Food and Bioprocess Technology

, Volume 12, Issue 5, pp 769–780 | Cite as

Optimizing Oxygen Input Profiles for Efficient Estimation of Michaelis-Menten Respiration Models

  • Arno Strouwen
  • Bart M. Nicolaï
  • Peter GoosEmail author
Original Paper


Models based on mass balances and Michaelis-Menten respiration kinetics are increasingly used to determine optimal storage conditions of fresh fruits and vegetables. The model parameters are usually estimated from respiration experiments at different, but fixed, gas conditions according to a response surface design. This is a tedious procedure that requires a gas mixing facility or a series of gas cylinders with appropriate composition. In this paper, we consider a simpler approach, in which the respiration kinetics of pear fruit are modeled using a single experiment with a time-varying O2 input profile. To optimize the information content produced by the O2 profile, we apply optimal dynamic experimental design principles and present a modified coordinate-exchange algorithm to achieve this goal. Finally, we demonstrate the added value of our approach by comparing the optimal O2 input profiles to several intuitive benchmark experiments.


Optimal experimental design Dynamic experiment Michaelis-Menten respiration Post-harvest storage 



Author Arno Strouwen is a PhD fellow Strategic Basic Research (SB) of the Fund for Scientific Research, Flanders (FWO), project 1S58717N.

Funding Information

The authors received financial support from KU Leuven (project C16/16/002).


  1. Atkinson, A., Donev, A., Tobias, R. (2007). Optimum experimental designs, with SAS Vol. 34. Oxford: Oxford University Press.Google Scholar
  2. Balsa-Canto, E., Alonso, A.A., Banga, J.R. (2010). An iterative identification procedure for dynamic modeling of biochemical networks. BMC Systems Biology, 4(1), 11.CrossRefGoogle Scholar
  3. Balsa-Canto, E., Rodriguez-Fernandez, M., Banga, J.R. (2007). Optimal design of dynamic experiments for improved estimation of kinetic parameters of thermal degradation. Journal of Food Engineering, 82(2), 178–188.CrossRefGoogle Scholar
  4. Bauer, I., Bock, H.G., Körkel, S., Schlöder, J.P. (2000). Numerical methods for optimum experimental design in DAE systems. Journal of Computational and Applied Mathematics, 120(1-2), 1–25.CrossRefGoogle Scholar
  5. Berg, J.M., Tymoczko, J.L., Gatto, G. Jr. (2002). Biochemistry, WH Freeman.Google Scholar
  6. Bernaerts, K., Servaes, R.D., Kooyman, S., Versyck, K.J., Van Impe, J.F. (2002). Optimal temperature input design for estimation of the square root model parameters: parameter accuracy and model validity restrictions. International Journal of Food Microbiology, 73(2), 145–157.CrossRefGoogle Scholar
  7. Bernaerts, K., Versyck, K.J., Van Impe, J.F. (2000). On the design of optimal dynamic experiments for parameter estimation of a Ratkowsky-type growth kinetics at suboptimal temperatures. International Journal of Food Microbiology, 54(1), 27–38.CrossRefGoogle Scholar
  8. Bessemans, N., Verboven, P., Verlinden, B., Nicolaï, B.M. (2016). A novel type of dynamic controlled atmosphere storage based on the respiratory quotient (RQ-DCA). Postharvest Biology and Technology, 115, 91–102.CrossRefGoogle Scholar
  9. Chaloner, K., & Verdinelli, I. (1995). Bayesian experimental design: a review. Statistical Science, 10(3), 273–304.CrossRefGoogle Scholar
  10. Efron, B., & Hastie, T. (2016). Computer age statistical inference. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  11. Fedorov, V.V., & Leonov, S.L. (2013). Optimal design for nonlinear response models. Boca Raton: CRC Press.CrossRefGoogle Scholar
  12. Fidler, J., & North, C. (1967). The effect of conditions of storage on the respiration of apples: I. the effects of temperature and concentrations of carbon dioxide and oxygen on the production of carbon dioxide and uptake of oxygen. Journal of Horticultural Science, 42(2), 189–206.CrossRefGoogle Scholar
  13. Fonseca, S.C., Oliveira, F.A., Brecht, J.K. (2002). Modelling respiration rate of fresh fruits and vegetables for modified atmosphere packages: a review. Journal of Food Engineering, 52(2), 99–119.CrossRefGoogle Scholar
  14. Goos, P., & Jones, B. (2011). Optimal design of experiments: a case study approach. Chichester: Wiley.CrossRefGoogle Scholar
  15. Hertog, M.L., Peppelenbos, H.W., Evelo, R.G., Tijskens, L.M. (1998). A dynamic and generic model of gas exchange of respiring produce: the effects of oxygen, carbon dioxide and temperature. Postharvest Biology and Technology, 14(3), 335–349.CrossRefGoogle Scholar
  16. Ho, Q.T., Hertog, M.L., Verboven, P., Ambaw, A., Rogge, S., Verlinden, B.E., Nicolaï, B.M. (2018). Down-regulation of respiration in pear fruit depends on temperature. Journal of Experimental Botany, 69 (8), 2049–2060.CrossRefGoogle Scholar
  17. Ho, Q.T., Verboven, P., Verlinden, B.E., Herremans, E., Wevers, M., Carmeliet, J., Nicolaï, B.M. (2011). A three-dimensional multiscale model for gas exchange in fruit. Plant Physiology, 155(3), 1158–1168.CrossRefGoogle Scholar
  18. Jacxsens, L., Devlieghere, F., De Rudder, T., Debevere, J. (2000). Designing equilibrium modified atmosphere packages for fresh-cut vegetables subjected to changes in temperature. LWT-Food Science and Technology, 33(3), 178–187.CrossRefGoogle Scholar
  19. Lammertyn, J., Scheerlinck, N., Jancsok, P., Verlinden, B.E., Nicolaï, B.M. (2003). A respiration–diffusion model for conference pears: II. simulations and relation to core breakdown. Postharvest Biology and Technology, 30 (1), 43–55.CrossRefGoogle Scholar
  20. Meyer, R.K., & Nachtsheim, C.J. (1995). The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics, 37(1), 60–69.CrossRefGoogle Scholar
  21. Michaelis, L., & Menten, M.L. (1913). Die Kinetik der Invertinwirkung, vol. 49, Universitätsbibliothek Johann Christian Senckenberg.Google Scholar
  22. Munack, A., & Posten, C. (1989). Design of optimal dynamical experiments for parameter estimation. In American control conference, 1989 (pp. 2010–2016): IEEE.Google Scholar
  23. Nahor, H.B., Scheerlinck, N., Van Impe, J.F., Nicolaï, B.M. (2003). Optimization of the temperature sensor position in a hot wire probe set up for estimation of the thermal properties of foods using optimal experimental design. Journal of Food Engineering, 57(1), 103–110.CrossRefGoogle Scholar
  24. Nahor, H.B., Scheerlinck, N., Verniest, R., De Baerdemaeker, J., Nicolaï, B.M. (2001). Optimal experimental design for the parameter estimation of conduction heated foods. Journal of Food Engineering, 48(2), 109–119.CrossRefGoogle Scholar
  25. Peppelenbos, H.W., & van’t Leven, J. (1996). Evaluation of four types of inhibition for modelling the influence of carbon dioxide on oxygen consumption of fruits and vegetables. Postharvest Biology and Technology, 7(1-2), 27–40.CrossRefGoogle Scholar
  26. Saltveit, M.E. (2003). Is it possible to find an optimal controlled atmosphere? Postharvest Biology and Technology, 27(1), 3–13.CrossRefGoogle Scholar
  27. Shampine, L.F., & Reichelt, M.W. (1997). The Matlab ODE suite. SIAM Journal on Scientific Computing, 18(1), 1–22.CrossRefGoogle Scholar
  28. Telen, D., Logist, F., Van Derlinden, E., Tack, I., Van Impe, J. (2012). Optimal experiment design for dynamic bioprocesses: a multi-objective approach. Chemical Engineering Science, 78, 82–97.CrossRefGoogle Scholar
  29. Vassiliadis, V.S. (1993). Computational solution of dynamic optimization problems with general differential-algebraic constraints, PhD thesis, Imperial College, University of London.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of Bioscience EngineeringKU Leuven: BIOSYST-MeBioSLeuvenBelgium
  2. 2.Faculty of Business and Economics, Department of Engineering ManagementUniversity of AntwerpAntwerpBelgium

Personalised recommendations