Food Science of Animal Resources (한국축산식품학회지)

Korean Society for Food Science of Animal Resources (한국축산식품학회)
권호 표지
DOI QR코드

DOI QR Code

Mathematical Simulation of the Temperature Dependence of Time Temperature Integrator (TTI) and Meat Qualities

육류의 품질과 Time Temperature Integrator(TTI) 온도의존성에 대한 수학적 Simulation

  • Park, Han-Jo (Department of Food Science and Technology, Dongguk University) ;
  • Shim, Soo-Dong (Department of Food Science and Technology, Dongguk University) ;
  • Min, Sang-Gi (Department of Food Science and Biotechnology of Animal Resources, Konguk University) ;
  • Lee, Seung-Ju (Department of Food Science and Technology, Dongguk University)
  • Published : 2009.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

The temperature dependence of time temperature integrator (TTI) was investigated in terms of the Arrhenius activation energy (Ea) to determine TTI requirements to accurately predict meat quality during storage. Mathematical simulation was conducted using a numerical analysis. First, using Euler's method and MS Excel VBA, the TTI color change was kinetically modeled and numerically calculated under several storage conditions. From the TTI color variable profiles calculated from the storage time-temperature profiles, $T_{eff}$, which is a constant temperature representing the whole temperature profiles, was calculated. Upon predicting Pseudomonas spp. concentrations (one of the meat qualities) from $T_{eff}$, it was found that if $Ea_{microbial\;spoilage}=Ea_{TTI}$ be true, then Pseudomonas concentrations were calculated to be constant with the same TTI color values, regardless of time-temperature profiles, whereas if $Ea_{microbial\;spoilage}{\neq}Ea_{TTI}$ then Pseudomonas concentrations varied even with the same TTI color values. This indicates that each TTI color value represents its own fixed degree of meat quality, only if $Ea_{meat\;qualities}=Ea_{TTI}$.

육류의 품질예측에 가장 적합한 TTI의 조건을 분석하기 위하여, 온도-시간 이력에 따른 TTI의 색 변화와 Pseudomonas spp.의 증식수준을 수학적으로 Simulation 하였다. 일련의 kinetics 및 온도의존성 관련 함수식의 연산에는 수치해석 기법인 Euler's method를 적용하였으며, MS Excel VBA기반 컴퓨터 프로그램을 작성하여 계산하였다. 쇠고기의 저장 유통에 대한 몇 가지 온도-시간 경로에 대하여, 저장 시간에 따른 TTI 색 함수 및 $T_{eff}$(해당 온도-시간 이력에 대한 일종의 대표적 온도 값)의 변화를 simulation 하였다. 온도의존성(활성화에너지)가 서로 다른 TTI에 대하여 Simulation한 결과, 먼저 Pseudomonas 증식의 활성화 에너지와 같은 활성화에너지를 갖는 TTI의 경우 같은 색에 대하여 온도-시간 이력에 상관없이 항상 같은 증식수준을 나타냈다. 반면에 활성화에너지가 서로 다른 경우 TTI가 같은 색에 대하여 온도-시간 이력에 따라 서로 다른 증식수준을 나타냈다. 결론적으로 육류의 특정 품질에 대한 적합한 TTI는 서로 온도의존성이 일치할 때 가장 정확한 예측 값을 얻을 수 있음을 알 수 있었다.

Keywords

References

  1. Bin, F. U., Taoukis, P. S., and Labuza, T. P.(1991) Predictive microbiology for monitoring spoilage of daily products with time-temperature integrators. J. Food Sci. 56, 1209-1215 https://doi.org/10.1111/j.1365-2621.1991.tb04736.x
  2. Bobelyn, E., Hertog, M., and Nicolaï, B. M. (2006) Applicability of an enzymatic time temperature integrator as a quality indicator for mushrooms in the distribution chain. Postharvest Biol. Tec. 42, 104-114 https://doi.org/10.1016/j.postharvbio.2006.05.011
  3. Claeys, W.L., Vanloey, A. M., and Hendrickx, M. E. (2002) Intrinsic time temperature integrators for heat treatment of milk. Trends Food Sci. Tech. 13, 293-311 https://doi.org/10.1016/S0924-2244(02)00164-4
  4. Emmanuel, P. and Viviana, O. S. (2009) Bread baking as a moving boundary problem. Part 2: Model validation and numerical simulation. J. Food Eng. 91, 434-442 https://doi.org/10.1016/j.jfoodeng.2008.09.038
  5. Geankoplis, C. J. (1983) Transport processes and unit operations, Second Edition. Allyn and Bacon, Inc., Lodon, pp. 29-33
  6. Giannakourou, M. C. and Taoukis, P. S. (2002) Systematic application of time temperature integrators as tools for control of frozen vegetable quality. J. Food Sci. 67, 2221-2228 https://doi.org/10.1111/j.1365-2621.2002.tb09531.x
  7. Giannakourou, M. C., Koutsoumanis K., Nychas, G. J. E., and Taoukis, P. S. (2005) Field evaluation of the application of time temperature integrators for monitoring fish quality in the chill chain. Int. J. Food Microbiol. 102, 323-336 https://doi.org/10.1016/j.ijfoodmicro.2004.11.037
  8. Hathaway, S. (1999) Management of food safety in international trade. Food Control 10, 247-254 https://doi.org/10.1016/S0956-7135(99)00006-7
  9. James, M. L., Smith, G. M., and Wolfond, J. C. (1977) Applied numerical methods for digital computation with FORTRAN and CSMP, Second Edition. Harper & Row, Publishers, Inc., Lodon, pp. 368-379
  10. Jung, H. M., Kim, G. S., Kim, M. S., Lee, Y. H., and Choi, D. S. (2008) Quality change of the pears using processed packaging materials by charcoal during storage and distribution. Korean J. Soc. Agr. Mach. 13, 272-278
  11. Lee, J. M. and Lee, S. J. (2008) Kinetic modelling for predicting the qualities of beef and color of enzyme time-temperature integrator during storage. Food Eng. Prog. 12, 241-246
  12. Lee, Y. S., Ji, H. H., Park, K. H., Lee, S. Y., Choi, Y. J., Lee, D. H., Park, S. H., Moon, E. S., Ryu, K., Shin, H. S., and Ha, S. D. (2008) Survey on storage temperature of domestic major chilled foods in refrigerator. J. Food Hyg. Safety 23, 304-308
  13. Macdonald, C. B., Gottlieb, S., and Ruuth, S. J. (2008) A numerical study of diagonally split Runge-Kutta methods for PDEs with discontinuities. J. Sci Comput. 35, 89-112
  14. Mendoza, T. F., Welt, B. A., Otwell, S., Teixeira, A. A., Kristonsson, H., and Balaban, M. M. (2004) Kinetic parameter estimation of time-temperature integrators intended for use with packaged fresh seafood. J. Food Sci. 69, 90-96 https://doi.org/10.1111/j.1365-2621.2004.tb13377.x
  15. Park, S.Y., Kim, Y. G., Kim, J. W., Lee, S. G., Lim, H. J., Joo, S. T., and Choi, Y. I. (2000) Dairy processing. Yu Han Publisher, Co, Seoul, pp. 69-80
  16. Rhee, S. Y., Cheon, D. W., and Park, J. W. (1996) An economic study on Korean native cattle marketing and stage price formation. Korean Agr. Policy Rev. 23, 109-121
  17. Taoukis, P. S. and Labuza, T. P. (1989) Applicability of timetemperature indicators as shelf life monitors of food products. J. Food Sci. 54, 783-788 https://doi.org/10.1111/j.1365-2621.1989.tb07882.x
  18. Taoukis, P. S., Koutsoumanis, K., and Nychas, G. J. E. (1999) Use of time-temperature integrators and predictive modeling for shelf life control of chilled fish under dynamic storage conditions. Int. J. Food Microbiol. 53, 21-31 https://doi.org/10.1016/S0168-1605(99)00142-7
  19. Taoukis, P. S. (2001) Modeling the use of time-temperature indicators in distribution and stock rotation. In: Food process modelling, 3rd ed. Tijskens, L. M. M., Hertog, M. L. A. T. M., and Nicoliai, B. M. (eds), CRC Press, Washington DC, pp. 402-432
  20. VITSAB. 2008. Home page.
  21. Yoon, S. H., Lee, C. H., Kim, D. Y., Kim, J. W., and Park, K. H. (1994) Time-temperature indicator using phospholipidsphospholipase system and application to storage of frozen pork. J. Food Sci. 20, 490-493

Cited by

  1. Virtual Simulation of Temperature Distribution throughout Beef Packages with Time-temperature Indicator (TTI) Labels vol.33, pp.1, 2013, https://doi.org/10.5851/kosfa.2013.33.1.31
  2. Applications of Time-Temperature Integrator (TTI) as a Quality Indicator of Grounded Pork Patty vol.33, pp.4, 2013, https://doi.org/10.5851/kosfa.2013.33.4.439
  3. Dynamic Modeling and Sensitivity Analysis for Predicting the Pseudomonas spp. Concentration in Alaska Pollack along the Distribution Path vol.43, pp.3, 2010, https://doi.org/10.5657/kfas.2010.43.3.205
  4. Mathematical Evaluation of Prediction Accuracy for Food Quality by Time Temperature Integrator of Intelligent Food Packaging through Virtual Experiments vol.2013, 2013, https://doi.org/10.1155/2013/950317
  5. A feasibility study of application of laccase-based time-temperature indicator to kimchi quality control on fermentation process vol.57, pp.6, 2014, https://doi.org/10.1007/s13765-014-4178-x
  6. Polymer-based time-temperature indicator for high temperature processed food products vol.21, pp.5, 2012, https://doi.org/10.1007/s10068-012-0196-9
  7. 다양한 산소 투과도를 가진 커버필름과 산소지시물질로 제작된 인쇄형 TTI vol.24, pp.2, 2009, https://doi.org/10.20909/kopast.2018.24.2.41
  8. 천연 색소인 안토시아니딘 기반의 인쇄형 시간-온도이력 지시계 개발 vol.24, pp.2, 2009, https://doi.org/10.20909/kopast.2018.24.2.49