Analysis and Validation of a Predictive Model for Growth and Death ofAeromonas hydrophilaunder Modified Atmospheres at Refrigeration Temperatures

Abstract

Specific growth and death rates of Aeromonas hydrophila were measured in laboratory media under various combinations of temperature, pH, and percent CO 2 and O 2 in the atmosphere. Predictive models were developed from the data and validated by means of observations obtained from (i) seafood experiments set up for this purpose and (ii) the ComBase database (http://www.combase.cc; http://wyndmoor.arserrc.gov/combase/). Two main reasons were identified for the differences between the predicted and observed growth in food: they were the variability of the growth rates in food and the bias of the model predictions when applied to food environments. A statistical method is presented to quantitatively analyze these differences. The method was also used to extend the interpolation region of the model. Most predictive models in food microbiology focus on the specific growth and/or death rate (or the doubling time [D value]) of a microorganism as a function of the main environmental factors, such as temperature, pH, and others. These models are commonly based on observations made in a welldefined and controlled laboratory environment, using microbiological media. It is also vital to validate the predictions in food environments, which can be highly complex and sometimes difficult to characterize.The overall error of a model is defined by means of the mean square error (MSE) between predictions and observations made in food (19). If extrapolations are omitted from the predictions, as they should be, then the overall error refers only to the interpolation region. Sometimes, depending on the experimental design and available data, it is difficult to determine the interpolation region of a multivariate empirical model based purely on observations. Baranyi et al. (3) defined it as a minimum convex polyhedron (MCP), or convex hull, in the space of environmental factors. As Fig. 1 shows, the MCP encompasses those combinations of the environmental conditions for which observations were made to generate the model. Its vertices can be calculated as described previously (3). Model predictions outside the MCP are extrapolations.Often, conditions observed in food fall outside of the interpolation region but are close enough to it that they can be useful for model validation. These observations can also help to extend the interpolation region of the model.In this paper, we report new experimental data about the growth and death rates of Aeromonas hydrophila which vary with temperature, pH, and percent CO 2 and O 2 in the atmosphere. Both death and growth data were used to estimate the growth-no growth boundary of the organism. The growth data were used to generate a predictive growth model, which was then extensively validated by comparing its predictions with various observations in food. Some observations were outside of but close enough to the interpolation region of the growth model to be useful for the validation procedure. We developed an algorithm to extend the interpolation region of the model in order to utilize those origina...

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