Nonlinear Survival Curves Research Articles

Lethality of heat to Escherichia coli O157:H7: D- and z-value determinations in turkey, lamb and pork

Thermal inactivation of a four-strain mixture of E. coli O157:H7 was determined in lean ground turkey, lamb and pork. Inoculated meat was packaged in bags completely immersed in a circulating water bath and held at 55, 57.5, 60, 62.5, and 65°C for predetermined lengths of time. The surviving cell population was enumerated by spiral plating meat samples on tryptic soy agar overlaid with Sorbitol MacConkey agar. D-values, determined by linear regression, in turkey were 11.51, 3.59, 1.89, 0.81 and 0.29 min at 55, 57.5, 60, 62.5 and 65°C, respectively ( z=6.5°C). When a survival model was fitted to the non-linear survival curves, D-values in turkey ranged from 11.26 min at 55°C to 0.23 min at 65°C ( z=6°C). When the E. coli O157:H7 four-strain cocktail was heated in ground pork or lamb, D-values calculated by both approaches were similar at all temperatures. Thermal-death-times from this study will assist the retail food industry to design cooking regimes that ensure safety of ground muscle foods contaminated with E. coli O157:H7.

A mathematical model for bacterial inactivation

The first order kinetic model, the Buchanan model and Cerf's model, can model a linear survival curve, a survival curve with a shoulder and a survival curve with a tailing, respectively. However, they are not suitable for fitting a sigmoidal survival curve. The three models were integrated into a new model that was capable of fitting the four most commonly observed survival curves: linear curves, curves with a shoulder, curves with a tailing (biphasic curves) and sigmoidal curves. The new model was compared with the Whiting–Buchanan model using the survival curves of Staphylococcus aureus. The goodness-of-fit of the proposed model is practically as good as that of the Whiting–Buchanan model. Compared with the Whiting–Buchanan model, the proposed model has a more mechanistic background. Since for non-linear survival curves, such as biphasic and sigmoidal curves, the t m−D value (the time required for an m-log-cycle reduction of microorganisms under a given condition) cannot be estimated accurately by the existing or traditional method, a new method is also proposed to predict accurately the t m−D value for non-linear survival curves.

Model of the influence of time and mild temperature on Listeria monocytogenes nonlinear survival curves

Heat treatment has long been regarded as one of the most widely used and most effective means of destroying pathogens in food. Up to now the linear relationship between the death rate and the temperature has been used when choosing the best heat treatment to apply. However, the information given by this linear relationship is no longer sufficient when nonlinear survival curves are observed. Consequently, the agri-food industry needs a tool to choose the best mild heat treatment to apply in the case of nonlinear survival curves. This study deals with the temperature-induced death of Listeria monocytogenes CIP 7831 in the stationary phase of growth. Eleven temperatures were tested. With the proposed primary and secondary models good fits of our data were obtained. A model describing both the effect of the duration of treatment and the temperature on the logarithm of the number of survivors was then built. A clear increase in the precision of the estimation of the parameters was obtained with this model. Moreover, with this model a new graphical strategy to choose a mild heat increase regarding a maximal survivor number has been proposed.

Thermal destruction of Escherichia coli O157:H7 in beef and chicken: determination of D- and Z-values

Thermal inactivation of a four-strain mixture of E. coli 0157:H7 was determined in 90% lean ground beef and lean ground chicken. Inoculated meat was packaged in bags which were completely immersed in a circulating water bath and held at 55, 57.5, 60, 62.5, and 65 °C for predetermined lengths of time. D-values, determined by linear regression, in beef were 21.13, 4.95, 3.17, 0.93 and 0.39 min, respectively ( z = 6.0 °C). Using a survival model for non-linear survival curves, D-values in beef ranged from 20.45 min (D 1; and there was no D 2) at 55 °C to 0.16 min (D 1) and 1.45 min (D 2) at 65 °C. When E. coli O157:H7 four-strain cocktail was heated in chicken, D-values calculated by both approaches were consistently less at all temperatures. The heat resistance of E. coli O157:H7 was not altered after refrigerated or frozen storage of inoculated beef for 48 h. The results of this study will be beneficial to the food industry in designing HACCP plans to effectively eliminate E. coli 0157:H7 in the meat products used in this study.

Use of a Modified Gompertz Equation to Model Nonlinear Survival Curves for Listeria monocytogenes Scott A

The heat resistance of Listeria monocytogenes was determined in 0.1M KH2PO4 buffer at three temperatures (50, 55, and 60°C), three pH levels (5, 6, and 7), and three NaCl concentrations (0, 2, and 4%). Survival curves were fit using nonlinear regression with a modified Gompertz equation. The Gompertz equation is capable of fitting survival curves which are linear, those which display an initial lag region followed by a linear region, and those which are sigmoidal. Parameter estimates were used to describe the lag region, death rate, and the tailing region of a survival curve. These estimates were also used to predict single and interactive effects of temperature, pH, and percentage of NaCl on the log surviving fraction (LSF) of bacteria. Interactions among these variables significantly (P < .05) affected the LSF. Generally, increased pH or NaCl concentration lead to an increased (P < .05) LSF, where as increased time or temperature lead to a decreased (P < .05) LSF. All multiple factor interactions significantly (P < .05) affected the LSF. These interactions differed depending on the heating medium and the region of the survival curve. The correlation of observed LSF and predicted LSF (R2 = .89) indicated that the Gompertz equation was in close agreement with the observations. This study demonstrated that the Gompertz equation and nonlinear regression can be used as an effective means to predict survival curve shape and response to heat of L. monocytogenes in many different environmental conditions.

Nonlinear Survival Curves for Cells of Solid Tumors after Large Doses of Fast Neutrons and γ Rays

We have previously proposed that survival curves for cells of murine NFSa fibrosarcomas after exposure to fast neutrons might demonstrate curvature when the neutron doses reach a level high enough to cure the fibrosarcomas. We report here that this is the case. Murine NFSa fibrosarcomas growing in the hind legs of syngeneic mice were exposed to either gamma rays or fast neutrons. The tumors were removed and retransplanted into fresh recipients to obtain 50% tumor cell doses, from which the dose-cell survival relationship was constructed. Survival curves showed continuous bending down to 10(-7), and were well fitted using the linear-quadratic model. The alpha and beta values for neutrons were larger than those for gamma rays. When the surviving fractions at experimental TCD50 doses were calculated using these values, comparable figures were obtained for neutrons and gamma rays. The RBEs for neutrons were comparable for the TCD50 and TD50 assays. Neutron RBE was independent of dose within a range of 5-28 Gy. The capacity of the tumors to repair the damage caused by large doses of neutrons was identical to that for small doses of neutrons, indicating that cells retained the capacity to repair neutron damage irrespective of the size of the dose.