A recent study by the Centers for Disease Control and Prevention reported that between 1998 and 2008, leafy greens outbreaks accounted for 22.3% of foodborne outbreaks in the United States. Several studies on the growth of bacteria at different temperatures have been conducted; however, there is a need for the prediction of bacterial growth when leafy greens are transported without temperature control. Food products, when taken out of refrigeration, undergo a temperature change, with the rate of temperature change being proportional to the difference in the temperature of food and its surroundings. The objective of this study was to estimate the growth of Escherichia coli O157:H7, Salmonella enterica, and L. monocytogenes in leafy greens during transportation from retail to home at ambient temperatures ranging from 10 to 40°C for up to 10 h. Experiments were conducted to monitor the temperature increase in fresh spinach taken from refrigeration temperature to ambient temperature. The growth of pathogens was predicted using these changing temperature profiles with the three-phase linear model as a primary model and the square root model as the secondary model. The levels of E. coli O157:H7, S. enterica, and L. monocytogenes increased by 3.12, 2.43, and 3.42 log CFU at 40°C for the 10-h period, respectively, when no lag phase was assumed. If leafy greens are not kept out of refrigeration for more than 3 h, when the air temperature is 40°C or more, pathogen growth should be less than 1 log CFU. These results would assist in developing recommendations for food transportation without refrigeration.

There has been a noticeable increase in the consumption of leafy green vegetables in the United States and a marked increase in the global distribution of produce in the last two decades (16). At the same time, because leafy greens receive minimal processing, any contamination arising in the field or during harvest or transport can result in products containing pathogens hazardous to human health. Recent data from the Centers for Disease Control and Prevention revealed that leafy greens were responsible for 22.3% of all foodborne outbreaks and about 46% of all foodborne disease in the United States between 1998 and 2008 (13, 25). Escherichia coli O157:H7 and Salmonella enterica were often implicated with the largest number of leafy green outbreaks in the United States during 1973 and 2012 (15). Although Listeria monocytogenes is seldom implicated in leafy green outbreaks, it can grow on leafy greens held at refrigeration temperatures (27) and is often isolated from fresh vegetables (14).

The temperature during transportation can be controlled (e.g., from processing plant to retail store) in refrigerated trucks or uncontrolled (e.g., transportation from retail store to home). If the duration of transportation without temperature control from retail to home is considerably long, there is risk of growth of pathogenic bacteria in contaminated leafy greens. Many studies on the growth of pathogens at different temperatures have been conducted; however, there is a need for more research on the prediction of bacterial growth when the food is transported without temperature control (28). The time-temperature profile during transportation has a critical impact on growth of pathogens in leafy greens. The pH, water activity, available moisture, and nutrients of leafy greens support the growth of foodborne pathogens, and refrigeration at ≤41°F (5°C) inhibits growth of some pathogens, such as E. coli O157:H7 and S. enterica (8, 18, 20, 31). Other studies suggest that psychrotrophic pathogens, such as L. monocytogenes, exhibit minimal growth in leafy greens ≤5°C (6, 9).

Food products undergo a temperature change when taken out of refrigeration, continuing until the product temperature approaches ambient air temperature. The rate of temperature change of a food is proportional to the driving force, i.e., the temperature differential between the food temperature and surrounding environment (19), which means that the rate of temperature change is greatest when the food is first placed in the environment and gradually slows as the food and environmental temperatures converge (28). The objective of this study was to characterize the temperature change in spinach once removed from refrigeration and to understand the effect of this temperature change on the growth of E. coli O157:H7, S. enterica, and L. monocytogenes.

Newton's law of heating. The temperature rise in a food is a function of food temperature, ambient air temperature, and the time that the food is out of refrigeration. We assumed a spinach bunch of mass m, volume V, surface area As, density q, and specific heat cp initially at temperature T0. At time t = 0, the food is placed into air temperature Ta, and heat transfer begins to take place between the food and its environment, with a heat transfer coefficient h.

Newton's law of heating can be expressed as

formula

or

formula

Equation 2 can be written as equation 3

formula

where B = hAsVcp, B is constant (min−1), t is time (min), Ta is outside air temperature (°C), T(t) is product temperature (°C) at time t, and T0 is initial food temperature (°C).

Estimation of the constant B. In equations 1 through 3, the food temperature (T) is a function of time, ambient air temperature (Ta), initial temperature (T0) and B. Experiments were conducted to estimate the value of B for fresh spinach, which was then used to predict the time-temperature profiles of spinach when removed from retail displays and transported without temperature control. Fresh bunches of unpackaged spinach (~0.75 lb or 0.34 kg each) were purchased from a retail store in Maryland, placed in plastic bags, and maintained at 5°C for 24 h, then transferred to the incubators with controlled temperatures of 10, 20, 30, and 40°C. Temperature data loggers with K-type probes (Lascar Electronics, Erie, PA) were used to monitor ambient temperature and spinach temperature for each bunch of spinach. Temperature measurements were made by using the probe located near the surface of the food (~0.5 cm inside the outer leaves). Spinach temperatures were recorded at 1-min interval for 10 h. Experiments were repeated six times at each temperature (10, 20, 30, and 40°C). The value of B was calculated by using least-squares regression in JMP software (Version 9.0, JMP, SAS, NC). One-way analysis of variance was performed in JMP software to test for significant differences among the values of B measured at temperatures 10, 20, 30, and 40°C, with the significance level set at 0.05 (1).

Primary growth model. The lag phase and log phase of the three-phase linear model (5) was used as the primary growth model because of its simplicity and wider application. The three-phase linear model fits lag phase, log phase, and stationary phase as straight lines. Equations 4 and 5 represent lag and log phases of the three-phase linear model.

formula
formula

where Nt is cell concentration (CFU g−1) at time t, t is time (h), tlag is lag time (h), tmax is the time required for maximum growth (h), and μ is the specific growth rate (ln CFU g−1 h−1).

E. coli O157:H7 and S. enterica populations are known to decline at temperatures lower than 5°C (10, 20, 21, 24, 31, 32), while L. monocytogenes can survive at 3°C (7, 9, 17). Survival modeling was not used in this study because the initial food temperature at retail display was assumed to be 5°C, and only the rise in temperature after the food was taken out of retail storage was considered.

Secondary growth model. The square root model was selected as the secondary growth model (26).

formula

In equation 6, μ is the specific growth rate in equation 5, b is the temperature coefficient, T is the food temperature (°C), and Tmin is the theoretical minimum temperature (°C). The values of b and Tmin are dependent on the microbe and the food. The square root model parameters for E. coli O157:H7, S. enterica, and L. monocytogenes were taken from the literature (Table 1). The minimum temperature for growth of pathogens has been reported as 5°C for E. coli O157:H7 (21), 7°C for S. enterica (22, 27), and 3°C for L. monocytogenes (7, 22). Because temperature and the specific growth rate μ change with respect to time, the modified square root model equation can be written as

formula
TABLE 1.

Parameters for square root model for growth of E. coli O157:H7, S. enterica, and L. monocytogenes in leafy greens

Parameters for square root model for growth of E. coli O157:H7, S. enterica, and L. monocytogenes in leafy greens
Parameters for square root model for growth of E. coli O157:H7, S. enterica, and L. monocytogenes in leafy greens

Lag-phase duration. The lag time (tlag) is also a function of food temperature. Lag-time data were obtained from the stand-alone software of the U.S. Department of Agriculture (USDA)–Agricultural Research Service's Pathogen Modeling Program (Version 7.0). The lag-time values given by Pathogen Modeling Program software for E. coli O157:H7, S. enterica, and L. monocytogenes for pH of 7.0, and water activity of 0.99 were used to predict the lag time for these pathogens at different temperatures (3, 4, 12). Because the food temperature gradually changes over time when the food is taken out of refrigeration, the expected lag time also changes with changing temperature. The percentage of lag time elapsing in each 1-min interval was estimated by dividing the interval time by the lag time for the interval temperature and multiplying the resulting value by 100. The percentage of lag time contributed by each minute interval was accumulated until 100% of the time in the lag phase elapsed, as shown by equation 8 (2):

formula

Prediction of bacterial growth. Two scenarios were considered for each pathogen: with lag phase and without lag phase. Pathogen growth was calculated by using equation 9 at every 1-min interval. Calculations for lag time and growth of pathogens were conducted by using MATLAB software (version 2015b, MathWorks, Natick, MA).

formula

Lag-phase duration. The lag-time values given by the Pathogen Modeling Program fitted the power-law equation for E. coli O157:H7 and S. enterica and exponential equation for L. monocytogenes. Table 2 shows the fitted equations for predicting lag time for these pathogens at different temperatures.

TABLE 2.

Fitted equations for predicting lag time for bacteria as a function of temperature

Fitted equations for predicting lag time for bacteria as a function of temperature
Fitted equations for predicting lag time for bacteria as a function of temperature

Value of B. The values of B were not significantly different at the four temperatures (P > 0.05), so the average value of B (0.017 min−1) was used. Figure 1 shows the measured and predicted change in food temperature as a function of time and ambient temperature, assuming the initial temperature of 5°C. The changes in leafy greens temperatures were calculated at constant ambient temperatures of 10, 20, 30, and 40°C for an initial temperature of 5°C, and these temperature profiles were subsequently used to predict the bacterial growth for up to 10 h (Fig. 2).

FIGURE 1.

Measured and predicted temperatures for fresh spinach as a function of ambient temperature and time out of refrigeration.

FIGURE 1.

Measured and predicted temperatures for fresh spinach as a function of ambient temperature and time out of refrigeration.

Close modal
FIGURE 2.

Predicted growth of (a) E. coli O157:H7 with lag phase, (b) E. coli O157:H7 without lag phase (c) S. enterica with lag phase, (d) S. enterica without lag phase, (e) L. monocytogenes with lag phase, and (f) L. monocytogenes without lag phase.

FIGURE 2.

Predicted growth of (a) E. coli O157:H7 with lag phase, (b) E. coli O157:H7 without lag phase (c) S. enterica with lag phase, (d) S. enterica without lag phase, (e) L. monocytogenes with lag phase, and (f) L. monocytogenes without lag phase.

Close modal

Prediction of E. coli O157:H7 growth with lag phase. The models predicted that the bacteria would remain in lag phase for at least 10 h, if the air temperature was less than 19°C when lag phase was assumed. The expected lag-phase duration at 19°C was 9.93 h. As air temperature increased, lag-phase duration decreased, and the bacterial growth increased. The lag times for 25, 30, 35, and 40°C temperatures for E. coli O157:H7 was predicted to be 4.47, 2.75, 2.40, and 1.40 h, respectively. The predicted growth in the E. coli O157:H7 population for 25, 30, 35, and 40°C ambient temperatures was 0.66, 1.29, 2.00, and 2.81 log CFU g−1, respectively, at the end of 10 h (Fig. 2a).

Prediction of E. coli O157:H7 growth without lag phase. When no lag phase was considered, the expected growth of E. coli O157:H7 at 10°C ambient temperature was 0.13 log CFU g−1. For 20, 30, and 40°C ambient temperatures, the growth of the pathogen was 0.68, 1.68, and 3.12 log CFU g−1, respectively (Fig. 2b).

Prediction of S. enterica growth with lag phase. When lag phase was considered, it was predicted that the lag phase did not complete in the first 10 h if the air temperature was less than 21°C (Fig. 2c). At the ambient temperature of 21°C, the lag-phase duration was predicted as 9.03 h. The lag time for 25, 30, 35, and 40°C ambient temperatures was estimated to be 5.48, 3.38, 2.30, and 1.70 h, respectively, whereas the growth of S. enterica for these temperatures was 0.43, 0.93, 1.49, and 2.12 log CFU g−1, respectively, at the end of 10 h.

Prediction of S. enterica growth without lag phase. At 10°C air temperature, the increase in the S. enterica population was very minimal (0.09 log CFU g−1) at the end of 10 h. For 20, 30, and 40°C ambient temperatures, the growth of S. enterica in spinach was predicted as 0.62, 1.32, and 2.44 log CFU g−1, respectively, at the end of 10 h (Fig. 2d).

Prediction of L. monocytogenes growth with lag phase. Lag-phase duration was predicted more than 10 h when the ambient temperature was less than 18°C. The expected lag time for L. monocytogenes in spinach was estimated as 9.80, 4.38, 2.63, 1.72, and 1.18 h, respectively, for 18, 25, 30, 35, and 40°C ambient temperature, respectively (Fig. 2e). Growth in the bacteria population at the end of 10 h was estimated as 0.01, 0.78, 1.48, 2.27, and 3.16 log CFU g−1 for ambient temperatures of 18, 25, 30, 35, and 40°C, respectively.

Prediction of L. monocytogenes growth without lag phase. When lag phase was not considered, the growth of L. monocytogenes was estimated as 0.20, 0.84, 1.90, and 3.43 log CFU g−1 at the end of 10 h for ambient temperatures of 10, 20, 30, and 40°C, respectively (Fig. 2f).

The focus of the current study is on the transition from the retail display to the home when leafy greens are present as individual packages. Early in the food chain, boxing and palletizing of the product would likely change the temperature profiles and require further data on heat transfer rates. The predictions of this study are useful in real-life situations in which refrigerated products are kept out of temperature control for a considerably long duration after purchase from retail stores and before storage in home refrigerators. The EcoSure 2007 survey (11) reported that the mean and the maximum durations of all refrigerated products out of refrigeration during transition from retail to home were 1 h 10 min and ~4 h, respectively.

When the ambient temperature was 20°C or below, the time needed for 1-log growth was predicted to be more than 10 h, with no lag-phase consideration for all three pathogens. For E. coli O157:H7, S. enterica, and L. monocytogenes, 1-log growth was achieved in 6.18, 7.68, and 5.50 h at 30°C and 3.57, 4.41, and 3.28 h at 40°C ambient temperature, respectively. Thus, based on 1-log growth time prediction without consideration of the lag phase, leafy greens should not be kept out of refrigeration for more than 3 h during summer afternoons, when the air temperature rises to 40°C or more in some parts of the world. These results are in close agreement with a U.S. Food and Drug Administration (FDA) position paper on quantitative risk assessment of relative risk to public health from foodborne L. monocytogenes among selected categories of ready-to-eat foods (29), which recommends that to limit the pathogen growth below 1 log, a conservative 4-h limit for keeping foods without temperature control allows for a needed margin of safety if the temperature of the environment is higher than 24°C.

McKellar and Delaquis (21) and Mishra et al. (22) validated their models shown in Table 1 by using the available nonisothermal time-temperature profiles in the literature. These studies (21, 22) reported that their model predictions were good without consideration of lag phase, indicating that bacterial growth on leafy greens started quickly after inoculation in the time-temperature profiles used for model validation. The prediction of bacterial growth without considering lag time could provide conservative results. However, Muñoz-Cuevas et al. (23) reported that when a food in lag time is taken to a fluctuating temperature, the system may be reset with a new lag phase. They concluded that the predictions were considerably more accurate when lag time was included in the model. In real-life situations, the lag phase may occur if the temperature fluctuation is too high or if bacteria undergo stressed conditions, such as chlorine washing. Thus, we performed the bacterial growth predictions considering the possibilities of both scenarios, with or without lag phase.

The starting retail temperature was considered to be 5°C because the FDA Food Code requires that ready-to-eat fruits and vegetables be refrigerated at 5°C or lower to minimize the growth of foodborne pathogens (30). In addition, in a large-scale U.S. study surveying 3,799 time-temperature profiles, Zeng et al. (32) found that distributions of mean temperature during retail display was 4 to 6°C in more than 55% cases. In the EcoSure 2007 survey (11), the mean temperature for refrigerated products at retail was reported as 4.5°C.

A large value of B indicates that the food approaches the environment temperature in a short time. B is proportional to the surface area, but inversely proportional to the mass and the specific heat of the food. The value of B was calculated for refrigerated food products in the EcoSure 2007 survey (11), taking the mean temperature at retail and mean change in product temperature from store to home based on time out of refrigeration, and the calculated value of B was 0.0034 min−1. The value of B for fresh spinach (0.017 min−1) was higher than the calculated value (0.0034 min−1) for the EcoSure 2007 survey. Fresh-cut leafy vegetables and spinach have a higher surface area to mass ratio than products such as fresh meat or packaged deli products, which were part of the EcoSure 2007 survey. The temperature of spinach bunches was taken at the surface, which is likely to reach ambient temperature faster than the inner leaves. Because the spinach leaves are loose (unlike ground beef or block cheese), inner spinach leaves likely attain ambient temperatures in a short time. Measuring the temperature of the surface leaves provides fail-safe results. Our predictions for 10°C ambient temperature without the consideration of lag phase are in good agreement with Koseki and Isobe (18), who reported about a 1-log growth of E. coli O157:H7 and L. monocytogenes and almost no growth of S. enterica in leafy greens kept at temperatures varying from 5 to 15°C (average ~10°C) for about 65 h during the storehouse storage, transportation to retail, and retail display.

We estimated that the lag phase for E. coli O157:H7, S. enterica, and L. monocytogenes is more than 10 h if spinach is kept in the ambient temperature of 18°C or lower. We also estimate that bacterial growth will not exceed 3.5 log/g at 40°C for 10 h when a lag phase is assumed. If we assume a 1-log growth per g allowed increase and no lag phase, our predictions show that leafy greens should not be kept out of refrigeration for more than 3 h at ambient temperatures of 40°C or more. The results of this study will be useful for estimating the risk to human health because of keeping leafy greens out of refrigeration for extended durations.

This work was supported through a grant (award 2011-51181-30767) from the USDA, National Institute of Food and Agriculture. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the view of the USDA–National Institute of Food and Agriculture.

1.
Alkalay
,
R. N.
, and
T. P.
Harrigan
.
2016
.
Mechanical assessment of the effects of metastatic lytic defect on the structural response of human thoracolumbar spine
.
J. Orthop. Res
.
doi:10.1002/jor.23154
.
2.
Borneman
,
D. L.
,
S. C.
Ingham
, and
C.
Ane
.
2009
.
Mathematical approaches to estimating lag-phase duration and growth rate for predicting growth of Salmonella serovars, Escherichia coli O157:H7, and Staphylococcus aureus in raw beef, bratwurst, and poultry
.
J. Food Prot
.
72
:
1190
1200
.
3.
Buchanan
,
R. L.
, and
K. L.
Klawitter
.
1992
.
The effect of incubation temperature, initial pH, and sodium chloride on the growth kinetics of Escherichia coli O157:H7
.
Food Microbiol
.
9
:
185
196
.
4.
Buchanan
,
R. L.
, and
J. G.
Phillips
.
2000
.
Updated models for the effect of temperature, initial pH, NaCl, and NaNO2 on the aerobic and anaerobic growth of Listeria monocytogenes
.
Quant. Microbiol
.
2
:
103
128
.
5.
Buchanan
,
R. L.
,
R. C.
Whiting
, and
W. C.
Damert
.
1997
.
When is simple good enough: a comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves
.
Food Microbiol
.
14
:
313
326
.
6.
Carlin
,
F.
,
C.
Nguyen-the
, and
A.
Abreu Da Silva
.
1995
.
Factors affecting growth of Listeria monocytogenes on minimally processed fresh endive
.
J. Appl. Bacteriol
.
78
:
636
646
.
7.
Carlin
,
F.
,
C.
Nguyen-the
,
A.
Abreu Da Silva
, and
C.
Cochet
.
1996
.
Effects of carbon dioxide on the fate of Listeria monocytogenes, of aerobic bacteria and on the development of spoilage in minimally processed fresh endive
.
Int. J. Food Microbiol
.
32
:
159
172
.
8.
Chang
,
J.-M.
, and
T. J.
Fang
.
2007
.
Survival of Escherichia coli O157:H7 and Salmonella enterica serovars Typhimurium in iceberg lettuce
.
Food Microbiol
.
24
:
745
751
.
9.
Ding
,
T.
,
Y.-G.
Jin
, and
D.-H.
Oh
.
2010
.
Predictive model for growth of Listeria monocytogenes in untreated and treated lettuce with alkaline electrolyzed water
.
World J. Microbiol. Biotechnol
.
26
:
863
869
.
10.
Ding
,
T.
,
J.
Wang
,
F.
Forghani
,
S.-D.
Ha
,
M.-S.
Chung
,
G.-J.
Bahk
, and
D.-H.
Oh
.
2012
.
Development of predictive models for the growth of Escherichia coli O157:H7 on cabbage in Korea
.
J. Food Sci
.
77
:
M257
M263
.
11.
EcoSure
.
2008
.
EcoSure 2007 cold temperature database
. .
12.
Gibson
,
A. M.
,
N.
Bratchell
, and
T. A.
Roberts
.
1988
.
Predicting microbial growth: growth responses of Salmonella in a laboratory medium as affected by pH, sodium chloride and storage temperature
.
Int. J. Food Microbiol
.
6
:
155
178
.
13.
Gould
,
L. H.
,
K. A.
Walsh
,
A. R.
Vieira
,
K.
Herman
,
I. T.
Williams
,
A. J.
Hall
, and
D.
Cole
.
2013
.
Surveillance for foodborne disease outbreaks—United States, 1998–2008
.
Morb. Mortal. Wkly. Rep
.
62
:
1
34
.
14.
Hanning
,
I. B.
,
M. G.
Johnson
, and
S. C.
Ricke
.
2008
.
Precut prepackaged lettuce: a risk for listeriosis?
Foodborne Pathog. Dis
.
5
:
731
746
.
15.
Herman
,
K. M.
,
A. J.
Hall
, and
L. H.
Gould
.
2015
.
Outbreaks attributed to fresh leafy vegetables, United States, 1973–2012
.
Epidemiol. Infect
.
143
:
3011
3021
.
16.
Jacxsens
,
L.
,
P. A.
Luning
,
J. G. A. J.
van der Vorst
,
F.
Devlieghere
,
R.
Leemans
, and
M.
Uyttendaele
.
2010
.
Simulation modelling and risk assessment as tools to identify the impact of climate change on microbiological food safety–the case study of fresh produce supply chain
.
Food Res. Int
.
43
:
1925
1935
.
17.
Kaminski
,
C. N.
,
G. R.
Davidson
, and
E. T.
Ryser
.
2014
.
Listeria monocytogenes transfer during mechanical dicing of celery and growth during subsequent storage
.
J. Food Prot
.
77
:
765
771
.
18.
Koseki
,
S.
, and
S.
Isobe
.
2005
.
Prediction of pathogen growth on iceberg lettuce under real temperature history during distribution from farm to table
.
Int. J. Food Microbiol
.
104
:
239
248
.
19.
Li
,
Y.
,
J. P.
Schrade
,
H.
Su
, and
J. J.
Specchio
.
2014
.
Transportation of perishable and refrigerated foods in mylar foil bags and insulated containers: a time-temperature study
.
J. Food Prot
.
77
:
1317
1324
.
20.
Ma
,
L.
,
G.
Zhang
,
P.
Gerner-Smidt
,
R. V
Tauxe
, and
M. P.
Doyle
.
2010
.
Survival and growth of Salmonella in salsa and related ingredients
.
J. Food Prot
.
73
:
434
444
.
21.
McKellar
,
R. C.
, and
P.
Delaquis
.
2011
.
Development of a dynamic growth–death model for Escherichia coli O157:H7 in minimally processed leafy green vegetables
.
Int. J. Food Microbiol
.
151
:
7
14
.
22.
Mishra
,
A.
,
M.
Guo
,
R. L.
Buchanan
,
D. W.
Schaffner
, and
A. K.
Pradhan
.
2017
.
Development of growth and survival models for Salmonella and Listeria monocytogenes during non-isothermal time-temperature profiles in leafy greens
.
Food Control
71
:
32
41
.
23.
Muñoz-Cuevas
,
M.
,
P. S.
Fernández
,
S.
George
, and
C.
Pin
.
2010
.
Modeling the lag period and exponential growth of Listeria monocytogenes under conditions of fluctuating temperature and water activity values
.
Appl. Environ. Microbiol
.
76
:
2908
2915
.
24.
Oliveira
,
M.
,
J.
Usall
,
C.
Solsona
,
I.
Alegre
,
I.
Viñas
, and
M.
Abadias
.
2010
.
Effects of packaging type and storage temperature on the growth of foodborne pathogens on shredded “Romaine” lettuce
.
Food Microbiol
.
27
:
375
380
.
25.
Painter
,
J. A.
,
R. M.
Hoekstra
,
T.
Ayers
,
R. V.
Tauxe
,
C. R.
Braden
,
F. J.
Angulo
, and
P. M.
Griffin
.
2013
.
Attribution of foodborne illnesses, hospitalizations, and deaths to food commodities by using outbreak data, United States, 1998–2008
.
Emerg. Infect. Dis
.
19
:
407
415
.
26.
Ratkowsky
,
D. A.
,
J.
Olley
,
T. A.
McMeekin
, and
A.
Ball
.
1982
.
Relationship between temperature and growth rate of bacterial cultures
.
J. Bacteriol
.
149
:
1
5
.
27.
Sant'Ana
,
A. S.
,
B. D. G. M.
Franco
, and
D. W.
Schaffner
.
2012
.
Modeling the growth rate and lag time of different strains of Salmonella enterica and Listeria monocytogenes in ready-to-eat lettuce
.
Food Microbiol
.
30
:
267
273
.
28.
Schaffner
,
D. W.
2013
.
Utilization of mathematical models to manage risk of holding cold food without temperature control
.
J. Food Prot
.
76
:
1085
1094
.
29.
U.S. Food and Drug Administration
.
2003
.
Quantitative assessment of relative risk to public health from foodborne Listeria monocytogenes among selected categories of ready-to-eat foods
.
U.S. Food and Drug Administration, Center for Food Safety and Applied Nutrition
,
College Park, MD
.
30.
U.S. Food and Drug Administration
.
2013
.
Food Code 2013
. .
31.
Vandamm
,
J. P.
,
D.
Li
,
L. J.
Harris
,
D. W.
Schaffner
, and
M. D.
Danyluk
.
2013
.
Fate of Escherichia coli O157:H7, Listeria monocytogenes, and Salmonella on fresh-cut celery
.
Food Microbiol
.
34
:
151
157
.
32.
Zeng
,
W.
,
K.
Vorst
,
W.
Brown
,
B. P.
Marks
,
S.
Jeong
,
F.
Pérez-Rodríguez
, and
E. T.
Ryser
.
2014
.
Growth of Escherichia coli O157:H7 and Listeria monocytogenes in packaged fresh-cut romaine mix at fluctuating temperatures during commercial transport, retail storage, and display
.
J. Food Prot
.
77
:
197
206
.