Efstathios Z. Panagou, Institute of Technology of Agricultural Products, National Agricultural Research Foundation, 1. Sof. Venizelou, Lycovrissi GR-141 23, Greece. E-mail: email@example.com
Aims: The aim of this research was to: (i) determine the inactivation pattern of a pressure-resistant strain of Pediococcus damnosus by high hydrostatic pressure in phosphate buffer (pH 6·7) and gilt-head seabream using the linear, biphasic and Weibull models; and (ii) validate the applicability of the Weibull model to predict survival curves at other experimental pressure levels.
Methods and Results: A pressure-resistant strain of P. damnosus was exposed to a range of pressures (500, 550, 600 and 650 MPa) in phosphate buffer (pH 6·7) and gilt-head seabream for up to 8 min at ambient temperature (23°C). Inactivation kinetics were described by the linear, biphasic and Weibull models. Increasing the magnitude of the pressure applied resulted in increasing levels of inactivation. Pronounced tailing effect was observed at pressures over 600 MPa. The Weibull and biphasic models consistently produced better fit than the linear model as inferred by the values of the root mean squared error, coefficient of determination (R2) and accuracy factor (Af). The scale factor (b) of the Weibull model was linearly correlated with pressure (P) treatment in the whole pressure range. Substituting the b parameter in the initial Weibull function and calculating the shape factor (n) by linear interpolation, high pressure (P) was directly incorporated into the model providing reasonable predictions of the survival curves at 570 and 630 MPa. Comparison between the survival curves in phosphate buffer and gilt-head seabream showed a clear protective effect of the food matrix on the resistance of the micro-organism, especially at 500 and 550 MPa.
Conclusions: The Weibull and biphasic models were more flexible to describe the survival curves of P. damnosus in the experimental pressure range, taking also into account the tailing effect that could not be included in the linear model. The Weibull model could also give reasonable predictions of the survival curves at other experimental pressures in both pressure menstrua. As the food matrix has a protective effect in microbial inactivation, the development of accurate mathematical models should be done directly on real food to avoid under- or over-processing times.
Significance and Impact of the Study: The development of accurate models to describe the survival curves of micro-organisms under high hydrostatic pressure treatment would be very important to the food industry for process optimisation, food safety and extension of the applicability of high pressure processing.
Over the last years, high hydrostatic pressure has been employed as an emerging and promising technology for non-thermal processing of foods, allowing inactivation of pathogenic and spoilage micro-organisms with fewer changes in texture, colour and flavour when compared with conventional technologies (Cheftel 1992; Hoover 1993; Smelt 1998). Thus, high pressure treatment of foods has the potential to produce high quality foods that are microbiologically safe and with extended shelf-life (Spilimbergo et al. 2002; Patterson 2005; Torres and Velazquez 2005). Today, a variety of pressure-treated products such as jams, fruit juices, avocado salad (guacamole), fresh-cut fruit salads, fresh whole oysters, etc. are commercially available in the USA, Europe and Japan (Torres and Velazquez 2005). However, because of the high cost of initial investment and the fact that the process is mainly batch-type, target applications include heat-sensitive products or products in which quality superiority and marketability compensates for the additional processing cost.
To establish a process that is sufficiently good for the safety of a food commodity, the pressure-destruction kinetics of spoilage and pathogenic micro-organisms related to the specific product should be established (Stoforos and Taoukis 2001). The inactivation of micro-organisms by heat and other stress factors has been traditionally assumed to follow first-order kinetics (Raffalli et al. 1994; Schaffner and Labuza 1997; Ponce et al. 1998; Peleg 1999). This approach is based on the assumption that the survival time is identical for all the cells of the population. However, this is hardly the case and several papers have been published reporting deviation from linearity (Cerf 1977; Peleg and Cole 1998; Xiong et al. 1999; van Boekel 2002; van Opstal et al. 2005). In the conventional first-order kinetics approach, when survival curves are not linear, the D-value is usually determined by considering the linear segment of the curve, resulting thus in over- or under-estimation of processing times for the commodity (Peleg and Cole 1998). To overcome this problem several other models have been proposed for the description of the inactivation curve, such as the modified Gompertz (Bhaduri et al. 1991), log-logistic (Cole et al. 1993), Baranyi (Baranyi et al. 1996) and Weibull (Peleg and Cole 1998) models. In addition, the performance of several nonlinear models on the inactivation kinetics of Bacillus cereus, Yersinia enterocolitica, Escherichia coli O157:H7, Listeria monocytogenes and Lactobacillus sake has been reported by Geeraerd et al. (2000).
In the last years, the model based on the Weibull frequency distribution has gained wide acceptance because of its simplicity and flexibility. Peleg and Cole (1998) expressed this model in the following logarithmic form:
where N0, the initial number of cells (CFU ml−1 or g−1); N, the number of survivals after an exposure time t (CFU ml−1 or g−1); t, the holding time (min) at pressure and b, n are the scale and shape factors respectively. This modelling approach assumes that the survival time of each cell of the population follows a Weibull distribution. The model describes both convex (n > 1) and concave (n < 1) survival curves. In the special case of n = 1 the model describes the traditional first-order curve (Mafart et al. 2002). Nowadays, the Weibull model has been successfully used to describe microbial inactivation by different methods such as heat, high hydrostatic pressure, pulsed electric fields and chemical agents (Fernández et al. 1999; Álvarez et al. 2002, 2003; Chen and Hoover 2003a; Virto et al. 2005, 2006).
Nonlinear inactivation curves can also be described by a biphasic model proposed by Cerf (1977), based on the assumption of two populations, a sensitive (fast inactivating) and a resistant (slow inactivating). This leads to a curve with two distinct segments of linearly decreasing populations, the second (more resistant) with a less negative slope. This model can be formulated as follows (Geeraerd et al. 2005):
where f is the fraction of the initial population in a major subpopulation, (1 − f) is the fraction of the initial population in a minor (more heat resistant) subpopulation, and kmax1 and kmax2 are the inactivation rates of the two populations respectively.
Gilt-head seabream (Sparus aurata) is a Mediterranean fish of high consumption and hence commercial interest in the region. Spoilage of fish is the result of the production of off-odours and -flavours mainly caused by bacterial activity (Koutsoumanis and Nychas 2000). Lactic acid bacteria are typically involved in a large number of food fermentations but also play an important role as spoilage microflora. Although lactic acid bacteria are not considered to belong to aquatic environments, species of certain genera are not rare in freshwater fish (González et al. 2000) and river water (Stiles and Holzapfel 1997), while some species have been isolated from diseased fish (Baya et al. 1991). A pressure-resistant strain of Pediococcus damnosus was isolated and identified in our laboratory from the spoilage microflora of high pressure-treated gilt-head seabream. The strain was screened together with 18 other strains of lactic acid bacteria and it was found to tolerate 450 MPa for 10 min with a reduction in viable counts of only 1·8 log10.
The objective of this research was to: (i) model the survival curves of the pressure-resistant strain of P. damnosus in phosphate buffer (pH 6·7) and gilt-head seabream using the linear, biphasic and Weibull models and compare the goodness-of-fit of these models; (ii) determine whether the Weibull model could be used successfully to predict survival curves at pressures other than the experimental pressure levels; and (iii) compare survival curves derived from phosphate buffer and gilt-head seabream.
Materials and methods
Preparation of the inoculum
A pressure-resistant strain of P. damnosus was isolated and identified from previous experiments carried out in our laboratory on gilt-head seabream. Stock cultures of the organism were maintained in vials of treated beads in a cryoprotective fluid (Protect Bacterial Preservers; Technical Service, Lancashire, UK) at −80°C. For revival, five separate beads were transferred in 10 ml of MRS broth (Merck 1·10661, Darmstadt, Germany) and incubated at 30°C for 24 h. The culture was renewed three times at the same conditions and kept at 4°C until use. For growth, a loopful of the culture was transferred in 100 ml of MRS broth and incubated at 30°C for 18–20 h. The cells were harvested by centrifugation at 4500 g for 10 min and washed twice with sterile phosphate-buffered solution (pH 6·7). The suspension [c. 108 cells ml−1 assessed by the microscopic count with a Neubauer counting chamber (Brand, Wertheim, Germany)] served as the inoculum for all the experiments.
The high-pressure system (Resato International B.V., Roden, Holland) consists of a high-pressure intensifier unit for the buildup of pressure in the system and an electric motor to drive a hydraulic pump. The oil in the pump is used to propel the oil-driven double-acting intensifier, which is actually a hydraulically driven reciprocating pump. In the intensifier, the pressure of the high-pressure fluid (Resato International B.V. high-pressure fluid-glycol emulsion) is ranged up to 1000 MPa. The pressure is adjustable in steps of c. 25 MPa.
The system consists of a block of six small (42 ml) high-pressure vessels measuring 2·5 cm in diameter and 10 cm in length respectively. The vessels are closed with a unique Resato thread connection on the top of the vessel. The pressure is transmitted from the intensifier to the vessels by the pressure fluid through high-pressure stainless steel tubing. Air-operated high-pressure needle valves are used for the control of circulation of pressure fluid, so that each vessel operates independently. Each vessel is equipped with a heating/cooling jacket to control experimental temperature in a range from −40 to +100°C. Temperature transmitters are mounted in each vessel to monitor temperature. Finally, two pressure transducers are used to monitor the pressure in the system.
In phosphate buffer (pH 6·7): Aliquots of 3·3 ml of sample containing 0·3 ml of cell suspension and 3·0 ml of phosphate-buffered solution (pH 6·7) were transferred in polyethylene pouches (20 mm width × 80 mm length) and heat sealed. Every pouch was placed in a second slightly bigger one to prevent accidental leakage of cell suspension and contamination of the pressurizing liquid. The pouches were placed in each of the six small vessels of the high-pressure unit and the system was pressurized at 500, 550, 600 and 650 MPa respectively. The initial temperature of the vessel jacket was adjusted to 23°C by means of a water–glycerol solution circulating from a water bath. The pressure in the system and the temperature in each vessel was monitored and recorded through the PLC system (Resato International, Roden, Holland). The come-up rate was approximately 100 MPa per 7 s and the pressure release time was <3 s. At selected time intervals, pressure vessels were isolated individually from the pressure system and the pressure of this vessel was released. Each experiment was repeated two times and duplicate pouches were used for each treatment.
In gilt-head seabream fish: Fresh, gilt-head seabream fish was obtained from a local super-market and transported in ice into the laboratory within 30–45 min. On arrival, the fish was dipped in alcohol and flamed for a few seconds to sterilize the outside part of the skin and thus avoid contamination during the preparation of fillets. A square piece of skin was removed aseptically and a muscle fillet was cut from the dorsal part of the fish. The fillet was cut into pieces and portions weighing 3 g were transferred aseptically into the pouches and were inoculated with 0·3 ml of the prepared cell suspension. The pouches were finally subjected to the same pressurization levels as above. Immediately after the pressure treatment the pouches were aseptically opened and the content homogenized with 27 ml of 1/4 sterile Ringer's solution in a Stomacher (Lab-Blender 400; Seward Medical, London, UK) for 2 min.
Enumeration of survivors
Pressurized pouches were serially diluted in 1/4 sterile Ringer's solution (Merck 1·15525). One millilitre of at least three serial dilutions was poured in duplicate on MRS agar plates (Merck 1·10660). The plates were incubated at 30°C for 96 h before enumeration to allow injured cells to form visible colonies. The data from the plate counts were transformed to log10 values prior to further analysis.
Survival curves were fitted using the nonlinear regression procedure of Statistica (Release 6·0; StatSoft Inc., Tulsa, OK, USA) to determine the parameters of the biphasic and Weibull models and the regression procedure for the linear model. The goodness-of-fit of the models was assessed using coefficient of determination (R2), root mean squared error (RMSE) and accuracy (Af) factors (Ross 1996).
The Weibull model was evaluated to see whether it could predict survival curves at pressures other than the experimental pressure levels. To this end, two pressure levels within the range used to develop the model were selected, namely 570 and 630 MPa. Pressurization of inoculated samples of both buffer and gilt-head seabream fish was performed at room temperature (23°C). At predetermined time intervals, counts of the micro-organism were determined and compared with the survival curves predicted by the Weibull model. The goodness of predictions was estimated by the RMSE, Bf and Af indices.
The survival curves of P. damnosus in phosphate buffer (pH 6·7) fitted with the linear, biphasic and Weibull models are presented in Fig. 1. Tailing was observed, particularly at high-pressure levels, indicating that the traditional linear model was not appropriate in describing the experimental data, and thus non-linear models were better for this purpose. More specifically, at 500 and 550 MPa the inactivation pattern was close to linearity; however, at 600 and 650 MPa a pronounced downward curvature was observed followed by tailing after 2-min treatment time corresponding to c. 5-log10 reductions. Extending the treatment time to 5 min only increased reduction by 0·4 and 0·8 log10 at 600 and 650 MPa respectively. Among the three models compared, the biphasic model consistently produced the best fit to all the survival curves, as indicated by the lowest RMSE and Af values and the highest R2 values at all pressures studied (Table 1). The linear model produced the poorest fit to the experimental data as inferred by the systematically higher RMSE and Af values and the lowest R2 values, regardless of pressure applied. The linear model gave reasonably good fit at 500 and 550 MPa but failed to describe the tailing effect at 600 and 650 MPa. Finally, the Weibull model gave better performance than the linear model; however, it was not as efficient as the biphasic model to describe the tailing effect at 600 and 650 MPa (Fig. 1).
Table 1. Comparison of goodness of fit of the linear, biphasic and Weibull models for the survival curves of Pediococcus damnosus in phosphate buffer (pH 6·7)
Root mean squared error
Accuracy factor (Af)
As the linear model could not produce good fit in the experiments conducted in phosphate buffer, it was decided to apply only the biphasic and Weibull models in the high-pressure treatment of gilt-head seabream (Fig. 2). The shape of the curves was again depended on the pressure applied, being close to linear at 500 and 550 MPa and concave at 600 and 650 MPa. A tailing effect was noticeable in the experimental data after 2-min treatment at 600 and 650 MPa. The goodness-of-fit of the two models was assessed by calculating the R2, RMSE and Af values. Comparing the individual values in Table 2, it can be concluded that the Weibull model produced good fit to the survival data at 500 and 550 MPa but it was less accurate in describing the tailing effect at 600 and 650 MPa compared with the biphasic model that produced better fit of the tailing effect (Fig. 2, Table 2).
Table 2. Goodness-of-fit of the biphasic and Weibull models for the survival curves of Pediococcus damnosus in gilt-head seabream
Root mean squared error
Accuracy factor (Af)
As the Weibull model produced a reasonably good fit to the survival curves at this pressure range, additional experiments were undertaken to determine whether this model could be used to predict the survival of P. damnosus at other pressure levels (570 and 630 MPa) in phosphate buffer and gilt-head seabream. Both b and n values were pressure dependent (Fig. 3). In the pressure range studied, the b values had a linear relationship with pressure, expressed by the following equation:
Substituting eqn (3) into eqn (1) we get eqn (4) that can predict the survival curves at other pressure levels:
The n values corresponding to 570 and 630 MPa pressure levels were estimated by linear interpolation from Fig. 3 and applied directly in eqn (4). The predicted survival curves are presented in Fig. 4. The model produced relatively good predictions at both pressure levels, as indicated by the calculated values of RMSE, Bf and Af that were 0·67, 1·01, 1·12 and 0·57, 1·04, 1·09 at 570 and 630 MPa respectively.
In the case of gilt-head seabream the factor b had also a linear trend with pressure given by eqn (5):
The n values were estimated again by linear interpolation as in the case of phosphate buffer. The model produced reasonably good predictions at 630 MPa, as indicated by the values of RMSE, Bf and Af being 0·42, 1·04 and 1·12 respectively. However, at 570 MPa, the model could not describe satisfactorily the tailing effect observed after 4 min (Fig. 4) (RMSE 1·11, Bf 1·19, Af 1·22).
A comparison of the survival curves of P. damnosus in phosphate buffer and gilt-head seabream showed that at 500 and 550 MPa the shape of the curves was close to linear while at 600 and 650 MPa all survival curves were concave. Moreover, the survival curves of the fish were constantly higher at all treatment times in comparison with phosphate buffer. This difference was minimized at higher-pressure levels and a pronounced tailing effect was observed after 2-min treatment time in both cases.
Determination of the kinetic parameters during microbial inactivation, whether through thermal high pressure, chemical or other processes, is a rather complicated task. So far, the industry has employed the approach of first-order kinetics to determine D and z values for food processing. This approach is based on the assumption that the cells of a population are homogeneous with identical inactivation times. Interestingly, many survival curves do not follow linear trend and exceptions occur in the form of shoulders and/or tailing (Cerf 1977), suggesting that this approach is not always correct. Even in the case of a pure culture, biological heterogeneity among the cells results in subpopulations with individual inactivation kinetics. As a result, inactivation curves could be regarded as the cumulative form of underlying distribution of individual inactivation times (van Boekel 2002; Avsaroglu et al. 2005; Buzrul et al. 2005).
In our work, it was evident that survival curves deviated from linearity in both phosphate buffer and gilt-head seabream and the shapes of the curves changed considerably according to the treatment pressure level (Figs 1 and 2). Consequently, forcing a straight line through the data points and taking into consideration first-order kinetics, considerable errors could have arisen in the determination of inactivation time, since the linear model did not produce a good fit to the survival curves in terms of RMSE, R2 and Af values (Table 1). For instance, if the target reduction of P. damnosus in phosphate buffer was 4 log10, the processing time would be 1·7 min at 600 MPa and 1·25 min at 650 MPa based on the Weibull model (Fig. 1). The relevant figures for the biphasic model would be 1·55 and 1·35 min at 600 and 650 MPa respectively. However, based on the linear model the corresponding time would be 2·5 min at 600 MPa and 1·99 min at 650 MPa, i.e. a 47% and 59% increase in processing time compared with the Weibull model.
In the Weibull model scale (b) and shape (n) factors were pressure dependent in both phosphate buffer and gilt-head seabream (Fig. 3). This observation is in agreement with other researchers (Peleg and Cole 2000; Mattick et al. 2001) who reported temperature dependence of b and n during thermal inactivation treatment of Clostridium botulinum and Salmonella spp. The b values presented an almost linear relationship in the entire set of pressure range (R2 = 0·94 in both pressure menstrua) (Fig. 3). This linear trend has been reported elsewhere (Chen and Hoover 2003b) for pressure inactivation of Y. enterocolitica and thermal inactivation of C. botulinum (Peleg and Cole 2000), L. monocytogenes, Salmonella typhimurium and Lactobacillus delbruecki (van Boekel 2002). The transformation of the initial Weibull model [eqn (1)] in which the b parameter was substituted by the linear relationship of pressure (P) produced an equation that could predict the survival curves of P. damnosus at pressures other than the experimental pressure levels. The shape (n) factors for the new pressure levels (570 and 630 MPa) were calculated by linear interpolation as reported elsewhere (Chen and Hoover 2003a). This model produced reasonably good prediction of the survival curves at 570 and 630 MPa for both phosphate buffer and gilt-head seabream as shown both graphically (Fig. 4) and numerically by the calculated RMSE, Bf and Af indices.
Although the nature of the model is empirical, n values can be associated with microbial inactivation (van Boekel 2002). Values of n > 1 indicate that the remaining cells become increasingly damaged over time, so there is cumulative damage occurring making survival increasingly difficult, whereas values of n < 1 indicate that the remaining cells are adaptive to the applied stress. Therefore, concave (n < 1) survival curves observed in both phosphate buffer and gilt-head seabream particularly at 600 and 650 MPa (Figs 1 and 2) could be regarded as evidence that sensitive subpopulations of P. damnosus were inactivated at a relatively fast rate leaving behind surviving cells of higher resistance to high pressure. Because of the differences in the resistance to pressure between the pressure-sensitive and pressure-resistant subpopulation, a tailing effect was observed at above 550 MPa. In the literature, both convex and concave survival curves fitted with the Weibull model have been reported for other food commodities and micro-organisms (van Boekel 2002; Mafart et al. 2002; Chen and Hoover 2003a, 2004; Avsaroglu et al. 2005; Buzrul et al. 2005; van Opstal et al. 2005; Virto et al. 2005, 2006).
Pressure sensitivity of vegetative bacteria is influenced by the composition of the food matrix, as certain food constituents such as proteins, lipids and carbohydrates can have a protective effect (Simpson and Gilmour 1997). This is well exemplified in our work (Figs 1 and 2) where differences in the survival curves of P. damnosus in phosphate buffer and gilt-head seabream were evident. They were more pronounced at 500 and 550 MPa, where the protective effect of the fish structure over the buffer was clear, but increasing the pressure to 600 and 650 MPa resulted in less distinct differences. Apparently, the protective effect of food structure was overcome by higher pressures. So, studying the survival of P. damnosus in phosphate buffer and extrapolating the data to gilt-head seabream is an error prone approach, resulting in considerable underestimation of the surviving population in the food and hence it would result in under-processing times. For instance, a treatment of 500 MPa for 4·5 min in phosphate buffer (pH 6·7) gave a 4-log10 reduction of the micro-organism (Fig. 1). However, the same treatment gave only a 2·4-log10 reduction in gilt-head seabream, whereas a 4-log10 reduction would have been achieved in 6·8 min (Fig. 2). Consequently, inactivation data obtained using buffers or other synthetic media should not be extrapolated to real food situations where a more severe pressure treatment would be necessary to achieve the same level of inactivation (Patterson 2005). Our findings are consistent with several authors who reported that bacteria are more resilient in a complex food matrix than a buffer at the same pH (Styles et al. 1991; Patterson et al. 1995; Garcia-Graells et al. 1999; Hugas et al. 2002; Chen and Hoover 2003b). However, this observation is not supported by all researchers (Garcia-Risco et al. 1998; Gervilla et al. 2000) complicating thus the development of safe preservation process by high hydrostatic pressure.
In conclusion, the biphasic and Weibull models gave more accurate predictions of inactivation of P. damnosus at different high pressure levels compared with the linear model, with the biphasic model being better in describing the tailing effect observed at 600 and 650 MPa in both phosphate buffer and gilt-head seabream. In addition, the Weibull model allowed reasonable predictions to be made at pressures different from experimental pressures. A comparison of the survival curves in buffer and gilt-head seabream indicated a protective effect of the food matrix in the survival of the micro-organism.
The present work is part of the EPAN-TR24 ‘Systematic study of the applicability of the novel non-thermal technology of High Hydrostatic Pressure for the production of Greek products of optimum quality’ project funded by the General Secretariat of Research and Technology of the Greek Ministry for Development.