An Artificial Neural Network Approach to Escherichia Coli O157:H7 Growth Estimation

Fundamentals and Applications of Artificial Neural Network Modelling of Continuous Bifidobacteria Monoculture at a Low Flow Rate

The application of artificial neural networks (ANNs) to mathematical modelling in microbiology and biotechnology has been a promising and convenient tool for over 30 years because ANNs make it possible to predict complex multiparametric dependencies. This article is devoted to the investigation and justification of ANN choice for modelling the growth of a probiotic strain of Bifidobacterium adolescentis in a continuous monoculture, at low flow rates, under different oligofructose (OF) concentrations, as a preliminary study for a predictive model of the behaviour of intestinal microbiota. We considered the possibility and effectiveness of various classes of ANN. Taking into account the specifics of the experimental data, we proposed two-layer perceptrons as a mathematical modelling tool trained on the basis of the error backpropagation algorithm. We proposed and tested the mechanisms for training, testing and tuning the perceptron on the basis of both the standard ratio between the training and test sample volumes and under the condition of limited training data, due to the high cost, duration and the complexity of the experiments. We developed and tested the specific ANN models (class, structure, training settings, weight coefficients) with new data. The validity of the model was confirmed using RMSE, which was from 4.24 to 980% for different concentrations. The results showed the high efficiency of ANNs in general and bilayer perceptrons in particular in solving modelling tasks in microbiology and biotechnology, making it possible to recommend this tool for further wider applications.

Modeling for Predicting the Time to Detection of Staphylococcal Enterotoxin A in Cooked Chicken Product

Staphylococcal enterotoxins (SEs) produced by Staphylococcus aureus (S. aureus) are the cause of Saphylococcal food poisoning (SFP) outbreaks. Thus, estimation of the time to detection (TTD) of SEs, that is, the time required to reach the SEs detection limit, is essential for food preservation and quantitative risk assessment. This study was conducted to explore an appropriate method to predict the TTD of SEs in cooked chicken product under variable environmental conditions. An S. aureus strain that produces staphylococcal enterotoxin A (SEA) was inoculated into cooked chicken meat. Initial inoculating concentrations (approximately 102, 103, 104 CFU/g) of S. aureus and incubation temperatures (15 ± 1, 22 ± 1, 29 ± 1, and 36 ± 1°C) were chosen as environmental variables. The counting of S. aureus colonies and the detection of SEA were performed every 3 or 6 h during the incubation. The TTD of SEA was considered a response of S. aureus to environmental variables. Linear polynomial regression was used to model the effects of environmental variables on the TTD of SEA. Result showed that the correlation coefficient (R2) of the regressed equation is higher than 0.98, which means the obtained equation was reliable. Moreover, the minimum concentration of S. aureus for producing a detectable amount of SEA under various environmental conditions was approximately 6.32 log CFU/g, which was considered the threshold for S. aureus to produce SEA. Hence, the TTD of SEA could be obtained by calculating the time required to reach the threshold by using an established S. aureus growth predictive model. Both established methods were validated through internal and external validation. The results of graphical comparison, RMSE, SEP, Af , and Bf showed that the accuracy of both methods were acceptable, and linear polynomial regression method showed more accurately.

Modeling the Combined Effects of Temperature, pH, and Sodium Chloride and Sodium Lactate Concentrations on the Growth Rate of Lactobacillus plantarum ATCC 8014

Nowadays, microorganisms with probiotic or antimicrobial properties are receiving major attention as alternative resources for food preservation. Lactic acid bacteria are able to synthetize compounds with antimicrobial activity against pathogenic and spoilage flora. Among them, Lactobacillus plantarum ATCC 8014 has exhibited this capacity, and further studies reveal that the microorganism is able to produce bacteriocins. An assessment of the growth of L. plantarum ATCC 8014 at different conditions becomes crucial to predict its development in foods. A response surface model of the growth rate of L. plantarum was built in this study as a function of temperature (4, 7, 10, 13, and 16°C), pH (5.5, 6.0, 6.5, 7.0, and 7.5), and sodium chloride (0, 1.5, 3.0, 4.5, and 6.0%) and sodium lactate (0, 1, 2, 3, and 4%) concentrations. All the factors were statistically significant at a confidence level of 90%  (p<0.10). When temperature and pH increased, there was a corresponding increase in the growth rate, while a negative relationship was observed between NaCl and Na-lactate concentrations and the growth parameter. A mathematical validation was carried out with additional conditions, demonstrating an excellent performance of the model. The developed model could be useful for designing foods with L. plantarum ATCC 8014 added as a probiotic.

Predictive Model of Listeria Monocytogenes’ Growth Rate Under Different Temperatures and Acids

A response surface model of Listeria monocytogenes’ growth rate was built in this study under different temperatures (10 °C, 15 °C, 20 °C, 25 °C and 30 °C) and acid concentrations: citric acid (0–0.4%) and ascorbic acid (0–0.4%); two ingredients which are often used in the food industry as preservatives. Mathematical validation was performed with additional samples at different conditions within the range of the model, obtaining acceptable values of root mean square error (0.0466), standard error of prediction (18.84%), bias factor (1.05) and accuracy factor (1.16). The inhibitory effect on growth was more effective with citric acid than ascorbic acid, possibly due to the major dissociation of citric acid occurring inside microbial cells. The different conditions considered in the model will potentially allow L. monocytogenes’ response to be predicted in foods having a similar composition to the chemical and physical factors set out in this paper.

Effect of temperature, pH, and water activity on Mucor spp. growth on synthetic medium, cheese analog and cheese

The Mucor genus includes a large number of ubiquitous fungal species. In the dairy environment, some of them play a technological role providing typical organoleptic qualities to some cheeses while others can cause spoilage. In this study, we compared the effect of relevant abiotic factors for cheese production on the growth of six strains representative of dairy technological and contaminant species as well as of a non cheese related strain (plant endophyte). Growth kinetics were determined for each strain in function of temperature, water activity and pH on synthetic Potato Dextrose Agar (PDA), and secondary models were fitted to calculate the corresponding specific cardinal values. Using these values and growth kinetics acquired at 15 °C on cheese agar medium (CA) along with three different cheese types, optimal growth rates (μopt) were estimated and consequently used to establish a predictive model. Contrarily to contaminant strains, technological strains showed higher μopt on cheese matrices than on PDA. Interestingly, lag times of the endophyte strain were strongly extended on cheese related matrices. This study offers a relevant predictive model of growth that may be used for better cheese production control but also raises the question of adaptation of some Mucor strains to the cheese.

Effects of climate change on Salmonella infections

BACKGROUND

Climate change and global warming have been reported to increase spread of foodborne pathogens. To understand these effects on Salmonella infections, modeling approaches such as regression analysis and neural network (NN) were used.

METHODS

Monthly data for Salmonella outbreaks in Mississippi (MS), Tennessee (TN), and Alabama (AL) were analyzed from 2002 to 2011 using analysis of variance and time series analysis. Meteorological data were collected and the correlation with salmonellosis was examined using regression analysis and NN.

RESULTS

A seasonal trend in Salmonella infections was observed (p<0.001). Strong positive correlation was found between high temperature and Salmonella infections in MS and for the combined states (MS, TN, AL) models (R(2)=0.554; R(2)=0.415, respectively). NN models showed a strong effect of rise in temperature on the Salmonella outbreaks. In this study, an increase of 1°F was shown to result in four cases increase of Salmonella in MS. However, no correlation between monthly average precipitation rate and Salmonella infections was observed.

CONCLUSION

There is consistent evidence that gastrointestinal infection with bacterial pathogens is positively correlated with ambient temperature, as warmer temperatures enable more rapid replication. Warming trends in the United States and specifically in the southern states may increase rates of Salmonella infections.

Development of Predictive Models for the Growth Kinetics of Listeria monocytogenes on Fresh Pork under Different Storage Temperatures

This study was conducted to develop a predictive model to estimate the growth of Listeria monocytogenes on fresh pork during storage at constant temperatures (5, 10, 15, 20, 25, 30, and 35°C). The Baranyi model was fitted to growth data (log CFU per gram) to calculate the specific growth rate (SGR) and lag time (LT) with a high coefficient of determination (R(2) > 0.98). As expected, SGR increased with a decline in LT with rising temperatures in all samples. Secondary models were then developed to describe the variation of SGR and LT as a function of temperature. Subsequently, the developed models were validated with additional independent growth data collected at 7, 17, 27, and 37°C and from published reports using proportion of relative errors and proportion of standard error of prediction. The proportion of relative errors of the SGR and LT models developed herein were 0.79 and 0.18, respectively. In addition, the standard error of prediction values of the SGR and LT of L. monocytogenes ranged from 25.7 to 33.1% and from 44.92 to 58.44%, respectively. These results suggest that the model developed in this study was capable of predicting the growth of L. monocytogenes under various isothermal conditions.

Modeling of Bacillus cereus growth in brown rice submitted to a combination of ultrasonication and slightly acidic electrolyzed water treatment

The combined effects of ultrasonication and slight acidic electrolyzed water were investigated to improve the microbial safety of brown rice against Bacillus cereus infection and to evaluate the growth kinetics of these bacteria during storage of untreated and treated rice at various temperatures (5, 10, 15, 20, 25, 30, and 35°C). The results indicate that this combination treatment was bactericidal against B. cereus, resulting in an approximately 3.29-log reduction. Although B. cereus can be efficiently reduced by treatment, temperature abuse during storage can allow B. cereus to recover and grow. A primary growth model (Baranyi and Roberts equation) was fitted to the raw growth data from untreated (control) and treated samples to estimate growth rate, lag time, and maximum population density, with a low standard error of the residuals (≤0.140) and high adjusted coefficient of determination (>0.990). The growth curves obtained from the Baranyi and Roberts model indicated that B. cereus grew more slowly on treated brown rice than on untreated brown rice. Secondary models predicting the square root of the maximum growth rate and the natural logarithm of the lag time as a function of temperature were satisfactory (bias factor = 0.993 to 1.013; accuracy factor = 1.290 to 1.352; standard error of prediction = 18.828 to 36.615%). Inactivation results and the model developed and validated in this study provided reliable and valuable growth kinetics information for quantitative microbiological risk assessment studies of B. cereus on brown rice.

Growth model of Escherichia coli O157:H7 at various storage temperatures on kale treated by thermosonication combined with slightly acidic electrolyzed water

This study was conducted to investigate the disinfection efficacy of hurdle treatments (thermosonication plus slightly acidic electrolyzed water [SAcEW]) and to develop a model for describing the effect of storage temperatures (4, 10, 15, 20, 25, 30, and 35°C) on the growth of Escherichia coli O157:H7 on fresh-cut kale treated with or without (control) thermosonication combined with SAcEW. The hurdle treatments of thermosonication plus SAcEW had strong bactericidal effects against E. coli O157:H7 on kale, with approximately 3.3-log reductions. A modified Gompertz model was used to describe growth parameters such as specific growth rate (SGR) and lag time (LT) as a function of storage temperature, with high coefficients of determination (R(2) > 0.98). SGR increased and LT declined with rising temperatures in all samples. A significant difference was found between the SGR values obtained from treated and untreated samples. Secondary models were established for SGR and LT to evaluate the effects of storage temperature on the growth kinetics of E. coli O157:H7 in treated and untreated kale. Statistical evaluation was carried out to validate the performance of the developed models, based on the additional experimental data not used for the model development. The validation step indicated that the overall predictions were inside the acceptable prediction zone and had lower standard errors, indicating that this new growth model can be used to assess the risk of E. coli O157:H7 contamination on kale.

Comparative analyses of response surface methodology and artificial neural network on medium optimization for Tetraselmis sp. FTC209 grown under mixotrophic condition

Mixotrophic metabolism was evaluated as an option to augment the growth and lipid production of marine microalga Tetraselmis sp. FTC 209. In this study, a five-level three-factor central composite design (CCD) was implemented in order to enrich the W-30 algal growth medium. Response surface methodology (RSM) was employed to model the effect of three medium variables, that is, glucose (organic C source), NaNO₃ (primary N source), and yeast extract (supplementary N, amino acids, and vitamins) on biomass concentration, X_max, and lipid yield, P_max/X_max. RSM capability was also weighed against an artificial neural network (ANN) approach for predicting a composition that would result in maximum lipid productivity, Pr_lipid. A quadratic regression from RSM and a Levenberg-Marquardt trained ANN network composed of 10 hidden neurons eventually produced comparable results, albeit ANN formulation was observed to yield higher values of response outputs. Finalized glucose (24.05 g/L), NaNO₃ (4.70 g/L), and yeast extract (0.93 g/L) concentration, affected an increase of X_max to 12.38 g/L and lipid a accumulation of 195.77 mg/g dcw. This contributed to a lipid productivity of 173.11 mg/L per day in the course of two-week cultivation.

Leuconostoc mesenteroides growth in food products: prediction and sensitivity analysis by adaptive-network-based fuzzy inference systems

Background

An adaptive-network-based fuzzy inference system (ANFIS) was compared with an artificial neural network (ANN) in terms of accuracy in predicting the combined effects of temperature (10.5 to 24.5°C), pH level (5.5 to 7.5), sodium chloride level (0.25% to 6.25%) and sodium nitrite level (0 to 200 ppm) on the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions.

Methods

The ANFIS and ANN models were compared in terms of six statistical indices calculated by comparing their prediction results with actual data: mean absolute percentage error (MAPE), root mean square error (RMSE), standard error of prediction percentage (SEP), bias factor (B_f), accuracy factor (A_f), and absolute fraction of variance (R²). Graphical plots were also used for model comparison.

Conclusions

The learning-based systems obtained encouraging prediction results. Sensitivity analyses of the four environmental factors showed that temperature and, to a lesser extent, NaCl had the most influence on accuracy in predicting the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions. The observed effectiveness of ANFIS for modeling microbial kinetic parameters confirms its potential use as a supplemental tool in predictive mycology. Comparisons between growth rates predicted by ANFIS and actual experimental data also confirmed the high accuracy of the Gaussian membership function in ANFIS. Comparisons of the six statistical indices under both aerobic and anaerobic conditions also showed that the ANFIS model was better than all ANN models in predicting the four kinetic parameters. Therefore, the ANFIS model is a valuable tool for quickly predicting the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions.

Development and validation of a predictive microbiology model for survival and growth of Salmonella on chicken stored at 4 to 12 °C

Salmonella spp. are a leading cause of foodborne illness. Mathematical models that predict Salmonella survival and growth on food from a low initial dose, in response to storage and handling conditions, are valuable tools for helping assess and manage this public health risk. The objective of this study was to develop and to validate the first predictive microbiology model for survival and growth of a low initial dose of Salmonella on chicken during refrigerated storage. Chicken skin was inoculated with a low initial dose (0.9 log) of a multiple antibiotic-resistant strain of Salmonella Typhimurium DT104 (ATCC 700408) and then stored at 4 to 12 °C for 0 to 10 days. A general regression neural network (GRNN) model that predicted log change of Salmonella Typhimurium DT104 as a function of time and temperature was developed. Percentage of residuals in an acceptable prediction zone, from -1 (fail-safe) to 0.5 (fail-dangerous) log, was used to validate the GRNN model by using a criterion of 70% acceptable predictions. Survival but not growth of Salmonella Typhimurium DT104 was observed at 4 to 8 °C. Maximum growth of Salmonella Typhimurium DT104 during 10 days of storage was 0.7 log at 9 °C, 1.1 log at 10 °C, 1.8 log at 11 °C, and 2.9 log at 12 °C. Performance of the GRNN model for predicting dependent data (n=163) was 85% acceptable predictions, for predicting independent data for interpolation (n=77) was 84% acceptable predictions, and for predicting independent data for extrapolation (n=70) to Salmonella Kentucky was 87% acceptable predictions. Thus, the GRNN model provided valid predictions for survival and growth of Salmonella on chicken during refrigerated storage, and therefore the model can be used with confidence to help assess and manage this public health risk.

General regression neural network and monte carlo simulation model for survival and growth of salmonella on raw chicken skin as a function of serotype, temperature, and time for use in risk assessment

A general regression neural network (GRNN) and Monte Carlo simulation model for predicting survival and growth of Salmonella on raw chicken skin as a function of serotype (Typhimurium, Kentucky, and Hadar), temperature (5 to 50 degrees C), and time (0 to 8 h) was developed. Poultry isolates of Salmonella with natural resistance to antibiotics were used to investigate and model survival and growth from a low initial dose (<1 log) on raw chicken skin. Computer spreadsheet and spreadsheet add-in programs were used to develop and simulate a GRNN model. Model performance was evaluated by determining the percentage of residuals in an acceptable prediction zone from -1 log (fail-safe) to 0.5 log (fail-dangerous). The GRNN model had an acceptable prediction rate of 92% for dependent data (n = 464) and 89% for independent data (n = 116), which exceeded the performance criterion for model validation of 70% acceptable predictions. Relative contributions of independent variables were 16.8% for serotype, 48.3% for temperature, and 34.9% for time. Differences among serotypes were observed, with Kentucky exhibiting less growth than Typhimurium and Hadar, which had similar growth levels. Temperature abuse scenarios were simulated to demonstrate how the model can be integrated with risk assessment, and the most common output distribution obtained was Pearson5. This study demonstrated that it is important to include serotype as an independent variable in predictive models for Salmonella. Had a cocktail of serotypes Typhimurium, Kentucky, and Hadar been used for model development, the GRNN model would have provided overly fail-safe predictions of Salmonella growth on raw chicken skin contaminated with serotype Kentucky. Thus, by developing the GRNN model with individual strains and then modeling growth as a function of serotype prevalence, more accurate predictions were obtained.

Determination of optimal growth parameters for the bioincising fungus Physisporinus vitreus by means of response surface methodology

AIM

To evaluate the influence of water activity (a(w)), temperature and pH on the radial growth and lag phase of Physisporinus vitreus (E-642), a basidiomycete was used in the biotechnological process of bioincising.

METHODS AND RESULTS

Radial growth was monitored for 20 days on malt extract agar medium. Five levels of a(w) (0.998, 0.982, 0.955, 0.928, 0.892) were combined with three incubation temperatures (10, 15, 20 degrees C) and three pH values (4, 5, 6). Data analyses showed a highly significant effect of a(w) and temperature (P < 0.0001) and a significant effect of pH (P < 0.05). The radial growth rate and lag phase of P. vitreus were very sensitive to a(w) reduction. Although P. vitreus was able to grow at all the selected temperatures and pH values, the lag phase increased with decreasing a(w) and growth became inhibited at a(w) = 0.955. Optimal conditions for growth of P. vitreus were a(w) = 0.998, 20 degrees C and pH 5. The response surface model provided reliable estimates of these growth parameters and confirmed a greater dependence on a(w) than on temperature or pH under in vitro conditions.

CONCLUSIONS

Low levels of a(w) can prevent growth of P. vitreus, so wood moisture content should be adjusted accordingly.

SIGNIFICANCE AND IMPACT OF THE STUDY

Implementation of these results should contribute towards the optimization and efficiency of bioincising.

A radial basis function neural network approach to determine the survival of Listeria monocytogenes in Katiki, a traditional Greek soft cheese

A radial basis function neural network was developed to determine the kinetic behavior of Listeria monocytogenes in Katiki, a traditional white acid-curd soft spreadable cheese. The applicability of the neural network approach was compared with the reparameterized Gompertz, the modified Weibull, and the Geeraerd primary models. Model performance was assessed with the root mean square error of the residuals of the model (RMSE), the regression coefficient (R2), and the F test. Commercially prepared cheese samples were artificially inoculated with a five-strain cocktail of L. monocytogenes, with an initial concentration of 10(6) CFU g(-1) and stored at 5, 10, 15, and 20 degrees C for 40 days. At each storage temperature, a pathogen viability loss profile was evident and included a shoulder, a log-linear phase, and a tailing phase. The developed neural network described the survival of L. monocytogenes equally well or slightly better than did the three primary models. The performance indices for the training subset of the network were R2 = 0.993 and RMSE = 0.214. The relevant mean values for all storage temperatures were R2 = 0.981, 0.986, and 0.985 and RMSE = 0.344, 0.256, and 0.262 for the reparameterized Gompertz, modified Weibull, and Geeraerd models, respectively. The results of the F test indicated that none of the primary models were able to describe accurately the survival of the pathogen at 5 degrees C, whereas with the neural network all fvalues were significant. The neural network and primary models all were validated under constant temperature storage conditions (12 and 17 degrees C). First or second order polynomial models were used to relate the inactivation parameters to temperature, whereas the neural network was used a one-step modeling approach. Comparison of the prediction capability was based on bias and accuracy factors and on the goodness-of-fit index. The prediction performance of the neural network approach was equal to that of the primary models at both validation temperatures. The results of this work could increase the knowledge basis for the applicability of neural networks as an alternative tool in predictive microbiology.

Predicting survival of Escherichia coli O157:H7 in dry fermented sausage using artificial neural networks

The Canadian Food Inspection Agency required the meat industry to ensure Escherichia coli O157:H7 does not survive (experiences > or = 5 log CFU/g reduction) in dry fermented sausage (salami) during processing after a series of foodborne illness outbreaks resulting from this pathogenic bacterium occurred. The industry is in need of an effective technique like predictive modeling for estimating bacterial viability, because traditional microbiological enumeration is a time-consuming and laborious method. The accuracy and speed of artificial neural networks (ANNs) for this purpose is an attractive alternative (developed from predictive microbiology), especially for on-line processing in industry. Data from a study of interactive effects of different levels of pH, water activity, and the concentrations of allyl isothiocyanate at various times during sausage manufacture in reducing numbers of E. coli O157:H7 were collected. Data were used to develop predictive models using a general regression neural network (GRNN), a form of ANN, and a statistical linear polynomial regression technique. Both models were compared for their predictive error, using various statistical indices. GRNN predictions for training and test data sets had less serious errors when compared with the statistical model predictions. GRNN models were better and slightly better for training and test sets, respectively, than was the statistical model. Also, GRNN accurately predicted the level of allyl isothiocyanate required, ensuring a 5-log reduction, when an appropriate production set was created by interpolation. Because they are simple to generate, fast, and accurate, ANN models may be of value for industrial use in dry fermented sausage manufacture to reduce the hazard associated with E. coli O157:H7 in fresh beef and permit production of consistently safe products from this raw material.

Food as a vehicle for transmission of Shiga toxin-producing Escherichia coli

Contaminated food continues to be the principal vehicle for transmission of Escherichia coli O157:H7 and other Shiga toxin-producing E. coli (STEC) to humans. A large number of foods, including those associated with outbreaks (alfalfa sprouts, fresh produce, beef, and unpasteurized juices), have been the focus of intensive research studies in the past few years (2003 to 2006) to assess the prevalence and identify effective intervention and inactivation treatments for these pathogens. Recent analyses of retail foods in the United States revealed E. coli O157:H7 was present in 1.5% of alfalfa sprouts and 0.17% of ground beef but not in some other foods examined. Differences in virulence patterns (presence of both stx1 and stx2 genes versus one stx gene) have been observed among isolates from beef samples obtained at the processing plant compared with retail outlets. Research has continued to examine survival and growth of STEC in foods, with several models being developed to predict the behavior of the pathogen under a wide range of environmental conditions. In an effort to develop effective strategies to minimize contamination, several influential factors are being addressed, including elucidating the underlying mechanism for attachment and penetration of STEC into foods and determining the role of handling practices and processing operations on cross-contamination between foods. Reports of some alternative nonthermal processing treatments (high pressure, pulsed-electric field, ionizing radiation, UV radiation, and ultrasound) indicate potential for inactivating STEC with minimal alteration to sensory and nutrient characteristics. Antimicrobials (e.g., organic acids, oxidizing agents, cetylpyridinium chloride, bacteriocins, acidified sodium chlorite, natural extracts) have varying degrees of efficacy as preservatives or sanitizing agents on produce, meat, and unpasteurized juices. Multiple-hurdle or sequential intervention treatments have the greatest potential to minimize transmission of STEC in foods.

Modelling fungal growth using radial basis function neural networks: The case of the ascomycetous fungus Monascus ruber van Tieghem

A radial basis function (RBF) neural network was developed and evaluated against a quadratic response surface model to predict the maximum specific growth rate of the ascomycetous fungus Monascus ruber in relation to temperature (20-40 degrees C), water activity (0.937-0.970) and pH (3.5-5.0), based on the data of Panagou et al. [Panagou, E.Z., Skandamis, P.N., Nychas, G.-J.E., 2003. Modelling the combined effect of temperature, pH and aw on the growth rate of M. ruber, a heat-resistant fungus isolated from green table olives. J. Appl. Microbiol. 94, 146-156]. Both RBF network and polynomial model were compared against the experimental data using five statistical indices namely, coefficient of determination (R(2)), root mean square error (RMSE), standard error of prediction (SEP), bias (B(f)) and accuracy (A(f)) factors. Graphical plots were also used for model comparison. For training data set the RBF network predictions outperformed the classical statistical model, whereas in the case of test data set the network gave reasonably good predictions, considering its performance for unseen data. Sensitivity analysis showed that from the three environmental factors the most influential on fungal growth was temperature, followed by water activity and pH to a lesser extend. Neural networks offer an alternative and powerful technique to model microbial kinetic parameters and could thus become an additional tool in predictive mycology.

Response surface model for prediction of growth parameters from spores of Clostridium sporogenes under different experimental conditions

Clostridium sporogenes is considered to be a non-toxingenic equivalent of proteolytic Clostridium botulinum, and it also causes food spoilage. The effects of temperature (16.6-33.4 degrees C), pH value (5.2-6.8) and concentration of sodium chloride (0.6-7.4%) on the growth parameters of C. sporogenes spores were investigated. The growth curves generated within different conditions were fitted using Baranyi function. Two growth parameters (growth rate, GR; lag-time, LT) of the growth curves under combined effects of temperature, pH and sodium chloride were modeled using a quadratic polynomial equation of response surface (RS) model. Mathematical evaluation demonstrated that the standard error of prediction (%SEP) obtained by RS model was 1.033% for GR and was 0.166% for LT for model establishing. The %SEP for model validation were 43.717% and 5.895% for GR and LT, respectively. The root-mean-squares error (RMSE) was in acceptable range which was less than 0.1 for GR and was less than 8.0 for LT. Both the bias factor (B(f)) and accuracy factor (A(f)) approached 1.0, which were within acceptable range. Therefore, RS model provides a useful and accurate method for predicting the growth parameters of C. sporogenes spores, and could be applied to ensure food safety with respect to proteolytic C. botulinum control.

Modelling the growth of Leuconostoc mesenteroides by Artificial Neural Networks

The combined effect of temperature (10.5 to 24.5 degrees C), pH level (5.5 to 7.5), sodium chloride level (0.25% to 6.25%) and sodium nitrite level (0 to 200 ppm) on the predicted specific growth rate (Gr), lag-time (Lag) and maximum population density (yEnd) of Leuconostoc mesenteroides under aerobic and anaerobic conditions, was studied using an Artificial Neural Network-based model (ANN) in comparison with Response Surface Methodology (RS). For both aerobic and anaerobic conditions, two types of ANN model were elaborated, unidimensional for each of the growth parameters, and multidimensional in which the three parameters Gr, Lag, and yEnd are combined. Although in general no significant statistical differences were observed between both types of model, we opted for the unidimensional model, because it obtained the lowest mean value for the standard error of prediction for generalisation. The ANN models developed provided reliable estimates for the three kinetic parameters studied; the SEP values in aerobic conditions ranged from between 2.82% for Gr, 6.05% for Lag and 10% for yEnd, a higher degree accuracy than those of the RS model (Gr: 9.54%; Lag: 8.89%; yEnd: 10.27%). Similar results were observed for anaerobic conditions. During external validation, a higher degree of accuracy (Af) and bias (Bf) were observed for the ANN model compared with the RS model. ANN predictive growth models are a valuable tool, enabling swift determination of L. mesenteroides growth parameters.