A mathematical model for predicting growth/no-growth of psychrotrophic C. botulinum in meat products with five variables

Abstract

The objective of this study was to develop a mathematical model for predicting growth/no-growth of psychrotrophic Clostridium botulinum in pasteurised meat products packed in modified atmosphere for combinations of storage temperature, pH, NaCl, added sodium nitrite and sodium lactate.Data for developing and training the artificial neural network (ANN) were generated in meat products. A total of 249 growth experiments were carried out in three different meat products with different combinations of storage temperature, pH, NaCl, sodium nitrite and sodium lactate. The meat batter was inoculated with approx. 104 spores/g using a 4-strain cocktail of gas-producing C. botulinum. The meat products were sliced, packed in modified atmosphere (30% CO2/70% N2) and stored at 4 °C, 8 °C and 12 °C, respectively, for up to 8 weeks. The enumeration of C. botulinum was performed when the volume of the package had increased by 9% or more, or at the end of the storage period.Based on 10–20 replicates for each combination, the “frequency of growth” was calculated. An ANN with 5 input neurons, 3 hidden and a single output neuron was trained using the 5 hurdle values as inputs and the observed “frequency of growth” as target value.The inputs for the final model are the five variables: temperature, pH, added sodium nitrite, NaCl and sodium lactate within the ranges 4–12 °C, 5.4–6.4, 0–150 ppm, 1.2–2.4% and 0–3% respectively. As reference a logistic regression method was also applied and subsequently compared to the full neural network model. Based on RMSEC value of 0.104 and 0.144 for ANN and the logistic regression model respectively, the ANN was preferred. On a separate set of test data (n = 60) the ANN model was validated by comparing the predicted “probability of growth” with the observed growth. A bias of 0.0166 was obtained, indicative of a model that is slightly fail-safe.