Skip to main content
Log in

Evaluation of alternative model structures of metabolic systems: two case studies on model identification and validation

  • Published:
Medical and Biological Engineering and Computing Aims and scope Submit manuscript

Abstract

In the paper some quantitative criteria for evaluating alternative linear model structures are presented and applied to two metabolic systems. Linear time-invariant structured models and input/output descriptions are proposed for the two metabolic processes considered, bilirubin and riphamicin kinetics, and maximum likelihood parameter estimates are obtained from input/output test data. The considered criteria include model plausibility and quantitative measures, e.g. the F-test, Akaike information criterion and the inverse of the information matrix, which are based on the results of model identification from input/output data. The combined use of the Akaike criterion and of the inverse of the information matrix proves to be, in conjunction with model plausibility, a very reliable tool in the metabolic model structure determination.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Afifi, A. A. andAzen, S. P. (1979)Statistical Analysis. Academic Press, New York.

    MATH  Google Scholar 

  • Akaike, H. (1969) Fitting autoregressive models for prediction.Ann. Inst. Statist. Math.,21, 243–247.

    MATH  MathSciNet  Google Scholar 

  • Akaike, H. (1972) Information theory and an extension of the maximum likelihood principle. Proceedings of the2nd International Symposium on Information Theory, Supplementary to Problems of Control and Information Theory 267–281.

  • Allsop, J. R., Wolfe, R., Di Stefano III, J. J. andBurke, J. F. (1979) The reliability of rates of glucose appearancein vivo calculated from single tracer injections.Can. J. Physiol. Pharmacol.,57, 1267–1274.

    Google Scholar 

  • Aström, K. J. (1967) On the achievable accuracy in identification problems. Preprints 1st IFAC Symposium on Identification and System Parameter Estimation, Academia, Prague,I, 1. 8.

    Google Scholar 

  • Bergman, R. N., Bowden, C. R. andCobelli, C. (1981) The minimal model approach to quantification of factors controlling glucose disposal in man. InCarbohydrate metabolism,Cobelli,C. andBergman,R. N. (Eds.), Wiley, Chichester, 269–296.

    Google Scholar 

  • Bergman, R. N., Ider, Y. Z., Bowden, C. R. andCobelli, C. (1979) Quantitative estimation of insulin sensitivity.Am. J. Physiol.,236, E667-E677.

    Google Scholar 

  • Berk, P. D., Howe, R. B., Bloomer, J. R. andBerlin, N. I. (1969) Studies of bilirubin kinetics in normal adults.J. Clin. Invest.,48, 2176–2190.

    Article  Google Scholar 

  • Brown, R. F., Carson, E. R., Finkelstein, L., Godfrey, K. R. andJones, R. P. (1979) Adequacy of measurements in compartmental modelling of metabolic systems,Med. & Biol. Eng. & Comput.,17, 216–222.

    Google Scholar 

  • Carson, E. R. andFinkelstein, L. (1973) Problems of identification in metabolic systems. InIdentification and System Parameter Estimation Eykhoff (Ed.), part I, North Holland, Amsterdam, 195–202.

    Google Scholar 

  • Carson, E. R., Cobelli, C. andFinkelstein, L. (1981) Modeling and identification of metabolic systems.Am. J. Physiol.,240, R120-R129.

    Google Scholar 

  • Cobelli, C. andDi Stefano III, J. J. (1980) Parameter and structural identifiability concepts and ambiguities: a critical review and analysis.Am. J. Physiol.,239, R7-R24.

    Google Scholar 

  • Fletcher, R. (1971) A modified Marquardt subroutine for nonlinear least squares. Atomic Energy Reserch Establishment, Harwell, Report AERE-R 6799.

    Google Scholar 

  • Frezza, M. (1980) Unpublished results.

  • Genesio, R andMilanese, M. (1979) Methods for the selection of approximating class of models. In Preprints of5th IFAC Symposium on Identification and System Parameter Estimation,Isermann,R. (Ed.), Pergamon Press, Oxford,1, 549–560.

    Google Scholar 

  • Goodwin, C. andPayne, R. L. (1977)Dynamic system identification. Academic Press, New York.

    MATH  Google Scholar 

  • Kelman, A. W. andWhiting, B. (1980) Modelling of drug response in individual subjects.J. Pharmacokin. Biopharm.,8, 115–130.

    Article  Google Scholar 

  • Okolicsanyi, L., Orlando, R. Venuti, M., Dal Brun, G., Cobelli, C., Ruggeri, A. andSalvan, A. (1981) A modelling study of the effect of fasting on bilirubin kinetics in Gilbert's syndrome.Am. J. Physiol.,240, R266-R271.

    Google Scholar 

  • Söderström, T. (1977) On model structure testing in system identification.Int. J. Control.,26, 1–18.

    MATH  Google Scholar 

  • Tranberg, K. G. andDencker, H. (1978) Modelling of plasma disappearance of unlabelled insulin in man.Am. J. Physiol.,235, E577-E585.

    Google Scholar 

  • Yamaoka, K., Nakagawa, T. andUno, T. (1978) Application of Akaike's information criterion (AIC) in the evaluation of linear pharmacokinetic equations.J. Pharmacok. Biopharm.,6, 165–175.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cobelli, C., Ruggeri, A. Evaluation of alternative model structures of metabolic systems: two case studies on model identification and validation. Med. Biol. Eng. Comput. 20, 444–450 (1982). https://doi.org/10.1007/BF02442404

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02442404

Keywords

Navigation