Survival curves of Listeria monocytogenes in chorizos modeled with artificial neural networks.

Using artificial neural networks (ANNs), a highly accurate model was developed to simulate survival curves of Listeria monocytogenes in chorizos as affected by the initial water activity (a(w0)) of the sausage formulation, temperature (T), and air inflow velocity (F) where the sausages are stored. The ANN-based survival model (R(2)=0.970) outperformed the regression-based cubic model (R(2)=0.851), and as such was used to derive other models (using regression) that allow prediction of the times needed to drop count by 1, 2, 3, and 4 logs (i.e., nD-values, n=1, 2, 3, 4). The nD-value regression models almost perfectly predicted the various times derived from a number of simulated survival curves exhibiting a wide variety of the operating conditions (R(2)=0.990-0.995). The nD-values were found to decrease with decreasing a(w0), and increasing T and F. The influence of a(w0) on nD-values seems to become more significant at some critical value of a(w0), below which the variation is negligible (0.93 for 1D-value, 0.90 for 2D-value, and <0.85 for 3D- and 4D-values). There is greater influence of storage T and F on 3D- and 4D-values than on 1D- and 2D-values.

Modeling the survival of Salmonella spp. in chorizos.

The survival of Salmonella spp. in chorizos has been studied under the effect of storage conditions; namely temperature (T=6, 25, 30 degrees C), air inflow velocity (F=0, 28.4 m/min), and initial water activity (a(w0)=0.85, 0.90, 0.93, 0.95, 0.97). The pH was held at 5.0. A total of 20 survival curves were experimentally obtained at various combinations of operating conditions. The chorizos were stored under four conditions: in the refrigerator (Ref: T=6 degrees C, F=0 m/min), at room temperature (RT: T=25 degrees C, F=0 m/min), in the hood (Hd: T=25 degrees C, F=28.4 m/min), and in the incubator (Inc: T=30 degrees C, F=0 m/min). Semi-logarithmic plots of counts vs. time revealed nonlinear trends for all the survival curves, indicating that the first-order kinetics model (exponential distribution function) was not suitable. The Weibull cumulative distribution function, for which the exponential function is only a special case, was selected and used to model the survival curves. The Weibull model was fitted to the 20 curves and the model parameters (alpha and beta) were determined. The fitted survival curves agreed with the experimental data with R(2)=0.951, 0.969, 0.908, and 0.871 for the Ref, RT, Hd, and Inc curves, respectively. Regression models relating alpha and beta to T, F, and a(w0) resulted in R(2) values of 0.975 for alpha and 0.988 for beta. The alpha and beta models can be used to generate a survival curve for Salmonella in chorizos for a given set of operating conditions. Additionally, alpha and beta can be used to determine the times needed to reduce the count by 1 or 2 logs t(1D) and t(2D). It is concluded that the Weibull cumulative distribution function offers a powerful model for describing microbial survival data. A comparison with the pathogen modeling program (PMP) revealed that the survival kinetics of Salmonella spp. in chorizos could not be adequately predicted using PMP which underestimated the t(1D) and t(2D). The mean of the Weibull probability density function correlated strongly with t(1D) and t(2D), and can serve as an alternative to the D-values normally used with first-order kinetic models. Parametric studies were conducted and sensitivity of survival to operating conditions was evaluated and discussed in the paper. The models derived herein provide a means for the development of a reliable risk assessment system for controlling Salmonella spp. in chorizos.

A hybrid Bayesian-neural network approach for probabilistic modeling of bacterial growth/no-growth interface.

A hybrid probabilistic modeling approach that integrates artificial neural networks (ANNs) with statistical Bayesian conditional probability estimation is proposed. The suggested approach benefits from the power of ANNs as highly flexible nonlinear mapping paradigms, and the Bayes' theorem for computing probabilities of bacterial growth with the aid of Parzen's probability distribution function estimators derived for growth and no-growth (G/NG) states. The proposed modeling approach produces models that can predict the probability of growth of targeted microorganism as affected by a set of parameters pertaining to extrinsic factors and operating conditions. The models also can be used to define the probabilistic boundary (interface) between growth and no-growth, and as such can define and predict the values of critical parameters required to keep a desired pre-specified bacterial growth risk in check. A modular system incorporating the various computational modules was constructed to illustrate the application of the hybrid approach to the probabilistic modeling of growth of pathogenic Escherichia coli strain as affected by temperature and water activity. The proposed approach was compared to other techniques including the traditional linear and nonlinear logistic regression. Results indicated that the hybrid approach outperforms the other approaches in its accuracy as well as flexibility to extract the implicit interrelationships between the various parameters. Advantages and limitations of the approach were also discussed and compared to those of other techniques.

A probabilistic neural network approach for modeling and classification of bacterial growth/no-growth data.

In this paper, we propose to use probabilistic neural networks (PNNs) for classification of bacterial growth/no-growth data and modeling the probability of growth. The PNN approach combines both Bayes theorem of conditional probability and Parzen's method for estimating the probability density functions of the random variables. Unlike other neural network training paradigms, PNNs are characterized by high training speed and their ability to produce confidence levels for their classification decision. As a practical application of the proposed approach, PNNs were investigated for their ability in classification of growth/no-growth state of a pathogenic Escherichia coli R31 in response to temperature and water activity. A comparison with the most frequently used traditional statistical method based on logistic regression and multilayer feedforward artificial neural network (MFANN) trained by error backpropagation was also carried out. The PNN-based models were found to outperform linear and nonlinear logistic regression and MFANN in both the classification accuracy and ease by which PNN-based models are developed.

Artificial neural networks: fundamentals, computing, design, and application.

Artificial neural networks (ANNs) are relatively new computational tools that have found extensive utilization in solving many complex real-world problems. The attractiveness of ANNs comes from their remarkable information processing characteristics pertinent mainly to nonlinearity, high parallelism, fault and noise tolerance, and learning and generalization capabilities. This paper aims to familiarize the reader with ANN-based computing (neurocomputing) and to serve as a useful companion practical guide and toolkit for the ANNs modeler along the course of ANN project development. The history of the evolution of neurocomputing and its relation to the field of neurobiology is briefly discussed. ANNs are compared to both expert systems and statistical regression and their advantages and limitations are outlined. A bird's eye review of the various types of ANNs and the related learning rules is presented, with special emphasis on backpropagation (BP) ANNs theory and design. A generalized methodology for developing successful ANNs projects from conceptualization, to design, to implementation, is described. The most common problems that BPANNs developers face during training are summarized in conjunction with possible causes and remedies. Finally, as a practical application, BPANNs were used to model the microbial growth curves of S. flexneri. The developed model was reasonably accurate in simulating both training and test time-dependent growth curves as affected by temperature and pH.

Computational neural networks for predictive microbiology: I. Methodology.

Artificial neural networks are mathematical tools inspired by what is known about the physical structure and mechanism of the biological cognition and learning. Neural networks have attracted considerable attention due to their efficacy to model wide spectrum of challenging problems. In this paper, we present one of the most popular networks, the backpropagation, and discuss its learning algorithm and analyze several issues necessary for designating optimal networks that can generalize after being trained on examples. As an application in the area of predictive microbiology, modeling of microorganism growth by neural networks will be presented in a second paper of this series.

Computational neural networks for predictive microbiology. II. Application to microbial growth.

The growth of a specific microorganism on a certain food is influenced by a number of environmental factors such as temperature, pH, and salt concentration. Methods that delineate the history of the growth of microorganisms are always subject to a considerable debate and scrutiny in the field of predictive microbiology. Regardless of its types, a growth model (e.g., modified Gompertz model) contains several parameters that vary depending on the microorganisms/food combination and the associated prevailing environmental conditions. The growth model parameters for a set of operating conditions are commonly determined from expressions developed via multiple linear regressions. In the present study, a substitute for the nonlinear regression-based equations is developed using computational neural networks. Computational neural networks are applied herein on experimental data pertaining to the anaerobic growth of Shigella flexneri. Results have indicated that predictions by neural networks offer better agreement with experimental data as compared to predictions obtained via corresponding regression equations.