the problem could be reduced to the solution of only two simultaneous equations. This can be done by progressively changing the value of n by small increments or decrements and solving for k and T(c). The iterations continue until the model constructed with the calculated k and T(c) values correctly predicts the survival ratio obtained in a third heat treatment with a known temperature profile. Once n, k, and T(c) are established in this way, the resulting model can be used to predict the complete survival curves of the organism or spore under almost any contemplated or actual UHT treatment in the same medium. The potential of the method is demonstrated with simulated inactivation patterns and its predictive ability with experimental survival data of Bacillus sporothermodurans. Theoretically at least, the shown calculation procedure can be applied to other thermal preservation methods and to the prediction of collateral biochemical reactions, like vitamin degradation or the synthesis of compounds that cause discoloration. The concept itself can also be extended to non-Weibullian inactivation or synthesis patterns, provided that they are controlled by only three or fewer kinetic parameters.

Characterization of Bacillus sporothermodurans IC4 spores; putative indicator microorganism for optimisation of thermal processes in food sterilisation

“…(6) is valid only for a fixed value of the parameter b. Indeed, it has been previously reported that the parameter b is practically constant over the lethal temperature range (Mafart et al, 2002;Peleg et al, 2008). Therefore, in this study, for the global optimisation, Eq.…”

Dynamic Model of Heat Inactivation Kinetics for Bacterial Adaptation

“…(Equation 7 can also be converted into a difference equation and solved with general-purpose software like MS Excel [19].) The validity of the WeLL model has been demonstrated by its ability to correctly predict dynamic inactivation patterns from experimental isothermal survival data (6,16,24) or from dynamic data not used in its parameter calculations (4,17,20).…”

“…The temperature dependence of the "rate parameter," b(T), can be described by the empirical log-logistic model (16,17,20):…”

Comparing the effectiveness of thermal and non-thermal food preservation processes: the concept of equivalent efficacy

“…Moreover, Eq. 20.12 can be used not only to simulate and correctly predict dynamic inactivation patterns (e.g., Corradini and Peleg, 2004;Periago et al, 2004;Pardey et al, 2005;Peleg, 2006), but also to serve as a model for extracting the survival parameters, n, k and T c , from experimental survival curves determined under non-isothermal conditions Peleg, 2006;Peleg et al, 2008a;Corradini et al, 2008Corradini et al, , 2009a. A modified version of the WeLL model, could also be used to correctly predict dynamic survival patterns in chemical disinfection and there is evidence that it might be applicable to HHP as well (Corradini and Peleg, 2003b;Doona et al 2007).…”