Classic and Reaction-Diffusion Models Used in Modified Atmosphere Packaging (MAP) of Fruit and Vegetables

Abstract

Fruits and vegetables continue metabolic processes after being harvested. In some produce, mainly climacteric fruits, these processes cause deterioration of the produce during storage. To reduce the deterioration rate, several strategies have been implemented for postharvest handling. One of these preservation strategies is modified atmosphere packaging (MAP). In this technology, the respiration rate of the produce and the gas permeability of the storage film are the two fundamental kinetic processes accounted for in designing the packaging system. To understand the relationship of these two kinetic processes during packaging in modified atmospheres, two major techniques have been presented from the standpoint of mathematical modeling: the classic respiration rate models and the reaction-diffusion model. In the classic model of respiration rate, four types of black box model approaches have been proposed: linear, polynomial, exponential, and the Michaelis–Menten kinetic models. For the last black box model, four types of inhibition approaches are considered: competitive, uncompetitive, noncompetitive, and, finally, a combination of competitive and uncompetitive inhibition. In the reaction-diffusion model, it has been considered that the transport of a species in modified atmosphere packaging (mass transport in the headspace and the film used as packaging) obeys strictly diffusive transport models. For this reason, the main objective of this review is to show the advances in the two major techniques (classic respiration rate models and the reaction-diffusion model) implemented to describe the MAP of fruit and vegetables, as described in specialized literature.

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References

  1. 1.

    Liu RH (2013) Health-promoting components of fruits and vegetables in the diet. Adv Nutr Int Rev J 4:384S–392S

    CAS  Google Scholar 

  2. 2.

    Singh R, Giri SK, Kulkarni SD (2013) Respiratory behavior of turning stage mature tomato (Solanum lycopersicum L.) under closed system at different temperature. Croatian journal of food science and technology 5(2):78–84

    Google Scholar 

  3. 3.

    Singh R, Giri Kumar S, Kulkarni S (2015) Respiratory behaviour of mature light green guava (Psidium guajava L.) under closed system. Poljoprivredna tehnika 38(1):23–29

    Google Scholar 

  4. 4.

    Ghidelli C, Pérez-Gago MB (2018) Recent advances in modified atmosphere packaging and edible coatings to maintain quality of fresh-cut fruits and vegetables. Crit Rev Food Sci Nutr 58(4):662–679

    CAS  PubMed  Google Scholar 

  5. 5.

    Guillard V, Guillaume C, Destercke S (2012) Parameter uncertainties and error propagation in modified atmosphere packaging modelling. Postharvest Biol Technol 67:154–166

    CAS  Google Scholar 

  6. 6.

    Rennie, T. J., & Sunjka, P. S. (2017). Modified atmosphere for storage, transportation, and packaging. In Novel Postharvest Treatments of Fresh Produce (pp. 433-480). CRC press

  7. 7.

    Singh R, Giri SK, Rao KR (2014) Respiration rate model for mature green capsicum (Capsicum annum L.) under closed aerobic atmospheric conditions. Croatian Journal of Food Science and Technology 6(2):110–115

    Google Scholar 

  8. 8.

    Zhang M, Meng X, Bhandari B, Fang Z, Chen H (2015) Recent application of modified atmosphere packaging (MAP) in fresh and fresh-cut foods. Food Reviews International 31(2):172–193

    Google Scholar 

  9. 9.

    Caleb OJ, Mahajan PV, Opara UL, Witthuhn CR (2012a) Modeling the effect of time and temperature on respiration rate of pomegranate arils (cv. “Acco” and” Herskawitz”). J Food Sci 77: 80–87

  10. 10.

    Caleb OJ, Mahajan PV, Opara UL, Withuhn CR (2012b) Modelling the respiration rates of pomegranate fruit and arils. Postharvest Biol Technol 64:49–54

    Google Scholar 

  11. 11.

    Caleb OJ, Opara UL, Witthuhn CR (2012c) Modified atmosphere packaging of pomegranate fruit and arils: a review. Food Bioprocess Technol 5:15–30. https://doi.org/10.1007/s11947-011-0525-7

    CAS  Article  Google Scholar 

  12. 12.

    Fonseca SC, Oliveira FA, Brecht JK (2002) Modelling respiration rate of fresh fruits and vegetables for modified atmosphere packages: a review. J Food Eng 52(2):99–119

    Google Scholar 

  13. 13.

    Gavara R, Catalá R, Cerisuelo J, Hernandez P (2018) Gas transport properties in packaging applications. In: Thomas S, Wilson R, Anil Kumar S, George SC (eds) Transport Properties of Polymeric Membranes, vol 30. Elsevier, Amsterdam, Chapter, pp 651–672

    Google Scholar 

  14. 14.

    Zhang Y, Liu Q, Rempel C (2011) Mathematical modeling of modified atmosphere packaging. In: Brody AL, Zhuang H, Han JH (eds) Modified atmosphere packaging for fresh-cut fruits and vegetables. Blackwell Publishing, Oxford, pp 11–30

    Google Scholar 

  15. 15.

    Caleb OJ, Mahajan PV, Al-Said FA, Opara UL (2013) Modified atmosphere packaging technology of fresh and fresh-cut produce and the microbial consequences—a review. Food Bioprocess Technology 6:303–329

    CAS  PubMed  Google Scholar 

  16. 16.

    Del Nobile MA, Baiano A, Benedetto A, Massignan L (2006) Respiration rate of minimally processed lettuce as affected by packaging. J Food Eng 74:60–69

    Google Scholar 

  17. 17.

    Mangaraj S, Goswami TK (2011a) Measurement and modeling of respiration rate of guava (CV. Baruipur) for modified atmosphere packaging. Int J Food Prop 14(3):609–628

    CAS  Google Scholar 

  18. 18.

    Mangaraj S, Goswami TK (2011b) Modeling of respiration rate of litchi fruit under aerobic conditions. Food Bioprocess Technol 4(2):272

    Google Scholar 

  19. 19.

    Hayakawa KI, Henig YS, Gilbert SG (1975) Formulae for predicting gas exchange of fresh produce in polymeric film package. J Food Sci 40(1):186–191

    CAS  Google Scholar 

  20. 20.

    Mangaraj S, Goswami TK, Giri SK, Joshy CG (2014) Design and develoepeemnt of a modified atmosphere packaging system for guava (cv. Baruipur). Journal of Food Science Technology 51(11):2925–2946

    CAS  PubMed  Google Scholar 

  21. 21.

    Mangaraj S, Goswami TK, Mahajan PV (2015) Development and validation of a comprehensive model for map of fruits based on enzyme kinetics theory and Arrhenius relation. J Food Sci Technol 52(7):4286–4295

    CAS  PubMed  Google Scholar 

  22. 22.

    Zhang Y, Liu Q, Geng X (2017) Modelling of modified atmosphere packaging based on conventional polymeric films and perforated films. In: Pareek S (ed) Novel postharvest treatments of fresh produce, 1st edn. CRC Press, Boca Raton, pp 533–556

    Google Scholar 

  23. 23.

    Ho QT, Hertog M, Verboven P, Ambaw A, Rogge S, Verlinden BE, Nicolaï BM (2018) Down-regulation of respiration in pear fruit depends on temperature. J Exp Bot 69(8):2049–2060

    CAS  PubMed  PubMed Central  Google Scholar 

  24. 24.

    Belay ZA, Caleb OJ, Opara UL (2016) Modelling approaches for designing and evaluating the performance of modified atmosphere packaging (MAP) systems for fresh produce: a review. Food Packag Shelf Life 10:1–15

    Google Scholar 

  25. 25.

    De Bonis MV, Cefola M, Pace B, Ruocco G (2013) Mass and heat transfer modeling of bio-substrates during packaging. Heat Mass Transf 49:799–808

    Google Scholar 

  26. 26.

    Ho QT, Verboven P, Verlinden BE, Schenk A, Delele MA, Rolletschek H, Nicolaï BM (2010b) Genotype effects on internal gas gradients in apple fruit. J Exp Bot 61(10):2745–2755

    CAS  PubMed  Google Scholar 

  27. 27.

    Mendoza F, Verboven P, Mebatsion HK, Kerckhofs G, Wevers M, Nicolaı¨ BM. (2007) Three-dimensional pore space quantification of apple tissue using x-ray computed microtomography. Planta 226:559–570

    CAS  PubMed  Google Scholar 

  28. 28.

    Ho QT, Verlinden BE, Verboven P, Nicolaï BM (2006a) Gas diffusion properties at different positions in the pear. Postharvest Biol Technol 41:113–120

    Google Scholar 

  29. 29.

    Ho QT, Verlinden BE, Verboven P, Vandewalle S, Nicolai BM (2006b) A permeation–diffusion–reaction model of gas transport in cellular tissue of plant materials. J Exp Bot 57(15):4215–4224

    CAS  PubMed  Google Scholar 

  30. 30.

    Ho QT, Verboven P, Verlinden BE, Lammertyn J, Vandewalle S, Nicolaï BM (2008) A continuum model for metabolic gas exchange in pear fruit. PLoS Comput Biol 4(3)

  31. 31.

    Ho QT, Verboven P, Mebatsion HK, Verlinden BE, Vandewalle S, Nicolaï BM (2009) Microscale mechanisms of gas exchange in fruit tissue. New Phytol 182(1):163–174

    CAS  PubMed  Google Scholar 

  32. 32.

    Lammertyn J, Scheerlinck N, Jancso’k P, Verlinden BE, Nicolaı̈ BM (2003a) A respiration–diffusion model for ‘Conference’ pears. I. Model development and validation. Postharvest Biol Technol 30:29–42

    Google Scholar 

  33. 33.

    Lammertyn J, Scheerlinck N, Jancso’k P, Verlinden BE, Nicolaı̈ BM (2003b) A respiration–diffusion model for ‘Conference’ pears. II. Simulation and relation to core breakdown. Postharvest Biol Technol 30:43–55

    Google Scholar 

  34. 34.

    Rao CG (2015) Engineering for storage of fruits and vegetables: cold storage, controlled atmosphere storage, modified atmosphere storage. Academic Press, Cambridge

    Google Scholar 

  35. 35.

    Ho QT, Verboven P, Verlinden BE, Herremans E, Wevers M, Carmeliet J, Bart MN (2011) A 3-D multiscale model for gas exchange in fruit. Plant Physiol 155:1158–1168

    CAS  PubMed  PubMed Central  Google Scholar 

  36. 36.

    Verboven P, Pedersen O, Herremans E, Ho QT, Nicolaï BM, Colmer TD, Teakle N (2012) Root aeration via aerenchymatous phellem: three-dimensional micro-imaging and radial O2 profiles (in Melilotus siculus.). New Phytol 193:420–431

    CAS  PubMed  Google Scholar 

  37. 37.

    Klee HJ, Giovannoni JJ (2011) Genetics and control of tomato fruit ripening and quality attributes. Annual Review of Genetics (45):41–59

  38. 38.

    Kubo Y (2015) Ethylene, oxygen, carbon dioxide, and temperature in postharvest physiology. In: Kanayama Y, Kochetov A (eds) Abiotic Stress Biology in Horticultural Plants. Springer, Tokyo, pp 17–33

    Google Scholar 

  39. 39.

    Watson JA, Treadwell D, Sargent SA, Brecht JK, Pelletier W (2015) Postharvest storage, packaging and handling of specialty crops: a guide for Florida small farm producers. University of Florida, Florida

    Google Scholar 

  40. 40.

    Wills RBH, McGlasson WB, Graham D, Joyce DC. (2007). Physiology and biochemistry. In: postharvest: an introduction to physiology and handling of fruits, vegetables and ornamentals, 5th: UNSW Press, Randwick p 29

  41. 41.

    Paul V, Pandey R, Srivastava GC (2012) The fading distinctions between classical patterns of ripening in climacteric and non-climacteric fruit and the ubiquity of ethylene—an overview. J Food Sci Technol 49(1):1–21

    CAS  PubMed  Google Scholar 

  42. 42.

    Gapper NE, McQuinn RP, Giovannoni JJ (2013) Molecular and genetic regulation of fruit ripening. Plant Mol Biol 82(6):575–591

    CAS  PubMed  Google Scholar 

  43. 43.

    Conesa A, Verlinden BE, Artes F, Nicolai B, Artes F (2007) Respiration rates of fresh-cut bell peppers under super atmospheric and low oxygen with or without high carbon dioxide. Postharvest Biol Technol 45:81–88

    CAS  Google Scholar 

  44. 44.

    Goyette B, Vigneault C, Raghavan V, Charles MT (2012) Hyperbaric treatment on respiration rate and respiratory quotient of tomato. Food Bioprocess Technol 5(8):3066–3074

    Google Scholar 

  45. 45.

    Zhang Y, Liu Z, Han JH (2007) In: Wilson CL (ed) Intelligent and active packaging for fruits and vegetables. New York, CRC Press

    Google Scholar 

  46. 46.

    Caleb, O.J., Herppich, W.B., P.V. Mahajan (2016a). The basics of respiration for horticultural products. Reference Module in Food Science (1st ed.), pp. 1–7

  47. 47.

    Caleb, O.J., Ilte, K., Fröhling, A., Geyer, M., P.V. Mahajan (2016b). Integrated modified atmosphere and humidity package design for minimally processed Broccoli (Brassica oleracea L. var. italica).Postharvest Biology and Technology, 121, pp. 87–100

  48. 48.

    Mahajan PV, Luca A, Edelenbos M (2016) Development of a small and flexible sensor-based respirometer for real-time determination of respiration rate, respiratory quotient and low O2 limit of fresh produce. Comput Electron Agric 121:347–353

    Google Scholar 

  49. 49.

    Iqbal T, Rodrigues S, Mahajan PV, Kerry JP (2009a) Mathematical modeling of the influence of temperature and gas composition on the respiration rate of shredded carrots. Journal Food Engineering 91:325–332

    CAS  Google Scholar 

  50. 50.

    Iqbal T, Rodrigues FAS, Mahajan PV, Kerry JP (2009b) Effect of time, temperature, and slicing on respiration rate of mushrooms. J Food Sci 74(6):E298–E303

    CAS  PubMed  Google Scholar 

  51. 51.

    Mahajan PV, Mezdad T (2013) Engineering packaging design accounting for transpiration rate: model development and validation with strawberries. J Food Eng 119:370–376

    Google Scholar 

  52. 52.

    Bovi GG, Caleb OJ, Linke M, Rauh C, Mahajan PV (2016) Transpiration and moisture evolution in packaged fresh horticultural produce and the role of integrated mathematical models: a review. Biosyst Eng 150:24–39

    Google Scholar 

  53. 53.

    Mahajan PV, Caleb OJ (2017) Modeling MAP of fruits and vegetables. Reference Module in Food Science. https://doi.org/10.1016/b978-0-08-100596-5.21461-3

  54. 54.

    Mangaraj S, Goswami TK, Giri SK, Chandra P, Pajnoo RK (2013) Development and evaluation of modified atmosphere (MA) packages employing lamination technique for Royal Delicious apple. Emirates Journal of Food and Agriculture 25(5):358–375

    Google Scholar 

  55. 55.

    Sousa AR, Oliveira JC, Sousa-Gallagher MJ (2017) Determination of the respiration rate parameters of cherry tomatoes and their joint confidence regions using closed systems. J Food Eng 206:13–22

    Google Scholar 

  56. 56.

    Finnegan E, Mahajan PV, O’Connell M, Francis GA, O’Beirne D (2013) Modelling respiration in fresh-cut pineapple and prediction of gas permeability needs for optimal modified atmosphere packaging. Postharvest Biol Technol 79:47–53

    CAS  Google Scholar 

  57. 57.

    Gomes MH, Beaudry RM, Almeida DP, Malcata FX (2010) Modelling respiration of packaged fresh-cut ‘Rocha’ pear as affected by oxygen concentration and temperature. J Food Eng 96(1):74–79

    CAS  Google Scholar 

  58. 58.

    Ghosh T, Dash KK (2018) Respiration rate model and modified atmosphere packaging of bhimkol banana. Engineering in Agriculture, Environment and Food 11(4):186–195

    Google Scholar 

  59. 59.

    Ravindra MR, Goswami TK (2008) Modelling the respiration rate of green mature mango under aerobic conditions. Biosyst Eng 99:239–248

    Google Scholar 

  60. 60.

    Zhao, X., Xia, M., Wei, X., Xu, C., Luo, Z., & Mao, L. (2019). Consolidated cold and modified atmosphere package system for fresh strawberry

  61. 61.

    Jalali A, Seiiedlou S, Linke M, Mahajan P (2017) A comprehensive simulation program for modified atmosphere and humidity packaging (MAHP) of fresh fruits and vegetables. J Food Eng 206:88–97

    CAS  Google Scholar 

  62. 62.

    Afifi EH (2016) Effect of active and passive modified atmosphere packaging on quality attributes of strawberry fruits during cold storage. Arab Universities Journal of Agricultural Sciences 24(1):157–168

    Google Scholar 

  63. 63.

    Agudelo C, Restrepo C, Zapata JE (2016) Respiration kinetic of mango (Mangifera indica L.) as function of storage temperature. Revista Facultad Nacional de Agronomía Medellín 69(2):7985–7995

    Google Scholar 

  64. 64.

    Barrios S, Lema P, Lareo C (2014b) Modeling respiration rate of strawberry (cv. San Andreas) for modified atmosphere packaging design. Int J Food Prop 17(9):2039–2051

    CAS  Google Scholar 

  65. 65.

    Nath P, Bouzayen M, Mattoo AK, Claude Pech J (eds) (2014) Fruit ripening: physiology, signalling and genomics. CABI, Wallingford

    Google Scholar 

  66. 66.

    Banks NH, Cleland DJ, Cameron AC, Beaudry RM, Kader AA (1995) Proposal for a rationalized system of units for postharvest research in gas exchange. HortScience 30(6):1129–1131

    Google Scholar 

  67. 67.

    Singh RK, Singh N (2005) In: Han JH (ed) Innovations in food packaging. New York, Elsevier Academic Press

    Google Scholar 

  68. 68.

    Singh R, Giri SK, Kulkarni SD, Ahirwar R (2012) Study on respiration rate and respiration quotient of green mature mango (mangifera indica L.) under aerobic conditions. Asian J of Bio Sci 7(2):210–213

    Google Scholar 

  69. 69.

    Bhande SD, Ravindra MR, Goswami TK (2008) Respiration rate of banana fruit under aerobic conditions at different storage temperatures. J Food Eng 87(1):116–123

    Google Scholar 

  70. 70.

    Nakamura N, SHIINA TDVS, NAWA Y (2004) Respiration properties of tree-ripe mango under CA condition. Japan Agricultural Research Quarterly: JARQ 38(4):221–226

    Google Scholar 

  71. 71.

    Torrieri E, Cavella S, Masi P (2009) Modelling respiration rate of Annurca apple for development of modified atmosphere packaging. Int J Food Sci Technol 44:890–899

    CAS  Google Scholar 

  72. 72.

    Dash KK, Ravindra MR, Goswami TK (2009) Modeling of respiration rate of sapota fruit under aerobic conditions. J Food Process Eng 32:528–543

    Google Scholar 

  73. 73.

    Bessemans, N., Verboven, P., Verlinden, B. E., & Nicolaï, B. M. (2016, June). RQ-based dynamic controlled atmosphere storage of apple fruit. In VIII International Postharvest Symposium: Enhancing Supply Chain and Consumer Benefits-Ethical and Technological Issues 1194 (pp. 681-688)

  74. 74.

    Rocculi P, Del Nobile MA, Romani S, Baiano A, Dalla M (2006) Use of a simple mathematical model to evaluate dipping and MAP effects on aerobic respiration of minimally processed apples. J Food Eng 76:334–340

    Google Scholar 

  75. 75.

    Heydari, A., Alemzadeh, I., & Vossoughi, M. (2012). Study and mathematical modeling of transient gas compositions for modified atmosphere packaging. In Analysis and Design of Biological Materials and Structures (pp. 163–174). Springer, Berlin, Heidelberg

  76. 76.

    Wang ZW, Duan HW, Hu CY (2009) Modelling the respiration rate of guava (Psidium guajava L.) fruit using enzyme kinetics, chemical kinetics and artificial neural network. Eur Food Res Technol 229:495–503

    CAS  Google Scholar 

  77. 77.

    Barrios S, Lema P, Marra F (2014a) Modelling passive modified atmosphere packaging of strawberries: numerical analysis and model validation. Int Food Res J 21(2):507–515

    CAS  Google Scholar 

  78. 78.

    Elhalwagy M, Dyck N, Straatman AG (2019) A multi-level approach for simulation of storage and respiration of produce. Appl Sci 9(6):1052

    CAS  Google Scholar 

  79. 79.

    Sousa MJ, Mahajan PV (2013) Integrative mathematical modelling for MAP design of fresh-produce: theoretical analysis and experimental validation. Food Control 29:444–450

    Google Scholar 

  80. 80.

    Kaur P, Rai DR, Paul S (2010) Nonlinear estimation of respiratory dynamics of fresh-cut spinach (spinacia oleracea) based on enzyme kinetics. J Food Process Eng 34:2137–2155

    Google Scholar 

  81. 81.

    Ho QT, Verboven P, Verlinden BE, Nicolaï BM (2010a) A model for gas transport in pear fruit at multiple scales. J Exp Bot 61(8):2071–2081

    CAS  PubMed  Google Scholar 

  82. 82.

    Lee DS, Haggar PE, Lee J, Yam KL (1991) Model for fresh products respiration in modified atmosphere based on principles of enzyme kinetics. J Food Sci 56(6):1580–1585

    CAS  Google Scholar 

  83. 83.

    Ersan S, Gunes G, and Zor AO (2010) Respiration rate of pomegranate arils as affected by O2 and CO2 and design of modified atmosphere packaging. Proc.10th Intern.Controlled and modified atmosphere. Acta Hort 876–889

  84. 84.

    Heydari AMIR, Shayesteh K, Eghbalifam N, Bordbar HOSSEIN, Falahatpisheh S (2010) Studies on the respiration rate of banana fruit based on enzyme kinetics. Int J Agric Biol 12(1):145–149

    CAS  Google Scholar 

  85. 85.

    Makino Y, Iwasaki K, Hirata T (1996) Oxygen consumption model for fresh produce on the basis of adsorption theory. Trans Am Soc Agric Eng 39:1067–1073

    Google Scholar 

  86. 86.

    Rennie TJ, Tavoularis S (2009b) Perforation-mediated modified atmosphere packaging. Part II. Implementation and numerical solution of a mathematical model. Postharvest Biology and Technology 51(1):10–20

    CAS  Google Scholar 

  87. 87.

    Ho QT, Verboven P, Verlinden BE, Schenk A, Nicolai BM (2013) Controlled atmosphere storage may lead to local ATP deficiency in apple. Postharvest Biol Technol 78:103–112

    CAS  Google Scholar 

  88. 88.

    Rennie TJ, Tavoularis S (2009a) Perforation-mediated modified atmosphere packaging. Part I. development of a mathematical model. Postharvest Biol Technol 51:1–9

    CAS  Google Scholar 

  89. 89.

    Torrieri E, Perone N, Cavella C, Masi P (2010) Modelling the respiration rate of minimally processed broccoli (Brassica rapa var. sylvestris) for modified atmosphere package design. Int J Food Sci Technol 45:2186–2193

    CAS  Google Scholar 

  90. 90.

    Barbosa NC, Vieira RAM, de Resende ED (2018) Modeling the respiration rate of golden papayas stored under different atmosphere conditions at room temperature. Postharvest Biol Technol 136:152–160

    CAS  Google Scholar 

  91. 91.

    Rahman EAA, Talib RA, Aziz MG, Yusof YA (2013) Modelling the effect of temperature on respiration rate of fresh cut papaya (Carica papaya L.) fruits. Food Sci Biotechnol 22(6):1581–1588

    Google Scholar 

  92. 92.

    Benítez S, Chiumenti M, Sepulcre F, Achaerandio I, Pujolá M (2012) Modeling the effect of storage temperature on the respiration rate and texture of fresh cut pineapple. J Food Eng 113(4):527–533

    Google Scholar 

  93. 93.

    Aindongo WV, Caleb OJ, Mahajan PV, Manley M, Opara UL (2014) Modelling the effects of storage temperature on the respiration rate of different pomegranate fractions. South African Journal of Plant and Soil 31(4):227–231

    Google Scholar 

  94. 94.

    Waghmare RB, Mahajan PV, Annapure US (2013) Modelling the effect of time and temperature on respiration rate of selected fresh-cut produce. Postharvest Biol Technol 80:25–30

    Google Scholar 

  95. 95.

    Muftuoglu F, Ayhan Z, Esturk O (2012) Modified atmosphere packaging of Kabaasi apricot (Prunus armeniaca L.‘Kabaaşı’): effect of atmosphere, packaging material type and coating on the physicochemical properties and sensory quality. Food Bioprocess Technol 5(5):1601–1611

    CAS  Google Scholar 

  96. 96.

    Castellanos DA, Cerisuelo JP, Hernandez-Muñoz P, Herrera AO, Gavara R (2016) Modelling the evolution of O2 and CO2 concentrations in MAP of a fresh product: application to tomato. J Food Eng 168:84–95

    CAS  Google Scholar 

  97. 97.

    Larsen H, Liland KH (2013) Determination of O2 and CO2 transmission rate of whole packages and single perforations in micro-perforated packages for fruit and vegetables. J Food Eng 119(2):271–276

    CAS  Google Scholar 

  98. 98.

    Kartal S, Aday MS, Caner C (2012) Use of microperforated films and oxygen scavengers to maintain storage stability of fresh strawberries. Postharvest Biol Technol 71:32–40

    CAS  Google Scholar 

  99. 99.

    Brody, A. L. (2005). What’s fresh about fresh-cut. Food Technol

  100. 100.

    Ozdemir I, Monnet F, Gouble B (2005) Simple determination of the O2 and CO2 permeances of microperforated pouches for modified atmosphere packaging of respiring foods. Postharvest Biol Technol 36(2):209–213

    CAS  Google Scholar 

  101. 101.

    Chung D, Papadakis SE, Yam KL (2003) Simple models for evaluating effects of smalls leaks on the gas barrier properties of food packages. Packaging Technology Science 16:77–86

    Google Scholar 

  102. 102.

    Techavises N, Hikida Y (2008) Development of a mathematical model for simulating gas and water vapor exchanges in modified atmosphere packaging with macroscopic perforations. J Food Eng 85:94–104

    Google Scholar 

  103. 103.

    González J, Ferrer A, Oria R, Salvador ML (2009) A mathematical model for packaging with microperforated films of fresh-cut fruits and vegetables. J Food Eng 95:158–165

    Google Scholar 

  104. 104.

    Marsh K, Bugusu B (2007) Food packaging-roles, materials, and environmental issues. J Food Sci 72:39–55

    Google Scholar 

  105. 105.

    González J, Ferrer A, Oria R, Salvador ML (2008) Determination of O2 and CO2 transmission rates through microperforated films for modified atmosphere packaging of fresh fruits and vegetables. J Food Eng 86(2):194–201

    Google Scholar 

  106. 106.

    Xanthopoulos G, Koronaki ED, Boudouvis AG (2012) Mass transport analysis in perforation-mediated modified atmosphere packaging of strawberries. J Food Eng 111(2):326–335

    CAS  Google Scholar 

  107. 107.

    Piringer OG, Baner AL (eds) (2008) Plastic packaging materials for food: barrier function, mass transport, quality assurance, and legislation. Wiley, Hoboken, pp 183–218

    Google Scholar 

  108. 108.

    Abdul-Baki AA, Solomos T (1994) Diffusivity of carbon dioxide through the skin and flesh of ‘Russet Burbank’ potato tubers. J Am Soc Hortic Sci 119(4):742–746

    Google Scholar 

  109. 109.

    Mannapperuma JD, Singh RP, Montero ME (1991) Simultaneous gas diffusion and chemical reaction in foods stored in modified atmospheres. J Food Eng 14(3):167–183

    Google Scholar 

  110. 110.

    Xia B, Sun D (2002) Applications of computational fluid dynamics (CFD) in the food industry: a review. Comput Electron Agric 34:5–24

    Google Scholar 

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Acknowledgements

This work was supported by the Chilean Council of Science and Technology [CONICYT-FONDECYT Regular project (1120342)].

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Correspondence to Luis A. Segura-Ponce.

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Badillo, G.M., Segura-Ponce, L.A. Classic and Reaction-Diffusion Models Used in Modified Atmosphere Packaging (MAP) of Fruit and Vegetables. Food Eng Rev 12, 209–228 (2020). https://doi.org/10.1007/s12393-020-09214-3

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Keywords

  • Modified atmosphere packaging
  • Classic MAP modeling
  • Reaction-diffusion model
  • Enzyme kinetics
  • Mass transport modeling