Meta-analysis of Kinetic Parameter Uncertainty on Shelf Life Prediction in the Frozen Fruits and Vegetable Chain

  • Maria C. GiannakourouEmail author
  • Petros S. Taoukis
Review Article


Most studies on frozen foods’ deterioration focus on measurements of selected quality determining indices at the reference frozen storage conditions at limited time points (e.g., 6 and 12 months). This information is not sufficient to predict the frozen system behavior under a different storage temperature, or under the real, dynamic conditions of the actual cold chain. For this purpose, a systematic kinetic study is essential; additionally, the real uncertainty of model parameters needs to be taken into account, in order to proceed to realistic shelf life estimations. In this review work, published findings on kinetic data of deterioration of frozen food of plant origin were analyzed. Kinetic parameters (e.g., activation energy, shelf life, etc.) were extracted and some of them incorporated to a further investigation. The scope is to provide a critical assessment and a comprehensive meta-analysis of the literature information on quality loss modeling of frozen foods. Therefore, common quality indices for specific systems are reviewed, fundamental methodologies used to build kinetic models are assessed, and alternative approaches to improve practical applications of these models are proposed. Alternative methodologies are described in order to take into account the calculated uncertainty of models’ parameters when assessing the remaining shelf life of the product at any point within the cold chain. This was implemented in a FORTRAN code through a Monte Carlo scheme, on literature data of vitamin C loss in different frozen matrices, as well as for other quality indices (e.g., color). Results demonstrated the improved predictions obtained, with broader and more realistic confidence intervals.


Quality kinetics Meta-analysis Frozen foods Parameter uncertainty Cold chain 



  1. 1.
    Bonat Celli G, Ghanem A, Su-Ling Brooks M (2016) Influence of freezing process and frozen storage on the quality of fruits and fruit products. Food Rev Int 32:280–304. CrossRefGoogle Scholar
  2. 2.
    Corradini MG, Peleg M (2006b) Prediction of vitamins loss during non-isothermal heat processes and storage with non-linear kinetic models. Trends Food Sci Technol 17(1):24–34CrossRefGoogle Scholar
  3. 3.
    Mattick KL, Legan JD, Humphrey TJ, Peleg M (2001) Calculating Salmonella inactivation in nonisothermal heat treatments from isothermal nonlinear survival curves. J Food Prot 64(5):606–613CrossRefGoogle Scholar
  4. 4.
    Periago PM, van Zuijlen A, Fernandez PS, Klapwijk PM, ter Steeg PF, Corradini MG, Peleg M (2004) Estimation of the non-isothermal inactivation patterns of Bacillus sporothermodurans IC4 spores in soups from their isothermal survival data. Int J Food Microbiol 95(2):205–218CrossRefGoogle Scholar
  5. 5.
    Valdramidis VP, Geeraerd AH, Bernaerts K, Van Impe JF (2006) Microbial dynamics versus mathematical model dynamics: the case of microbial heat resistance induction. Innov Food Sci Emerg 7:80–87. CrossRefGoogle Scholar
  6. 6.
    Charoenrein S, Harnkarnsujarit N (2016) Food Freezing and Non-Equilibrium States. In: Non-Equilibrium States and Glass Transitions in Foods: Processing Effects and Product-Specific Implications. pp 39–62. doi: CrossRefGoogle Scholar
  7. 7.
    Reid DS, Sajjaanantakul T, Lillford PJ, Charoenrein S (2010) Water Properties in Food, Health, Pharmaceutical and Biological Systems: ISOPOW 10. Water properties in food, health, pharmaceutical and biological systems: ISOPOW 10. doi: Google Scholar
  8. 8.
    Biliaderis CG, Swan RS, Arvanitoyannis I (1999) Physicochemical properties of commercial starch hydrolyzates in the frozen state. Food Chem 64:537–546. CrossRefGoogle Scholar
  9. 9.
    Manzocco L, Nicoli MC, Anese M, Pitotti A, Maltini E (1998) Polyphenoloxidase and peroxidase activity in partially frozen systems with different physical properties. Food Res Int 31:363–370. CrossRefGoogle Scholar
  10. 10.
    Terefe NS, Hendrickx M (2002) Kinetics of the pectin Methylesterase catalyzed De-esterification of pectin in frozen food model systems. Biotechnol Prog 18:221–228. CrossRefPubMedGoogle Scholar
  11. 11.
    Terefe NS, Van Loey A, Hendrickx M (2004) Modelling the kinetics of enzyme-catalysed reactions in frozen systems: the alkaline phosphatase catalysed hydrolysis of di-sodium-p-nitrophenyl phosphate. Innov Food Sci Emerg 5:335–344. CrossRefGoogle Scholar
  12. 12.
    Syamaladevi RM, Sablani SS, Tang J, Powers J, Swanson BG (2011) Stability of anthocyanins in frozen and freeze-dried raspberries during long-term storage: in relation to glass transition. J Food Sci 76:E414–E421. CrossRefPubMedGoogle Scholar
  13. 13.
    Syamaladevi RM, Manahiloh KN, Muhunthan B, Sablani SS (2012) Understanding the influence of state/phase transitions on ice recrystallization in Atlantic Salmon (Salmo salar) during frozen storage. Food Biophys 7:57–71. CrossRefGoogle Scholar
  14. 14.
    Zhang Y, Zhao J-H, Ding Y, Nie Y, Xiao H-W, Zhu Z, Tang X-M (2017) Effects of state/phase transitions on the quality attributes of mango (Mangifera indica L.) during frozen storage. Int J Food Sci Technol 52:239–246. CrossRefGoogle Scholar
  15. 15.
    Huang K, Tian H, Gai L, Wang J (2012) A review of kinetic models for inactivating microorganisms and enzymes by pulsed electric field processing. J Food Eng 111:191–207. CrossRefGoogle Scholar
  16. 16.
    DerSimonian R, Laird N (1986) Meta-analysis in clinical trials. Control Clin Trials 7:177–188. CrossRefGoogle Scholar
  17. 17.
    Sutton AJ, Abrams KR, Jones DR (2001) An illustrated guide to the methods of meta-analysis. J Eval Clin Pract 7:135–148. CrossRefPubMedGoogle Scholar
  18. 18.
    Van Boekel MAJS (1996) Statistical aspects of kinetic modeling for food science problems. J Food Sci 61:477–486. CrossRefGoogle Scholar
  19. 19.
    Gonçalves EM, Abreu M, Brandão TRS, Silva CLM (2011a) Degradation kinetics of colour, vitamin C and drip loss in frozen broccoli (Brassica oleracea L. ssp. Italica) during storage at isothermal and non-isothermal conditions. Int J Refrig 34:2136–2144. CrossRefGoogle Scholar
  20. 20.
    Gonçalves EM, Pinheiro J, Abreu M, Brandão TRS, Silva CLM (2011b) Kinetics of quality changes of pumpkin (Curcurbita maxima L.) stored under isothermal and non-isothermal frozen conditions. J Food Eng 106:40–47. CrossRefGoogle Scholar
  21. 21.
    Huang L (2015a) Direct construction of predictive models for describing growth of Salmonella Enteritidis in liquid eggs - a one-step approach. Food Control 57:76–81. CrossRefGoogle Scholar
  22. 22.
    Valdramidis VP, Geeraerd AH, Bernaerts K, Van Impe JFM (2008) Identification of non-linear microbial inactivation kinetics under dynamic conditions. Int J Food Microbiol 128:146–152. CrossRefPubMedGoogle Scholar
  23. 23.
    Valdramidis VP, Taoukis PS, Stoforos NG, Van Impe JFM (2012) In: Cullen PJ, Tiwari BK, Valdramidis VP (eds) novel thermal and non-thermal technologies for fluid foods. Academic Press, London, UK doi: CrossRefGoogle Scholar
  24. 24.
    Taoukis PS, Giannakourou MC (2018) Modelling food quality. Food Sci Technol (London) 32:38–43Google Scholar
  25. 25.
    Giannakourou MC, Stoforos NG (2016) In: Carvajal-Millan E, Mohan CO, Ravishankar CN (eds) food process engineering and quality assurance, apple academic press Inc., NJ, USAGoogle Scholar
  26. 26.
    Peleg M, Normand MD, Dixon WR, Goulette TR (2018) Modeling the degradation kinetics of ascorbic acid. Crit Rev Food Sci 58:1478–1494. CrossRefGoogle Scholar
  27. 27.
    Peleg M (2003) Microbial survival curves: interpretation, mathematical modeling, and utilization. Comments on Theoretical Biology 8:357–387CrossRefGoogle Scholar
  28. 28.
    Peleg M, Normand MD, Corradini MG (2005) Generating microbial survival curves during thermal processing in real time. J Appl Microbiol 98:406–417CrossRefGoogle Scholar
  29. 29.
    Taoukis PS, Labuza TP, Saguy S (1997) In: Valentas KJ, Rotstein E,Singh RP (Eds) Handbook of food engineering practice. New York: CRC PressGoogle Scholar
  30. 30.
    Van Boekel MAJS (2008) Kinetic modeling of food quality: a critical review. Compr Rev Food Sci Food 7:144–158. CrossRefGoogle Scholar
  31. 31.
    Fu B, Labuza TP (1993) Shelf life prediction: theory and applications. Food Prot 4(3):125–133Google Scholar
  32. 32.
    Corradini MG, Peleg M (2006a) On modeling and simulating transitions between microbial growth and inactivation or vice versa. Int J Food Microbiol 108:22–35CrossRefGoogle Scholar
  33. 33.
    Arrhenius SA (1889) Über die Dissociationswärme und den Einfluß der Temperatur auf den Dissociationsgrad der Elektrolyte. Z Phys Chem 4:96–116. CrossRefGoogle Scholar
  34. 34.
    Peleg M, Normand MD, Corradini MG (2012a) The Arrhenius equation revisited. Crit Rev Food Sci 52(9):830–851CrossRefGoogle Scholar
  35. 35.
    Peleg M, Normand MD, Corradini MG (2017) A new look at kinetics in relation to food storage. Annu Rev Food Sci Technol 8:135–153CrossRefGoogle Scholar
  36. 36.
    Williams ML, Landel RF, Ferry JD (1955) The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J Chem Eng 77:3701–3707Google Scholar
  37. 37.
    Peleg M (1992) On the use of the WLF model in polymers and foods. Crit Rev Food Sci Nutr 32:59–66. CrossRefPubMedGoogle Scholar
  38. 38.
    Peleg M, Engel R, Gonzalez-Martinez C, Corradini MG (2002) Non-Arrhenius and non-WLF kinetics in food systems. J Sci Food Agric 82(12):1346–1355CrossRefGoogle Scholar
  39. 39.
    Nelson KA, Labuza TP (1994) Water activity and food polymer science: implications of state on Arrhenius and WLF models in predicting shelf life. J Food Eng 22:271–289. CrossRefGoogle Scholar
  40. 40.
    Taoukis PS, Tsironi TS, Giannakourou MC (2015) handbook of food processing and engineering. In: Tzia K, Varzakas T (eds) food engineering fundamentals, vol I. CRC press, Boca Raton, Florida, USAGoogle Scholar
  41. 41.
    Peleg M, Normand MD, Corradini MG (2012b) On Quantifying Nonthermal Effects on the Lethality of Pressure-Assisted Heat Preservation Processes. J Food Sci 77:R47–R56. CrossRefPubMedGoogle Scholar
  42. 42.
    Giannakourou MC, Taoukis PS (2003c) Stability of dehydrofrozen green peas pretreated with nonconventional osmotic agents. J Food Sci 68:2002–2010CrossRefGoogle Scholar
  43. 43.
    Labuza TP (1982) Shelf-Life Dating of Foods. Food & Nutrition Press, Inc., WestportGoogle Scholar
  44. 44.
    Taoukis PS (2011) In: Heldman DR, Moraru CI (eds) Encyclopedia of Agricultural, Food and Biological Engineering, Vol. II, 2nd edn. CRC Press, Taylor & Francis Group, New YorkGoogle Scholar
  45. 45.
    Dermesonluoglu E, Katsaros G, Tsevdou M, Giannakourou M, Taoukis P (2015) Kinetic study of quality indices and shelf life modelling of frozen spinach under dynamic conditions of the cold chain. J Food Eng 148:13–23. CrossRefGoogle Scholar
  46. 46.
    Giannakourou MC, Taoukis PS (2003b) Kinetic modelling of vitamin C loss in frozen green vegetables under variable storage conditions. Food Chem 83:33–41. CrossRefGoogle Scholar
  47. 47.
    Martins RC, Silva CLM (2004) Frozen green beans (Phaseolus vulgaris, L.) quality profile evaluation during home storage. J Food Eng 64:481–488. CrossRefGoogle Scholar
  48. 48.
    Gonçalves EM, Cruz RMS, Abreu M, Brandão TRS, Silva CLM (2009) Biochemical and colour changes of watercress (Nasturtium officinale R. Br.) during freezing and frozen storage. J Food Eng 93:32–39. CrossRefGoogle Scholar
  49. 49.
    Dermesonlouoglou EK, Giannakourou M, Taoukis PS (2016) Kinetic study of the effect of the osmotic dehydration pre-treatment with alternative osmotic solutes to the shelf life of frozen strawberry. Food Bioprod Process 99:212–221. CrossRefGoogle Scholar
  50. 50.
    Dermesonlouoglou E, Zachariou I, Andreou V, Taoukis PS (2018) Quality assessment and shelf life modeling of pulsed electric field pretreated osmodehydrofrozen kiwifruit slices. Int J Food Stud 7:34–51. CrossRefGoogle Scholar
  51. 51.
    Martins RC, Lopes IC, Silva CLM (2005) Accelerated life testing of frozen green beans (Phaseolus vulgaris, L.) quality loss kinetics: colour and starch. J Food Eng 67:339–346. CrossRefGoogle Scholar
  52. 52.
    Giannakourou MC, Taoukis PS (2002) Systematic application of time temperature integrators as tools for control of frozen vegetable quality. J Food Sci 67(6):2221–2228CrossRefGoogle Scholar
  53. 53.
    Dermesonlouoglou E, Giannakourou M, Taoukis P (2007) Kinetic modelling of the quality degradation of frozen watermelon tissue: effect of the osmotic dehydration as a pre-treatment. Int J Food Sci Technol 42:790–798. CrossRefGoogle Scholar
  54. 54.
    Cruz RMS, Vieira MC, Silva CLM (2009) Effect of cold chain temperature abuses on the quality of frozen watercress (Nasturtium officinale R. Br.). J Food Eng 94:90–97. CrossRefGoogle Scholar
  55. 55.
    Corradini MG, Peleg M (2007) Shelf-life estimation from accelerated storage data. Trends Food Sci Technol 18:37–47CrossRefGoogle Scholar
  56. 56.
    Giannakourou MC, Taoukis PS (2003a) Application of a TTI-based distribution management system for quality optimization of frozen vegetables at the consumer end. J Food Sci 68:201–209CrossRefGoogle Scholar
  57. 57.
    Gogou E, Derens E, Alvarez G, Taoukis P (2014) Field test monitoring of the food cold chain in European markets. Refr Sci Technol 548–554Google Scholar
  58. 58.
    Gogou E, Katsaros G, Derens E, Alvarez G, Taoukis PS (2015) Cold chain database development and application as a tool for the cold chain management and food quality evaluation. Int J Refrig 52:109–121. CrossRefGoogle Scholar
  59. 59.
    Gwanpua SG, Verboven P, Leducq D, Brown T, Verlinden BE, Bekele E, Aregawi W, Evans J, Foster A, Duret S, Hoang HM, Van Der Sluis S, Wissink E, Hendriksen LJAM, Taoukis P, Gogou E, Stahl V, El Jabri M, Le Page JF, Claussen I, Indergård E, Nicolai BM, Alvarez G, Geeraerd AH (2015) The FRISBEE tool, a software for optimising the trade-off between food quality, energy use, and global warming impact of cold chains. J Food Eng 148:2–12. CrossRefGoogle Scholar
  60. 60.
    Labuza TP (1985) In: Fennema OR (ed) food chemistry, 2nd edn. Marcel Dekker, New YorkGoogle Scholar
  61. 61.
    Aspridou Z, Koutsoumanis KP (2015) Individual cell heterogeneity as variability source in population dynamics of microbial inactivation. Food Microbiol 45(Part B):216–221. CrossRefPubMedGoogle Scholar
  62. 62.
    Huang L (2015b) Dynamic determination of kinetic parameters, computer simulation, and probabilistic analysis of growth of Clostridium perfringens in cooked beef during cooling. Int J Food Microbiol 195:20–29. CrossRefPubMedGoogle Scholar
  63. 63.
    Lianou A, Koutsoumanis KP (2011) A stochastic approach for integrating strain variability in modeling Salmonella enterica growth as a function of pH and water activity. Int J Food Microbiol 149:254–261. CrossRefPubMedGoogle Scholar
  64. 64.
    Channon HA, Hamilton AJ, D'Souza DN, Dunshea FR (2016) Estimating the impact of various pathway parameters on tenderness, flavour and juiciness of pork using Monte Carlo simulation methods. Meat Sci 116:58–66. CrossRefPubMedGoogle Scholar
  65. 65.
    Evrendilek GA, Avsar YK, Evrendilek F (2016) Modelling stochastic variability and uncertainty in aroma active compounds of PEF-treated peach nectar as a function of physical and sensory properties, and treatment time. Food Chem 190:634–642. CrossRefPubMedGoogle Scholar
  66. 66.
    Giannakourou MC, Koutsoumanis K, Dermesonlouoglou E, Taoukis PS (2001) Applicability of the shelf life decision system (SLDS) for control of nutritional quality of frozen vegetables. Acta Hortic 566:275–280CrossRefGoogle Scholar
  67. 67.
    Giannakourou MC, Stoforos NG (2017) A theoretical analysis for assessing the variability of secondary model thermal inactivation kinetic parameters. Foods 6:7CrossRefGoogle Scholar
  68. 68.
    Wesolek N, Roudot AC (2016) Assessing aflatoxin B1 distribution and variability in pistachios: validation of a Monte Carlo modeling method and comparison to the codex method. Food Control 59:553–560. CrossRefGoogle Scholar
  69. 69.
    Efron B, Tibshirani RJ (1993) An introduction to the bootstrap, 1st edn. Chapman & Hall/CRC Monographs on Statistics & Applied Probability, Boca Raton, FL, USACrossRefGoogle Scholar
  70. 70.
    Poschet F, Bernaerts K, Geeraerd AH, Scheerlinck N, Nicolaı̈ BM, Van Impe JF (2004) Sensitivity analysis of microbial growth parameter distributions with respect to data quality and quantity by using Monte Carlo analysis. Math Comput Simul 65:231–243. CrossRefGoogle Scholar
  71. 71.
    Poschet F et al (2003) Monte Carlo analysis as a tool to incorporate variation on experimental data in predictive microbiology. Food Microbiol 20:285–295. CrossRefGoogle Scholar
  72. 72.
    Poschet F, Geeraerd AH, Van Loey AM, Hendrickx ME, Van Impe JF (2005) Assessing the optimal experiment setup for first order kinetic studies by Monte Carlo analysis. Food Control 16:873–882. CrossRefGoogle Scholar
  73. 73.
    Mishra DK, Dolan KD, Yang L (2011) Bootstrap confidence intervals for the kinetic parameters of degradation of anthocyanins in grape pomace. J Food Process Eng 34:1220–1233. CrossRefGoogle Scholar
  74. 74.
    Dolan KD, Yang L, Trampel CP (2007) Nonlinear regression technique to estimate kinetic parameters and confidence intervals in unsteady-state conduction-heated foods. J Food Eng 80:581–593CrossRefGoogle Scholar
  75. 75.
    Sui X, Zhou W (2014) Monte Carlo modelling of non-isothermal degradation of two cyanidin-based anthocyanins in aqueous system at high temperatures and its impact on antioxidant capacities. Food Chem 148:342–350. CrossRefPubMedGoogle Scholar
  76. 76.
    Rodríguez-Martínez V, Velázquez G, Welti-Chanes J, Torres, JA (2018) In: Barbosa-Cánovas GV, Fontana AJ, Schmidt SJ, Labuza TP (eds.), water activity in foods, Fundamental and applications. Wiley-Blackwell, New YorkGoogle Scholar
  77. 77.
    Destercke S, Chojnacki E (2009) Safety, reliability and risk analysis: theory. In: Martorell S, Soares CG, Barnett J (eds) Methods and applications. Taylor & Francis Group, LondonGoogle Scholar
  78. 78.
    Smid JH, Verloo D, Barker GC, Havelaar AH (2010) Strengths and weaknesses of Monte Carlo simulation models and Bayesian belief networks in microbial risk assessment. Int J Food Microbiol 139:S57–S63. CrossRefPubMedGoogle Scholar
  79. 79.
    Cassin MH, Paoli GM, Lammerding AM (1998) Simulation modeling for microbial risk assessment. J Food Prot 61(11):1560–1566CrossRefGoogle Scholar
  80. 80.
    Jaykus LA (1996) The Application of Quantitative Risk Assessment to Microbial Food Safety Risks. Crit Rev Microbiol 22(4):279–293. CrossRefPubMedGoogle Scholar
  81. 81.
    Singh M, Markeset T (2009) In: Martorell S, Soares CG, Barnett J (eds) Safety, reliability and risk analysis: theory, methods and applications, Taylor & Francis Group, LondonGoogle Scholar
  82. 82.
    Barreto H, Howland FM (2006) Introductory econometrics: using Monte Carlo simulation with Microsoft excel®. Cambridge University Press, New YorkGoogle Scholar
  83. 83.
    Lammerding AM, Fazil A (2000) Hazard identification and exposure assessment for microbial food safety risk assessment. Int J Food Microbiol 58:147–157. CrossRefPubMedGoogle Scholar
  84. 84.
    Taoukis PS (2001). In: Tijkskens LMM, Hertog MLATM, Nicolai BM (Eds) Food process modeling. New York: CRC PressGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Food Science and TechnologyUniversity of West Attica (former Technological Educational Institute of Athens)EgaleoGreece
  2. 2.School of Chemical Engineering, Laboratory of Food Chemistry and TechnologyNational Technical University of AthensAthensGreece

Personalised recommendations