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.
Similar content being viewed by others
References
Afifi, A. A. andAzen, S. P. (1979)Statistical Analysis. Academic Press, New York.
Akaike, H. (1969) Fitting autoregressive models for prediction.Ann. Inst. Statist. Math.,21, 243–247.
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.
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.
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.
Bergman, R. N., Ider, Y. Z., Bowden, C. R. andCobelli, C. (1979) Quantitative estimation of insulin sensitivity.Am. J. Physiol.,236, E667-E677.
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.
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.
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.
Carson, E. R., Cobelli, C. andFinkelstein, L. (1981) Modeling and identification of metabolic systems.Am. J. Physiol.,240, R120-R129.
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.
Fletcher, R. (1971) A modified Marquardt subroutine for nonlinear least squares. Atomic Energy Reserch Establishment, Harwell, Report AERE-R 6799.
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.
Goodwin, C. andPayne, R. L. (1977)Dynamic system identification. Academic Press, New York.
Kelman, A. W. andWhiting, B. (1980) Modelling of drug response in individual subjects.J. Pharmacokin. Biopharm.,8, 115–130.
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.
Söderström, T. (1977) On model structure testing in system identification.Int. J. Control.,26, 1–18.
Tranberg, K. G. andDencker, H. (1978) Modelling of plasma disappearance of unlabelled insulin in man.Am. J. Physiol.,235, E577-E585.
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.
Author information
Authors and Affiliations
Rights 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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02442404