Identification of the Listeria monocytogenes survival curves in UHT whole milk utilising local linear wavelet neural networks

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Abstract

The aim of the present work is to investigate the capabilities of a wavelet neural network for describing the inactivation pattern of Listeria monocytogenes by high hydrostatic pressure in milk, and to compare its performance against classic neural network architectures and models utilised in food microbiology. A new wavelet network is being proposed that includes a “product operation” layer between wavelet functions and output layer, while the connection output-layer weights have been replaced by a local linear model. Milk was artificially inoculated with an initial population of the pathogen and exposed to a range of high pressures (350, 450, 550, 600 MPa) for up to 40 min at ambient temperature (25 °C). Models were validated at 400 and 500 MPa with independent experimental data. First or second order polynomial models were employed to relate the inactivation parameters to pressure, whereas all learning-based networks were utilised in a standard identification approach. The prediction performance of the proposed local linear wavelet network was better at both validation pressures. The development of accurate models to describe the survival curves of microorganisms in high pressure treatment would be very important to the food industry for process optimisation, food safety and would eventually expand the applicability of this non-thermal process.

Highlights

► Modelling of the Listeria monocytogenes survival curves in UHT whole milk. ► Development of a novel wavelet neural network (WNN) architecture. ► Comparison of the WNN scheme against other “classic” neural network architecture and models used in food microbiology. ► Evaluation made using well known performance indices.

Introduction

There has been continued interest in the food industry in using high hydrostatic pressure processing as a non-thermal preservation technique. Its primary advantage is that it can inactivate microorganisms and certain enzymes at ambient temperature, thus avoiding the detrimental effects of cooking temperatures on various food quality attributes, such as nutritional value, flavour and taste (Smelt, 1998). A variety of pressure-treated commercial products such as jams, fruit juices, guacamole, and fresh whole oysters, are already commercially available in the United States, Japan and Europe (Torres & Velazquez, 2005), whereas another potential application in the food industry is the production of novel meat, poultry, fish and dairy products. However, as foods are frequently implicated as carriers of foodborne pathogens, it is important to provide information on the effect of high-pressure processing on these micro-organisms. The inactivation of micro-organisms by high pressure is well documented; typically, vegetative pathogens can be inactivated at a pressure range of 200–700 MPa (Patterson & Kilpatrick, 1998; Tholozan, Ritz, Jugiau, Federighi, & Tissier, 2000). The exact mechanism of high pressure inactivation has been fully elucidated, but it is generally accepted that high pressure results in morphological, genetic and biochemical alterations causing cell death due to accumulated damage (Simpson & Gilmour, 1997).

Listeria monocytogenes is a ubiquitous foodborne pathogen associated with outbreaks of listeriosis from consumption of various food commodities, such as vegetables, dairy products, seafood and meat (Gandhi & Chikindas, 2007). The pathogen is of great health concern for the food industry, because it is characterised by high mortality rates, especially in pregnant women, neonates, elderly and immune-compromised (McLauchlin, Mitchell, Smerdon, & Jewell, 2004). The pathogen can grow at refrigeration temperatures and survive in foods for prolonged periods of time under adverse conditions (Little et al., 2007). It is a very hardy micro-organism that can grow over a wide range of pH values (4.3–9.1) and temperature ranges from 0 to 45 °C. In addition, it is relatively resistant to desiccation and can grow at aw values as low as 0.90 (Nolan, Chamblin, & Troller, 1992). 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 and described in detail (Stoforos & Taoukis, 2001). The inactivation of micro-organisms by heat and other processing methods has been traditionally assumed to follow first-order kinetics. All cells or spores in a population are assumed to have equal resistance to lethal treatments, and therefore a linear relationship between the fall in the logarithm of the number of survivors over treatment time would be expected (Schaffner & Labuza, 1997). However, significant deviations from linearity have frequently been reported (Peleg & Cole, 1998). Three kinds of deviations have been observed: curves with a shoulder, curves with tailing, and sigmoid-type curves. A number of models have been proposed to describe these nonlinear survival curves, such as the Weibull (Van Boekel, 2002), modified Gompertz (Bhaduri et al., 1991), Baranyi (Baranyi & Roberts, 1994), Chiruta (Geeraerd, Herremans, & Van Impe, 2000), and the Xiong (Xiong, Xie, Edmonson, & Sheard, 1999) models. This is also the case with high pressure processing, where recent studies indicate that microbial survival curves do not necessarily follow first-order kinetics. A quasi-chemical model was used by Ross, Taub, Doona, Feeherry, & Kustin (2005) for describing nonlinear survival curves. Chen and Hoover used a linear and three nonlinear models, Weibull, log-logistic, and modified Gompertz functions, to fit the pressure inactivation data of Yersinia enterocolitica and viruses (Chen & Hoover, 2003). The Weibull and log-logistic models consistently produced better fits than the linear and modified Gompertz models for these two micro-organisms.

Developing models from observed data is a fundamental problem in many fields, such as statistical data analysis, signal processing, control, forecasting, and computational intelligence. This problem is also frequently referred to as function estimation or approximation and system identification. There are two general approaches to function learning, namely, the parametric and the non-parametric approach. When the observed data is contaminated (such that it does not follow a pre-selected parametric family of functions or distributions closely) or when there are no suitable parametric families, the non-parametric approach provides more robust results and hence, is more appropriate.

Neural networks have become a popular tool in non-parametric function learning due to their ability to learn rather complicated functions. The multi-layer perceptron (MLP), along with the back-propagation (BP) training algorithm, is probably the most frequently used type of neural network in practical applications (Haykin, 1999). However, due to its multilayered structure and the greedy nature of the BP algorithm, the training processes often settle in undesirable local minima of the error surface or converge too slowly. The radial basis function (RBF) network (Ham & Kostanic, 2001), as an alternative to the MLP, has a simpler structure. With some pre-processing on the training data, such as clustering, the training of RBF networks can be much easier than MPL networks. From the point of view of function representation, an RBF network is a scheme that represents a function of interest by using members of a family of compactly (or locally) supported basis functions. The locality of the basis functions makes the RBF network more suitable in learning functions with local variations and discontinuities (Chen, Cowan, & Grant, 1991). Furthermore, the RBF networks can represent any function that is in the space spanned by the family of basis functions. However, the basis functions in the family are generally not orthogonal and are redundant. This means that for a given function, its RBF network representation is not unique and is probably not the most efficient. In literature, some unsupervised clustering techniques were widely used for RBF centre determination according to the input disturbances (Uykan, Guzelis, Celebi, & Koivo, 2000).

In recent years, wavelets have become a very active subject in many scientific and engineering research areas. Especially, wavelet neural networks (WNN), inspired by both the feed-forward neural networks and wavelet decompositions, have received considerable attention and have become a popular tool for function approximation (Zhang & Gilbert, 1995). The main characteristic of WNNs is that some kinds of wavelet functions are used as the nonlinear transformation function in the hidden layer, instead of the usual sigmoid function. Incorporating the time-frequency localisation properties of wavelets and the learning abilities of general neural network, WNN has shown its advantages over the regular methods such as NN for complex nonlinear system modelling (Stephen & Wei, 2005).

The aim of the current research study is to investigate the feasibility of utilising WNN methodology as an alternative to classical neural networks in the area of food microbiology. The proposed, in this paper, WNN scheme incorporates some modifications compared to classic WNNs, in order to enhance its performance. A classic WNN employs nonlinear wavelet basis functions (named wavelets) instead of using common sigmoid activation functions. The output of the network is a weighted sum of a number of wavelet functions. The proposed multiplication wavelet neural network with local linear weight coefficients (MWNN-LCW) incorporates a “product-operation” layer adopted from the basic neuro-fuzzy Larsen architecture (Rutkowska, 2002). In addition, the connection weights between the hidden layer neurons and output neurons are replaced by a local linear model, similar to the output layer appeared in ANFIS neuro-fuzzy system (Jang, 1993). The overall objective of this study is to design an accurate one-step-ahead prediction scheme to model the survival of Listeria monocytogenes in ultra high-temperature (UHT) whole milk during high pressure treatment using the proposed MWNN-LCW structure. The proposed prediction scheme is compared against multilayer neural perceptron (MLP), radial basis function network (RBF) and a dynamic recurrent Elman network. Similarly, an assessment will be made against three well-known for the food microbiology, nonlinear conventional models (Weibull, Gompertz, Geeraerd) and an evaluation will be conducted to compare the goodness-of-fit of these models.

Section snippets

Bacterium and preparation of cell suspension

Listeria monocytogenes NCTC 10527 from the collection of the Laboratory of Microbiology and Biotechnology of Foods was used throughout this study. Stock cultures were maintained in vials of treated beds in a cryoprotective fluid (Protect Bacterial Preservers, Technical Service Consultants Ltd., Heywood, UK) at -80°C until use. The culture was revived by inoculation in 9 ml of Tryptic Soy Broth (TSB, 402155, Biolife, Milan, Italy) supplemented with 0.6% yeast extract and incubation at 30 °C for 24 

Primary modelling

The survival curves of L. monocytogenes during high pressure inactivation were fitted with three primary models to determine the kinetic parameters of L. monocytogenes in UHT whole milk. The first model applied was the re-parameterized Gompertz equation (Zwietering, Jongenburger, Rombouts, & Van’t Riet, 1990) determined by the following equation:log10N(t)=log10N(0)+A·exp-expk·eA·(ts-t)+1where ts (min) is the duration of the shoulder, k (min−1) is the maximum specific inactivation rate, N(0) (log

Wavelet transform

Wavelet techniques can offer added insight and performance in data analysis situations where Fourier techniques have previously been used (Young, 1993). The basis functions of the Fourier transform consist of sine and cosine, while basis functions of wavelet transform consist of the dilated and translated versions of the mother wavelet. The basis functions for both transforms are localised in frequency, but wavelet functions are also localised in space. The time–frequency resolution differences

Model validation

The proposed wavelet network, classic neural network approaches as well as statistical models were comparatively evaluated to determine whether they could successfully predict the responses of the pathogen at pressure levels other than those initially selected for model development. For this reason, two different high pressure levels, within the range employed to develop the models, were selected, namely 400 and 500 MPa. Additional milk pouches were prepared, inoculated with the pathogen and

Nonlinear dynamic system identification

In general, dynamic systems are complex and nonlinear. An important step in nonlinear systems identification is the development of a nonlinear model. In recent years, computational-intelligence techniques, such as neural networks, fuzzy logic and combined hybrid systems algorithms have become very effective tools of identification of nonlinear plants. The problem of identification consists of choosing an identification model and adjusting the parameters, such that the response of the model

Discussion of results

The objective of this study was to investigate the feasibility of using a WNN scheme for the development a series–parallel model of survival curves of L. monocytogenes under high pressure in whole milk. The survival curves of L. monocytogenes inactivated by high hydrostatic pressure were obtained at six pressure levels (350, 400, 450, 500, 550 and 600 MPa) in UHT whole milk (Fig. 6). Interestingly, the shapes of the survival curves that follow those experimental data change considerably

Conclusion

In conclusion, the survival curves of L. monocytogenes in UHT whole milk could have different shapes depending on the treatment pressure levels. The development of accurate mathematical models to describe and predict pressure inactivation kinetics of microorganisms, such L. monocytogenes should be very beneficial to the food industry for optimisation of process conditions and improved dependability of HACCP programs. In this research study we have developed a new type of wavelet neural network,

Acknowledgements

The authors would like to thank Dr. C. Tassou and Dr. K. Mallidis from the Institute of Technology of Agricultural Products (ITAP) of the National Agricultural Research Foundation (NAGREF) for providing the high pressure equipment for the experiment. The assistance of Dr. E.Z. Panagou from AUA is also greatly appreciated.

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      First, an overview of inactivation kinetic models is presented, followed by a discussion on the different factors influencing the inactivation of L. monocytogenes induced by the application of HHP technology, which include technological parameters, food matrix characteristics and culture conditions. Various predictive models are available for HHP inactivation of L. monocytogenes or Listeria innocua (a L. monocytogenes surrogate for processing plant safety purposes) in food simulated systems (Ates, Rode, Skipnes, & Lekang, 2016; Doona, Feeherry, Ross, & Kustin, 2012), meat products (Bover-Cid et al., 2011, 2015;; Carlez, Rosec, Richard, & Cheftel, 1993; Hereu, Dalgaard, et al., 2012; Lerasle et al., 2014; Rubio, Possas, Rincón, García-Gímeno, & Martínez, 2018), fish (Ramaswamy, Zaman, & Smith, 2008), seafood (Das et al., 2016; Fletcher, Youssef, & Sravani, 2008), milk (Amina, Kodogiannis, Petrounias, Lygouras, & Nychas, 2012; Buzrul, Alpas, Largeteau, & Demazeau, 2008; Chen & Hoover, 2003, 2004), dairy products (Shao, Ramaswamy, & Zhu, 2007) and RTE vegetables (Jung, Lee, Kim, Cho, & Ahn, 2014; Muñoz, Ancos, Sa, & Cano, 2006). Although bacterial resistance to HHP has been reported to be higher in solid foods than in culture media and liquid foods (Ates et al., 2016; Bover-Cid et al., 2015), a substantial number of modelling approaches developed in buffered solution and culture media is available in literature (Muñoz-Cuevas et al., 2013).

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