Colour stability and lipid oxidation of fresh beef. Development of a response surface model for predicting the effects of temperature, storage time, and modified atmosphere composition

Meat Science 54 (2000) 49±57

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Colour stability and lipid oxidation of fresh beef. Development of a response surface model for predicting the e€ects of temperature, storage time, and modi®ed atmosphere composition Marianne Jakobsen*, Grete Bertelsen Department of Dairy and Food Science, Food Chemistry, The Royal Veterinary and Agricultural University, Rolighedsvej 30, DK-1958 Frederiksberg C, Denmark Received 23 December 1998; received in revised form 19 May 1999; accepted 19 May 1999

Abstract Samples of fresh beef muscles (Longissimus dorsi) were packed under varying modi®ed atmosphere conditions (20±80% oxygen) and stored at 2±8 C for 10 days. At 2 day intervals meat samples were analysed for surface colour and extent of lipid oxidation (TBARS). Response surface models for predicting the e€ects of temperature, storage time and modi®ed atmosphere composition on colour stability and lipid oxidation were developed. Temperature and time were found to be the most important factors for retaining meat colour and minimizing lipid oxidation. However, the oxygen content also had a signi®cant e€ect on both quality parameters. A stable interval of maintaining a good meat colour was found between 55 and 80% O2. Response surface modelling was found to be very promising for modelling of chemical quality changes in meat stored under di€erent conditions, but the large biological di€erences between animals may complicate the development of generally valid models. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: Mathematical modelling; Colour stability; Lipid oxidation; Modi®ed atmosphere packaging (MAP); Beef

1. Introduction Modi®ed atmosphere packaging (MAP) is widely used to extend the shelf life and quality of chill stored beef. Colour, microbial growth, and lipid oxidation are important factors for the shelf life and consumer acceptance of fresh meat. Shelf life and quality of fresh beef are strongly in¯uenced by initial meat quality, package parameters, and storage conditions (Zhao, Wells & McMillin, 1994). It is well known that elevated levels of carbon dioxide inhibit microbial growth (Gill & Tan, 1980; Marshall, Wiese-Lehigh, Wells & Farr, 1991; Wimpfheimer, Altman & Hotchkiss, 1990), whereas elevated levels of oxygen prolong colour stability (Asensio, Ordonez & Sanz, 1988; Bartkowski, Dryden & Marchello, 1982; Taylor, 1972). The gas composition normally used for modi®ed atmosphere packaged beef is 20±30% CO2 and 70±80% O2 (Blakistone, 1998; Taylor, 1996).

* Corresponding author. Fax: +45-3528-3344. E-mail address: [email protected] (M. Jakobsen)

Lipid oxidation causes a rancid o€-¯avour and o€odour in meat. Numerous factors a€ect lipid oxidation including light, oxygen concentration, temperature, presence of anti- and prooxidants, degree of unsaturation of the fatty acids and the presence of enzymes (Skibsted, Mikkelsen & Bertelsen, 1998). Lipid oxidation is normally not considered to be a limiting factor for shelf life of aerobic packed chill stored meat, as lipid oxidation occurs at a slower rate than discoloration or microbial growth (Zhao, Wells & McMillin, 1994). However, when modi®ed atmosphere packaging represses the other deteriorative mechanisms in meat, lipid oxidation might limit shelf life (McMillin, 1993). While an elevated oxygen level is known to prolong colour stability, it is also expected to increase the rate of lipid oxidation (Zhao et al., 1994). Increased lipid oxidation has been reported for meat stored at elevated oxygen concentrations (Jackson, Acu€, Vanderzant, Sharp & Savell, 1992; Jensen, Guidera, et al., 1998; Taylor, 1985), although other researchers did not ®nd any increase in lipid oxidation under similar conditions (Asenio, Ordonez & Sanz, 1988; Lopez-Lorenzo, Hernandez, Sans-Perez & Ordonez, 1980; Ordonez & Ledward, 1977).

0309-1740/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0309-1740(99)00069-8

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Mathematical techniques can be of help in predicting the e€ects of environmental variables, such as temperature and initial gas composition, on deterioration reactions in meats. Attempts have been made to develop predictive equations to describe the quantitative relationships between bacterial growth and the combined e€ects of storage time, temperature and initial gas composition on modi®ed atmosphere stored beef (Zhao et al., 1992). However, corresponding models for predicting chemical changes such as discoloration and lipid oxidation are not available. The object of the present study was to develop mathematical models describing the relationship between discoloration and lipid oxidation in beef and the combined e€ect of time, temperature and partial pressure of oxygen. These models should form the basis for proposing an optimal MAP gas composition to maintain the bright red colour preferred by the consumer and at the same time keeping lipid oxidation at a minimum. 2. Materials and methods 2.1. Meat samples Longissimus dorsi muscles containing approximately 3% intramuscular fat (IMF) were used. The muscles were removed from the animal before 4 days post slaughter at less than 7 C and matured for one week in vacuum bags at 2 C. Subsequently, the muscles were trimmed of external fat and cut into 1.5 cm thick steaks. Prior to packaging the samples were allowed to bloom for approximately one hour at 5 C. Meat from four di€erent animals was used. The meat from the di€erent animals had been handled the same after slaughter, e.g. maturing time, transportation conditions, etc., and all animals had passed the normal quality control at the slaughterhouse. However, the animals may have been of di€erent age, breed etc. 2.2. Packaging parameters and storage conditions Storage temperature, storage time, and the ratio between oxygen and carbon dioxide in the headspace were varied (Table 1). To minimize changes in headspace due to di€usion of gases, microbial metabolism, and CO2 absorption by the meat, a high barrier packaging material, with respect to O2 and CO2 permeability was used, good hygiene was maintained, and a high ratio of headspace to meat (of about 9:1) was used. The meat samples were placed in polystyrene trays and packed in pouches of a laminated packaging material of 40 mm PA/EVOH/PA/75 mm LDPE/LLDPE (Danisco Flexible ON, Lyngby, Denmark) with an oxygen transmission rate of 0.5 cm3/m2/24 h/atm, a carbon dioxide transmission rate of 2 cm3/m2/24 h/atm and a water-vapour transmission rate of 4 g/m2/24 h.

Table 1 Levels of storage temperature and storage time content of oxygen and carbon dioxide in headspace in the experiment used Temperature ( C)

O2 (%)

CO2

Days

2 5 8 2 8 2 5 2 8 2 5 8

20 20 20 35 35 50 50 65 65 80 80 80

80 80 80 65 65 50 50 35 35 20 20 20

2,4,6,8,10 2,4,6,8,10 2,4,6,8,10 2,4,6,8,10 2,4,6,8,10 2,4,6,8,10 2,4,6,8,10 2,4,6,8,10 2,4,6,8,10 2,4,6,8,10 2,4,6,8,10 2,4,6,8,10

The pouches were ®lled with gas using a chamber type packaging machine (Komet, Plochingen, Germany). After ®lling, the O2 levels in the pouches were found to be 22.8, 39.7, 53.0, 67.1, and 80.9%. Gas compositions were measured by inserting a needle into the pouches, withdrawing approximately 3 ml of the headspace for analysis in a CheckMate gas analyser. On the days of analysis, leaking packages were found by measuring the headspace composition before opening. Headspace composition remained constant during the entire experiment except for samples stored at 8 C where a reduced oxygen level (5±10% less) was observed on days 8 and 10, due to microbial action and/or biochemical reactions in the meat. The meat samples had a volume of approximately 80 ml, and the headspace in the individual packs was approximately 750 ml. The samples were stored in the dark in refrigerators (Termaks series 6000, Termaks A/S, Solheimsviken, Norway), and the temperature monitored continuously during storage at two di€erent places in each refrigerator using data loggers (Tinytalk II-Temp Loggers, RS Radio Parts, Copenhagen, Denmark). The mean storage temperatures were 1.6, 5.2, and 8.2 C. The whole experiment was replicated four times with meat from four di€erent animals. On the day of packaging (day 0), four additional samples were analysed resulting in 12(combinations)5(days)+4=64 samples per animal. Only one replicate could be made as one muscle yielded 30±35 samples and left and right side muscles were used. 2.3. Analysis On days 0, 2, 4, 6, 8 and 10 the following analyses were carried out: . Gas composition of the package headspace was measured using a CheckMate 9900 gas analyser (PBI Dansensor, Ringsted, Denmark) expressed as %O2 and %CO2. . Colour was measured on the meat surface immediately after opening of the package using a Minolta

M. Jakobsen, G. Bertelsen / Meat Science 54 (2000) 49±57

Colorimeter CR-300 (Minolta, Osaka, Japan) using the L; a; b coordinates (CIELAB colour system). Red colour was expressed as the a-value, the higher the a-value the redder the sample. The measurement was repeated on ®ve randomly selected locations on each sample. . Lipid oxidation was measured using the 4 mm top layer of each sample, removed using a commercial slicer, and homogenised with a kitchen blender. The extent of lipid oxidation was estimated as TBARS (thiobarbituric acid reactive substances) by the extraction method of Sorensen and Jorgensen (1996). TBARS were measured on two replicates from each sample and were expressed as moles malonaldehyde(MA)/kg meat. On day 0, four randomly selected samples were further analysed for: . Total fat (as g fat/100 g meat) by the method of Folch, Lees, and Stanley (1957). . Fatty acid composition (as g unsaturated or saturated fatty acids/100 g meat) by the method of Jart (1997). . Vitamin E (as mg a-tocopherol/kg meat) in two replicates from each sample by the method of Jensen et al. (1997). . pH was measured in a 1:1 meat±water homogenate. 2.3.1. Experimental errors The repeatability (repeated measurements made on the same meat sample) of the TBARS analyses was 0.3 m-moles MA/kg meat. The repeatability of the colour avalue measurements was 0.8. In addition there would be a (non quanti®ed) variation due to natural biological di€erences. 2.4. Mathematical and statistical analyses All models were developed using Unscrambler 6.11 (Camo AS, Trondheim, Norway). Unscrambler's response surface algorithm using MLR (Multiple Linear Regression) was applied. The resulting response surface models contain linear, interaction and quadratic e€ects yielding models of the form (1). Y ˆ 0 ‡ 1
D ‡ 2
T ‡ 3
O ‡ 4
D
T ‡ 5
D
O ‡ 6
T
O ‡ 7
D
D ‡ 8
T
T ‡ 9
O
O

…1†

where Y is the predicted response variable and the treatment variables day …D†, temperature …T†, and oxygen level …O† are mean-centered (by subtracting the average value of the variable). s are regression coecients. Distinct outlying samples were removed prior to modelling. A few samples displayed abnormal behaviour, and since no extra beef samples had been packed, it was not

51

possible to redo the chemical analyses. Approximately 5% of the samples were removed before modelling due to leaking packages or errors in analysis. The validity of the models was assessed using ANOVA (Analysis of Variance), enabling a check to be made for the signi®cance of all the e€ects. Response surface plots displaying the levels of a response when varying two variables and keeping the third variable constant were used for ®nal interpretation of the models. Means were compared using the procedure GLM in SAS 6.08 (SAS Institute, Inc., Cary, NC). Signi®cant di€erences were estimated by Duncan's multiple range test (P<0.05). 3. Results Development of lipid oxidation during chill storage varied signi®cantly between muscles at all storage temperatures, the di€erences being most pronounced at 8 C. As can be seen from Fig. 1(a), lipid oxidation was most pronounced in animal A followed by animals B, C and D. The di€erences may partly be explained by varying levels of endogenous vitamin E, lipid content and fatty acid composition of the lipids (Table 2), parameters all known to a€ect lipid oxidation (Skibsted et al., 1998). Di€erences in colour stability between individual animals were also observed, but mainly at 8 C (Fig. 1b). At 2 and 5 C only samples from animal A showed a better colour stability than samples from the other animals. It appears that meat with the poorest oxidative stability has the best colour stability. This is interesting since a direct relationship between pigment and lipid oxidation has been found in several studies (for reviews see e.g. Faustman & Cassens, 1990; Skibsted et al., 1998). No obvious explanation can be given for the opposite results found in the present study, however, it deserves attention and will be pursued in future studies. Due to the large di€erences between muscles from the individual animals, response surface models were ®rst developed considering the four animals separately. According to Table 3 colour stability models for animals B, C and D show good correlation between measured and predicted a-values. The SED (Standard Error of Deviation between measured and predicted response values) conforms well with the above-mentioned analysis performance. The colour stability model for animal A is not as good as the other models probably because of the small variations in a-values throughout storage (i.e. structured variances in a-value are not larger than the random variances in a-value) (see Fig. 1b). Models for lipid oxidation for animals A, B, and C also show good correlation and SED between measured and predicted TBARS-values. The model for animal D is less good, as the variation in TBARS-values for animal D is approximately the same during the whole experiment.

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M. Jakobsen, G. Bertelsen / Meat Science 54 (2000) 49±57

The colour stability models for the four di€erent animals are similar with respect to signi®cant e€ects. Main e€ects of D (days), T (temperature), O (oxygen content) and the interaction e€ect of DT recur in all four models (except main e€ect of D for animal A). Furthermore, the b-coecients for all four models show the same tendencies except the levels di€er (results not shown). The lipid oxidation models for the four di€erent animals are also similar with respect to signi®cant e€ects. Main e€ects of D; T; O recur in all four models (except main e€ect of O; T for animal D), and the b-coecients of these e€ects also show the same tendencies except for the level of the coecients (results not shown). Consequently, the following response surface models for predicting changes in colour a-values (2) and TBARS (3) are given as the average of the four individual models: a ÿ value ˆ 29:018 ÿ 0:409
D ÿ 0:499
T ‡ 0:021
O ÿ 0:124
D
T ‡ 0:004
D
O ‡ 0:002
T
O ÿ 0:066
D
D ÿ 0:054
T
T

…2†

R-Square=0.950 and SED=0.60 compared to the average of the four animals. Table 3 Results of response surface models considering the four animals separately Animal

Samples dl

R-Square

Model for colour stability A 67 0.545 B 66 0.847 C 72 0.882 D 70 0.902 Model for lipid oxidation A 67 0.931 B 66 0.831 C 69 0.903 D 66 0.686 Fig. 1. Lipid oxidation (a) dl measured as TBARS [mmoles(MA)/kg meat] and a-values (b) of steaks from M.Longissimus dorsi from four di€erent animals (A, B, C and D). The samples were packed in 80% O2 and 20% CO2 and stored at 8 C.

SEDa

E€ects of signi®canceb,c

0.95 0.92 1.31 1.21

T,O,DT,DO D,T,O,DT D,T,O,DT,DO,TO,DD,TT D,T,O,DT,DO,DD,TT

1.01 0.71 0.22 0.48

D,T,O,DT,DD,TT D,T,O,DT,TO D,T,O,DO,DD,TT D,TT

a SED (Standard Error of Deviation) between measured and predicted response values. b Signi®cance accepted at the 5% level. c T=temperature ( C), O=oxygen content (%), D=day.

Table 2 Total fat content, fatty acid composition, vitamin E and pH of beef muscles (Longissimus dorsi) of the four animals Animal

Total fata (g/100 g meat)

Fatty acidsa 42 double bonds (g/100 g meat)

Fatty acidsa >2 double bonds (g/100 g meat)

Vitamin Eb (mg a-toc./kg meat)

pHa

A B C D

3.7c‹1.3d 3.3c‹1.2 1.6d‹0.4 2.5c,d‹0.7

3.6c‹1.2 3.2c‹1.3 1.5d‹0.4 2.4c,d‹0.6

0.08c‹0.04 0.07c‹0.04 0.05c‹0.01 0.03c‹0.02

2.4d‹0.2 3.0c,d‹0.4 3.5c‹0.5 3.2c‹0.4

5.60c‹0.03 5.58c‹0.03 5.57c‹0.01 5.60c‹0.02

a

Calculated as the mean of single analyses made on four di€erent samples ‹SD. Calculated as the mean of two replicate analyses made on four di€erent samples ‹SD. c,d Means with the same letter are not signi®cantly di€erent at a 5% level. b

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53

TBARS ˆ 2:935 ‡ 0:416
D ‡ 0:187
T ‡ 0:009
O ‡ 0:042
D
T ‡ 0:001
D
O ‡ 0:002
T
O ‡ 0:003
D
D ‡ 0:066
T
T

…3†

R-Square=0.955 and SED=0.36 compared to the average of the four animals, where D; T and O are mean-centered and Dmean ˆ 5:000; Tmean ˆ 4:683 and Omean ˆ 52:156. As expected, both day …D† and temperature …T† had pronounced e€ects on colour and oxidative stability. The a-value decreased with increasing temperature and time, whereas TBARS increased with increasing temperature and time. The level of TBARS increased considerably more from 5 to 8 C than from 2 to 5 C. The level of oxygen in the headspace also a€ected colour stability and lipid oxidation during chill storage. Fig. 2(a) shows that the samples stored in 20% O2 were not able to retain as good a colour as samples stored in higher O2 contents, on the other hand samples stored with 20% O2 became less rancid than samples stored at higher O2 contents (Fig. 2b). Measured values and the corresponding predicted values in both models showed good agreement (Fig. 3a and b). The pronounced e€ect of the storage temperature, 2 C versus 8 C, on colour stability and lipid oxidation is clearly seen (Fig. 3a and b). Interpretation of the e€ects of the treatment factors is best seen in the response surface plots of the models (Fig. 4a and b), which may be used to predict a compromising O2 level, to give optimal colour stability and an acceptable level of lipid oxidation. The average a-value is relatively stable between 55 and 80% O2. Thus colour stability is not markedly increased on elevating the O2 level from 55 to 80%, regardless of temperature (Fig. 4a). It is seen from Fig. 4b that from day six samples were susceptible to lipid oxidation when stored at the higher temperatures. At the lower temperatures lipid oxidation is largely repressed, and thus the O2 level is less important. The predicted response values shown in Fig. 4(a) and (b) can be calculated from the regression models (2) and (3). For example, the average TBARS-value for samples packed with 60% O2 and stored at 6 C for 6 days is calculated as: 2:935 ‡ 0:416
…6:0 ÿ 5:0† ‡ 0:187
…6:0 ÿ 4:683† ‡ 0:009
…60:0 ÿ 52:156† ‡ 0:042
…6:0 ÿ 5:0†
…6:0 ÿ 4:683† ‡ 0:001
…6:0 ÿ 5:0†
…60:0 ÿ 52:156† ‡ 0:002
…6:0 ÿ 4:683†
…60:0 ÿ 52:156† ‡ 0:003
…6:0 ÿ 5:0†
…6:0 ÿ 5:0† ‡ 0:066
…6:0 ÿ 4:683†
…6:0 ÿ 4:683† ˆ 3:9 ÿ moles MA=kg meat:

Normally, refrigerated beef is stored in 70±80% O2 and 20±30% CO2 (Blakistone, 1998; Taylor, 1996).

Fig. 2. Colour a-values (a) and lipid oxidation (b) measured as TBARS [mmoles(MA)/kg meat] of steaks from M. Longissimus dorsi (average of four animals). The samples were packed at four di€erent O2 levels (20, 35, 65, 80%) and stored at 8 C.

Assuming that 3 C is a realistic storage temperature, the models allow us to estimate how packaging with di€erent O2 levels a€ects colour stability and lipid oxidation at 3 C. Reducing the oxygen level from 80 to 55% does not really a€ect the colour stability of the meat when stored at 3 C (Fig. 5a). Samples packed in 55±80% O2 gain in a-value (blooming) from day 0 to a maximum on day 4. Then, the red colour begins to fade, but after day 8 the sample is as red as the starting value. However, samples packed in 20% O2 retain the same a-value to day 4, but

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M. Jakobsen, G. Bertelsen / Meat Science 54 (2000) 49±57

Fig. 4. Response surface plot of predicted average a-values (a) and TBARS (b) of steaks from M. Longissimus dorsi (average of four animals) stored for six days at di€erent chill storage temperatures and stored in di€erent levels of oxygen. The plot in (a) is divided into four areas of increasing a-values. E.g. [23.9±25.5] refers to an area of avalues between 23.9 and 25.5, etc. The plot in (b) is divided into four areas of increasing TBARS. E.g. [2.8±3.4] refers to an area of a-values between 2.8 and 3.4, etc. Fig. 3. Colour a-values (a) and TBARS (b) of steaks from M. Longissimus dorsi (average of the four animals). 20,2 mea refers to measured values for samples stored in 20% O2 at 2 C; 20,2 pre refers to predicted values for samples stored in 20% O2 at 2 C. 20,8 mea refers to measured values for samples stored in 20% O2 at 8 C. 20,8 pre refers to predicted values for samples stored in 20% O2 at 8 C.

then become less red. O2 contents of 55±80% give a superior colour stability compared to 20% O2. Although the O2 level can be reduced without a€ecting colour stability this reduction does not have much in¯uence on lipid oxidation in meat (Fig. 5b), the predicted TBARS-value on day 10 decreases from 4.8 mmols MA/kg meat to 4.6 m-moles MA/kg meat when the O2 level is reduced from 80 to 55%. It appears that a further decrease is needed to obtain reduced lipid oxidation at 3 C.

4. Discussion The developed models can be used to predict the e€ect of di€erent packaging (oxygen content) and storage parameters (time and temperature) on the meat quality parameters. The models can also identify the most important factors for these meat quality parameters. The most important factor for maintaining the red oxymyoglobin colour and keeping lipid oxidation to a minimum is the temperature. A low temperature (below approximately 4 C) almost prevents lipid oxidation, regardless of oxygen level (Fig. 4b). When the temperature is raised, the oxygen level becomes more critical. At 8 C, storage for 10 days in 20% oxygen gives an estimated TBARS-value of 6.5 m-moles MA/kg meat, whereas storage in 80% oxygen gives an estimated TBARS-value of 7.7 m-moles MA/kg meat [calculated using Eq. (3)].

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Fig. 5. Colour a-values (a) and TBARS (b) of steaks from beef M. Longissimus dorsi (average of four animals) predicted for three packaging and storage conditions. 20,3 refers to samples stored in 20% O2 at 3 C; 55,3 refers to samples stored in 55% O2 at 3 C; 80,3 refers to samples stored in 80% O2 at 3 C.

Nevertheless, the TBARS-value does not reach an unacceptable level as regards o€-¯avour (except for meat from animal A at the most extreme temperature, 8 C) (Boles & Parrish, 1990; Greene & Cumuze, 1981), but it could represent a problem in meat products with more oxidative stress, e.g. heat treated meat products. To maintain a cherry red meat colour throughout storage a low temperature and an oxygen level above 20% are needed. However, the model reveals, that raising the oxygen level above approximately 55% does not improve the colour stability further (Fig. 4a). Storage of the meat for 10 days in 55% oxygen at 2 C maintains a

55

red meat colour throughout the whole period (avalue=28), but if the temperature is raised to 5 C the meat can only maintain this colour for 6 1/2 days [calculated using Eq. (2)]. The response surface method is suitable for developing predictive models describing the chemical changes in meat quality, but due to the large biological variation in meat from di€erent animals, experiments with a larger number of animals and di€erent muscles must be performed, before more generally valid models can be developed. The developed models are only valid for meat similar to that used in this study, and the predicted values represent the average of the four animals. The models cannot be extrapolated to levels of variables outside those used in this study. At the beginning of the storage period the total fat content, fatty acid composition and the content of vitamin E were measured (Table 2). Meat containing a large amount of polyunsaturated fatty acids is more susceptible to lipid oxidation than meat containing a small amount of these fatty acids, and a large content of vitamin E is known to inhibit lipid oxidation (Faustman, Chan, Schaefer & Havens, 1998; Jensen, FlenstedJensen, et al., 1998). Models which incorporate these parameters can be developed. For example, a model for development of lipid oxidation using the content of polyunsaturated fatty acids and vitamin E as additional input variables was developed which gives a good description of the di€erences in the tendency of the meat to undergo lipid oxidation among the four animals. At ®rst we tried to ®t one response surface model of the form (1) to data from the four di€erent animals at the same time [the response variable being log(TBARS)]. As expected this model gave a very poor ®t, R2 ˆ 0:490 (Fig. 6a), due to the large biological di€erences between the four animals. Thus, a response surface model of the form (4) was ®tted to the same data. (The model is a reduced model containing only signi®cant e€ects instead of all possible interaction e€ects.) log…TBARS† ˆ 0 ‡ 1
u:fat ‡ 2
vitE ‡ 3
D ‡ 4
T ‡ 5
O ‡ 6
u:fat
T ‡ 7
vitE
D ‡ 8
T
D

…4†

where s are regression coecients, u:fat is the content of polyunsaturated fatty acids (g/100 g meat), vitE is the content of vitamin E (mg a-toc./kg meat) and D; T; O are the treatment variables day, temperature and oxygen content. All variables are mean-centered. The result was a large improvement in the ®t of the model, R2 ˆ 0:897 (Fig. 6b). The resulting model is given in Eq. (5).

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M. Jakobsen, G. Bertelsen / Meat Science 54 (2000) 49±57

(positive b-coecient) to the level of lipid oxidation, whereas the variable corresponding to the vitamin E content negatively in¯uenced the level of lipid oxidation. In conclusion, response surface models seem promising for predicting the e€ect of the head space gas composition and time and temperature on chemical changes in meat (discoloration and lipid oxidation). However, due to large biological di€erences between samples originating from di€erent animals more experimental units are needed and more emphasis should be put on describing the initial meat quality and its susceptibility to oxidative changes, before more generally valid models can be developed. To reduce discoloration in chill stored beef steaks the developed models suggest that the oxygen content should be more than approximately 55%. To keep lipid oxidation low, the temperature should be less than approximately 4 C. Acknowledgements This work was sponsored by the FéTEK program through LMCÐCentre for Advanced Food Studies. The authors are grateful to Bente Sùrensen for excellent technical assistance. Also thanks to AGA A/S, Danisco Flexible ON and Danish Crown, Hvidovre for providing materials for this experiment. References

Fig. 6. Predicted values of log(TBARS) plotted against measured values of log(TBARS) for steaks from four di€erent animals (A, B, C and D) packed under the conditions shown in Table 1: (a) model not incorporating the content of unsaturated fatty acids (>two double bonds) and vitamin E; (b) model incorporating the content of unsaturated fatty acids (>two double bonds) and vitamin E (5). The line y ˆ x is shown in both ®gures.

log…TBARS† ˆ 0:441 ‡ 3:286
u:fat ÿ 0:285
vitE ‡ 0:052
D ‡ 0:015
T ‡ 0:001
O ‡ 0:049
u:fat
T ÿ 0:038
vitE
D ‡ 0:019
T
D

…5†

where all the variables signi®cantly a€ect the model (P 0.05). u:fatmean ˆ 0:058; vitEmean ˆ 3:025; Dmean ˆ 5:0; Tmean ˆ 4:683 and Omean ˆ 52:156. As expected, the variable corresponding to the content of polyunsaturated fatty acids contributed positively

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