Advertisement

Successive complementary model-based experimental designs for parameter estimation of fed-batch bioreactors

  • Jung Hun Kim
  • Jong Min Lee
Research Paper

Abstract

When a dynamic model is used for the description of (fed-)batch bioreactors, it is typical that the model parameters are highly correlated to each other. In this case, it is important to keep the parameter correlation as small as possible to obtain a reliable set of parameter estimates. In this study, we propose an anticorrelation parameter estimation scheme that can be best utilized when a number of different batch experiments are sequentially processed. The scheme iteratively performs parameter estimation and model-based design of experiment (MBDOE) at the beginning and between the batches. The important difference from the existing approaches is that the MBDOE objective is defined according to the system analysis performed a priori, so that each new batch supplements what is lacking from the previous batches combined, in terms of information. The use of the scheme is illustrated on a fed-batch bioreactor model.

Keywords

Model-based design of experiment Sequential design of experiment Parameter estimation Parameter correlation Bioreactor 

Notes

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2015R1A1A1A05001310). This research was also respectfully supported by Engineering Development Research Center (EDRC) funded by the Ministry of Trade, Industry and Energy (MOTIE) (No. N0000990).

References

  1. 1.
    Franceschini G, Macchietto S (2008) Model-based design of experiments for parameter precision: state of the art. Chem Eng Sci 63(19):4846–4872CrossRefGoogle Scholar
  2. 2.
    Martinez EC, Cristaldi MD, Grau RJ (2009) Design of dynamic experiments in modeling for optimization of batch processes. Ind Eng Chem Res 48(7):3453–3465CrossRefGoogle Scholar
  3. 3.
    Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingmüller U, Timmer J (2009) Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25(15):1923–1929CrossRefGoogle Scholar
  4. 4.
    Holmberg A (1982) On the practical identifiability of microbial growth models incorporating Michaelis–Menten type nonlinearities. Math Biosci 62(1):23–43CrossRefGoogle Scholar
  5. 5.
    Chappell MJ, Godfrey KR (1992) Structural identifiability of the parameters of a nonlinear batch reactor model. Math Biosci 108(2):241–251CrossRefGoogle Scholar
  6. 6.
    Walter E, Lecourtier Y, Happel J, Kao JY (1986) Identifiability and distinguishability of fundamental parameters in catalytic methanation. AIChE J 32(8):1360–1366CrossRefGoogle Scholar
  7. 7.
    Walter E, Pronzato L (1996) On the identifiability and distinguishability of nonlinear parametric models. Math Comput Simul 42(2–3):125–134CrossRefGoogle Scholar
  8. 8.
    Li P, Vu QD (2013) Identification of parameter correlations for parameter estimation in dynamic biological models. BMC Syst Biol 7(1):91CrossRefGoogle Scholar
  9. 9.
    Raue A, Becker V, Klingmüller U, Timmer J (2010) Identifiability and observability analysis for experimental design in nonlinear dynamical models. Chaos Interdiscip J Nonlinear Sci 20(4):045105CrossRefGoogle Scholar
  10. 10.
    Kravaris C, Hahn J, Chu Y (2013) Advances and selected recent developments in state and parameter estimation. Comput Chem Eng 51:111–123CrossRefGoogle Scholar
  11. 11.
    Chu Y, Hahn J (2008) Parameter set selection via clustering of parameters into pairwise indistinguishable groups of parameters. Ind Eng Chem Res 48(13):6000–6009CrossRefGoogle Scholar
  12. 12.
    Lee D, Singla A, Wu HJ, Kwon JSI (2018) An Integrated numerical and experimental framework for modeling of CTB and GD1b Ganglioside binding kinetics. AIChE JGoogle Scholar
  13. 13.
    Lee D, Ding Y, Jayaraman A, Kwon JS (2018) Mathematical modeling and parameter estimation of intracellular signaling pathway: application to LPS-induced NFκB activation and TNFα production in macrophages. Processes 6(3):21CrossRefGoogle Scholar
  14. 14.
    Galvanin F, Ballan CC, Barolo M, Bezzo F (2013) A general model-based design of experiments approach to achieve practical identifiability of pharmacokinetic and pharmacodynamic models. J Pharmacokinet Pharmacodyn 40(4):451–467CrossRefGoogle Scholar
  15. 15.
    Franceschini G, Macchietto S (2008) Novel anticorrelation criteria for design of experiments: algorithm and application. AIChE J 54(12):3221–3238CrossRefGoogle Scholar
  16. 16.
    Bernaerts K, Versyck KJ, Van Impe JF (2000) On the design of optimal dynamic experiments for parameter estimation of a Ratkowsky-type growth kinetics at suboptimal temperatures. Int J Food Microbiol 54(1–2):27–38CrossRefGoogle Scholar
  17. 17.
    Versyck K, Claes J, Van Impe J (1998) Optimal experimental design for practical identification of unstructured growth models. Math Comput Simul 46(5–6):621–629CrossRefGoogle Scholar
  18. 18.
    Sidoli F, Mantalaris A, Asprey S (2004) Modelling of mammalian cells and cell culture processes. Cytotechnology 44(1–2):27–46CrossRefGoogle Scholar
  19. 19.
    Pritchard DJ, Bacon DW (1978) Prospects for reducing correlations among parameter estimates in kinetic models. Chem Eng Sci 33(11):1539–1543CrossRefGoogle Scholar
  20. 20.
    Franceschini G, Macchietto S (2008) Novel anticorrelation criteria for model-based experiment design: Theory and formulations. AIChE J 54(4):1009–1024CrossRefGoogle Scholar
  21. 21.
    Franceschini G, Macchietto S (2008) Anti-correlation approach to model-based experiment design: application to a biodiesel production process. Ind Eng Chem Res 47(7):2331–2348CrossRefGoogle Scholar
  22. 22.
    Galvanin F, Macchietto S, Bezzo F (2007) Model-based design of parallel experiments. Ind Eng Chem Res 46(3):871–882CrossRefGoogle Scholar
  23. 23.
    Fedorov VV, Hackl P (2012) Model-oriented design of experiments, vol 125. Springer, BerlinGoogle Scholar
  24. 24.
    Walter É, Pronzato L (1990) Qualitative and quantitative experiment design for phenomenological models—a survey. Automatica 26(2):195–213CrossRefGoogle Scholar
  25. 25.
    Nihtilä M, Virkkunen J (1977) Practical identifiability of growth and substrate consumption models. Biotechnol Bioeng 19(12):1831–1850CrossRefGoogle Scholar
  26. 26.
    Bates DM, Watts DG (1988) Nonlinear regression: iterative estimation and linear approximations. Nonlinear regression analysis and its applications. Wiley, New York, pp 33–66CrossRefGoogle Scholar
  27. 27.
    Chu Y, Hahn J (2007) Parameter set selection for estimation of nonlinear dynamic systems. AIChE J 53(11):2858–2870CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Chemical and Biological Engineering, Institute of Chemical ProcessesSeoul National UniversitySeoulRepublic of Korea

Personalised recommendations