Calculating microbial survival parameters and predicting survival curves from non-isothermal inactivation data

Irrespective of whether the isothermal semi-logarithmic survival curves of heat inactivated microbial cells or spores are linear or nonlinear, it is theoretically possible to numerically calculate their survival parameters from inactivation data obtained under non-isothermal conditions. A method to do the calculation, when the temperature history ('profile') is expressed algebraically, is demonstrated with simulated survival curves. It has been tested with the published survival data of Salmonella, whose nonlinear semi-logarithmic isothermal survival curves can be described by a power law model. The reported survival ratios of Salmonella, determined during non-isothermal heat treatments in a broth and in ground chicken breast, were used to estimate its isothermal survival parameters in the two media and their temperature dependence. These, in turn, were used to predict the cells' survival curves under different temperature 'profiles.' There was a good agreement between the predicted and the reported experimental survival curves in the broth case and reasonable agreement in the ground chicken breasts, where the database was considerably smaller The development of a mathematical method to calculate survival parameters from non-isothermal inactivation data will eliminate the need to determine these parameters under isothermal conditions, which can only be approximated and are technically difficult to perform. In many cases, the proposed method will also enable the determination of the survival parameters in the actual food or medium of interest, which may contain particles, or is too viscous to be heated and cooled effectively using the currently available experimental procedures. In principle, the described mathematical method can also be used to assess organisms' survival parameters in nonthermal inactivation processes, such as exposure to a dissipating chemical agent or the application of ultra high-pressure.     

A numerical algorithm for calculating microbial survival curves during thermal processing

Assuming that the targeted microorganism’s isothermal survival curves follow the Weibullian pattern, which describes a large number of microbial isothermal survival curves, a simple numerical algorithm was developed to calculate the momentary survival ratio during non-isothermal thermal processes. The algorithm is based on a mathematical expression derived from a non-isothermal survival rate model proposed in the literature.Simulations indicated that the proposed algorithm generated the same results as those obtained from other non-isothermal models found in the literature. However, compared to the published models, the proposed algorithm has two advantages. One is that the calculation speed is very fast because only simple algebraic operations are involved, and the other is that it can be programmed very easily in different computer languages and spreadsheets. In addition, the algorithm provides an effective way to estimate changes of microbial survival ratio with time from product temperatures that are either directly measured during thermal processing or predicted by proper heat transfer models. Thus, the algorithm can also be easily incorporated into control systems of commercial thermal process equipment.     

Prediction of an organism's inactivation patterns from three single survival ratios determined at the end of three non-isothermal heat treatments

Traditionally, an organism's heat resistance parameters have been determined from a set of experimental isothermal survival data. Sometimes, however, even approximating an isothermal profile, and/or obtaining counts at sufficiently short time intervals, is extremely difficult for technical and logistic reasons. The problem would be avoided if the survival parameters could be calculated from the final survival ratios determined at the end of non-isothermal heat treatments with known temperature profiles. Theoretically, if the heat resistance were characterized by three unknown survival parameters, they could be extracted by solving three simultaneous dynamic survival curves' equations. In practice, because of the three equation's complexity - they are themselves the numerical solutions of three differential rate equations - and because the experimental final survival ratios might have a scatter, realistic estimates of the survival parameters require short cut and averaging methods for their calculation. Such a method has been tried with published dynamic inactivation data on Salmonella enteritidis and Escherichia coli. The concept was validated by the ability of the Weibullian-Log logistic model, whose three survival parameters had been obtained directly from final experimental survival ratios only, to predict entire non-isothermal survival curves that had not been used in the model's formulation. The methodology need not be restricted to Weibullian and simpler survival patterns but its practicality might be lost if there are more than three survival parameters. In principle, the same procedure can be extended to biochemical processes that occur during heat preservation, especially at very high temperatures. Estimating inactivation kinetic parameters without isothermal data could also facilitate the quantification of microbial survival under realistic processing conditions and in the actual food rather than in a surrogate medium.     

Numerical and Statistical Methodology to Analyze Microbial Spoilage of Refrigerated Solid Foods Exposed to Temperature Abuse

Numerical and statistical procedures based on pseudo-zero for the lag and first order reaction kinetics for the exponential growth phase were developed to analyze non-isothermal microbial spoilage. Arrhenius model parameters and their accuracy were estimated for a mixture of Pseudomonas fluorescens, Staphylococcus aureus andAchromobacter lwoffi growing in a seafood model. Linear regressions used with isothermal experiments generated initial values for nonlinear estimations of the frequency (K₀) and activiation energy (E_a) constants. An optimization technique was used to minimize the square difference between experimental and estimated values while parameter accuracy was assessed using a bootstrap method. E_a and In(K₀) were 109±3.4 and 48.3±1.5 kJ/mole for the exponential, and 152±4.0 and 64.4±1.7 kJ/mole for the lag phase, respectively. The Mann-Whitney-Wilcoxon rank sum test showed no significant differences between parameters generated by two different temperature profiles (5% significance level).     

Calculation of the non-isothermal inactivation patterns of microbes having sigmoidal isothermal semi-logarithmic survival curves

Sigmoidal isothermal semi-logarithmic survival curves are of two main types; starting with a downward and changing to upward concavity and vice versa. Both can be described by a variety of mathematical models having 3-4 adjustable parameters. The temperature dependence of these models' parameters can be described by empirical models, which account for the progressive change in the sigmoidal shape, including its disappearance at either high or low temperatures. If the temperature history of a heat-treated population of microbial cells or spores ('temperature profile') can be described algebraically, then there is a way to estimate the survival pattern under these non-isothermal conditions without invoking the traditional D and z values, which require forcing straight lines through the curved experimental data. The described method is based on the assumption that the local slope of the non-isothermal survival curve is that of the isothermal curve at the momentary temperature, at a time, which corresponds to the momentary survival ratio. It is similar to the method previously proposed for microbial populations with a 'power law' type isothermal survival curves, except that the time, which corresponds to the momentary survival ratio, is calculated either symbolically or numerically as a procedure incorporated in the governing differential equation. The method's capabilities are demonstrated with simulated survival curves under temperature histories that resemble thermal processing of foods. They include heating to different target temperatures and starting the cooling at different times.     

Evaluation of selected mathematical models to predict the inactivation of Listeria innocua by pulsed electric fields

The inactivation of Listeria innocua ATCC 51742 by pulsed electric fields was investigated at 35, 40 and 45 kV/cm. Results indicate that at treatment times shorter than 37 μs at 40 and 45 kV/cm, and 49 μs at 35 kV/cm, there is a linear relationship between the logarithm of the survivor fraction and the treatment time. However, longer times result in an abrupt increase in the slope of the inactivation curve and in inactivation values greater than six logarithmic cycles. A model based on Weibull's survival function was used to describe microbial inactivation and then compared to a first-order kinetic model. Distribution parameters of Weibull's survival function and kinetic constant for the first-order kinetic model were calculated by fitting experimental data. Calculated mean times for microbial inactivation from Weibull's distribution were 11.55, 8.65 and 5.39 μs at 35, 40 and 45 kV/cm, respectively. The goodness-of-fit between experimental and predicted values was determined using an accuracy factor. The model based on the Weibull survival distribution provided better accuracy factors than first-order kinetics. The model based on Weibull's survival function seems promising for describing survival curves that exhibit concavity.     

Pressure inactivation kinetics of Yersinia enterocolitica ATCC 35669

The survival curves of Yersinia enterocolitica ATCC 35669 inactivated by high hydrostatic pressure were obtained at four pressure levels (300, 350, 400, and 450 MPa) in sodium phosphate buffer (0.1 M, pH 7.0) and four pressure levels (350, 400, 450, 500 MPa) in UHT whole milk. Tailing was observed in all the survival curves. A linear model and three nonlinear models were fitted to these data and the performances of these models were compared. The linear regression model for survival curves at four pressure levels had regression coefficients (R2) values of 0.785-0.962 and mean square error (MSE) of 0.265-0.893. A residual plot strongly suggested that a linear regression function was not appropriate as there was strong curvature in the plotted data. The nonlinear regression model using the log-logistic had R2 values of 0.946-0.982 and MSE values of 0.110-0.320. The Weibull model had R2 values of 0.944-0.975 and MSE values of 0.153-0.349. These results indicated that both were better models to describe the pressure inactivation kinetics of Y. enterocolitica in milk and buffer. Among the three nonlinear models studied, the modified Gompertz model produced the poorest fit to data. The number of parameters of the log-logistic model was reduced from four to two so that the model was greatly simplified. The reduced log-logistic model still produced a fit comparable to the full model. Since pressure had no significant effect on the shape factors of the Weibull model at the pressure levels of 300-400 MPa for buffer and 400-500 MPa for milk, models were developed to predict survival curves of Y. enterocolitica at pressures different from the experimental pressures.     

Modeling the survival of Salmonella spp. in chorizos

The survival of Salmonella spp. in chorizos has been studied under the effect of storage conditions; namely temperature (T=6, 25, 30 degrees C), air inflow velocity (F=0, 28.4 m/min), and initial water activity (a(w0)=0.85, 0.90, 0.93, 0.95, 0.97). The pH was held at 5.0. A total of 20 survival curves were experimentally obtained at various combinations of operating conditions. The chorizos were stored under four conditions: in the refrigerator (Ref: T=6 degrees C, F=0 m/min), at room temperature (RT: T=25 degrees C, F=0 m/min), in the hood (Hd: T=25 degrees C, F=28.4 m/min), and in the incubator (Inc: T=30 degrees C, F=0 m/min). Semi-logarithmic plots of counts vs. time revealed nonlinear trends for all the survival curves, indicating that the first-order kinetics model (exponential distribution function) was not suitable. The Weibull cumulative distribution function, for which the exponential function is only a special case, was selected and used to model the survival curves. The Weibull model was fitted to the 20 curves and the model parameters (alpha and beta) were determined. The fitted survival curves agreed with the experimental data with R(2)=0.951, 0.969, 0.908, and 0.871 for the Ref, RT, Hd, and Inc curves, respectively. Regression models relating alpha and beta to T, F, and a(w0) resulted in R(2) values of 0.975 for alpha and 0.988 for beta. The alpha and beta models can be used to generate a survival curve for Salmonella in chorizos for a given set of operating conditions. Additionally, alpha and beta can be used to determine the times needed to reduce the count by 1 or 2 logs t(1D) and t(2D). It is concluded that the Weibull cumulative distribution function offers a powerful model for describing microbial survival data. A comparison with the pathogen modeling program (PMP) revealed that the survival kinetics of Salmonella spp. in chorizos could not be adequately predicted using PMP which underestimated the t(1D) and t(2D). The mean of the Weibull probability density function correlated strongly with t(1D) and t(2D), and can serve as an alternative to the D-values normally used with first-order kinetic models. Parametric studies were conducted and sensitivity of survival to operating conditions was evaluated and discussed in the paper. The models derived herein provide a means for the development of a reliable risk assessment system for controlling Salmonella spp. in chorizos.     

Estimating microbial growth parameters from non-isothermal data: a case study with Clostridium perfringens

Microbial growth parameters are usually calculated from the fit of a growth model to a set of isothermal growth data gathered at several temperatures. In principle at least, it is also possible to derive them from non-isothermal ('dynamic') growth data. This requires the numerical solution of a rate model whose coefficients are nested terms that include the temperature profile. The methodology is demonstrated with simulated non-isothermal growth data on which random noise had been superimposed to emulate the scatter found in experimental microbial counts. The procedure has been validated by successful retrieval of the known generation parameters from the simulated growth curves. The method was then applied to experimental non-isothermal growth data of C. perfringens cells in cooled ground beef. The growth data collected under one cooling regime were used to predict the organism's growth patterns under different temperature histories. The practicality of the method is currently limited because of the relatively large scatter found in experimental microbial growth data and the relatively low frequency at which they are collected. But if and when the scatter could be reduced and the counts taken at short time intervals, the method could be used to determine the growth model in situ thus enabling to translate the changing temperature during processing, transportation or storage into a corresponding growth curve of the organism in question.     

Pressure inactivation kinetics of Enterobacter sakazakii in infant formula milk

Survival curves of Enterobacter sakazakii inactivated by high hydrostatic pressure were obtained at four pressure levels (250, 300, 350, and 400 MPa), at temperatures below 30 degrees C, in buffered peptone water (BPW; 0.3%, wt/vol) and infant formula milk (IFM; 16%, wt/vol). A linear model and four nonlinear models (Weibull, log-logistic, modified Gompertz, and Baranyi) were fitted to the data, and the performances of the models were compared. The linear regression model for the survival curves in BPW and IFM at 250 MPa has fitted regression coefficient (R2) values of 0.940 to 0.700, respectively, and root mean square errors (RMSEs) of 0.770 to 0.370. For the other pressure levels, the linear regression function was not appropriate, as there was a strong curvature in the plotted data. The nonlinear regression models with the log-logistic and modified Gompertz equations had R2 values of 0.960 to 0.992 and RMSE values of 0.020 to 0.130 within pressure levels of 250 to 400 MPa, respectively. These results indicate that they are both better models for describing the pressure inactivation kinetics of E. sakazakii in IFM and BPW than the Weibull distribution function, which has an R2 minimum value of 0.832 and an RMSE maximum value of 0.650 at 400 MPa. On the other hand, the parameters for the Weibull distribution function, log-logistic model, and modified Gompertz equation did not have a clear dependence on pressure. The Baranyi model was also analyzed, and it was concluded that this model provided a reasonably good fit and could be used to develop predictions of survival data at pressures other than the experimental pressure levels in the range studied. The results provide accurate predictions of survival curves at different pressure levels and will be beneficial to the food industry in selecting optimum combinations of pressure and time to obtain desired target levels of E. sakazakii inactivation in IFM.     

Estimating microbial survival parameters from dynamic survival data using Microsoft Excel

Reliable survival parameter estimation is an essential part of building predictive models for microbial survival. It has been demonstrated that these parameters can be accurately identified using a one‐step regression approach that fits a survival model to multiple dynamic data sets at once. However, the existing methods are not quite user‐friendly because their application requires relatively high computer skills. In this study, a recursive equation for the Weibull model was used to construct microbial survival curves under dynamic conditions. Based on this, a procedure was developed to estimate survival parameters by fitting the equation to dynamic survival data sets using the built‐in functions and Solver of Microsoft Excel. The results showed that the method provided an easy and accurate way for estimating microbial survival parameters.     

Effect of temperature on microbial growth rate-mathematical analysis: the Arrhenius and Eyring-Polanyi connections

The objective of this work is to develop a mathematical model for evaluating the effect of temperature on the rate of microbial growth. The new mathematical model is derived by combination and modification of the Arrhenius equation and the Eyring-Polanyi transition theory. The new model, suitable for both suboptimal and the entire growth temperature ranges, was validated using a collection of 23 selected temperature-growth rate curves belonging to 5 groups of microorganisms, including Pseudomonas spp., Listeria monocytogenes, Salmonella spp., Clostridium perfringens, and Escherichia coli, from the published literature. The curve fitting is accomplished by nonlinear regression using the Levenberg-Marquardt algorithm. The resulting estimated growth rate (μ) values are highly correlated to the data collected from the literature (R(2) = 0.985, slope = 1.0, intercept = 0.0). The bias factor (B(f) ) of the new model is very close to 1.0, while the accuracy factor (A(f) ) ranges from 1.0 to 1.22 for most data sets. The new model is compared favorably with the Ratkowsky square root model and the Eyring equation. Even with more parameters, the Akaike information criterion, Bayesian information criterion, and mean square errors of the new model are not statistically different from the square root model and the Eyring equation, suggesting that the model can be used to describe the inherent relationship between temperature and microbial growth rates. The results of this work show that the new growth rate model is suitable for describing the effect of temperature on microbial growth rate. Practical Application: Temperature is one of the most significant factors affecting the growth of microorganisms in foods. This study attempts to develop and validate a mathematical model to describe the temperature dependence of microbial growth rate. The findings show that the new model is accurate and can be used to describe the effect of temperature on microbial growth rate in foods.     

Inactivation Kinetics of Listeria monocytogenes by High-Pressure Processing: Pressure and Temperature Variation

The enhanced quasi-chemical kinetics (EQCK) model is presented as a methodology to evaluate the nonlinear inactivation kinetics of baro-resistant Listeria monocytogenes in a surrogate protein food system by high-pressure processing (HPP) for various combinations of pressure (P= 207 to 414 MPa) and temperature (T= 20 to 50 °C). The EQCK model is based on ordinary differential equations derived from 6 "quasi-chemical reaction" steps. The EQCK model continuously fits the conventional stages of the microbial lifecycle: lag, growth, stationary phase, and death; and tailing. Depending on the conditions, the inactivation kinetics of L. monocytogenes by HPP show a lag, inactivation, and tailing. Accordingly, we developed a customized, 4-step subset version of the EQCK model sufficient to evaluate the HPP inactivation kinetics of L. monocytogenes and obtain values for the model parameters of lag (λ), inactivation rate (μ), rate constants (k), and "processing time" (tp). This latter parameter was developed uniquely to evaluate kinetics data showing tailing. Secondary models are developed by interrelating the fitting parameters with experimental parameters, and Monte Carlo simulations are used to evaluate parameter reproducibility. This 4-step model is also compared with the empirical Weibull and Polylog models. The success of the EQCK model (as its 4-step subset) for the HPP inactivation kinetics of baro-resistant L. monocytogenes showing tailing establishes several advantages of the EQCK modeling approach for investigating nonlinear microbial inactivation kinetics, and it has implications for determining mechanisms of bacterial spore inactivation by HPP. Practical Application: Results of this study will be useful to the many segments of the food processing industry (ready-to-eat meats, fresh produce, seafood, dairy) concerned with ensuring the safety of consumers from the health hazards of Listeria monocytogenes, particularly through the use of emerging food preservation technologies such as high-pressure processing.     

Fractional Differential Equations Based Modeling of Microbial Survival and Growth Curves: Model Development and Experimental Validation

ABSTRACT: A fractional differential equations (FDEs)‐based theory involving 1‐ and 2‐term equations was developed to predict the nonlinear survival and growth curves of foodborne pathogens. It is interesting to note that the solution of 1‐term FDE leads to the Weibull model. Nonlinear regression (Gauss–Newton method) was performed to calculate the parameters of the 1‐term and 2‐term FDEs. The experimental inactivation data of Salmonella cocktail in ground turkey breast, ground turkey thigh, and pork shoulder; and cocktail of Salmonella, E. coli, and Listeria monocytogenes in ground beef exposed at isothermal cooking conditions of 50 to 66 °C were used for validation. To evaluate the performance of 2‐term FDE in predicting the growth curves—growth of Salmonella typhimurium, Salmonella Enteritidis, and background flora in ground pork and boneless pork chops; and E. coli O157:H7 in ground beef in the temperature range of 22.2 to 4.4 °C were chosen. A program was written in Matlab to predict the model parameters and survival and growth curves. Two‐term FDE was more successful in describing the complex shapes of microbial survival and growth curves as compared to the linear and Weibull models. Predicted curves of 2‐term FDE had higher magnitudes of R² (0.89 to 0.99) and lower magnitudes of root mean square error (0.0182 to 0.5461) for all experimental cases in comparison to the linear and Weibull models. This model was capable of predicting the tails in survival curves, which was not possible using Weibull and linear models. The developed model can be used for other foodborne pathogens in a variety of food products to study the destruction and growth behavior.     

Survival curves of heated bacterial spores: effect of environmental factors on Weibull parameters

The classical D-value of first order inactivation kinetic is not suitable for quantifying bacterial heat resistance for non-log linear survival curves. One simple model derived from the Weibull cumulative function describes non-log linear kinetics of micro-organisms. The influences of environmental factors on Weibull model parameters, shape parameter "p" and scale parameter "delta", were studied. This paper points out structural correlation between these two parameters. The environmental heating and recovery conditions do not present clear and regular influence on the shape the parameter "p" and could not be described by any model tried. Conversely, the scale parameter "delta" depends on heating temperature and heating and recovery medium pH. The models established to quantify these influences on the classical "D" values could be applied to this parameter "delta". The slight influence of the shape parameter p variation on the goodness of fit of these models can be neglected and the simplified Weibull model with a constant p-value for given microbial population can be applied for canning process calculations.     

Heat resistance kinetics variation among various isolates of Escherichia coli

This paper reports an investigation of serotype-specific differences in heat resistance kinetics of clinical and food isolates of Escherichia coli. Heat resistance kinetics for 5 serotypes of E. coli at 60 °C were estimated in beef gravy using a submerged coil heating apparatus. The observed survival curves were sigmoidal and there were significant differences (p=0.05) of the survival curves among the serotypes. Consequently, a model was developed that accounted for the sigmoidal shape of the survival curves and the serotype effects. Specifically, variance components for serotypes and replicates within serotypes were estimated using mixed effect nonlinear modeling. If it is assumed that the studied serotypes represent a random sample from a population of E. coli strains or serotypes, then, from the derived estimates, probability intervals of the expected lethality for random selected serotypes can be computed. For example, expected serotype-specific lethalities at 60 °C for 10 min are estimated to range between 5 and 9 log₁₀ with 95% probability. On the other hand, to obtain a 6-log₁₀ lethality, the expected minutes range, with 95% probability, from 6 to 12 min. The results from this study show that serotypes of E. coli display a wide range of heat resistance with nonlinear survival curves.Industrial relevanceThis paper is of high current interest since it deals with the ongoing international debate on log linear vs. non-log linear microbial inactivation curves observed during thermal and non-thermal processing. The data on 5 serotypes of E. coli indicate a clear need for further studies with more strains to fully characterize the heat resistance kinetics for E. coli.     

Thermal inactivation of Campylobacter jejuni in broth

New Zealand has a high rate of reported campylobacteriosis compared with other developed countries. One possible reason is that local strains have greater heat tolerance and thus are better able to survive undercooking; this hypothesis is supported by the remarkably high D-values reported for Campylobacter jejuni in The Netherlands. The objective of this study was to investigate the thermal inactivation of isolates from New Zealand in broth, using strains that are commonly found in human cases and food samples in New Zealand. Typed Campylobacter strains were heated to a predetermined temperature using a submerged-coil heating apparatus. The first-order kinetic model has been used extensively in the calculation of the thermal inactivation parameters, D and z; however, nonlinear survival curves have been reported, and a number of models have been proposed to describe the patterns observed. Therefore, this study compared the conventional first-order model with eight nonlinear models for survival curves. Kinetic parameters were estimated using both one- and two-step regression techniques. In general, nonlinear models fit the individual inactivation data sets better than the log-linear model. However, the log-linear and the (nonlinear) Weibull models were the only models that could be successfully fitted to all data sets. For seven relevant New Zealand C. jejuni strains, at temperatures from 51.5 to 60°C, D- and z-values were obtained, ranging from 1.5 to 228 s and 4 to 5.2°C, respectively. These values are in broad agreement with published international data and do not indicate that the studied New Zealand C. jejuni strains are more heat resistant than other strains, in contrast with some reports from The Netherlands.     

On calculating sterility in thermal and non-thermal preservation methods

There is growing evidence that the mortality of microbial cells, and the inactivation of bacterial spores, exposed to a hostile environment need not follow a first order kinetics. Consequently microbial semi-logarithmic survival curves are frequently non-linear, and their shape can change with temperature or under different chemical agent concentrations, for example. Experimental semi-logarithmic survival curves under unchanging conditions, can be described by an equation whose coefficients are determined by the particular temperature, agent concentration, etc. If the dependency of these coefficients on temperature, agent concentration, etc., can be expressed algebraically, then in principle one can construct the survival curve for the changing or transient conditions that exist in industrial thermal and non-thermal treatments. This is done by incorporating the lethal agent's mode of change, e.g. the heating or pressure curve into the survival curve equation parameters. The result is a mathematical model that would enable the calculation of the time needed to achieve any degree of microbial survival ratio numerically, without the need to assume any mortality kinetics. Such a model can be used to assess, or compare, the efficacy of different preservation processes where the intensity of the lethal agent changes with time. The concept is demonstrated with a special simple case using simulated thermal treatments. The outcome of the simulations is presented as planar log survival vs time relationships and as curves in a three-dimensional log survival–temperature–time or log survival–concentration–time space.     

Estimation of the non-isothermal inactivation patterns of Bacillus sporothermodurans IC4 spores in soups from their isothermal survival data

The isothermal survival curves of the heat resistant spores of Bacillus sporothermodurans IC4, in the range of 117-125 degrees C, were determined in chicken, mushroom and pea soups by the capillary method. They were all non-linear with a noticeable upper concavity and could be described by the equation log(10) [N(t)/N(0)]=-b(T)t(n) with a fixed power, n, of the order of 0.7-0.8. The temperature dependence of b(T) could be described by the equation b(T)=log(e)[1+exp[k(T-T(c))]], where T(c) is the temperature where intensive inactivation starts and k is the slope of b(T) at temperatures well above T(c). They were 121-123 degrees C and 0.2-0.4 degrees C(-1), respectively, depending on the soup. These parameters were used to estimate the survival curves of the spores in two non-isothermal heat treatments using the procedure originally proposed by Peleg and Penchina [Crit. Rev. Food Sci. Nutr. 40 (2000) 159]. The results were compared with experimental survival curves, determined by the direct injection method, in another laboratory. There was a general agreement, although not perfect, between the predicted and experimentally observed survival ratios. Also, the isothermal survival parameters, estimated directly from the non-isothermal inactivation data using the model, were in general agreement with those calculated from the isothermal data. This suggests that the heat inactivation patterns of B. sporothermodurans IC4 spores in soups can be at least roughly estimated using the same general survival model, which has until now only been experimentally validated for vegetative bacterial cells.     

INACTIVATION KINETICS AND REDUCTION OF BACILLUS COAGULANS SPORE BY THE COMBINATION OF HIGH PRESSURE AND MODERATE HEAT

The combination effect of high pressure (400, 500 and 600 MPa) and moderate heat (70 and 80C) on the inactivation kinetics and reduction of Bacillus coagulans spore in phosphate buffer and ultra-high temperature (UHT) whole milk was investigated. The pressure come-up time and corresponding logarithmic reduction of spore inactivation were considered during pressure-thermal treatment. B. coagulans spore had a much higher resistance to pressure in UHT whole milk than in phosphate buffer. Survival data were modeled using the linear, Weibull and log-logistic models to obtain relevant kinetic parameters. The tailing phenomenon occurred in all survival curves, indicating the linear model was not adequate for describing these curves. The mean square error and regression coefficient suggested that the log-logistic model produced best fits to all survival curves, followed by the Weibull model.

PRACTICAL APPLICATIONS

It becomes increasingly apparent that high-pressure treatment combined with moderate heat treatment for low acid and acid products is often required for effective bacterial spores' inactivation. Consequently, the prediction model of microbial survival curves is essential. Bacillus coagulans is a slightly pressure-resistant and relatively heat-resistant spoilage bacterium of considerable concern during the processing of acid foods. Spore inactivation effect during the pressure come-up time is sometimes considerable and should not beignored. The use of mathematical models to predict inactivation for spores could help the food industry further to develop optimum process conditions.