Dynamic gain matrix approach to modeling of dynamic modified atmosphere packaging systems

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Variations in food and biological systems create nonlinear interactions that increase complexity of mathematical models. A multivariable correlative mathematical modeling strategy, dynamic gain matrix (DGM) method, was derived using advanced process control concepts and it was applied to describe quality changes in beef loin steaks with postmortem fabrication time and modified atmosphere packaging (MAP) conditions altered by dynamic gas exchange. DGM was used for modeling of dynamic MAP to satisfy the special modeling requirements of relationships between the processing and packaging variables and quality parameters through consideration of multivariable interacting deterioration mechanism in mathematical terms. A normalization method was also developed and applied to eliminate initial condition effects arising from meat source differences. A total of 960 data points were analyzed, and the model is reported as a series of first order differential equations with respect to retail display time to describe changes in color, pH and microbial population as functions of postmortem fabrication time, distribution gas composition, gas exchange time and retail gas composition. The model was optimized to minimize prediction sum of residual errors, and a pairing and control strategy was proposed to be used for optimum control of quality parameters for a chosen display time by manipulation of processing and packaging variables. The strategy developed has specific use for prediction and design of dynamic gas exchange MAP systems as well as potential use in similar biological engineering systems.

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Journal of Food Process Engineering

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