Harry M. Marks

Modeling non-linear survival curves to calculate thermal inactivation of Salmonella in poultry of different fat levels

Survival curves of a cocktail of eight serotypes of Salmonella in ground poultry of different fat levels (1-12%), when heated rapidly to specified temperatures (58-65 degrees C), were examined. Because many of the survival curves were concave, values for two parameters: the asymptotic D-value and the lag times were estimated and used to develop secondary models for estimating the time needed to obtain a 7 log10 relative reduction as a function of fat level and temperature. To compute the necessary time, at a given temperature and fat level, the estimated lag time should be added to the product of 7 and the estimated asymptotic D-value. A model was also developed for estimating the standard error of the estimated times, so that upper confidence bounds for the necessary times can be computed. It was found that lag times increase with higher fat levels. The effect of fat on D-values depended on the species; it is estimated that, for a given increase of fat level, the increase of the D-value would be greater for ground chicken than that for ground turkey. In addition, there was a statistically significant species effect on D-values, with higher D-values for ground turkey than for ground chicken at the higher temperatures studied. The thermal death curves displayed a non-linear tendency, however, for estimation purposes, a linear curve was assumed. There was not a statistically significant interaction effect of fat levels and temperatures on D-values, thus, for modeling, it was assumed that z-values were not dependent on the fat levels. The z-values for ground chicken and turkey were estimated to be 5.5 degrees C and 6.1 degrees C, respectively, and are statistically significantly different. These findings should have substantial practical importance to food processors of cooked poultry, allowing them to vary their thermal treatment of ready-to-eat poultry products in a safe manner.

Growth of Clostridium perfringens from spore inocula in cooked cured beef: development of a predictive model ☆

Abstract The objective of this study was to develop a model to predict the growth of C. perfringens from spores at temperatures applicable to the cooling of cooked cured meat products. C. perfringens growth from spores was not observed at a temperature of 12 °C for up to 3 weeks. The two parameters: germination, outgrowth, and lag (GOL) time and exponential growth rate, EGR, were determined using a function derived from mechanistic and stochastic considerations and the observed relative growths at specified times. A general model to predict the amount of relative growth for arbitrary temperature was determined by fitting the exponential growth rates to a square root Ratkowsky function, and assuming a constant ratio of GOL and generation times. The predicted relative growth is sensitive to the value of this ratio. A closed form equation was developed that can be used to estimate the relative growth for a general cooling scenario and determine a standard error of the estimate. The equation depends upon microbiological assumptions of the effect of history of the GOL times for gradual changes in temperature. Applying multivariate statistical procedures, a confidence interval was computed on the prediction of the amount of growth for a given temperature. The model predicts, for example, a relative growth of 3.17 with an upper 95% confidence limit of 8.50 when cooling the product from 51 to 11 °C in 8 h, assuming a log linear decline in temperature with time.

Predictive Thermal Inactivation Model for Effects of Temperature, Sodium Lactate, NaCl, and Sodium Pyrophosphate on Salmonella Serotypes in Ground Beef

ABSTRACT Analyses of survival data of a mixture of Salmonella spp. at fixed temperatures between 55°C (131°F) and 71.1°C (160°F) in ground beef matrices containing concentrations of salt between 0 and 4.5%, concentrations of sodium pyrophosphate (SPP) between 0 and 0.5%, and concentrations of sodium lactate (NaL) between 0 and 4.5% indicated that heat resistance of Salmonella increases with increasing levels of SPP and salt, except that, for salt, for larger lethalities close to 6.5, the effect of salt was evident only at low temperatures (<64°C). NaL did not seem to affect the heat resistance of Salmonella as much as the effects induced by the other variables studied. An omnibus model for predicting the lethality for given times and temperatures for ground beef matrices within the range studied was developed that reflects the convex survival curves that were observed. However, the standard errors of the predicted lethalities from this models are large, so consequently, a model, specific for predicting the times needed to obtained a lethality of 6.5 log10, was developed, using estimated results of times derived from the individual survival curves. For the latter model, the coefficient of variation (CV) of predicted times range from about 6 to 25%. For example, at 60°C, when increasing the concentration of salt from 0 to 4.5%, and assuming that the concentration of SPP is 0%, the time to reach a 6.5-log10 relative reduction is predicted to increase from 20 min (CV = 11%) to 48 min (CV = 15%), a 2.4 factor (CV = 19%). At 71.1°C (160°F) the model predicts that more than 0.5 min is needed to achieve a 6.5-log10 relative reduction.

Predictive model for growth of Clostridium perfringens during cooling of cooked uncured meat and poultry.

Comparison of Clostridium perfringens spore germination and outgrowth in cooked uncured products during cooling for different meat species is presented. Cooked, uncured product was inoculated with C. perfringens spores and vacuum packaged. For the isothermal experiments, all samples were incubated in a water bath stabilized at selected temperatures between 10 and 51°C and sampled periodically. For dynamic experiments, the samples were cooled from 54.4 to 27°C and subsequently from 27 to 4°C for different time periods, designated as x and y hours, respectively. The growth models used were based on a model developed by Baranyi and Roberts (1994. A dynamic approach to predicting bacterial growth in food. Int. J. Food Micro. 23, 277-294), which incorporates a constant, referred to as the physiological state constant, q(0). The value of this constant captures the cells history before the cooling begins. To estimate specific growth rates, data from isothermal experiments were used, from which a secondary model was developed, based on a form of Ratkowskys 4-parameter equation. The estimated growth kinetics associated with pork and chicken were similar, but growth appeared to be slightly greater in beef; for beef, the maximum specific growth rates estimated from the Ratkowsky curve was about 2.7 log(10) cfu/h, while for the other two species, chicken and pork, the estimate was about 2.2 log(10) cfu/h. Physiological state constants were estimated by minimizing the mean square error of predictions of the log(10) of the relative increase versus the corresponding observed quantities for the dynamic experiments: for beef the estimate was 0.007, while those for pork and chicken the estimates were about 0.014 and 0.011, respectively. For a hypothetical 1.5h cooling from 54°C to 27° and 5h to 4°C, corresponding to USDA-FSIS cooling compliance guidelines, the predicted growth (log(10) of the relative increase) for each species was: 1.29 for beef; 1.07 for chicken and 0.95 log(10) for pork. However, it was noticed that for pork in particular, the model using the derived q(0) had a tendency to over-predict relative growth when the observed amount of relative growth was small, and under-predict the relative growth when the observed amount of relative growth was large. To provide more fail-safe estimate, rather than using the derived value of q(0), a value of 0.04 is recommended for pork.

Characterizing asymptotic D-values for Salmonella spp. subjected to different heating rates in sous-vide cooked beef

Abstract Inactivation rates of a cocktail of Salmonella spp. in sous vide cooked beef exposed to varied ‘come-up’ heating times of zero (control), and 1–3 h from 10 °C to the processing temperature of 58 °C were examined. The observed survival curves, determined for 58 °C, displayed a slight ‘shoulder’ followed by a non-zero asymptotic D -values. Comparisons of the survival curves confirm that the rate of heating can substantially influence the heat resistance of Salmonella spp. While there was no significant difference between the estimated asymptotic D -values for the control and 1-h come-up heating time survival curves, the estimated D -values were significantly larger for the 2- and 3-h come-up heating times curves. The estimated averages of the asymptotic D -values for the control and 1-h come-up time survival curves are approximately 5.7 min; for the 2-h come-up time curves, 7 min; and for the 3-h come-up time curves, 8 min. These findings could have substantial practical importance to food processors in sous vide cooked beef that are processed by slow heating rate/long come-up times and low heating temperatures.

Thermal Inactivation of Salmonella Serotypes in Red Meat as Affected by Fat Content

Survival curves of a cocktail of eight serotypes of Salmonella in ground beef and pork meat of different levels of fat (4% to 28%), at temperatures that ranged from 58°C to 65°C, were examined. Asymptotic D-values (D-values for large times) and initial D-values (D-values for small times, near zero) were estimated by identifying regions where the survival curves were linear, and performing linear regressions on data within the identified regions. The initial lag D-values increase with increasing fat levels for both beef and pork. The relationship of the asymptotic D-values with fat levels and temperature is complex, and definitive conclusions could not be made. It appears that, for ground beef, asymptotic D-values increase with increasing fat levels, but this was not the case for ground pork. The shapes of the survival curves were concave, convex, and sigmoidal, and depended upon the temperature, where for the lower temperatures studied (58°C and 60°C) the curves exhibited tailing. The Gompertz function was found to provide a good fit to the data over the range of temperatures and fat levels studied. These results, particularly for beef, suggest the importance of determining the shape of the survival curves (concave, convex or sigmoidal) when estimating times needed to obtain an adequate margin of safety for thermal processes of red meat.

Mathematical description of non-linear survival curves of Listeria monocytogenes as determined in a beef gravy model system at 57.5 to 65 °C

Abstract This paper presents a non-linear model for predicting the inactivation of Listeria monocytogenes, suspended in beef broth after heat treatment. A five-strain cocktail of L. monocytogenes was used in developing inactivation data at 57.5, 60, 62.5 and 65 °C, where maximum observed lethalities were more than 7 log10 for the latter three temperatures. For all four temperatures, the survival curves, i.e. the common logarithms (base 10) of the numbers of surviving cells vs. times, were distinctly convex. Four functions, based on different assumptions underlying the shape of the survival curves, were compared. The assumptions involve the asymptotic behavior of the survival curves. Mechanistic considerations were used in deriving some of the functions considered. The function selected for further modeling was the logistic function, where the natural logarithm of time is the independent variable. Using this function, a model for predicting the amount of inactivation for temperatures between 57.5 and 65 °C was determined. The model presented in this paper is different from models that have been presented in the predictive microbiology literature, in that the parameters that describe the model are assumed to be random variables. Thus, a full description of the model includes standard deviations of parameter values, which were estimated using a mixed-effects analysis. Other research has indicated a logistic function adequately describes survival curves of L. monocytogenes. The use of this function entails that there are not non-zero asymptotic D-values. In conclusion, there is a substantial body of evidence suggesting that non-linear models are needed for characterizing survival curves of L. monocytogenes.

Predictive Thermal Inactivation Model for Effects and Interactions of Temperature, NaCl, Sodium Pyrophosphate, and Sodium Lactate on Listeria monocytogenes in Ground Beef

The effects and interactions of heating temperature (60xa0°C to 73.9xa0°C), salt (0.0xa0% to 4.5xa0%u2009w/v), sodium pyrophosphate (0.0xa0% to 0.5xa0%u2009w/v), and sodium lactate (0.0xa0% to 4.5xa0%u2009w/v) on the heat resistance of a five-strain mixture of Listeria monocytogenes in 75xa0% lean ground beef were examined. Meat samples in sterile filtered stomacher bags were heated in a temperature controlled waterbath to determine thermal death times. The recovery medium was tryptic soy agar supplemented with 0.6xa0% yeast extract and 1xa0% sodium pyruvate. Weibull survival functions were employed to model the primary survival curves. Then, survival curve-specific estimated parameter values obtained from the Weibull model were used for determining a secondary model. The results indicate that temperature and salt have a large impact on the inactivation kinetics of L. monocytogenes, while sodium lactate (NaL) has an impact in the presence of salt. The model presented in this paper for predicting inactivation of L. monocytogenes can be used as an aid in designing lethality treatments meant to control the presence of this pathogen in ready-to-eat products.

Mechanistic modeling of salmonellosis: Update and future directions

ABSTRACT Microbial risk assessors often make simplifying assumptions that lead to the selection of simple concave functions with low-dose linearity, consistent with no-threshold and single-hit hypotheses, as default dose–response model forms. However, evidence is accumulating as the “microbiome revolution” progresses that challenge these assumptions that influence the estimates of the nature and magnitude of uncertainties associated with microbial risks. Scientific advances in the knowledge of the human “superorganism” (hybrid consortium of human plus microbial communities that cooperatively regulates health and disease) enable the design of definitive studies to estimate the pathogen doses overcome by the innate defenses, including the protective microbiota. The systematic investigation of the events of non-typhoid salmonellosis in humans undertaken nearly 2 decades ago was updated to incorporate recent scientific advances in the understanding of impact of the healthy superorganism that strengthens and extends the biological motivations for sublinear or convex dose–response curves in microbial risk assessment. The knowledge of colonization resistance (innate protection of the human superorganism from low doses of ingested pathogens) and microbiota-mediated clearance is advancing mechanistically for many pathosystems. However, until more detailed mechanistic data become available for salmonellosis, the consideration of a variety of empirical model forms is essential for depicting the uncertainty of the “true” dose–response model.