Direct Dynamic Kinetic Analysis and Computer Simulation of Growth ofClostridium perfringensin Cooked Turkey during Cooling

On optimum dynamic temperature profiles for thermal inactivation kinetics determination

Determination of inactivation kinetics, associated with thermal processing of foods and obtained from dynamic temperature experiments, requires carefully designed experiments, the primary element being the selection of the appropriate temperature profile along with a carefully planned sampling schedule. In the present work, a number of different dynamic temperature profiles were investigated in terms of their ability to generate accurate kinetic parameters with low confidence intervals (CIs). Although alternative models have been also tested, our work was concentrated on thermal inactivation kinetics that could be described by the classical D-z values. A pair of D and z values was assumed, and for each temperature profile tested, concentration data at different processing times were generated through the appropriate models. Next, an error (up to ±2.5% or ±5%) was introduced on these theoretical values to generate pseudo-experimental data, and the back-calculation of the assumed kinetic parameters by non-linear regression was performed. The accuracy and the 95% CIs of the estimated kinetic parameters were evaluated; joint confidence regions were also constructed to investigate parameters correlation. The effect of temperature profile pattern, level of error, number of experimental points, and reference temperature was assessed. A stepwise increasing and a single triangle-pattern temperature profile were the best profiles among those tested. As a general observation, based on different kinetic models investigated, temperature profiles and sampling intervals that result in concentration versus time diagrams having shapes as suggested by the primary model used when isothermally applied are not considered appropriate for parameter estimation.

Dynamic kinetic analysis of growth of Listeria monocytogenes in pasteurized cow milk

The objective of this study was to develop a dynamic model for predicting the growth of Listeria monocytogenes in pasteurized cow milk under fluctuating temperature conditions during storage and temperature abuse. Six dynamic temperature profiles that simulated random fluctuation patterns were designed to change arbitrarily between 4 and 30°C. The growth data collected from 3 independent temperature profiles were used to determine the kinetic parameters and construct a growth model combining the primary and secondary models using a 1-step dynamic analysis method. The results showed that the estimated minimum growth temperature and maximum cell concentration were 0.6 ± 0.2°C and 7.8 ± 0.1 log cfu/mL (mean ± standard error), with the root mean square error (RMSE) only 0.3 log cfu/mL for model development. The model and the associated kinetic parameters were validated using the data collected under both dynamic and isothermal conditions, which were not used for model development, to verify the accuracy of prediction. The RMSE of prediction was approximately 0.3 log cfu/mL for fluctuating temperature profiles, and it was between 0.2 and 1.1 log cfu/mL under certain isothermal temperatures (2-30°C). The resulting model and kinetic parameters were further validated using 3 growth curves at 4, 7, and 10°C arbitrarily selected from ComBase (www.combase.cc). The RMSE of prediction was 0.8, 0.4, and 0.5 log cfu/mL, respectively, for these curves. The validation results indicated the predictive model was reasonably accurate, with relatively small RMSE. The model was then used to simulate the growth of L. monocytogenes under a variety of continuous and square-wave temperature profiles to demonstrate its potential application. The results of this study showed that the model developed in this study can be used to predict the growth of L. monocytogenes in contaminated milk during storage.

Holistic Approach to the Uncertainty in Shelf Life Prediction of Frozen Foods at Dynamic Cold Chain Conditions

Systematic kinetic modeling is required to predict frozen systems behavior in cold dynamic conditions. A one-step procedure, where all data are used simultaneously in a non-linear algorithm, is implemented to estimate the kinetic parameters of both primary and secondary models. Compared to the traditional two-step methodology, more precise estimates are obtained, and the calculated parameter uncertainty can be introduced in realistic shelf life predictions, as a tool for cold chain optimization. Additionally, significant variability of the real distribution/storage conditions is recorded, and must be also incorporated in a kinetic prediction scheme. The applicability of the approach is theoretically demonstrated in an analysis of data on frozen green peas Vitamin C content, for the calculation of joint confidence intervals of kinetic parameters. A stochastic algorithm is implemented, through a double Monte Carlo scheme incorporating the temperature variability during distribution, drawn from cold chain databases. Assuming a distribution scenario of 130 days in the cold chain, 93 ± 110 days remaining shelf life was predicted compared to 180 days assumed based on the use by date. Overall, through the theoretical case study investigated, the uncertainty of models’ parameters and cold chain dynamics were incorporated into shelf life assessment, leading to more realistic predictions.

A Theoretical Analysis for Assessing the Variability of Secondary Model Thermal Inactivation Kinetic Parameters

Traditionally, for the determination of the kinetic parameters of thermal inactivation of a heat labile substance, an appropriate index is selected and its change is measured over time at a series of constant temperatures. The rate of this change is described through an appropriate primary model and a secondary model is applied to assess the impact of temperature. By this approach, the confidence intervals of the estimates of the rate constants are not taken into account. Consequently, the calculated variability of the secondary model parameters can be significantly lower than the actual variability. The aim of this study was to demonstrate the influence of the variability of the primary model parameters in establishing the confidence intervals of the secondary model parameters. Using a Monte Carlo technique and assuming normally distributed DT values (parameter associated with a primary inactivation model), the error propagating on the DTref and z-values (secondary model parameters) was assessed. When DT confidence intervals were broad, the secondary model's parameter variability was appreciably high and could not be adequately estimated through the traditional deterministic approach that does not take into account the variation on the DT values. In such cases, the proposed methodology was essential for realistic estimations.