Predictive modelling of inactivation of Listeria spp. in bovine milk during high-temperature short-time pasteurization

International Journal of Food Microbiology 39 (1998) 167–173

Predictive modelling of inactivation of Listeria spp. in bovine milk during high-temperature short-time pasteurization a,b

a

P. Piyasena , S. Liou , R.C. McKellar b

a ,b ,

*

a Centre for Food and Animal Research, Agriculture and Agri-Food Canada, Ottawa, ON K1 A 0 C6, Canada Southern Crop Protection and Food Research Centre – Food Research Program, Agriculture and Agri-Food Canada, 95 Stone Road West, P.O. Box 3650, Guelph, ON N1 H 8 J7, Canada

Received 14 February 1997; received in revised form 20 October 1997; accepted 11 November 1997

Abstract A linear model was derived to describe the thermal inactivation of Listeria innocua in bovine whole milk in a high-temperature short-time pilot scale pasteurizer. Integrated lethal effect, or pasteurization effect (PE), was obtained by converting times at different temperatures in the various sections of the pasteurizer to the equivalent time at the reference temperature (728C). PE was then related by a simple linear function to the log 10 of the % viable counts with a power transformation of the PE values to improve the linear fit. R 2 values for the five L. innocua trials varied from 0.728 to 0.974. Validation of this model with Listeria monocytogenes confirmed that L. monocytogenes was more heat sensitive. Inter-trial variation was incorporated into the model using the @RISK TM simulation software. Output from simulations confirmed that pasteurization at the IDF standard conditions of 728C for 15 sec can ensure at least an 11-log reduction of L. monocytogenes. The results showed that L. innocua may be used as a model microorganism to assess the thermal inactivation of L. monocytogenes, since its heat resistance is at least equal to or greater than that of the pathogenic species.  1998 Elsevier Science B.V. Keywords: Listeria; Innocua; Monocytogenes; High-temperature short-time; Pasteurization; Model

1. Introduction Listeria monocytogenes is of considerable concern to milk processors due to its presence in raw milk supplies and greater heat resistance relative to other food-borne pathogens (Griffiths, 1989; Farber and Peterkin, 1991). While there is general consensus *Corresponding author. Tel.: 11 5197676229; fax: 11 5197676334; e-mail: [email protected]

that L. monocytogenes does not survive proper pasteurization (Mackey and Bratchell, 1989; Farber and Peterkin, 1991), survival of this pathogen during thermal treatments is enhanced by prior exposure to environmental stress (Farber and Peterkin, 1991; Farber et al., 1992; Lou and Yousef, 1996) and recovery improved by thorough resuscitation techniques (Farber and Peterkin, 1991; Mendonca and Knabel, 1994; Patel and Beuchat, 1995). These findings support concerns regarding the effectiveness

0168-1605 / 98 / $19.00  1998 Elsevier Science B.V. All rights reserved. PII S0168-1605( 97 )00131-1

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of sub-pasteurization and pasteurization techniques against L. monocytogenes (D’Aoust, 1989). There is a need to establish appropriate processing conditions for milk and dairy products to reduce the risk posed by L. monocytogenes (Farber and Peterkin, 1991; Griffiths, 1989; Mackey and Bratchell, 1989). Batch methods for determining D-values of pathogens cannot be easily extrapolated to continuous processes such as high-temperature short-time (HTST) pasteurization, since the former do not take into account the possible effects of shear force and other physical stresses (Swartzel, 1984; Mackey and Bratchell, 1989; Fairchild et al., 1994). In earlier studies on the thermal stability of L. monocytogenes during HTST processing, we demonstrated that L. monocytogenes could not be recovered from whole milk after treatment at $ 698C for 16 s (Farber et al., 1988, 1992). Subsequently, we have focused on the development of novel mathematical models to describe the thermal inactivation of milk enzymes and food-borne pathogens in a pilot scale HTST pasteurizer. Models developed to date relate the logarithm of residual activity of several bovine milk enzymes to the pasteurization effect (PE). PE for each section of the pasteurizer was determined by converting time at the indicated temperature to the equivalent time at the reference temperature (728C) using the empirical Arrhenius equation as described in earlier publications (McKellar et al., 1994a; Hirvi et al., 1996; McKellar et al., 1996). The present study extends the previous work by: (1) developing a mathematical model for the continuous thermal inactivation of Listeria innocua as a model system; (2) validating the L. innocua model using experimental data from L. monocytogenes inactivation; and (3) applying the techniques of risk assessment to quantify variability of the model parameters and output.

2. Materials and methods

2.1. Strains and culture conditions L. innocua strain LA-1 and L. monocytogenes Scott A were maintained in glycerol at 2 208C and propagated on Tryptic Soy Broth containing 0.6% (w / v) Yeast Extract (TSBYE; Difco Laboratories, Detroit, MI). Strains were transferred twice into TSBYE at 308C for 24 h, then inoculated into 20 l of

TSBYE at 308C for 24 h. The cultures were concentrated to approximately 800 ml using a Pellicon filtration system with a HVMP000C5 0.45 mm filter (Millipore Corp. Bedford, MA), and stored overnight at 48C. The use of cold-adapted, stationary phase cells was intended to more closely resemble the natural environment to which Listeria spp. might be exposed.

2.2. Milk processing Design and operation of the HTST pasteurizer, and source of milk were described previously (McKellar et al., 1994a, 1996). Two Mueller tanks each containing 200 l whole milk were heated to 808C for 1 h. Each tank was inoculated with 400 ml of culture concentrate (to approximately 10 8 cfu / ml) as well as 100 ml of the dye Fast Green FCF (Sigma Chemical Co., St. Louis, MO) in distilled H 2 O (1% w / v) as a marker for inoculated milk. The temperature range studied was 60.5–69.58C at 0.58C increments. Holding tubes used in this study were nominally 3, 10, 16, 30 and 60 s; accurate determinations of holding times were made using the salt test as described previously (McKellar et al., 1994a; Hirvi et al., 1996; McKellar et al., 1996). Temperatures within the various sections of the pasteurizer were monitored using thermocouples and recorded using a Digistrip II recorder (Model DR-IA; Kaye Instruments Inc., Bedford, MA) as described previously (McKellar et al., 1994a; Hirvi et al., 1996; McKellar et al., 1996). For each temperature and holding tube, raw, uninoculated milk was run through the system until the desired temperature had been attained. The system was then switched over to inoculated milk, and a sample was taken after the temperature had equilibrated. Appropriate dilutions of the samples were surface plated onto TSAYE and incubated at 308C for 72 h. Random colonies were picked and examined microscopically to confirm the presence of Listeria spp.

2.3. Data analysis Calculation of PE and derivation of linear models were carried out as described previously (McKellar et al., 1994a; Hirvi et al., 1996; McKellar et al., 1996). The program to calculate PE was written in

P. Piyasana et al. / International Journal of Food Microbiology 39 (1998) 167 – 173

VisualBasic (Microsoft Corporation, Redmond, Washington). PE for each section of the pasteurizer was determined by converting time (t) at the indicated temperature (T ) to the equivalent time at the reference temperature (728C) using the empirical Arrhenius equation (Kessler, 1986; McKellar et al., 1994a): 1 PE 5 ] t0

E e s ds E

a 2 ] R

1 1 ]2 ] T T0

d dt

(1)

where: Ea 5energy of activation J / mol; R58.314 J / mol K; T5Temperature, K; T 0 5Reference temperature, 345 K; t5Time, s; t 0 5Reference time, 15 s. Thus, a PE of 1.0 corresponds to full pasteurization as defined by the IDF (728C for 15 s). The modelling process involved iterative selection of the best Ea / R value from an input range (usually 60 000 to 80 000) to minimize the error sum of squares (ESS) of the regression of log 10 % initial activity against PE. A power transformation (PE c where c50.2 to 1.0) was also included as part of the model selection process to obtain the optimum linear fit. A linear model for L. innocua was derived from five independent trials, and the model was validated using three independent trials conducted with L. monocytogenes. The model was of the form: log 10 % initial activity 5 intercept 1 slope 3 PE c where c was fixed at 0.8. There was some inter-trial

169

variability in the power transformation parameter with L. innocua. It was necessary to fit a single value of c to all the trials so that they could be grouped on the same graph. The mean value of c from the five L. innocua was chosen. The model provides a single output value for each set of processing conditions, but does not take into account inter-trial variability. In order to incorporate variability into the model, the risk analysis software @RISK TM V3.1a (Palisade Corporation, Newfield, NY), a Lotus 1-2-3W add-in, was used. @RISK TM expresses model parameters as distributions, and when simulations are performed, outputs are calculated as distributions. Thus, a range of probable output (e.g., survival) values for a specified set of processing conditions are obtained, and the probability of achieving a target log reduction can be estimated. A spreadsheet was prepared which contained the model and calculations of PE and log reduction which had been previously incorporated in the program PasTime (McKellar et al., 1994b). Model parameters (Ea /R, intercept and slope) were entered into the spreadsheet as normal distributions with mean and standard deviation values taken from Table 1. Parameter estimates from the five L. innocua trials were interdependent; significant correlations were observed between Ea /R and slope (r 2 50.647) and intercept (r 2 50.240). @RISK TM simulations were adjusted to include these correlations. Latin hypercube is a recent development in sampling technology which employs stratification of the

Table 1 Listeria innocua – Derivation of Model Trial

ESS

MESS

r2

c

Intercept

SD

Slope

SD

Ea /R

n

A B C D E

1.99 2.16 0.459 3.44 1.06

0.133 0.080 0.020 0.127 0.040

0.728 0.778 0.974 0.812 0.955

0.80 0.80 0.80 0.80 0.80

2.34 1.82 1.33 1.82 2.00

0.746 0.312 0.395 0.651 0.444

220.2 238.7 219.8 227.4 218.7

13.7 13.7 5.32 12.2 2.49

52,000 69,500 61,000 69,500 52,500

18 29 30 30 30

Avg. S.D.

1.86 0.366

log 10 % initial activity5intercept1slope3PE c , where c is fixed. ESS5Error Sum of Squares. MESS5Mean Error Sum of Squares (ESS /n23 for three degrees of freedom). r 2 5Coefficient of determination. Ea 5Activation Energy (J / mol). R5Universal Gas Constant (8.314 J / mol K). n5Number of Samples.

224.9 8.41

60.9 8.6

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input probability distributions, resulting in fewer iterations than the traditional Monte Carlo method (Palisade Corporation, 1995). Latin hypercube simulations were performed using temperatures of 67, 69.5, and (by extrapolation) 728C with a 16 s holding time, and a total of 1500 iterations were performed for each replicate simulation. Latin hypercube simulations were also performed using times and temperatures taken from the three L. monocytogenes trials. The temperatures were taken from the thermocouple readings at the end of the holding tube, with the time taken from the corresponding holding tube. A total of 82 time / temperature combinations were analyzed. Three replicate simulations were performed for each trial, and a total of 1500 iterations were performed for each replicate simulation.

and d-glutamyl transpeptidase (TP) (McKellar et al., 1996), and catalase (CA) (Hirvi et al., 1996). This might be due to the expected greater variation in heat stability found with microorganisms compared to enzymes. A combined linear model was derived using the average parameter values from the individual trials (Table 1). The L. innocua model was used to predict log reductions based on times and temperatures from each of the three L. monocytogenes trials. Regressed log (experimental) values were plotted against log(model) values and the slopes and the intercepts were compared (Fig. 2). Results from three trials with L. monocytogenes correlated well with the L. innocua model (Table 2). Slopes for each validation trial

3. Results Five independent trials were performed with L. innocua, and the results for the corresponding linear models are presented in Table 1. Linear models were derived for each trial and the average c value (0.8) was used to give the best fit. A scatter diagram of one trial is presented in Fig. 1. Significant inter-trial variation was noted. In particular, the variation in the slope parameter was considerably greater than was found for earlier models for alkaline phosphatase (AP) (McKellar et al., 1994a), lactoperoxidase (LP) Fig. 2. Validation of L. innocua model using data from a single Listeria monocytogenes trial.

Table 2 Listeria monocytogenes – Validation of Model Trial

ESS

MESS

r2

Intercept

Slope

n

F G H

8.83 43.5 21.4

0.315 1.55 0.764

0.802 0.812 0.789

20.207 21.19 20.720

0.978 1.04 0.942

30 30 30

20.706 0.492

0.987 0.051

Avg. S.D.

Fig. 1. Derivation of linear model for Listeria innocua using a single trial.

Regressed log(exp)5intercept1slope3log(model) ESS5Error Sum of Squares. MESS5Mean Error Sum of Squares (ESS /n22 for two degrees of freedom). r 2 5Correlation Coefficient. n5Number of Samples.

P. Piyasana et al. / International Journal of Food Microbiology 39 (1998) 167 – 173

were similar; however, intercepts varied considerably. Intercept values ,0 indicate that L. monocytogenes was more heat sensitive than L. innocua. It is clear that all points are below the line of equivalance, indicating that the experimental log reductions were greater than predicted by the L. innocua model. A Lotus 1-2-3 Version 5.0 spreadsheet was designed which incorporated calculations of PE and subsequent log reduction values using average parameter estimates (Table 1). Parameters were entered as @RISK TM normal distributions, and simulations were performed using times and temperatures taken from the three L. monocytogenes trials. Experimental L. monocytogenes log reductions were compared to

Table 3 Validation of Listeria innocua model using @RISK TM simulations with Listeria monocytogenes Percentile a

Number of Failures b Trial F (n530)

5 10 15 20 25 30 35 40 45 50

Trial G (n526)

Trial H (n526)

1c

2

3

1

2

3

1

2

3

0 0 2 3 5 7 9 11 15 19

0 0 2 3 5 7 10 12 18 22

0 0 3 4 7 8 10 13 18 21

0 0 1 1 1 1 2 2 2 2

0 0 1 1 1 1 2 2 2 2

0 0 1 1 1 1 2 2 2 2

0 0 0 1 1 2 2 3 3 3

0 0 0 0 1 2 2 2 3 3

0 0 0 1 1 2 2 2 3 3

a

Percentage of simulated values below the associated log reduction derived from the L. innocua model. b Instances where the experimental log reductions of L. monocytogenes were below the percentile values. c Replicate simulations.

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percentile values generated during simulation. Probability distributions generated by simulation were divided into equal probability increments called percentiles. Percentiles represent the percentage of generated results which are less than or equal to the associated log reduction. A failure was scored when the log reduction associated with a percentile was higher than the corresponding experimental log reduction (i.e., the model ‘failed dangerous’). Number of failures were totalled for each sample in each trial, and the results are presented in Table 3. For all trials, no failures were found at the 5 and 10 percentile, with the failure rate increasing to 22 / 30 at the 50 percentile with Trial F. Slight variation was noted between simulations for Trial F. There were fewer failures associated with Trials G and H, indicating that L. monocytogenes in these trials was considerably more heat sensitive, confirming the results from Table 2. Despite the variability between trials, the results suggest that the actual log reduction of L. monocytogenes will exceed the estimated log reduction associated with the 5th percentile. A 95% confidence interval was selected as an example; in general, higher confidence intervals would be required for risk analysis. Table 4 shows the results of simulations performed with some important temperatures, with a 16 s holding time. At 678C, an average log reduction for L. innocua of .4 was predicted by the model; however, the 95% confidence limits predict slightly greater than 1-log reduction. Increasing the temperature to 69.58C ensures that a 4-log reduction can be achieved with 95% confidence. At pasteurization conditions (728C for 16 s) there was a 95% probability of achieving a log reduction of .11. Further information can be obtained from the cumulative probability distribution for 728C for 16 s (Fig. 3).

Table 4 Examples of predictions made from @RISK TM simulations a Temperature (8C)

Average log reduction

95% confidence b

67 69.5 72

4.17 11.6 28.1

1.29 4.53 11.4

a b

All simulations were performed using a 16 s holding time. Log reduction achieved by 95% of the iterations (1500 total).

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Fig. 3. Cumulative probability distribution for 728C for 16 s holding conditions predicted by the L. innocua model.

Under these processing conditions, there was a 50% probability of at least a 28-log reduction of L. innocua.

4. Discussion The present study has confirmed our earlier work (Farber et al., 1992, 1988) in which we demonstrated that L. monocytogenes was not detected after HTST processing at .698C for 16 s. Simulations carried out with @RISK TM showed that these pasteurization conditions can ensure a .11-log reduction, in contrast to the results of Mackey and Bratchell (1989) who estimated a 5.2 D reduction for 71.78C for 15 s using a slug flow heat exchanger. In a recent review, Farber and Peterkin (1991) discussed discrepancies in reported values for thermal tolerance of L. monocytogenes. These authors reported that the heat-shock response exhibited by a pathogen might lead to dramatically increased heat resistance, while improved techniques for resuscitating heat-injured microorganisms would increase recovery. In support of these suggestions, Farber et al. (1992) demonstrated that L. monocytogenes grown at elevated temperatures (.308C) exhibited increased heat resistance. This same study was unable to establish a statistically significant improvement in recovery using anaerobic incubation. Thus, the apparent reduced heat resistance noted in the present study may be due to growth of L. monocytogenes at 308C, and the absence of any resuscitation methods. Considerable inter-trial variability was noted with

the parameters of the linear model. Earlier models developed for milk enzymes (McKellar et al., 1994a; Hirvi et al., 1996; McKellar et al., 1996) showed little variation between model development trials, and validation trials were in good agreement with derived models. Significant variability in heat resistance of microorganisms is not unusual, and has been confirmed in other studies on survival of Enterococcus faecium during HTST pasteurization (unpublished data). It is therefore difficult to validate foodborne pathogen models in the manner employed for milk enzyme models (McKellar et al., 1994a; Hirvi et al., 1996; McKellar et al., 1996). We chose to validate the L. innocua model using data from trials performed with L. monocytogenes. Simulations based on the L. innocua model were carried out using @RISK TM , with holding times and temperatures taken from the L. monocytogenes trials. Predicted log reductions were compared to experimental results. The model was considered to have failed when a simulated log reduction associated with a particular percentile over-predicted the actual log reduction. It has been reported that L. innocua is more heat resistant than L. monocytogenes (Foegeding and Stanley, 1991), and in agreement with this, no failures were reported at the lower percentiles. Thus, a simulated value corresponding to the 5th or 10th percentile will consistently under predict actual log reductions of L. monocytogenes. It has been proposed that L. innocua be used as a biological indicator for L. monocytogenes (Fairchild and Foegeding, 1993), with the higher heat resistance of L. innocua providing a margin of safety for a

P. Piyasana et al. / International Journal of Food Microbiology 39 (1998) 167 – 173

milk processor. Earlier results (McKellar, 1996), as well as those of the present study confirm these findings, and support the use of L. innocua strains as biological indicators of L. monocytogenes in milk processing experiments. The use of risk analysis software can extend the utility of predictive models by incorporating experimental variation into predictions. The present results have demonstrated that use of simulation models may provide an additional measure of confidence by expressing the output in terms of probability. The 95% confidence limits (5th percentile) from the L. innocua model define the extent of a conservative model which underestimates the thermal inactivation of L. monocytogenes (i.e. is ‘failsafe’). Thus, this procedure provides the processor with information to facilitate decisions based on the probability of a specific pathogen surviving a given thermal process.

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