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A mathematical model was developed from experimental measurements to describe the evolution of the O 2 , CO 2 and ethylene in a modified atmosphere packaging system for Cavendish bananas. The respiration and ethylene production in the fruits were experimentally obtained from a closed system method and then represented by Michaelis-Menten equations of enzyme kinetics. The gas transfer through the packaging was described by a Fick's diffusion equation, and the temperature dependence was represented based on the Arrhenius law. The model was validated by packaging the fruit in perforated bags of polypropylene and low density polyethylene at 12°C for a period of 8 days. With the developed model it was possible to satisfactorily describe the experimental evolution of the gas content in the headspace of the packages, obtaining coefficients of determination (R 2 ) of 0.93 for the O 2 levels, 0.90-0.91 for the CO 2 levels, and 0.89-0.93 for the ethylene levels.

A proper description of the respiration and ethylene generation is important in the development of package systems for the preservation of fresh fruits and vegetables. In this work, a model based on both Michaelis-Menten and chemical kinetics equations was developed and assessed in order to describe the respiration and ethylene generation of avocado (Persea americana cv. Hass) and feijoa fruits (Acca sellowiana Berg) from experimental data obtained at different temperatures by a closed system method. The temperature effect in both processes was described using Arrhenius-type relationships. After this, avocadoes and feijoas were packed in perforated low-density polyethylene (LDPE) and polypropylene (PP) bags for 8 days at 12°C and 80% RH to validate the usefulness of the model to describe the gas evolution in modified atmosphere packaging (MAP). For avocado fruits, respiration rates of 2680-3030 cm 3 kg-1 d-1 were obtained at 24°C and normal atmosphere, and 3650-4230 cm 3 kg-1 d-1 for feijoa fruits. As for ethylene production rates, at 24°C were obtained values of 3.11 cm 3 kg-1 d-1 for avocado and 0.50 cm 3 kg-1 d-1 for feijoa. At 6°C, respiration and ethylene production rates were up to 6 times lower. It was possible to describe properly the ethylene generation using a Michaelis-Menten simple equation and the respiration rates using a Michaelis-Menten uncompetitive kinetics for both fruits with coefficients of determination above 0.9 in each case. The overall model was validated in the MAP test being possible to predict successfully the O 2 , CO 2 and C 2 H 4 levels inside the packages.

In this study, 'Hass' avocado samples were stored at different temperatures to determine changes in firmness, color and other physicochemical support properties throughout the storage time and to represent shelf life depending on temperature from the evolution of these quality properties. From the experimental data, a set of models were adjusted to represent the change of each property as a function of time and temperature by using a first-order kinetics to represent the evolution of lightness (L*) and the chromatic coordinate b*, and a logistic equation to represent firmness and a*. The effect of temperature was represented by using Arrhenius equations. From the models of firmness and color, suitable equations were obtained to predict shelf life considering the relationship with the senescence stage (between 20 and 33 days). All the models were adjusted satisfactorily, obtaining regression coefficients higher than 0.95. In order to determine the predictive capacity of the proposed models, a validation experiment was carried out by storing fruits at 12 C until reaching the senescence stage. With the models, it was possible to satisfactorily predict the changes in color and firmness and it was possible to estimate the shelf life time at 12 C (28 AE 3.1 days).

Modified atmosphere packaging (MAP) is a useful preservation system that allows to significantly increase the shelf life of fruits and vegetables. The MAP results of changing the composition of the atmosphere in the packaging headspace due to the dynamic interaction between the metabolic processes of the packaged product on the one hand, in which O 2 is consumed and another gases such as CO 2 and water vapor are generated, and on the other hand, by transferring all of these gases through the package. The aim of the system is to balance these two processes in such a way that constant levels of these different gases are reached in the packaging headspace and that these equilibrium levels are as favorable as possible to preserve the product. This chapter describes design strategies to obtain a satisfactory gas transfer capacity in the MAP system through the configuration of several related variables such as the type of packing material, its thickness, the transfer surface area and the required number and diameter of perforations. For this, the necessary steps are proposed to estimate the appropriate transfer capacity according to the equilibrium gas concentrations desired to longer preserve the product by using the mass balance equations of the MAP system.

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