Assessment of Escherichia coli O157:H7 growth in ground beef in the Greek chill chain

Assessment of Escherichia coli O157:H7 growth in ground beef in the Greek chill chain

Food Research International 123 (2019) 590–600 Contents lists available at ScienceDirect Food Research International journal homepage: www.elsevier...

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Food Research International 123 (2019) 590–600

Contents lists available at ScienceDirect

Food Research International journal homepage: www.elsevier.com/locate/foodres

Assessment of Escherichia coli O157:H7 growth in ground beef in the Greek chill chain Myrsini Kakagianni, Konstantinos P. Koutsoumanis

T



Laboratory of Food Microbiology and Hygiene, Department of Food Science and Technology, School of Agriculture, Faculty of Agriculture, Forestry and Natural Environment, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

ARTICLE INFO

ABSTRACT

Keywords: E. coli O157:H7 Ground beef Predictive growth model Validation Chill chain Risk assessment

A predictive mathematical model of the effect of temperature (10–47 °C) on the growth of Escherichia coli O157:H7 in natural contaminated ground beef was developed. The estimated values for the cardinal parameters Tmin, Tmax, Topt and the optimum maximum specific growth rate (μopt) of E. coli O157:H7 were found to be 3.36, 46.87, 43.16 °C and 1.385/h, respectively. The developed model was further validated against observed growth of E. coli O157:H7 in ground beef at non – isothermal chilling conditions by using two periodically changing temperature profiles with temperature ranging from 0 to 15 °C. Overall the model predicted satisfactorily the growth of E. coli O157:H7 in ground beef at dynamic temperature conditions. The model was combined with temperature data collected from ground beef chill chain in Greece in order to assess the growth of the pathogen from purchase of the product at retail to consumption. Retail storage average temperature from 50 retail cabinets in Greek super markets ranged from 0.1 to 7.4 °C with a mean of 3.2 °C and a mean standard deviation of 1.7 °C. The predicted growth of the pathogen after 7 days of storage at retail ranged between 0 and 2.03 log10 CFU/g, with an average growth to 0.31 log10 CFU/g. The growth of the pathogen during transportation from retail to domestic refrigerators ranged between 0.03 and 0.45 log10 CFU/g, with an average growth to 0.16 log10 CFU/g. The average temperature of 160 domestic refrigerators ranged from −2.7 to 18.1 °C. Differences in the temperature among the shelves of the refrigerators were observed. The predicted growth of E. coli O157:H7 in ground beef stored in domestic refrigerators for 1 day ranged between 0.00 and 2.3 log10 CFU/g. For a scenario storage of ground beef in retail for 3 days, transportation from retail domestic refrigerators over a period of 6 h and storage in domestic refrigerators for 3 days the 99th percentile of the total growth was 4.83 log10 CFU/g for storage at the upper self of the domestic refrigerator. The data and models provided in the present work can be further used in a quantitative risk assessment model of E. coli O157:H7 in ground beef consumed in Greece.

1. Introduction Escherichia coli O157:H7 was first recognized as a human pathogen in 1982, during an investigation of two outbreaks of bloody diarrhoea in Oregon and Michigan (Doyle & Schoeni, 1984; Riley et al., 1983), attributed to the consumption of undercooked contaminated beef burgers (Byrne, Bolton, Sheridan, Blair, & McDowell, 2002). Since then, it continues to be considered as a microorganism of primary food safety concern for food industry, consumers and regulatory agencies with respect to public health worldwide (CDC, 2018), due to the pathogen's inherent acid tolerance, pathogenicity and very low infective dose (from 10 to 100 cells) (Leyer, Wang, & Johnson, 1995; Su & Li, 2004). In particular, the consumption of a variety of raw or undercooked foods of bovine origin, including ground beef, has been primarily implicated

in numerous well – documented and publicized outbreaks of the enterohemorrhagic strain O157:H7 (CDC, 2014, 2016). This pathogen, as an enterohaemorrhagic strain capable of producing verotoxins, may cause bloody diarrhoea and can progress to haemolytic uremic syndrome (HUS) and thrombotic thrombocytopenic purpura in infected young children and elders and immune – compromised patients, respectively (Su & Li, 2004; Yang, Li, & Chou, 2007). The Centers for Disease Control and Prevention has estimated that foodborne diseases caused by Shiga toxin – producing E. coli O157:H7 (O157 STEC) account for 265,000 cases of illnesses, 3600 hospitalizations and 30 deaths in the US each year (CDC, 2018). Thus, preventing food from the contamination, further cross – contamination and/or proliferation of this pathogen at all steps along the food chain remains a great challenge to the meat processors, as well as regulatory agencies (Buncic et al.,

⁎ Corresponding author at: Department of Food Science and Technology, School of Agriculture, Faculty of Agriculture, Forestry and Natural Environment, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece. E-mail addresses: [email protected] (M. Kakagianni), [email protected] (K.P. Koutsoumanis).

https://doi.org/10.1016/j.foodres.2019.05.033 Received 9 April 2019; Received in revised form 16 May 2019; Accepted 20 May 2019 Available online 21 May 2019 0963-9969/ © 2019 Elsevier Ltd. All rights reserved.

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fresh TSB and incubated at 37 °C for 18 h. The 18-h culture was centrifuged (model PK 120R, Thermo Electron Corporation, Waltham, MA, United States) at 6000 rpm for 20 min at 4 °C. The harvested cells were washed with 20 ml of quarterstrength Ringer's solution (Lab M Limited) and centrifuged as described previously. The harvested cells of the washed cultures were resuspended in 20 ml of Ringer's solution to yield an inoculum count of approximately 7–8 log10 CFU/g when 3 ml of inoculum were applied to 600 g of ground beef. In order to determine the exact initial concentration of the inoculum and check its purity, appropriate dilutions in Ringer's solution of the prepared inoculum were surface plated on TSA.

2014; Loukiadis et al., 2017; Yang et al., 2007; Yoon et al., 2009). Microbial risk analysis has been widely accepted as an effective tool to assess possible links between hazards in the food chain and actual risks to public health (FAO – WHO, 2006). In microbiological risk assessment the dynamics of pathogens' growth, survival, and inactivation in foods should be explicitly considered. Predictive microbiology has been recognized as an important component of the risk assessment process for estimating the changes in microbial levels in foods as the product moves through the farm – to – fork chain. Although many mathematical models describing the effect of temperature on the growth of E. coli O157:H7 have been published (Buchanan, Bagi, Goins, & Phillips, 1993; Cassin, Lammerding, Todd, Ross, & McColl, 1998; Sutherland, Bayliss, & Braxton, 1995; Tamplin, 2002; Tamplin, Paoli, Marmer, & Phillips, 2005; Walls & Scott, 1996) most of them have been developed and validated using data obtained from experiments conducted in a well – defined and controlled laboratory environment (Pin, Sutherland, & Baranyi, 1999; te Giffel & Zwietering, 1999) or sterile foods under static growth conditions. Such models often underestimate factors such as the food composition or the antagonistic microflora (Pin et al., 1999). In addition, as temperature fluctuations are common during transportation and storage validation of the models under dynamic conditions is required to evaluate their performance under realistic conditions (Koutsoumanis, Pavlis, Nychas, & Xanthiakos, 2010; Koutsoumanis, Stamatiou, Skandamis, & Nychas, 2006). The available risk assessment models of E.coli O157:H7 in ground beef indicate that growth of the pathogen during storage in among the most important factors affecting the final risk (Cassin et al., 1998; Signorini & Tarabla, 2009; Smith, Fazil, & Lammerding, 2013). Considering the impact of growth during storage in the final risk, the accuracy of the predicted growth in a risk assessment model is of great importance for realistic risk outputs. Apart from high performance, predictive models accurate predictions of growth require time – temperature data for the whole chill chain of ground beef which are not available for Greece. Based on the above, the objective of the present study was to develop a predictive model for the effect of storage temperature on the growth of E. coli O157:H7 in natural contaminated ground beef and combine it with temperature data of the Greek chill chain (retail, domestic, transportation from retail to domestic). The final goal was to assess the total growth of the pathogen from purchase of ground beef at retail to consumption by taking into variability the storage conditions.

2.1.2. Preparation of ground beef Fresh beef was purchased from a local retail premise and was transported to the laboratory within 1 h of purchase where it was washed and cut into pieces. Then, the beef pieces were kept under refrigeration (5 °C) and under aerobic conditions. During the 0 day, the cutting of the beef pieces into ground beef was followed and the ground beef was further divided into 3 portions of 600 g in order to have, finally, 3 replications (A, B, C). Immediately after preparation, a 3 ml aliquot of the suspension (final concentration 103–104 CFU/g) was inoculated in each portion of ground beef and, in order for the inoculum to be spread evenly, the portions were mixed by hand (for approximately 10 min). Then it was divided into 15 petri plates with 40 g/petri plates. The petri plates with inoculated ground beef were stored under controlled isothermal conditions (10, 12, 15, 20, 25, 35, 42, 45 and 47 °C) or programmed changing temperature conditions (0 °C/16 h and 15 °C/6 h, 5 °C/12 h, 10 °C/8 h and 15 °C/8 h) in high – precision ( ± 0.2 °C) low – temperature incubators (model MIR 153; Sanyo Electric Co., Ora – Gun, Gunma, Japan). The temperature of samples was monitored during the storage period using electronic temperature monitoring devices (Cox Tracer; Cox Technologies, Belmont, USA). Triplicate samples from each storage temperature were taken at appropriate time intervals to allow for efficient kinetic analysis of microbial growth. For each temperature condition, un – inoculated samples were periodically checked for the presence of E. coli O157:H7. No positive sample was found. 2.1.3. Ground beef analysis Ground beef samples were analyzed microbiologically on the day of inoculation. Ground beef (25 g) was transferred aseptically to a stomacher bag to a 400 – ml sterile filter bag (BagPage®, Interscience) containing 225 ml of Ringer's solution, and were homogenized for 2 min (BagMixer® 400 stomacher, Interscience). Appropriate serial decimal dilutions of samples in Ringer's solution were surface plated on the selective medium Sorbitol MacConkey Agar supplemented with the antibiotics cefixime – tellurite (SMAC – CT, Oxoid) for the enumeration of E. coli O157:H7 populations. Colonies were counted after incubation of plates at 37 °C for 24–32 h.

2. Materials and methods 2.1. Experimental design 2.1.1. Bacterial strain and preparation of inoculum The strain used in this study was the non – pathogenic strain Escherichia coli O157:H7 NCTC 12900, kindly provided by the strain collection of the Laboratory of Food Microbiology and Biotechnology (Department of Food Science and Human Nutrition, Agricultural University of Athens). The tested strain is phenotypically very similar to the toxigenic strains of E. coli O157:H7, but devoid of the ability to produce verotoxins (Skandamis & Nychas, 2000). The stock culture of the strain was stored frozen (−70 °C) onto Microbank™ porous beads (Pro-Lab Diagnostics, Ontario, Canada). The working culture was stored refrigerated (5 °C) on tryptone soy agar (TSA; Lab M Limited, Lancashire, United Kingdom) slants and was renewed bimonthly. The strain was activated by transferring a loopful from fresh TSA slants into 10 ml of tryptone soy broth (TSB; Lab M Limited) and incubating for 24 h at 37 °C. Portions of the activated culture were transferred into 10 ml of

2.2. Model development and validation 2.2.1. Model development Regarding the experiments at isothermal and dynamic temperature conditions, 3 ground beef samples (3 replications) from one experiment were analyzed for each temperature condition and each temperature profile. The observed growth data (log10 CFU/g) of E. coli O157:H7 in ground beef stored under isothermal chilling conditions were fitted to the primary model of Baranyi and Roberts (1994) using the program DMFit in order to estimate the kinetic parameter for growth, maximum specific growth rate, μmax, in ground beef and the physiological state

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(ho) of the cells. The original dynamic model has an explicit solution for static situations (when the model parameters do not depend on time), which describes the natural logarithm of the cell concentration, y (t) = ln x(t), by the equation:

y (t ) = y0 + µ max A (t )

1 emµmax A (t ) 1 ln 1 + m e m (ymax y0 )

Table 1 Estimated values and statistics for the parameters of the Cardinal Model with Inflection (Eq. (3)) describing the effect of temperature on the maximum specific growth rate (μmax) of Escherichia coli O157:H7 in ground beef.

(1)

where μmax is the maximum specific growth rate of the cell population; ymax is the natural logarithm of the maximum population's concentration; y0, the natural logarithm of the initial cell concentration; m is a curvature parameter characterizing the transition from the exponential to the stationary phase of growth and A(t) is a gradually delayed time variable described by the equation:

A (t ) = t +

1 µ max

ln (e

µmax t

+e

h0

+e

µmax t h 0 )

(Topt

Tmin)([(Topt

(T Tmax )(T Tmin )(T Topt ) 0

, Tmin )2 (Topt Tmax )(Topt + Tmin

2T )]

T

RMSEc

R2d

μopt (1/h) Tmax Tmin Topt

1.385 ± 0.047 46.87 ± 0.12 3.36 ± 2.35 43.16 ± 0.42

1.224 46.61 −1.17 42.09

1.435 47.14 3.63 44.01

0.0205

0.920

d

± : Standard Error. CL: Confidence Limits. RMSE: Root Mean Square Error. R2: Coefficient of determination.

2.3. Collection of temperature data of ground beef chill chain A survey of temperature conditions of the Greek chill chain of ground beef, including retail storage, transportation from retail to domestic storage and domestic storage, was performed. 2.3.1. Temperature during retail storage The temperature of retail cabinets for refrigerated meat products was recorded for 5–7 days using electronic temperature – monitoring data loggers (cox tracer, Cox Technologies, Belmont, NC, USA). In total Tmin

, Tmin

T

,

Tmax

T

Upper 95% CLb

c

(3) 0

( )=

Lower 95% CLb

b

(2)

( )

Estimated valuea

a

where h0 is a parameter characterizing the ‘adaptation work’ required by the cells to adjust to the new environment (Baranyi & Roberts, 1994). The effect of storage temperature on the kinetic parameter was further modelled using the Cardinal Model with Inflection (Rosso, Lobry, & Flandrois, 1993):

µ max (T ) = µopt

Parameter

Tmax

where μopt is the optimum value for the maximum specific growth rate (1/h) (when T = Topt); Tmin, Topt and Tmax are the theoretical minimum, optimum and maximum temperature (°C) for growth, respectively. Tmin and Tmax are theoretical, and may be far from the actual minimum and maximum growth temperatures of the pathogen. The values of Tmin, Topt and Tmax as well as the confidence and the predictions limits were determined by fitting the estimated μmax values for the tested microorganism to the above model using the Excel v4 format of the curve – fitting program TableCurve 2D (Systat Software Inc., San Jose, CA, USA). The adequacy of the developed models to fit data was evaluated graphically and also by the coefficient of determination R2 and the Root Mean Square Error (RMSE) (Ratkowsky, 2004).

(4) 50 retail cabinets from super markets in five different cities (Athens, Patra, Iraklio, Thessaloniki and Larisa) in Greece were tested. 2.3.2. Temperature during transportation from retail to domestic storage Electronic temperature – monitoring data loggers were provided to 30 consumers in 4 different cities (Thessaloniki, Volos, Larissa and Litochoro) in Greece who bought pre – packed ground beef from a super market. Consumers were asked to buy ground beef from supermarket as usual, transported it to their domestic refrigerator and record the temperature for 6 h. The data loggers were programmed to record both the environmental and the product temperature every 5 min for 24 h. 2.0 1.8

2.2.2. Model validation at dynamic temperature conditions Inoculated samples with the pathogen were stored at periodically changing temperature conditions (0 °C/16 h and 15 °C/6 h, 5 °C/12 h, 10 °C/8 h and 15 °C/8 h) in high – precision ( ± 0.2 °C) low – temperature incubators (model MIR 153; Sanyo Electric Co., Ora – Gun, Gunma, Japan), in order to simulate the distribution and storage conditions of the ground beef in Greece. Observed growth was compared graphically with the growth predicted by the model. Prediction of growth was based on the combination of the secondary model (Eq. (3)) with the differential equations of the Baranyi and Roberts primary model (Eqs. (1) and (2)), which were numerically integrated with respect to time. For the initial concentration (y0), the value determined by the plate count method was used. The physiological state (Baranyi & Roberts, 1994) of the cells (h0) was fixed to 1.0 based on the average of h0 values observed in ground beef at static temperature conditions (10–47 °C). Predicted growth was calculated using the explicit form of the above equations in an excel spreadsheet.

1.6

max (1/h)

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

10

20

30

40

50

Temperature (°C)

Fig. 1. Effect of temperature on the maximum specific growth rate (μmax) of Escherichia coli O157:H7 in ground beef, fitted to the Cardinal Model with Inflection (solid line) (Eq. (3)). Points (○) represent observed values of the μmax. The dotted lines depict the 95% confidence limits of the effect of temperature on maximum specific growth rate.

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10.0

16

9.0

14

University of Thessaloniki (Koutsoumanis et al., 2010). 2.4. Prediction of Escherichia coli O157:H7 growth in ground beef at temperature conditions of the Greek chill chain

12 10 7.0

8 6.0

6 5.0

The temperature data collected was used to predict the growth of E. coli O157:H7. The prediction of growth under the dynamic temperature profiles was based on the assumption that after a temperature shift, the growth rate is adopted instantaneously to the new temperature environment (Koutsoumanis et al., 2006). Eqs. (1) and (2) were used for the prediction of growth at dynamic temperature conditions based on the “momentary” μmax which was calculated from Eqs. (3) and (4). No lag phase was considered (ho = 0.01) based on the assumption that lag is consumed during transportation from the production centre to retail outlets. The latter represents a worst case scenario for pathogen's growth. The maximum population density was found to be independent of temperature and was therefore taken as the average of the values estimated during testing at isothermal conditions (ymax = 108.5 CFU/g). The overall growth of the tested pathogen in ground beef was calculated for various periods of storage and expressed in the form of frequency distributions with the average value, the standard deviation and the 90th, 95th and 99th percentiles provided. In addition, a comparison between the estimation of pathogen's growth predicted from the dynamic temperature profiles and from a constant temperature based on the average temperature of the profile was carried out.

Temperature (°C)

Log10 CFU/g

8.0

4 4.0

2 0

3.0

0

30

60

90 120 150 Time (hours)

180

210

Fig. 2. Comparison between observed (points) and predicted (lines) growth of Escherichia coli O157:H7 in ground beef stored under dynamic temperature conditions (16 h at 0 °C and 6 h at 15 °C).

10.0

16

9.0

14 3. Results and discussion

12 10 7.0

8 6.0

6 5.0

3.1. Model development

Temperature (°C)

Log10 CFU/g

8.0

The Baranyi model described well the growth curves of E. coli O157:H7 on ground beef at different storage temperatures (10, 12, 15, 19, 21, 25, 30, 35, 41, 45, 46 and 47 °C) providing good statistical fits to the data (R2 > 0.91 for all fitted curves). The μmax increased from 0.071/h (average value) at 10 °C to 1.43/h at 45 °C, while storage temperatures > 45 °C resulted in decrease of μmax. The μmax data obtained from the Baranyi model was further used to develop a cardinal parameter model in order to determine the effect of temperature on the growth kinetics of E. coli O157:H7 on ground beef (Eqs. (3) and (4)). The R2 and RMSE values (Table 1), as well as the graphical evaluation of the fitting curve (Fig. 1), indicated a satisfactory performance of the model in describing the effect of temperature on the μmax of the pathogen microorganism. The estimated values for the cardinal parameters Tmin, Tmax, Topt and the optimum maximum specific growth rate (μopt) of E. coli O157:H7 were found to be 3.36, 46.87, 43.16 °C and 1.385/h, respectively (Table 1). These values are in general different from those reported by Salter, Ross, and McMeekin (1998). In the latter study the authors modelled the effect of temperature on the growth of 10 E. coli strains and reported Tmin values ranging from 4.23 to 6.41 °C, which are significantly higher that the Tmin estimated in the present study. The Topt and Tmax values reported by Salter et al. (1998) ranged from 39.55 to 42.56 °C and 47.32 to 51.26 °C, respectively. The above differences in the cardinal parameters can be mainly attributed to fact that the models of Salter et al. (1998) were based on data derived from laboratory liquid media. Such models may often overestimate the microbial growth that actually occurs in real foods (Dalgaard & Jørgensen, 1998; Koutsoumanis et al., 2006; Pin et al., 1999; te Giffel & Zwietering, 1999), because they do not take into account factors such as the food structure and its resulting local effects, the possible microbial interactions or the concentration of minor (or

4 4.0

2 0

3.0

0

30

60

90 120 150 Time (hours)

180

210

Fig. 3. Comparison between observed (points) and predicted (lines) growth of Escherichia coli O157:H7 in ground beef stored under dynamic temperature conditions (12 h at 5 °C, 8 h at 10 °C and 8 h at 15 °C).

For this, the external sensor of the data logger was located in centre of ground beef package at the time of purchase. Depending on the transportation time, the 6 h profiles include a certain time of storage in the domestic refrigerator. This was done in order to record the decrease of product's temperature after placement in each domestic refrigerator. 2.3.3. Temperature during domestic storage One hyndred and sixty domestic refrigerators were surveyed in North Greece (Thessaloniki) using electronic temperature – monitoring data loggers. The data loggers were programmed to record the temperature every 5 min for 24 h and were located at the upper, middle and lower shelves of each refrigerator. These data was combined with previously collected temperatures of domestic refrigerators in Greece from the Laboratory of Food Microbiology and Hygiene of Aristotle

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15

13

13

11

11

Temperature (°C)

Temperature (°C)

M. Kakagianni and K.P. Koutsoumanis

9 7 5 3 1 -1

0

30

60

90

120

150

180

9 7 5 3 1 -1 0 -3

-3 -5

-5

Time (hours)

13

11

11

Temperature (°C)

15

13

Temperature (°C)

15

9 7 5 3 1 -1 0 -3

30

60

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30

120

150

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120

150

180

120

150

180

Time (hours)

9 7 5 3 1 -1 0 -3

180

60

30

60

90

-5

-5

Time (hours)

Time (hours)

Fig. 4. Representative temperature profiles of retail cabinets for meat products in Greece.

2.5

100

1st day

90

3rd day

80

5th day

70

7th day

% Retail refrigerators

Log10 (CFU/g)

2.0

1.5

1.0

0.5

60 50 40 30 20 10

0.0

0 0

30

60

90

120

150

180

0.00 0.16 0.32 0.48 0.64 0.80 0.96 1.12 1.28 1.44 1.60

Time (hours)

Log10 (CFU/g)

Fig. 5. Prediction of Escherichia coli O157:H7 growth in ground beef during storage for 7 days at temperature conditions observed in 50 retail refrigerators of meat products in Greece.

Fig. 6. Distribution of predicted Escherichia coli O157:H7 growth in ground beef during storage at temperature conditions observed in 50 retail refrigerators of meat products in Greece for 1, 3, 5 and 7 days.

major, from the bacterium point of view) constituents (antimicrobial compounds, natural inhibitors e.t.c.). In another study, Tamplin et al. (2005) modelled the effect of temperature on the growth of E. coli O157:H7 on sterile ground beef and reported Tmin value of 3.79 °C much closer to that observed in the present work. In the latter study the authors reported a significantly higher specific growth rate at optimum temperature (2.9/h), which could be attributed to the absence of background flora in ground beef which can inhibit the growth of the pathogen.

3.2. Model validation under dynamic temperature conditions The developed kinetic model was validated against observed growth of E. coli O157:H7 in ground beef at non – isothermal chilling conditions by using two periodically changing temperature profiles with temperature ranging from 0 to 15 °C. A graphical method was used to assess the performance of the model. The comparison between observed and predicted growth of E. coli O157:H7 in ground beef stored at dynamic temperature conditions is illustrated in Figs. 2 and 3. Fig. 2 shows the

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Table 2 Percentiles of predicted Escherichia coli O157:H7 growth in ground beef during storage at retail cabinets for 1, 3, 5 and 7 days. Predicted growth is based on the dynamic temperature profiles collected in the Greek chill chain.

0.50 0.45 0.40

Growth of E. coli O157:H7 (log10 CFU/g) 1st day

3rd day

5th day

0.35

7th day

Log10 (CFU/g)

Percentile

T profile 1 5 10 50 90 95 99

0.00 0.00 0.00 0.02 0.12 0.16 0.20

0.00 0.00 0.00 0.04 0.36 0.42 0.58

0.00 0.00 0.01 0.08 0.62 0.88 1.10

0.01 0.03 0.03 0.15 0.79 1.16 1.71

0.30 0.25 0.20 0.15 0.10 0.05

growth of the pathogen in ground beef under a periodic temperature profile of 16 h at 0 °C and 6 h at 15 °C. As shown the predictive growth model for E. coli O157:H7 showed a good performance with the predictive growth being very close to the observed data. Fig. 3 shows the growth of the pathogen in ground beef under a periodic temperature profile of 12 h at 5 °C, 8 h at 10 °C and 8 h at 15 °C. In this case the observed growth showed a higher variation with the prediction being closer to the lower values of the observed data. Overall, however, the model predicted satisfactorily the growth of E. coli O157:H7 in ground beef at dynamic temperature conditions. The comparison results for

25

0.00 0

2

3

4

5

6

Time (hours) Fig. 8. Prediction of Escherichia coli O157:H7 growth in ground beef during transportation from retail cabinets to domestic refrigerators.

both validation studies supported the assumption that the specific growth rate is adopted instantaneously. Baranyi, Robinson, Kaloti, and Mackey (1995) reported that the predictions of Brochothrix 30

External Temperature Internal Temperature in ground beef

25

Temperature (°C)

20

Temperature (°C)

1

15

10

5

20 15 10 5

0

0 0

1

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0

6

1

2

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3

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6

Time (hours) 35

30

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25

Temperature (°C)

Temperature (°C)

25 20 15 10 5

20 15 10 5 0

0 0

1

2

3

4

5

0

6

1

2

3

Time (hours)

Time (hours)

Fig. 7. Representative temperature profiles during transportation of ground beef from retail cabinets to domestic refrigerators over a period of 6 h. Depending on the transportation time the 6 h profiles include a certain time of storage in the domestic refrigerator. 595

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3.3. Prediction of E. coli O157:H7 growth in ground beef at temperature conditions of the Greek chill chain

Table 3 Percentiles of predicted Escherichia coli O157:H7 growth in ground beef during transportation from retail cabinets to domestic refrigerators over a period of 6 h. Predicted growth is based on the dynamic temperature profiles collected in the Greek chill chain.

The developed growth model and the temperature data collected were used to predict the growth of E. coli O157:H7 in ground beef stored under conditions of the Greek chill chain. Representative temperature profiles of retail storage are presented in Fig. 4. Retail storage average temperature ranged from 0.1 to 7.4 °C with a mean of 3.2 °C and a mean standard deviation of 1.7 °C. These results are in agreement with data on retail storage temperature available in the literature. In a previous survey study, Koutsoumanis et al. (2010) reported that retail storage temperature in Greece ranges from 0 to 11.7 °C with a mean of 4.98°C a median 5.44 °C and a standard deviation of 2.90 °C. Pierre (1996) reported a mean temperature of 4 °C in retail refrigerators in France, while Likar and Jevšnik (2006) examined 1286 retail refrigerators in Slovenia and found that temperature ranged between −2.2 and 12.2 °C with an average value (weighted mean) of 4.6 °C. A similar mean temperature at retail was also reported in the Canadian survey of Smith et al. (2013). The temperature in the majority of the 50 examined retail cabinets showed significant fluctuations over time with periodic upshifts of temperature. These fluctuations can be attributed to the defrost systems of the refrigerators which may lead to a short time temperature increase up to 10 °C during a defrost cycle (Bovill, Bew, & Baranyi, 2001; Koutsoumanis et al., 2010). In Fig. 5, the predicted growth of E. coli O157:H7 in ground beef during storage in 50 retail cabinets for meat products during the examination (168 h) based on the changing temperature profile is illustrated. The growth of the pathogen after 7 days of storage ranged

Growth of E. coli O157:H7 (log10 CFU/g) Percentile

Internal T of ground beef T profile

1 5 10 50 90 95 99

0.03 0.04 0.07 0.15 0.29 0.36 0.43

thermosphacta growth were good when the temperature profile contained step changes from 17 to 25 °C down to 5 °C, but the predictions no longer held for steps changes down to 3 °C. In the same study the authors attributed this observation to the alteration of the physiological state of the organism caused by the sudden cold – shock. In the present study, no additional lag phase was observed even for abrupt temperature downshifts from 15 to 0 °C.

Upper shelf Middle shelf

20

20

15

Temperature (°C)

Temperature (°C)

Lower shelf

10

5

15

10

5

0

0 0

4

8

12

16

20

24

0

4

8

12

16

20

24

20

24

Time (hours)

20

20

15

15

Temperature (°C)

Temperature (°C)

Time (hours)

10

5

10

5

0

0 0

4

8

12

16

20

24

0

Time (hours)

4

8

12

16

Time (hours)

Fig. 9. Representative 24 h temperature profiles of 160 domestic refrigerators in Greece. 596

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2.5

Upper shelf

1.0

Log10 (CFU/g)

Log10 (CFU/g)

1.5

1.5

1.0

0.5

0.5

0

4

8

12

16

20

24

1.5

1.0

0.5

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Lower shelf

2.0

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2.5

Middle shelf

0.0 0

4

Time (hours)

8

12

16

20

24

0

4

Time (hours)

8

12

16

20

24

Time (hours)

Fig. 10. Prediction of Escherichia coli O157:H7 growth of in ground beef during storage at temperature conditions observed in 160 domestic refrigerators in Greece.

provided to 30 consumers in Greece who buy pre – packed ground beef from a super market. Consumers were asked to buy ground beef from supermarket as usual, transported it to their domestic refrigerator and record the temperature for 6 h. Depending on the transportation time the 6 h profiles include a certain time of storage in the domestic refrigerator. This was done in order to record the decrease of product's temperature after placement in the domestic refrigerator. Representative temperature profiles during the transportation of ground beef from the retail cabinets to domestic refrigerators are shown in Fig. 7. Product's temperature showed an increase during transportation followed by a decrease after placement in the domestic refrigerator. The average temperature of the 6 h transportation profiles of 30 products tested ranged from 5.3 to 16.4 °C with a mean of 10.7 °C and a mean standard deviation of 1.9 °C. Fig. 8 shows the growth of E. coli O157:H7 in ground beef during transportation from retail cabinets to domestic refrigerators. The growth of the pathogen during the 6 h profile ranged between 0.03 and 0.45 log10 CFU/g, with an average growth to 0.16 log10 CFU/g. The 90th, 95th and 99th percentiles of growth of the pathogen were 0.29, 0.36 and 0.43 log10 CFU/g, respectively (Table 3). Fig. 9 shows representative storage temperature profiles in 3 different positions of 160 domestic refrigerators. The average temperature for the upper shelf of 160 domestic refrigerators ranged from −1.8 to 15.4 °C with a mean of 7.3 °C and a mean standard deviation of 1.0 °C. Average temperature for the middle shelf of 160 domestic refrigerators ranged from −0.9 to 13.1 °C with a mean of 6.1 °C and a mean standard deviation of 1.0 °C. Average temperature for the lower shelf of 160 domestic refrigerators ranged from −2.7 to 18.1 °C with a mean of 6.5 °C and a mean standard deviation of 0.9 °C. The predicted growth of E. coli O157:H7 in ground beef stored in domestic for 1 day is presented in Fig. 10. The growth of the pathogen in the upper shelf ranged between 0.00 and 1.54 log10 CFU/g, with an average growth to 0.25 log10 CFU/g. In the middle shelf the growth ranged from 0.00 to 1.00 log10

Table 4 Percentiles of predicted Escherichia coli O157:H7 growth in ground beef during storage at domestic refrigerators for 24 h. Predicted growth is based on the dynamic temperature profiles collected in the Greek chill chain. Growth of E. coli O157:H7 (log10 CFU/g) Percentile

Upper shelf

Middle shelf

Lower shelf

T profile 1 5 10 50 90 95 99

0.00 0.00 0.02 0.15 0.65 0.92 1.27

0.00 0.00 0.01 0.08 0.34 0.53 0.92

0.00 0.00 0.00 0.10 0.58 0.72 1.24

between 0.00 and 2.04 log10 CFU/g, with an average growth to 0.31 log10 CFU/g, The significant variability of E. coli O157:H7 growth during retail storage is shown in Fig. 6 where the distribution of the total prediction of growth of E. coli O157:H7 in ground beef for different storage times in the 50 tested retail cabinets is presented. The estimated growth of E. coli O157:H7 for 1, 3, 5 and 7 days was only 0.04, 0.12, 0.22 and 0.31 log10 CFU/g, respectively. The 90th, 95th and 99th percentiles of pathogen's growth for 7 days of storage were 0.79, 1.16 and 1.71 log10 CFU/g, respectively (Table 2). The storage conditions throughout the ground beef cold chain were important factors affecting the level of pathogen at the time of consumption and thus the risk to consumers. Most available risk assessments do not take into account the effect of food transportation from retail outlets to domestic refrigerators mainly due to the lack of data (Signorini & Tarabla, 2009). In the present study, electronic temperature – monitoring data loggers were

Table 5 Percentiles of predicted Escherichia coli O157:H7 growth in ground beef during storage for 5 days at retail, transportation from retail cabinets to domestic refrigerators over a period of 6 h and storage for 1 day at domestic refrigerator. Predicted growth is based on the dynamic temperature profiles collected in the Greek chill chain. Growth of E. coli O157:H7 (log10 CFU/g) Percentile

1 5 10 50 90 95 99

Retail (5 days)

0.00 0.00 0.01 0.08 0.62 0.88 1.10

Retail to domestic (6 h)

0.03 0.04 0.07 0.15 0.29 0.36 0.43

Domestic (1 day)

Total

Upper shelf

Middle shelf

Lower shelf

Upper shelf

Middle shelf

Lower shelf

0.00 0.00 0.02 0.15 0.65 0.92 1.27

0.00 0.00 0.01 0.08 0.34 0.53 0.92

0.00 0.00 0.00 0.10 0.58 0.72 1.24

0.03 0.04 0.10 0.37 1.56 2.15 2.80

0.03 0.04 0.09 0.31 1.25 1.77 2.45

0.03 0.04 0.09 0.32 1.48 1.95 2.77

Each bold number for each percentile corresponds to the sum of retail(5d)+retail to domestic(6h)+domestic(1) for the upper,middle and lower shelf. 597

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Table 6 Percentiles of predicted Escherichia coli O157:H7 growth in ground beef during storage for 3 days at retail, transportation from retail cabinets to domestic refrigerators over a period of 6 h and storage for 3 days at domestic refrigerator. Predicted growth is based on the dynamic temperature profiles collected in the Greek chill chain. Growth of E. coli O157:H7 (log10 CFU/g) Percentile

Retail (3 days)

1 5 10 50 90 95 99

Retail to domestic (6 h)

0.00 0.00 0.00 0.04 0.36 0.42 0.58

Domestic (3 days)

Total

Upper shelf

Middle shelf

Lower shelf

Upper shelf

Middle shelf

Lowershelf

0.00 0.01 0.06 0.44 1.96 2.75 3.82

0.00 0.00 0.02 0.24 1.03 1.60 2.75

0.00 0.00 0.01 0.29 1.73 2.15 3.71

0.03 0.04 0.13 0.63 2.61 3.53 4.83

0.03 0.04 0.10 0.44 1.68 2.38 3.76

0.03 0.04 0.09 0.48 2.38 2.93 4.72

0.03 0.04 0.07 0.15 0.29 0.36 0.43

Each bold number for each percentile corresponds to the sum of retail(5d)+retail to domestic(6h)+domestic(1) for the upper,middle and lower shelf. 1.0

1.0

5th Day

0.8

Percentiles

Percentiles

0.8

7th Day

0.6 0.4 0.2

Growth based on Temperature Profile 0.0

0.3

0.6

0.9

1.2

0.4 0.2

Growth Based on Mean Temperature

0.0

0.6

Growth Based on Mean Temperature Growth based on Temperature Profile

0.0 1.5

0.0

Growth (log10 CFU/g)

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

Growth (log10 CFU/g)

Fig. 11. Cumulative distributions of predicted Escherichia coli O157:H7 growth in ground beef during retail storage for 5 and 7 days, based on the dynamic temperature profile and average value of dynamic temperature profile.

CFU/g, with an average growth to 0.15 log10 CFU/g, while the growth of the pathogen in the lower shelf ranged between 0.00 and 2.30 log10 CFU/g, with an average growth to 0.20 log10 CFU/g. The 90th, 95th and 99th percentiles of growth during domestic storage of 1 day are presented in Table 4. Tables 5 and 6 present the overall growth of E.coli O157:H7 (log10 CFU/g) in the chill chain using different scenarios: (a) storage of ground beef at retail for 5 days, transportation from retail to domestic refrigerator over a period of 6 h and storage in domestic refrigerator for 1 day (Table 5); (b) storage of ground beef in retail for 3 days, transportation from retail domestic refrigerators over a period of 6 h and storage in domestic refrigerators for 3 days (Table 6). Comparing the results from Tables 5 and 6, it is obvious that the second scenario with the increased storage time in the domestic refrigerators resulted in a significantly higher total growth of the pathogen with the 99th percentile of the total growth being almost 2 log10 CFU/g higher for the upper and lower shelf compared to first scenario. This can be attributed to the higher temperature of domestic refrigerators in Greece compared to retail cabinets and indicates the important contribution of domestic storage in the total growth of the pathogens. Most available risk assessment of E.coli O157:H7 in ground beef indicate that growth of the pathogen during storage is among the most important factors affecting the final risk (Cassin et al., 1998; Signorini & Tarabla, 2009; Smith et al., 2013). Cassin et al. (1998) reported that the average probability of illness was predicted to be reduced by 80% under a hypothetical mitigation strategy directed at reducing microbial growth during storage through a reduction in storage temperature. They also stated that the latter strategy was predicted to be more effective than others tested such as a hypothetical intervention which estimated a plausible reduction in the concentration of E. coli O157:H7 in the feces of cattle shedding the pathogen and one aimed at

convincing consumers to cook hamburgers more thoroughly. Signorini and Tarabla (2009) reported that the risk of E.coli O157:H7 infection and HUS related to the consumption of ground beef were most sensitive to the type of storage at home (r = − 0.416), slaughterhouse storage temperature (r = 0.240) and bacterial concentration in the cattle hide (r = 0.239). They also showed that there was an association between home preparation of hamburgers (r = − 0.116) and the risk of illness, although this was a result of the type of storage at retail (r = − 0.110) and at home and not their intrinsic characteristics. Considering the impact of growth during storage in the final risk, the accuracy of the predicted growth in a risk assessment model is of great importance for realistic risk outputs. In most risk assessment studies growth is predicted based on the assumption that temperature during storage is constant using the average value. As shown in the present study, however, temperature during retail storage, transportation from retail to domestic and domestic storage may show significant fluctuations. In the present study a comparison between the growth of E.coli O157:H7 during domestic storage predicted based on the dynamic profiles of the 50 retail cabinets and the growth predicted based on the average value of the profiles was performed. Fig. 11 presents the cumulative distributions of the prediction of the total growth for the above comparison. As shown, prediction of growth based on the average temperature is significantly lower and less variable. For example, the 95th percentile of growth after storage at retail for 7 days was 0.7 log10 CFU/g when predicted based on the average temperature and 1.2 log10 CFU/g when predicted based on the temperature profiles (Table 7). These results are in agreement with Rajkowski and Marmer (1995) who reported that the use of mid – point temperatures in a fluctuating regime in a predictive model for E.coli O157:H7 resulted in underestimation of total growth. Most of the available data on retail and domestic storage 598

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Table 7 Comparison between predicted growth of Escherichia coli O157:H7 in ground beef during storage for 5 and 7 days at retail based on the dynamic temperature profiles and the average value of the profiles.

Buncic, S., Nychas, G.-J., Lee, M. R., Koutsoumanis, K., Hébraud, M., Desvaux, M., ... Antic, D. (2014). Microbial pathogen control in the beef chain: Recent research advances. Meat Science, 97(3), 288–297. https://doi.org/10.1016/j.meatsci.2013.04. 040. Byrne, C. M., Bolton, D. J., Sheridan, J. J., Blair, I. S., & McDowell, D. A. (2002). The effect of commercial production and product formulation stresses on the heat resistance of Escherichia coli O157:H7 (NCTC 12900) in beef burgers. International Journal of Food Microbiology, 79(3), 183–192. https://doi.org/10.1016/S01681605(02)00120-4. Cassin, M. H., Lammerding, A. M., Todd, E. C., Ross, W., & McColl, R. S. (1998). Quantitative risk assessment for Escherichia coli O157: H7 in ground beef hamburgers. International Journal of Food Microbiology, 41(1), 21–44. https://doi.org/10.1016/ S0168-1605(98)00028-2. CDC (Centers for Disease Control and Prevention). Multistate outbreak of Shiga toxin-producing Escherichia coli O157:H7 infections linked to ground beef (final update). (2014). Retrieved from https://www.cdc.gov/ecoli/2014/O157H7-05-14/index.html (accessed June 20, 2014). CDC (Centers for Disease Control and Prevention). Multistate outbreak of Shiga toxin-producing Escherichia coli O157:H7 infections linked to beef products produced by Adams farm (final update). (2016). Retrieved from https://www.cdc.gov/ecoli/2016/o157h7-0916/index.html (accessed October 19, 2016). CDC (Centers for Disease Control and Prevention). Reports of selected E. coli outbreak investigations. (2018). Retrieved from https://www.cdc.gov/ecoli/outbreaks.html (accessed March 13, 2018). Dalgaard, P., & Jørgensen, L. V. (1998). Predicted and observed growth of Listeria monocytogenes in seafood challenge tests and in naturally contaminated cold-smoked salmon. International Journal of Food Microbiology, 40(1–2), 105–115. https://doi. org/10.1016/S0168-1605(98)00019-1. Doyle, M. P., & Schoeni, J. L. (1984). Survival and growth characteristics of Escherichia coli associated with hemorrhagic colitis. Applied and Environmental Microbiology, 48(4), 855–856. FAO/WHO (Food and Agriculture Organisation of the United Nations/World Health Organisation) (2006). Food safety risk analysis: A guide for national food safety authorities. FAO Food and Nutrition Paper, 87, Rome, Italy. te Giffel, M. C., & Zwietering, M. H. (1999). Validation of predictive models describing the growth of Listeria monocytogenes. International Journal of Food Microbiology, 46(2), 135–149. https://doi.org/10.1016/S0168-1605(98)00189-5. Kennedy, J., Jackson, V., Blair, I. S., McDowell, D. A., Cowan, C., & Bolton, D. J. (2005). Food safety knowledge of consumers and the microbiological and temperature status of their refrigerators. Journal of Food Protection, 68(7), 1421–1430. https://doi.org/ 10.4315/0362-028X-68.7.1421. Koutsoumanis, K., Pavlis, A., Nychas, G.-J. E., & Xanthiakos, K. (2010). Probabilistic model for Listeria monocytogenes growth during distribution, retail storage, and domestic storage of pasteurized milk. Applied and Environmental Microbiology, 76(7), 2181–2191. https://doi.org/10.1128/AEM.02430-09. Koutsoumanis, K., Stamatiou, A., Skandamis, P., & Nychas, G.-J. (2006). Development of a microbial model for the combined effect of temperature and pH on spoilage of ground meat, and validation of the model under dynamic temperature conditions. Applied and Environmental Microbiology, 72(1), 124–134. https://doi.org/10.1128/ AEM.72.1.124-134.2006. Laguerre, O., Derens, E., & Palagos, B. (2002). Study of domestic refrigerator temperature and analysis of factors affecting temperature: A French survey. International Journal of Refrigeration, 25(5), 653–659. https://doi.org/10.1016/S0140-7007(01)00047-0. Leyer, G. J., Wang, L.-L., & Johnson, E. A. (1995). Acid adaptation of Escherichia coli O157: H7 increases survival in acidic foods. Applied and Environmental Microbiology, 61(10), 3752–3755. Likar, K., & Jevšnik, M. (2006). Cold chain maintaining in food trade. Food Control, 17(2), 108–113. https://doi.org/10.1016/j.foodcont.2004.09.009. Loukiadis, E., Bièche-Terrier, C., Malayrat, C., Ferré, F., Cartier, P., & Augustin, J.-C. (2017). Distribution of Escherichia coli O157: H7 in ground beef: Assessing the clustering intensity for an industrial-scale grinder and a low and localized initial contamination. International Journal of Food Microbiology, 250, 75–81. https://doi.org/ 10.1016/j.ijfoodmicro.2017.03.009. Pierre, O. (1996). Temperature de conservation de certaines denrees alimentaires tres perissables dans les rayons libre service des grandes et moyenne surfaces. Option Qualite, 138, 12–18. Pin, C., Sutherland, J. P., & Baranyi, J. (1999). Validating predictive models of food spoilage organisms. Journal of Applied Microbiology, 87(4), 491–499. https://doi.org/ 10.1046/j.1365-2672.1999.00838.x. Rajkowski, K. T., & Marmer, B. S. (1995). Growth of Escherichia coli O157: H7 at fluctuating incubation temperatures. Journal of Food Protection, 58(12), 1307–1313. https://doi.org/10.4315/0362-028X-58.12.1307. Ratkowsky, D. A. (2004). Model fitting and uncertainty. In R. C. McKellar, & X. Lu (Eds.). Modelling microbial responses in food (pp. 151–196). Boca Raton, FL: CRC Press. Riley, L. W., Remis, R. S., Helgerson, S. D., McGee, H. B., Wells, J. G., Davis, B. R., ... Hargrett, N. T. (1983). Hemorrhagic colitis associated with a rare Escherichia coli serotype. New England Journal of Medicine, 308(12), 681–685. https://doi.org/10. 1056/NEJM198303243081203. Rosso, L., Lobry, J., & Flandrois, J. (1993). An unexpected correlation between cardinal temperatures of microbial growth highlighted by a new model. Journal of Theoretical Biology, 162(4), 447–463. https://doi.org/10.1006/jtbi.1993.1099. Salter, M. A., Ross, T., & McMeekin, T. A. (1998). Applicability of a model for non-pathogenic Escherichia coli for predicting the growth of pathogenic Escherichia coli. Journal of Applied Microbiology, 85(2), 357–364. Signorini, M., & Tarabla, H. (2009). Quantitative risk assessment for verocytotoxigenic Escherichia coli in ground beef hamburgers in Argentina. International Journal of Food

Growth of E. coli O157:H7 (log10 CFU/g) Percentile (%)

5th day

7th day

T profile

Average T

T profile

Average T

0.00 0.00 0.01 0.08 0.62 0.88 1.10

0.00 0.00 0.00 0.00 0.45 0.53 0.78

0.01 0.03 0.03 0.15 0.79 1.16 1.71

0.00 0.00 0.00 0.00 0.52 0.72 1.18

1 5 10 50 90 95 99

temperature conditions refer to environmental (air) temperature (Kennedy et al., 2005; Koutsoumanis et al., 2010; Laguerre, Derens, & Palagos, 2002; Taoukis et al., 2016). In general it is expected that product's temperature profiles are smoother than air temperature. Depending on the profile, using air temperature for predicting microbial growth may lead to under- or over – estimation of growth. On the other hand, as shown in Fig. 11, prediction of growth using the average temperature may lead to under – estimation of growth. The main reason for this is that the average temperature may be lower than the minimum temperature for growth while growth may actually occur for periods of the profile where temperature is high. That was the case of 29 out of 50 retail temperature profiles obtained in the present study for which the average temperature (for 7 days of storage) was below the Tmin value (3.36 °C) estimated for E. coli O157:H7, while prediction based on the profile was up to 0.3 log CFU/g. However, the impact of the above difference on the final risk is to be assessed using a risk assessment model. Based on the above, it is clear that further research is required to assess the impact of temperature data use in predicting microbial growth based on comparative evaluation of air vs product temperature and dynamic profile vs average temperature of storage conditions. In conclusion, the present study presents the development of a predictive model for the effect of storage temperature on the growth of E. coli O157:H7 in raw ground beef. The model was combined with temperature data of the Greek chill chain (retail, domestic, transportation from retail to domestic) to assess the total growth of the pathogen by taking into variability the storage conditions. The data and models provided can be further used in a quantitative risk assessment model of E. coli O157:H7 in ground beef consumed in Greece. Acknowledgments This study has been carried out with the financial support of the Commission of the European Communities, Project ProSafeBeef “FoodCT-2006-36241”. It does not necessarily reflect the Commission's views and in no way anticipates its future policy in this area. References Baranyi, J., & Roberts, T. A. (1994). A dynamic approach to predicting bacterial growth in food. International Journal of Food Microbiology, 23(3–4), 277–294. https://doi.org/ 10.1016/0168-1605(94)90157-0. Baranyi, J., Robinson, T. P., Kaloti, A., & Mackey, B. M. (1995). Predicting growth of Brochothrix thermosphacta at changing temperature. International Journal of Food Microbiology, 27(1), 61–75. https://doi.org/10.1016/0168-1605(94)00154-X. Bovill, R. A., Bew, J., & Baranyi, J. (2001). Measurements and predictions of growth for Listeria monocytogenes and Salmonella during fluctuating temperature: II. Rapidly changing temperatures. International Journal of Food Microbiology, 67(1–2), 131–137. https://doi.org/10.1016/S0168-1605(01)00446-9. Buchanan, R. L., Bagi, L. K., Goins, R. V., & Phillips, J. G. (1993). Response surface models for the growth kinetics of Escherichia coli O157:H7. Food Microbiology, 10(4), 303–315. https://doi.org/10.1006/fmic.1993.1035.

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