INTRODUCTION

Top Abstract Introduction Materials and Methods Results and Discussion References

Fresh fish are among the most perishable food products, and the monitoring and controlling of fish quality is one of the main goals in the fish industry. Fish shelf life is influenced by a number of factors, such as initial microbiological quality, season, handling, and feeding (17, 37, 40, 41) and consequently can vary significantly from batch to batch. The limited and variable shelf lives of fish are major problems for fish quality assurance. This is the reason for the extensive research which has been carried out in the last few decades on the development of direct product methods (microbial, sensory, and biochemical) for the evaluation of fish spoilage (14, 15, 16). Nevertheless, several problems are related to the use of these methods mainly due to time and sensitivity limitations. An alternative to direct product testing is predictive microbiology. Predictions of food quality can improve significantly distribution and marketing, especially for chilled foods such as fish (28).

Application of mathematical modeling for shelf life prediction requires sufficient knowledge of the product spoilage mechanisms (20). In the case of fish and fish products, spoilage is caused by a fraction of the total fish microflora, the specific spoilage organisms (SSO) (16). Since temperature is one of the most important factors influencing microbial growth, modeling the growth of the SSO as a function of temperature is essential in shelf life prediction. Although a large number of models for the prediction of growth of spoilage organisms at various temperatures have been developed, the majority of these studies have been carried out under constant conditions (5, 26, 32, 47). However, unlike other factors affecting microbial growth (e.g., pH and water activity), temperature may vary extensively throughout the complete production and distribution chain. In practice, foods are frequently exposed to significant temperature fluctuations during transportation and storage before delivery to the consumer.

Several studies have been published predicting microbial growth at fluctuating temperatures (2, 12, 24, 42, 48). The aim of these studies was to test whether growth under nonisothermal conditions can be predicted from models based on growth data obtained isothermally. Zwietering et al. (48), after testing several hypotheses about the growth of Lactobacillus plantarum at changing temperatures, concluded that the bacteria are exposed to stress by a shift in temperature in the lag phase as well as in exponential phase. These authors also observed that temperature changes around the minimum of growth showed very large deviations from the model. The latter finding was also reported for the growth of Brochothrix thermosphacta in changing temperature conditions in a study where the dynamic model of Baranyi et al. (2) failed to predict growth accurately when the temperature profile contained step changes from a higher temperature of 17 to 25°C down to 3°C. The inability of the models to predict microbial growth after a shift to low temperature could be a significant problem in predicting the shelf life of foods since similar temperature fluctuations often occur during the chilled food chain. It needs to be noted, however, that both of these studies were conducted in liquid media under laboratory conditions. It has been shown that factors such as the preincubation temperature of the bacterial culture, as well as the structure and composition of the growth medium may play an important role on the bacterial behavior after a shift to low temperature (10, 13, 30, 45). Thus, studies with naturally contaminated actual foods would lead to the accumulation of more reliable information about microbial growth at fluctuating temperature.

The objectives of the present study were first of all to present a mathematical model for the effect of temperature on the growth of the SSO, i.e., pseudomonads, of aerobically stored gilt-head seabream. The data on pseudomonad growth from 23 experiments with gilt-head seabream stored at different isothermal conditions were collected and modeled as a function of temperature using a Belehradek type model. Second, we sought to evaluate the ability of the model to predict microbial growth at nonisothermal conditions. Gilt-head seabream was stored aerobically at dynamic temperature profiles designed in the laboratory or simulated real temperature profiles derived from field tests within the fish chill chain. Finally, the observed pseudomonad growth was compared to the model prediction using the indices of bias and accuracy factors to illustrate the validity of the model in predicting the shelf life of gilt-head seabream under conditions of varying temperature. The shelf life of fish derived from sensory analysis for each dynamic profile tested was compared to the shelf life estimated based on pseudomonad growth predicted by the model.

	MATERIALS AND METHODS

Top Abstract Introduction Materials and Methods Results and Discussion References

Studies at constant temperature conditions. Gilt-head Seabream (Sparus aurata), a Mediterannean fish of high consumption and commercial interest in Greece was studied. Eleven replicated storage experiments were carried out with ungutted fresh gilt-head seabream. Fish were bought from the Nireus Aquacultured Industry in Athens within 6 to 12 h after catch and then transported in ice, within 30 min, to the laboratory. The fish were then stored under controlled isothermal conditions (from 0 to 15°C) in high-precision low-temperature incubators (MIR Sanyo). Samples were taken at appropriate time intervals to allow for an efficient kinetic analysis of sensory quality and microbial growth.

Studies under dynamic temperature conditions. Five replicated storage experiments were carried out with ungutted fresh gilt-head seabream stored under dynamic temperature conditions. Four different temperature scenarios designed in the laboratory and one temperature profile derived from a field test within the real fish chilled chain were used. The field test was carried out in cooperation with a fish industry in Athens, and the temperature of the fish during a common distribution and storage procedure was recorded using temperature data loggers (Diligence Data Logger; Comark, Ltd.). The temperature profile derived from the data loggers was then simulated in the laboratory. All of the dynamic temperature experiments were carried out using the appropriate temperature program in high-precision low-temperature incubators.

Sample preparation. A 25-g portion from the dorsal half of the fish was transferred to a stomacher bag (Seward Medical, London, United Kingdom); 225 ml of 0.1% peptone water with salt (NaCl, 0.85% [wt/vol]) was added, and the mixture was homogenized for 60 s with a stomacher (Lab Blender 400; Seward).

Microbiological media and enumeration. Samples (0.1 ml) of serial dilutions of fish homogenates were spread on the surface of the appropriate media in Petri dishes for enumeration of the pseudomonads on cetrimide fusidin cephaloridine agar (Oxoid code CM 559, supplemented with SR103) and incubated at 20°C for 2 days (29).

Sensory evaluation of shelf life. Whole fish was evaluated by a trained sensory panel of five to eight judges who were asked to evaluate the odor of raw fish and the taste and odor of cooked fish. Fish were scaled, gutted, and gilled before cooking. Fish were cooked whole, individually wrapped tightly in aluminum foil, at 180°C for 30 min. An adaptation of a simple three-point scoring system (7, 43) was used. Taste and odor was judged and recorded in appropriate forms with descriptive terms reflecting the organoleptic evolution of quality deterioration. A rating was assigned on a continuous hedonic scale of from 0 to 3 (with "0" being the highest-quality score and "2" being the limit of acceptance).

Data analysis. The growth data from the enumeration of pseudomonads on gilt-head seabream were modeled as a function of time using the log-transformed form of the four-parameter logistic model (equation 1) (6). The calculated parameters allow estimates of the maximum specific growth rate (µ_max) and the lag phase (t_Lag).

(1)

In equation 1, t is the time (in hours), N(t) is the number of microorganisms at time t (CFU/gram), N_min and N_max are the minimum and maximum asymptotic cell concentration (CFU/gram), µ_max is the maximum specific growth rate (per hour), and t_i is the time (in hours) when half of the maximum cell concentration is reached. The duration of the lag phase (t_Lag) was calculated as described by Dalgaard (6).

1

(2)

(3)

Comparison between observed and predicted growth. The comparison between observed and predicted growth of pseudomonads on gilt-head seabream stored under dynamic temperature conditions was based on the bias and accuracy factors (39). The time to each observed pseudomonad count was compared to the time predicted to reach the same cell density as that observed. Accuracy and bias factors provide an indication of the average deviation between the model predictions and the observed results (39), and their closeness to a value of 1 is an effective and practical measure of predictive model validity. Bias and accuracy factors are defined as follows:

(4)

(5)

where t_observed (in hours) is the time to each observed pseudomonad count experimentally observed, t_predicted (in hours) is the time predicted to reach the same cell density as that observed, and n is the number of observations.

	RESULTS AND DISCUSSION

Top Abstract Introduction Materials and Methods Results and Discussion References

Experiments at constant temperature conditions. Pseudomonads have been established as the SSO of Mediterranean gilt-head seabream (Sparus aurata) stored under aerobic conditions at a temperature range from 0 to 15°C (20, 21, 22). In the present study, growth data from 23 experiments with aerobically stored gilt-head seabream under different isothermal conditions were collected, and the logistic function was used in order to calculate the kinetic parameters lag time (t_Lag), maximum growth rate (µ_max), and maximum cell concentration (N_max) of the pseudomonads (Table 1). The growth of pseudomonads, along with the fitted logistic curves, at five representative constant temperatures is shown in Fig. 1. Unlike t_Lag and µ_max, N_max was not affected significantly by the storage temperature, and it was found to be in the range of 8.4 ± 0.7 log CFU/g (average ± the standard deviation) (Table 1). At all temperatures tested, changes in the sensory characteristics of the fish followed closely the pseudomonad growth, and the end of shelf life was observed when pseudomonads reached an average value of 10⁷ CFU/g (Table 1). Similar results have reported in other studies with gilt-head seabream (20, 22), as well as with other Mediterranean fish species (21, 43).

View larger version (15K): [in this window] [in a new window]   FIG. 1.   Growth data and fitted logistic curves of pseudomonads on gilt-head seabream stored aerobically at 0 (), 2 (), 5 (), 8 (), 10 (), and 15 () °C.

View larger version (12K): [in this window] [in a new window]   FIG. 2.   Belehradek plots for the effect of temperature on µmax (a) and lag phase (b) of pseudomonad growth on aerobically stored gilt-head seabream.

View larger version (13K): [in this window] [in a new window]   FIG. 3.   Joint confidence intervals of the Belehradek model parameters for µmax (a) and lag phase (b) of pseudomonad growth on aerobically stored gilt-head seabream.

Prediction of lag time at dynamic temperature conditions. As can be seen from Table 1, the growth of pseudomonads on gilt-head seabream is characterized by a relatively significant lag phase that ranged from 7 to 40 h depending on the storage temperature. Considering that these lag values are approximately one-fifth of the total shelf life of the fish (Table 1), accurate predictions of lag time are crucial in shelf life modeling. In predicting lag time at changing temperatures, a better understanding of its determinant would be of great importance.

(6)

View larger version (13K): [in this window] [in a new window]   FIG. 4.   Linear regression between µmax and the lag phase of pseudomonad growth on gilt-head seabream stored under various isothermal conditions.

View larger version (13K): [in this window] [in a new window]   FIG. 5.   Theoretical graphical representation of microbial lag duration under nonisothermal conditions based on equation 6.

(7)

Prediction of growth under dynamic temperature conditions. Since temperature changes in a production and distribution chain are usually random and thus no mathematical expression can be used to describe the time-temperature variation, an accepted approach to predict microbial growth is to divide the time-temperature history into short assumed constant temperature time intervals (11). Microbial growth can then be simulated using one of the available sigmoid functions. In the present study, the growth of pseudomonads on gilt-head seabream at fluctuating temperatures was predicted using the logistic equation as follows:

(8)

where t_Lag is the duration of the pseudomonad lag phase and can be estimated from equation 7, N₀ is the initial pseudomonad cell concentration, dt_i (i = 1, 2, 3, etc.) is a short, assuming constant temperature time interval, N_ti is the cell concentration of pseudomonads at a time interval dt_i, µ_i is the maximum growth rate of pseudomonads at the temperature during dt_i, that can be estimated from the Belehradek equation (equation 2), and N_max is the maximum cell concentration of the pseudomonads. In addition, the 95% confidence intervals of the predicted pseudomonad growth curve were estimated based on the confidence intervals of the Belehradek plot regression lines for lag phase and maximum growth rate (Fig. 2). For example, the lower confidence interval of the predicted curve was estimated using the upper confidence interval of the lag phase and the lower confidence interval of the maximum growth rate. The confidence intervals of the predicted curve during the stationary phase were estimated based on the the confidence limits of the N_max calculated from the 23 replications.

Validation of the growth model under nonisothermal conditions. In order to evaluate the suitability of the model to predict the growth of pseudomonads under nonisothermal conditions, the predicted growth curves derived from equation 8 were compared to observed growth data from five experiments with gilt-head seabream at changing temperatures. The growth of pseudomonads at temperature scenarios that contained step temperature changes designed in the laboratory are shown in Fig. 6 to 9. A real temperature profile derived from the fish chilled chain is presented in Fig. 10. The latter profile corresponds to packaging of the fish and storage in the industry for 3 days. The fish were then transported to a distribution center, repacked, and stored for 1 week. A satisfactory agreement between predicted and observed growth for the profiles presented in Fig. 6, 8, 9, and 10 was obtained, and the observed growth data of pseudomonads were found to be within the confidence limits of the prediction lines. In Fig. 7 the observed datum points coincided with the lower confidence prediction line, mainly due to the underprediction of the lag-phase duration. In order to indicate the performance of the model, bias and accuracy factors were estimated for each temperature profile by treating each datum point as a separate observation. The observed time of each pseudomonad viable count was compared to the time required by the bacteria to reach the same population level, as predicted by the model. Although the latter approach is quite different from the one used for isothermal studies (39), it offers a useful index for the assessment of the model performance under changing temperature conditions (32). The bias and accuracy factors for all temperature profiles tested in the present study ranged from 0.91 to 1.17 and from 1.11 to 1.17, respectively (Table 3), indicating that there was a good agreement between predicted and observed growth. Other studies on bacterial growth at fluctuating temperature demonstrated that the bacteria were exposed to stress after a temperature shift resulted in an additional lag phase (1, 48). For example, Baranyi (1) reported that a step temperature change down to 3°C altered the physiological stage of B. thermosphacta and that the model failed to predict growth. This is not the case of the present study, where the model predicted satisfactory growth even after a temperature shift down to 0°C. These contradictory results could be due to the fact that the reference studies (1, 48) were conducted using laboratory media and pure cultures. The high preincubation temperature (25 or 30°C) of the bacterial cultures used in such studies, as well as the structure and composition of the growth medium may influence the behavior of microorganisms after a shift to low temperature (10, 13, 30). Indeed, temperature shifts close to 0°C did not cause any significant additional lag in the growth of endogenous bacteria on other real food products (32, 43).

View larger version (20K): [in this window] [in a new window]   FIG. 6.   Observed (datum points) and predicted (solid line) growth of pseudomonads on gilt-head seabream stored under nonisothermal conditions (profile 1). The dotted lines represent the 95% confidence limits of predicted growth.

View larger version (18K): [in this window] [in a new window]   FIG. 7.   Observed (datum points) and predicted (solid line) growth of pseudomonads on gilt-head seabream stored under nonisothermal conditions (profile 2). The dotted lines represent the 95% confidence limits of predicted growth.

View larger version (23K): [in this window] [in a new window]   FIG. 8.   Observed (datum points) and predicted (solid line) growth of pseudomonads on gilt-head seabream stored under nonisothermal conditions (profile 3). The dotted lines represent the 95% confidence limits of predicted growth.

View larger version (23K): [in this window] [in a new window]   FIG. 9.   Observed (datum points) and predicted (solid line) growth of pseudomonads on gilt-head seabream stored under nonisothermal conditions (profile 4). The dotted lines represent the 95% confidence limits of predicted growth.

View larger version (25K): [in this window] [in a new window]   FIG. 10.   Observed (datum points) and predicted (solid line) growth of pseudomonads on gilt-head seabream stored under nonisothermal conditions (profile 5). The dotted lines represent the 95% confidence limits of predicted growth.

Comparison between the shelf life observed and the shelf life predicted based on the pseudomonad growth model. The shelf life of fish can be predicted as the time required by the specific spoilage organisms to multiply from the initial level to a spoilage level (6, 20). In the present study, in order to evaluate the applicability of the pseudomonad growth model to predict the shelf life of gilt-head seabream at fluctuating temperatures, the time required by pseudomonads to reach 10⁷ CFU/g estimated with equation 7 was compared to the observed shelf life derived from the sensory analysis for each temperature profile tested. In addition, 95% confidence limits for the prediction of shelf life were estimated based on the time required by the confidence limits of the predicted pseudomonad growth to reach 10⁷ CFU/g. The results from the comparison are shown in Table 4. In four of five cases the difference between the observed and predicted shelf lives was <11% and in one case was 18%, while the average difference was 5.8%. The validation of the model showed that it is able to describe satisfactorily the growth of pseudomonads under nonisothermal conditions and to provide realistic shelf life predictions.