Mathematical modeling of the influence of temperature and gas composition on the respiration rate of shredded carrots

Measurement of the respiration rate of fresh produce under different gas composition and temperature, and respective mathematical modeling, are essential for the design of modified atmosphere packaging (MAP). In this work respiration rate of shredded carrots was measured at storage temperatures of 0, 4, 8, 12, 16 and 20 °C under different gas composition of O₂ and CO₂. As expected, temperature was the most influential factor on respiration rate, for all atmospheres tested; as it increased from 0 to 20 °C the values varied from 5.2 ± 0.5 to 51 ± 1 ml/(kg hr) for ambient air. The extreme gas mix (2% O₂ + 16% CO₂) reduced O₂ consumption and CO₂ production rates by 30-45%, when compared to the values observed for the samples stored in ambient air. Primary modelling showed that the effect of temperature followed an Arrhenius-type relationship and that the influence gas composition was best described by a Michaelis-Menten uncompetitive model. It was further observed that activation energy for both O₂ and CO₂, was not statistically different in the range of gas composition tested, thus RQ was considered to be constant (1.2). Monte Carlo simulations using respiration rate model parameters showed that the levels of O₂ and CO₂ in MAP containing shredded carrots were within the tolerance limits.