## Introduction

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 *N*_{0}, 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 *k*_{max1} and *k*_{max2} 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 log_{10}.

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.