Modelling of the microbiological quality of meat

PAPERS

Modelling of the microbiological quality of meat

M.L.T. Muermans”?, F.K. Stekelenburg*, M.H. Zwietering” and J.H.J. Huis in ‘t Veldt$

An alternative to challenge tests for the assessment of the shelf-life of food products is predictive microbiology, the development of mathematical models that describe the influence of predominant controlling factors (such as temperature, water activity and pH) on the lag phase and the growth rate of microorganisms. In this paper, modifications of the square-root model are tested to predict the relationship between growth rate and temperature, and between lag phase and temperature, of spoilage organisms growing in a vacuum-packed, cooked meat product and on aerobically packed fresh meat. The emphasis of the study was on examining the growth behaviour of the spoilage flora in the meat product, and on fresh meat rather than in liquid media. Results show that the square-root model in its modified forms can indeed be used to describe the effect of storage temperature on the growth rate and the lag phase of the organisms involved. Although predictions of the models have to be validated in practical situations, predictive microbiology has been shown to be a promising technique for the estimation of a product’s shelf- life and the impact of any modification of a product’s formulation on both its safety and its shelf-life.

Keywords: spoilage; meat microbiology; temperature

products; meat; lactic acid bacteria;

INTRODUCTION

Microbial spoilage of foods is of great concern to producers, retailers and consumers. Growth of either pathogenic and spoilage organisms is unwanted with regard to food safety as well as from an economic point of view. Growth and metabolic activity of spoilage microorganisms is also one of the main causes of

‘University of Utrecht, Faculty of Veterinary Science, Department of the Science of Food of Animal Origin, PO Box 80.175, 3508 TD Utrecht, The Netherlands. *TN0 Nutrition and Food Research, PO Box 360, 3700 AJ Zeist, The Netherlands. m Agricultural University, Department of Food Science, PO Box 8129, 6700 EV Wageningen, The Netherlands. Presented at the International Food Technology Exposition and Conference (IFTEC), 15-18 November 1992, The Hague, The Netherlands. *To whom correspondence should be addressed at: TN0 Nutrition and Food Research, PO Box 360, 3700 AJ Zeist, The Netherlands

216 Food Control 1993 Volume 4 Number 4

Pseudomonas spp.; predictive

spoilage of meat and meat products, with spoilage being indicated by formation of off-odours, off- flavours, slime and, possibly, a discoloration of the meat. Generally, spoilage of cooked or fresh meats becomes evident when the total bacterial cell count exceeds 107/cm2 and 108/g, respectively (Hayes, 1985; Lambert et al., 1991). Which part of the initial micro- flora eventually causes spoilage depends on such product characteristics as pH, glucose content and a, value, and on storage conditions (temperature, gaseous atmosphere). Normally, under chilled storage conditions, the spoilage flora of aerobically packed meat mainly consists of Pseudomonas spp., while the spoilage flora of anaerobically packed meat mainly consists of lactic acid bacteria (von Holy ef al., 1991; Lambert et al., 1991).

Assessment of shelf-life is traditionally carried out in challenge tests, in which all parameters, such as the composition of food, packaging and temperature, are fixed. Shelf-life is estimated by determining the number

0956-7135/93/040216-06 0 1993 Butterworth-Heinemann Ltd

Modelling meat microbial quality: M. L. T. Muermans et al.

of microorganisms, mostly using classical microbiological methods. The result of a challenge test is only applicable to the specific product and circumstances tested: if one parameter is altered, the shelf-life of the ‘new’ product should be determined again. The challenge test is therefore very expensive and time-consuming (Baird-Parker and Kilsby, 1987), and the results are of limited use.

An alternative method to determine shelf-life of food products is predictive microbiology, the development of mathematical models that describe the influence of predominant controlling factors (such as temperature, pH, water activity, gaseous atmosphere and preservatives) on the lag phase and growth rate of pathogenic and spoilage organisms. The models are often based on laboratory experiments, in which the bacterial growth response to different controlling factors is measured. Subsequently, the model can be used to predict the growth response under conditions that were not originally tested. These predictions, however, can only be made through interpolation within the range of factors examined (Ross and McMeekin, 1991).

Predictive models can be used in a number of different ways, for example in the field of product development. New product formulations with the required microbiological stability can be developed by performing only a limited number of challenge tests. Furthermore, the consequences on shelf-life of a product reformulation can be predicted. In addition, a wide variety of product formulations can be tested by simulations, without the necessity to prepare all the product formulations and to carry out challenge tests. Mathematical models can also be used to predict the effect on shelf-life of different time-temperature com- binations during production and distribution. Product temperature histories can be monitored with temperature data loggers. The temperature history, in combination with knowledge of the characteristics of the product, can be used to assess the elapsed or remaining shelf-life of the product at any stage in the production and distribution process. Storage and distribution conditions which are most critical to growth of microorganisms can be idenfitied relatively easily (Gibbs and Williams, 1990; Gould, 1989).

Generally, predictive models are constructed on the basis of data obtained from experiments conducted in liquid laboratory media. In these media, the values of different factors can be controlled more easily than in food products. Furthermore, no interference of, for example, food components will occur. However, it is quite possible that the growth behaviour of the microorganisms in the laboratory medium differs from their behaviour in a food product. The growth rate, and especially the length of the lag phase in a food product, can be quite different from the values obtained in liquid media, even under the same environmental conditions. Therefore, the predictive value of developed models has to be validated in practical situations before they can be used for predictive purposes.

In the past ten years, several models have been developed that describe the influence of one or more controlling factors on the growth of microorganisms. One of these models, which describes the influence of one of the most important controlling factors namely temperature, is the square-root model of Ratkowsky et al. (1982). When temperature is between the minimum

and the optimum value for a microorganism to grow, the square-root model gives a linear relationship between the square-root of the growth rate constant (r) and the temperature (T):

X.6 = b, (T- T,,) (I)

where b, is a regression coefficient, and 7’,, is the theoretical temperature (in K) at which the growth rate is zero. T, is a notional temperature that cannot be determined experimentally, and is considered to be an intrinsic property of the microorganism. This means that for every microorganism or group of microorganisms, To is a fixed value that is independent of the growth conditions (Ratkowsky et al., 1982).

In Ratkowsky’s work, growth rate was measured as the reciprocal of the time to reach a certain level of turbidity. The square-root model can be modified to include the maximum specific growth rate (P,,,~~) instead of the growth constant (I):

The temperature Tmin in Equation (2) corresponds to To in Equation (1).

Ratkowsky et al. (1983) extended the square-root model to cover the whole temperature range for growth:

where b3 and c3 are regression coefficients, and Tmin

and Tmax are the minimum and maximum temperatures, respectively, at which the growth rate is zero.

Besides the maximum growth rate (p,,,,,), the length of the lag phase or lag time (A) of a spoilage organism is also of importance when considering the shelf-life of a food product. A model describing the length of the lag phase as a function of controlling factors is, therefore, also needed in shelf-life predictions.

Zwietering et al. (1991) modified the extended Ratkowsky model to describe the lag time (A) as a function of temperature (T):

In (A) = In{[b, (T- Tmin) { l-

cxp ]cd(T- Tmax>1>1~2~ (4)

where b4 and c4 are parameters, and Trnin and T,,, are the minimum and maximum temperatures, respectively where the growth rate is zero.

In analogy to the relation between the square-root model and the extended model of Ratkowsky (Equa- tions 1 and 3), Equation (4) can be rewritten as:

ln(A)=ln{[bS(T-T,in)]-2} (5)

for temperatures between the minimum and the optimum temperature for growth.

The work presented here involves a study under- taken to examine the application of the modified square-root model for the growth rate (Equation 2) and the lag phase (Equation 5) to describe the effect of temperature on growth of spoilage flora in vacuum- packed, cooked meat products and aerobically packed fresh meat. A meat product (a Bologna-type sausage) and fresh meat (beef) was used instead of liquid media in order to approach practical situations as much as possible.

Food Control 1993 Volume 4 Number 4 217


MATERIALS AND METHODS

Vacuum-packed cooked meat products

Preparation of Bologna-type sausage Bologna-type sausage was prepared according to a

standard recipe. To limit the number of controlling factors, no nitrite was added to the sausage. The pH of the sausage was 6.2. The sausage was filled into cans and pasteurized in water of 78°C until a core temperature of 70°C was maintained for at least two minutes. After pasteurization, the cans were stored at 0°C until use.

Preparation of inoculum The Bologna-type sausage was inoculated with a

pure culture of a Lactobacillus curvatus. This culture was isolated from a spoiled sample of vacuum-packed cooked ham, and is one of the predominant Lacto- bacillus spp. in spoiled, vacuum-packed, cooked meat products. Before the start of the experiment, the deep- frozen culture (-40°C) was defrosted and cultivated twice at 30°C in MRS broth (Oxoid, code CM 359) for 24 hours. An appropriate dilution of this culture was used to inoculate the Bologna-type sausage.

Inoculation of the sausage The sausage was placed in a disinfected laboratorium

cutter (Stephanal, type FA.30), inoculated and minced for 2 min. In this way, the inoculated bacteria were distributed homogeneously over the sausage. The initial level in the sausage was 104c.f.u./g. Subse- quently, single packages of 40-5Og were prepared, vacuum-packed in a foil with an oxygen permeability of 1.5cm3m-2bar-’ d-i at 2O”C, and stored at 0, 3, 7, 15 or 25°C.

Microbiological analysis At different time intervals, varying with the storage

temperature, duplicate samples were taken. Growth of lactic acid bacteria was measured using the Man- Rogosa-Sharpe Agar (MRSA, Oxoid, code CM 361). Spread plates were incubated anaerobically (BBL, Gaspak plus) at 3O”C, and counted after 3 days.

Aerobically packed fresh meat

Preparation of the meat samples Fresh beef (eye of round) with a pH of 5.6 f 0.2 was

obtained from a slaughterhouse. In the laboratory, it was cut into pieces of 40 to 60g. Subsequently, all pieces were mixed together by hand using sterile gloves to distribute the naturally occurring flora as homogeneously as possible. Each single piece was placed into a sterile Petri dish, wrapped in a foil of very high oxygen permeability (f 10 000 cm3 me2 bar-’ d-r at 20°C) and stored at four different temperatures (0, 3, 7 and 1O’C).

Microbiological analysis At different time intervals, duplicate samples were

taken. Growth of the spoilage flora, Pseudomonas spp., was measured on Plate Count Agar (Oxoid, code CM 325). Spread plates were incubated aerobically at 25°C and counted after 3 days,

Fitting of the data

Growth curves were fitted using the modified Gompertz model (Zwietering et al., 1990), by non- linear regression with a Marquardt algorithm. This resulted in estimates of the length of the lag phase or lag time (A, in h); the maximum specific growth rate (/&ax 7 in h-l) and the asymptotic value (A = ln(N,l Na), with N, being the maximum number of bacteria reached (c.f.u./g) and No being the initial cell number (c.f.u./g).

The modified square-root model of Ratkowsky (Equation 2) was fitted to the square-root of the growth rate data using linear regression. This resulted in estimates of b2 and Tmin.

The lag-time model (Equation 5) was fitted to the logarithm of the lag time data using non-linear regression. This resulted in estimates of b5 and 7’min.

RESULTS

Modelling microbial growth in vacuum-packed cooked meat products

Figure I shows the datum points and fitted growth curves of L. curvatus in Bologna-type sausage at five different storage temperatures.

As expected, the temperature has a significant effect on the growth of L. curvatus. As the temperature decreases, the length of the lag phase (A) increases and the growth rate (pm,,) decreases. When the total number of lactic acid bacteria exceeds 107c.f.u./g, the onset of spoilage is imminent. Therefore, 107c.f.u./g can be used as a practical level to determine the product’s shelf-life. At 25°C this level is reached within 1 day; at 0°C the spoilage level is reached after 18 days.

The square-root model of Ratkowsky (Equation 2) and the lag-time model (Equation 5) were fitted to the square-root of the growth rate data and the logarithm of the lag-time data, respectively. Datum points and fitted curves are shown in Figures 2 and 3. For every datum point, error bars are given indicating the 95% confidence interval (95% C.I.) of the estimated values Of Pmax and A. For datum points without error bars, the 95% C.I. was too small to be seen in this graph. Values of the parameter estimations b2 and Tmin of

‘O r

0 5 10 15 20 25 30

Tme (days)

Figure 1 Datum points and fitted growth curves of L. curvurus in vacuum-packed Bologna-type 0, 15°C; +, 25°C

sausa, at: V, 0°C; ??, 3°C; A, 7°C;



Table 2 Observed and fitted data of the growth rate (y,,,) and the lag-time (A) (lag-time model 2) for L. curvatus

7

& 0.60 -

z -$ 0.40 -

S-

T (K) Figure 2 Relationship between the square-root of the growth rate (CL,,,,,) and the temperature (T) (Ratkowsky plot) for L. curvatus growing in vacuum-packed Bologna-type sausage

,^ 4 i

‘ - 3-

x

22

0' I

270 275 280 285 290 295 300

T Cc<)

Figure 3 Datum points and fitted curves for lag-time data of L. curvatus

Equation (2) and b5 and Tmin of Equation (5) are given in Table 1.

From Figure 2 it can be seen that the square-root model describes the data very well. The extrapolated Tmin value is 267.7K. This is in fair agreement with a Tmin value of 265.8K calculated from generation time data of a Lactobacillus spp. growing on vacuum- packed fresh beef (Zamora and Zaritzky, 1985).

The lag-time model also describes the data reason- ably well (see Figure 3). Here, the Tmin value is estimated 267.9 K. This Tmin estimation lies within the

Temperature

(“C)

Fitted Observed Fitted Observed Alax &lax h A

(h-‘) (h-l) (h) (h)

25.5 0.677 0.680 4.38 3.34 15.5 0.309 0.317 9.62 10.16 7.1 0.109 0.112 27.11 29.70 3.3 0.053 0.055 56.47 70.24 0.7 0.026 0.026 116.35 92.90

95% C.I. limits of Tmin in Equation (2) (see Table 2). This implies that the Tmin value estimated in Equation (2) can also be used in Equation (5). In Table I, the lag- time model with a Tmin value of 267.9 K is referred to as ‘lag-time model 1’; the lag-time model with a Tmin value of 267.7K is referred to as ‘lag-time model 2’. Observed and fitted values for P,,,~~ and A (lag-time model 2) are listed in Table 2.

Modelling microbial growth in aerobically packed fresh beef

Datum points and fitted growth curves of Pseudomonas on fresh beef at different temperatures are shown in Figure 4. The arrows in the figure indicate the time

2

0 5 10 15 20

Tme (days)

Figure 4 Datum points and fitted growth curves of Pseudomonas spp. in aerobically packed fresh beef at different temperatures. ??, 0°C; A, 3°C; .,7”C; +, 10°C

Table 1 Values of model parameters for L. curvatus and Pseudomonas

Microorganism Model Parameter

L. curvatus Square root bz T ml”

Lag-time model 1 b5 T ml”

Lag-time model 2 bs TIlli”

Pseudomonas spp. Square root bz T ml”

Lag-time model 1 b5 T,i”

Lag-time model 2 b.5 TIC”

Estimated value

0.026739 267.73

0.015759 267.90

0.015523 267.73

0.017629 262.30

0.008190 263.95

0.007299 262.30

95% C.I.

Min

0.026281 267.41

0.010087 264.43

0.013470

0.005132 250.73

0.003816 257.03

0.006628

Max

0.027198 268.04

0.021431 271.37

0.017576

0.030126 273.87

0.012563 270.87

0.007970



0.50

1 0.40 -

k 0.30 -

E 1 0.20 -

0.10 -

0.00 I

260 265 270 275 280 285

T (K) Figure 5 Ratkowsky plot for Pseudomonas spp. growing on aerobically packed fresh beef

C i

E x

4- &

;70 275 280 285 290

T (K)

Figure 6 Datum points and fitted curves for lag-time data of Pseudomonas spp. -, Lag-time model 1; ---, lag-time model 2

at which spoilage (discolouration, formation of off- odours) was obvious.

From Figure 4 it can be seen that temperature also has a pronounced effect on the growth of Pseudomonas spp. on beef. At lO”C, spoilage occurs after 6 days; at O”C, the time of spoilage is delayed to more than 3 weeks.

The square-root model of Ratkowsky (Equation 2) and the lag-time model (Equation 5) were fitted to the square-root of the growth rate and the logarithm of the lag-time data of Pseudomonas spp., respectively. Datum points and fitted curves are shown in Figures 5 and 6. For every datum point, error bars are given indicating the 95% C.I. of the estimated values of pmax and A. Values of the parameter estimations b2 and Tmin of Equation (2) and b5 and 7’min of Equation (5) are given in Table 1.

Although the number of datum points is limited, Figure 5 shows that the usefulness of the square-root model for describing the effect of temperature on the growth rate of Pseudomonas spp. on fresh beef is promising. The extrapolated Tmin value is 262.2 K. This is in close agreement with Tmin values found by other workers. For example, Chandler and McMeekin (1989) estimated a Tmin value of 263 K for Pseudomonas spp. growing in milk. From generation time data of Pseudo- monas spp. given by Lambert et al. (1991), Tmin values of 261.5 K and 262.4K were calculated for non- fluorescent and fluorescent Pseudomonas spp., respectively, growing on meat.

The lag-time model also describes the data very well. The Tmin value estimated in the lag-time model lies

within the 95% C.I. of the Tmin value estimated in Equation (2). Therefore, the estimated Tmin value in Equation (2) can also be used in the lag-time model (see Table 1 and Figure 6). In Table 3, observed and fitted values of p,,, and A are listed.

In Table 4, shelf-life predictions calculated from the observed values for growth rate and lag phase are compared to shelf-life predictions based on growth rate and lag-time data predicted using Equations (2) and (5). The data in Table 4 show that the observed and predicted shelf-life are almost the same. This implies that the modified square-root model for growth rate (Equation 2) and lag phase (Equation 5) can be used to predict the shelf-life of Bologna-type sausage and fresh beef under the conditions tested.

The shelf-life predictions for fresh beef in Table 4 give a good reflection of the shelf-life in practical situations. On the other hand, the shelf-life of Bologna- type sausage is underestimated. For example, in practical situations, the shelf-life of this product at 7°C is 14-28 days. This discrepancy may be explained by the fact that in our study, besides NaCl, no other preservatives such as nitrite and lactate were added. In practical situations additional preservatives are often added, and this could be one of the reasons that our shelf-life prediction is an underestimation of the real shelf-life. Currently, efforts are being made to determine the effect of a combination of several different controlling factors in the growth of the spoilage flora of vacuum- packed Bologna-type sausage.

The results presented here indicate that the growth of the spoilage flora of aerobically packed fresh beef and vacuum-packed Bologna-type sausage can be described by using two modifications of the square-root model. However, before models are used to predict shelf-life, they have to be thoroughly validated in practical situations. Furthermore, it could be important to include a relationship between the growth of the

Table 3 Observed and fitted data of the growth rate (P,,,~J and the lag-time (A) (lag-time model 2) for Pseudomonas spp.

Temperature

(“C)

9.4 7.1 3.3 0.7

Fitted Observed Fitted Observed

W max /&lax A h

(h-‘) (h-l) (h) (h)

0.126 0.133 46.46 43.96 0.098 0.099 59.24 59.20 0.061 0.052 95.77 82.71 0.040 0.048 144.44 163.43

Table 4 Shelf-life predictions of vacuum-packed Bologna-type sausage and aerobically packed fresh beef, based on observed and fitted growth rate (cc,,,,,) and lag-time (A) data

Product Temperature (“C)

Shelf-life (days)

Observed Fitted

Bologna-type sausage 25.5 I I 15.5 3 3 7.1 8 8 3.3 I6 I7 0.7 33 33

Fresh beef 9.4 5 5 7.1 6 6 3.3 10 11 0.7 15 15



spoilage flora and the concentratiotis of metabolites that cause sensory spoilage of the product. Sensory spoilage is a criterion enabling consumers to decide whether or not a food product is spoiled. If, however, food inspection services use a certain number of spoilage organisms as a level above which the product should not be sold, this level can be used in predictive microbiology to determine shelf-life.

CONCLUSION

In this preliminary study, it is shown that modifications of the square-root model can be applied to describe the effect of storage temperature on the maximum growth rate (P,,,,~) and the lag-time (A) of Lactobacillus curvatus in vacuum-packed cooked meat products and Pseudomonas spp. on aerobically packed fresh beef. Both models can be used to predict the growth rate and the lag phase of the microorganisms involved at any storage temperature within the experimental range tested. These models however, have to be tested extensively for their predictive value before using them for shelf-life predictions in practical situations.

ACKNOWLEDGEMENT

This research was funded by the Dutch Product Board for Livestock and Meat. The authors wish to thank W.L.J.M. Zomer and H.J. Pouw for technical assist- ante.

REFERENCES

Baird-Parker, A.C. and Kilsby, D.C. (1987) Principles of predictive food microbiology. J. Appl. Bacterial. Symposium Supplement, 43s-49s

Chandler, R.E. and McMeekin, A.T. (1989) Temperature function integration as the basis of an accelerated method to predict the shelf-life of pasteurized, homogenized milk. Food Microbial. 6, 105-111

Gibbs, P.A. and Williams, A.P. (1990) Using mathematics for shelf life prediction. Food Technology International Europe (Ed. Turner, A.) Sterling Publications International, London, pp. 287-290

Gould, G. (1989) Predictive mathematical modelling of microbial growth and survival in foods. Food Sci. Technol. Today 3, 89-92

Hayes, P.R. ( 1985) Food Spoilage. Food Microbiology and Hygiene. Elsevier Applied Science Publishers, London and New York, pp. 80-139

Lambert, A.D., Smith, J.P. and Dodds, K.L. (1991) Shelf-life extension and microbiological safety of fresh meat - a review. Food Microbial. 8, 267-297

Ratkowsky, D.A., Olley, J., McMeekin, T.A. and Ball, A. (1982) Relationship between temperature and growth rate of bacterial cultures. J. Bacterial. 149, l-5

Ratkowsky, D.A., Lowry, R.K., McMeekin, T.A., Stokes, A.N. and Chandler, R.E. (1983) Model for bacterial culture growth rate throughout the entire biokinetic temperature range. J. Bacterial. 154, 1222-1226

Ross, T. and McMeekin, T.A. (1991) Predictive microbiology - application of a square-root model. Food Amt. 43, 202-207

von Holy, A., Cloete, T.E. and Holzapfel, W.H. (1991) Quantification and characterization of microbial populations associated with spoiled, vacuum-packed Vienna sausages. Food Microbial. 8,95- 104

Zamora, M.C. and Zaritzky, N.E. (1985) Modeling of microbial growth in refrigerated packaged beef. J. Food Sci. 50, 1003-1006

Zwietering, M.H., Jongenburger, I., Rombouts, F.M. and van ‘t Riet, K. (1990) Modelling of the bacterial growth curve. Appl. Environ. Microbial. 56, 1875-1881

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Received I7 November 1992 Revised 3 June 1993 Accepted 3 June 1993


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Modelling of the microbiological quality of meat