Isothermal Survival Curves Research Articles

Analysis of methane hydrate nucleation in water-in-oil emulsions: Isothermal vs constant cooling ramp method and new method for data treatment

Temperature dependence of methane hydrate nucleation rate in 50 wt% water in oil emulsion was studied within the temperature range from +2 to −6 °C (supercooling values: 13–21 °C). It turned out that the temperature dependence of nucleation rate in this temperature interval cannot be described by the equations of the classical nucleation theory. This point is discussed with use of available literature data. An approach to the analysis of isothermal survival curves is suggested. Using the approach allows us to establish the amount of nucleation centers in the system and their relative activity. A probable number of nucleation centers and the effect of temperature on the manifestation activity of these centers were determined for the obtained experimental data.

Effect of pomegranate powder on the heat inactivation of Escherichia coli O104:H4 in ground chicken

Health concerns have led to a search for natural plant-based antimicrobials. Ellagic acid has been shown to have antimicrobial activity against foodborne pathogens. The objective of this study was to assess the effect of a high-ellagic acid commercial pomegranate on the heat resistance of Escherichia coli O104:H4 in ground chicken. A full 24 factorial design was used, consisting of temperature treatment with four levels (55.0, 57.5, 60.0, and 62.5 °C) and pomegranate with four levels (0.0, 1.0, 2.0, and 3.0 wt/wt. % containing 70% ellagic acid). Experiments were conducted twice, providing a total of 32 survival curves. A three-parameter Weibull primary model was used to describe survival kinetics. Secondary models were then developed to estimate the shape parameter β (i.e., curvature representing susceptibility of cells to stress), scale parameter γ (i.e., time to reach the first decimal reduction) and the 5.0-log lethality time t5.0 (i.e., time to reach a 5.0-log reduction), all as polynomial functions of temperature and pomegranate powder concentration. The positive effect of pomegranate concentration on both β and γ demonstrated that the phenolic-rich pomegranate powder causes E. coli O104:H4 cells to become more susceptible to heat, increasing the steepness and concavity of the isothermal survival curves. It was estimated that the 5.0-log reduction time would reach a minimum at a pomegranate powder concentration of 1%, producing a 50% decrease in lethality time, in comparison to that without added pomegranate powder. Nonetheless, a mixed-effect omnibus regression further confirmed that the greatest difference in the thermal resistance of E. coli O104:H4 happened between tests with and without pomegranate powder. In fact, adding more than 1.0% pomegranate powder, at a constant temperature, resulted only in a marginal decrease in thermal resistance. Meat processors can use the model to design lethality treatments in order to achieve specific reductions of E. coli O104:H4 in ground chicken.

Effect of the medium characteristics and the heating and cooling rates on the nonisothermal heat resistance of Bacillus sporothermodurans IC4 spores

In recent years, highly thermo-resistant mesophilic spore-forming bacteria belonging to the species Bacillus sporothermodurans have caused non-sterility problems in industrial sterilization processes. The aim of this research was to evaluate the effect of the heating medium characteristics (pH and buffer/food) on the thermal inactivation of B. sporothermodurans spores when exposed to isothermal and non-isothermal heating and cooling treatments and the suitability of non-linear Weibull and Geeraaerd models to predict the survivors of these thermal treatments. Thermal treatments were carried out in pH 3, 5 and 7 McIlvaine buffer and in a courgette soup. Isothermal survival curves showed shoulders that were accurately characterized by means of both models. A clear effect of the pH of the heating medium was observed, decreasing the D120 value from pH 7 to pH 3 buffer down to one third. Differences in heat resistance were similar, regardless of the model used and were kept at all temperatures tested. The heat resistance in courgette soup was similar to that shown in pH 7 buffer. When the heat resistance values obtained under isothermal conditions were used to predict the survival in the non-isothermical experiments, the predictions estimated the experimental data quite accurately, both with Weibull and Geeraerd models.

Heat resistance of Listeria species to liquid whole egg ultrapasteurization treatment

The lethality of ultrapasteurization treatments (70°C/1.5min.) applied at constant temperature (isothermal condition) and at a constantly raising temperature of 2°C/min (non-isothermal condition) in liquid whole egg (LWE) against two strains of Listeria monocytogenes (STCC 5672 and 4032) and one of Listeria innocua has been investigated. Isothermal survival curves up to 71°C were obtained, which followed first-order inactivation kinetics. The obtained Dt values indicated that L. innocua was significantly (p<0.05) more heat resistant than L. monocytogenes strains. Non-significant (p>0.05) differences were observed among z values (12.4±0.4°C, 13.1±0.4°C and 12.2±0.7°C for L. innocua and L. monocytogenes 5672 and 4032, respectively). Based on obtained Dt and z values, isothermal ultrapasteurization treatment (70°C/1.5min.) would provide 3.5-, 5.0-, and 6.5-Log10 cycles of L. innocua and L. monocytogenes 5672 and 4032, respectively. Non-isothermal heating lag phase increased the thermotolerance of Listeria species in LWE. The simulated industrial pasteurization treatment for LWE (heating-up phase from 25 to 70°C followed by 1.5min. at 70°C) would attain 5-Log10 reductions of L. monocytogenes 5672 and 4032, and 3.7-Log10 reductions of L. innocua. Therefore, the safety level of industrial ultrapasteurization concerning L. monocytogenes could be lower than that estimated with data obtained under isothermal conditions.

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

Spore-forming bacteria with high heat resistance increasingly challenge industrial sterilisation processes in foods. To ensure stability of manufactured foods, generally worst case scenarios are applied often leading to unwanted over processing of foods. This means bigger requirements of energy and larger emissions of CO2 into the atmosphere. A heat-resistant spore-forming bacterium, Bacillus sporothermodurans, was tested for its ability to produce consistently highly heat-resistant spore crops to be used to more precisely determine the minimal thermal process that is compatible with microbial stability, thus avoiding the indicated overprocessing. Isothermal survival curves of B. sporothermodurans IC4 spores were determined in distilled water at temperatures up to 125 °C using the capillary tube technique and a thermoresistometer Mastia. B. sporothermodurans consistently produced crops of heat-resistant spores with kmax values at 121 °C up to 0.46 min−1. After consecutive sporulation cycles, the measured heat resistance of B. sporothermodurans was not reduced. Survival curves showed shoulders that were characterized by means of existing models (Geeraerd, Weibull) that were compared with the classical, log-linear one. Shoulders are a common phenomenon in heat-resistant spore-forming bacteria and may be related to the need of more stringent processing conditions. B. sporothermodurans spores were considered adequate to optimize sterilisation processes of low acid foods under a wide variety of conditions. Establishing precise heat treatments can be a way to guarantee food safety and stability while reducing the use of energy and contaminating emissions.

Predictive Modeling of Salmonella Species Inactivation in Ground Pork and Turkey during Cooking

The objective of this study was to evaluate the ability of the Weibull distribution to predict the inactivation of Salmonella in three meat products cooked under isothermal and non-isothermal conditions. Ground turkey thigh (5.09% fat, pH 6.45), turkey breast (0.47% fat, pH 6.04) and pork (17.04% fat, pH 6.36) were inoculated with an 8 strain Salmonella cocktail. The meat was cooked isothermally at 50, 54, 58, 62 and 66ºC, and non-isothermally at two heating rates (5 or 10 ºC/min) to 54, 60 and 66 ºC. Surviving Salmonella were enumerated at intervals during the cooking process. Isothermal survival curves were described by the Weibull distribution, log S (t) = -b (T) tn(T), and its simplified form as a linear equation (n=1). Nonlinearity was observed in Salmonella survival curves. The Weibull distribution described pathogen inactivation better than its simplified linear form for all isothermal trials. The b and n parameters from isothermal data were used to predict the non-isothermal survival curves. Piecewise cubic hermite interpolating polynomial was used to estimate b and n in the non-isothermal program. At 54 and 66 ºC, the Weibull model well predicted the non-isothermal Salmonella survival curves for all meats. The model over-predicted the destruction of Salmonella in three meats at 60 ºC for both heating rates. The accurate prediction of Salmonella destruction at 66 ºC was at a higher temperature than the range of validity reported in the literature.

Thermal inactivation of Listeria monocytogenes in ground beef under isothermal and dynamic temperature conditions

The objective of this research was to compare the suitability of three kinetic models for describing the survival of a cocktail of Listeria monocytogenes in ground beef under both isothermal and dynamic temperature conditions. Ground beef (93% lean), inoculated with a 4-strain cocktail of L. monocytogenes, was subjected to heating at 57, 60, 63, or 66 °C to develop isothermal kinetic models. Experimental data showed that the isothermal survival curves were not strictly linear and were downwardly concaved. The isothermal inactivation of L. monocytogenes in ground beef was better described by two nonlinear kinetic models, the Weibull-type and the modified Gompertz models. Analytical results showed that root mean square error values (RMSE) of the Weibull-type and the modified Gompertz models were 0.19 and 0.20 log(CFU/g), both significantly smaller than that of the linear model (0.48 log(CFU/g)). Under linear heating dynamic conditions, however, only the modified Gompertz model, with a RMSE of only 0.71 log(CFU/g), was suitable for describing the survival of the pathogen. Both linear and Weibull-type models grossly underestimated the survival of L. monocytogenes in ground beef during dynamic heating.

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

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, Tc, a marker of the temperature where the inactivation accelerates and k, the slope of the rate parameter at temperatures well above Tc. 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 Tc. The iterations continue until the model constructed with the calculated k and Tc values correctly predicts the survival ratio obtained in a third heat treatment with a known temperature profile. Once n, k, and Tc 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.

Letter to the editor

Letter to the editor

A numerical algorithm for calculating microbial survival curves during thermal processing

Abstract 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.

Generating microbial survival curves during thermal processing in real time

To develop a method to calculate and record theoretical microbial survival curves during thermal processing of foods and pharmaceutical products simultaneously with the changing temperature. Moreover, to demonstrate that the method can be used to calculate nonisothermal survival curves, with widely available software such as Microsoft Excel. It has been assumed that the targeted organism's isothermal survival curves are not log linear and hence, the inactivation rate in nonisothermal processes is a function of the momentary temperature and the corresponding survival ratio. This could be expressed by a difference equation, which is an approximation to the continuous rate model. The concept was tested with the isothermal survival parameters of Clostridium botulinum and Bacillus sporothermodurans spores, and Salmonella enteritidis cells, using different kinds of survival models and under temperature profiles resembling those of commercial processes. As expected, there was an excellent agreement between the curves produced by solving the differential equation of the continuous model and by the incremental method, which has been posted on the web as freeware. It is possible to calculate nonisothermal survival curves, in real time, with an algorithm that can be written in the language of general purpose software, to follow the inactivation of one or more targeted organisms simultaneously and to simulate microbial survival patterns under existing or planned industrial thermal processes. Replacement of the traditional 'F0-value', which requires the log linearity of the organism's isothermal survival curves, by the more realistic theoretical survival ratio estimate as a measure of the thermal process efficacy.

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 °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 °C and 0.2–0.4 °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.

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.

Calculation of the Non-Isothermal Inactivation Patterns of Microbes Having Sigmoidal Isothermal Semi-Logarithmic Survival Curves

ABSTRACT 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.

A Model of Survival Curves Having an‘Activation Shoulder’

ABSTRACT: The ‘activation shoulder’ in the isothermal survival curves of B. stearothermophilus spores is probably an indication that the initial number is an undercount and that heat improves their recovery. The inactivation need not follow a first order kinetics. It is described by an empirical model, whose coefficients are determinded by the spores but not by any preconceived kinetic order. When the temperature‘profile ’ and the survival parameters’ temperature dependence are expressed algebraically, the slope of the corresponding non isothermal survival curve, which is initially positive, can be used to generate the survival ratios by numerical methods, as demonstrated with simulated stable and unstable heat treatments using published inactivation data.

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.