Structural identifiability of models characterizing saturable binding: Comparison of pseudo-steady-state and non-pseudo-steady-state model formulations

Mathematical Biosciences

Volumn 133, Issue 1, 1996, Pages 1-20

  Chappell, Michael J ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ASSOCIATION; BINDING KINETICS; CHEMICAL REACTION KINETICS; DISSOCIATION CONSTANT; MATHEMATICAL MODEL; STEADY STATE; STRUCTURE ANALYSIS;

EID: 0029968577     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/0025-5564(95)00064-X     Document Type: Article

References (23)

1. J. D. Murray, Mathematical Biology, Springer-Verlag, New York, 1989.
2. S. I. Rubinow, Mathematical Problems in the Biological Sciences (Regional Conf. Ser. Appl. Math., Vol. 10), Society for Industrial and Applied Mathematics, Philadelphia, 1973.
3. D. G. Grahame-Smith and J. K. Aronson, Oxford Textbook of Clinical Pharmacology and Drug Therapy, 2nd ed. Oxford Univ. Press, London, U.K., 1992.
4. J. A. Jacquez, Compartmental Analysis in Biology and Medicine, Univ. Michigan Press, Ann Arbor, 1985.
5. S. W. Benson, The Foundations of Chemical Kinetics (McGraw-Hill Ser. Adv. Chem.), McGraw-Hill, New York, 1960.
6. M. J. Chappell and K. R. Godfrey, Structural identifiability of the parameters of a nonlinear batch reactor model, Math. Biosci. 108:241-251 (1992).
7. M. J. Chappell, K. R. Godfrey, and S. Vajda, Global identifiability of the parameters of nonlinear systems with specified inputs: a comparison of methods, Math. Biosci. 102:41-73 (1990).
8. K. R. Godfrey, Compartmental Models and Their Application, Academic, New York, 1983.
9. B. Whiting and A. W. Kelman, The modelling of drug response, Clin. Sci. 59:311-315 (1980).
10. E. Walter, Identifiability of State Space Models (Lect. Notes Biomath. Vol. 46), Springer-Verlag, New York, 1982.
11. E. Walter and Y. Lecourtier, Unidentifiable compartmental models: what to do?, Math. Biosci. 56:1-25 (1981).
12. R. Hermann and A. J. Krener, Nonlinear controllability and observability, IEEE Trans. Autom. Control AC-22:728-740 (1977).
13. A. Isidori, Nonlinear Control Systems: An Introduction, Springer, New York, 1985.
14. S. Vajda and H. Rabitz, State isomorphism approach to global identifiability of nonlinear systems, IEEE Trans. Autom. Control AC-34:220-223 (1989).
15. S. Vajda, K. R. Godfrey, and H. Rabitz, Similarity transformation approach to structural identifiability of nonlinear models, Math. Biosci. 93:217-248 (1989).
16. S. Vajda, Identifiability of polynomial systems: structural and numerical aspects, in Identifiability of Parametric Models, E. Walter, Ed., Pergamon, Oxford, 1987, pp. 42-49.
17. H. Pohjanpalo, System identifiability based on the power series expansion of the solution, Math. Biosci. 41:21-33 (1978).
18. J. Delforge, A. Syrota, and B. M. Mayozer, Identifiability and error minimization in estimation of receptor model parameters with PET, in Positron Emission Tomography in Clinical Research and Clinical Diagnosis: Tracer Modelling and Radioreceptors, ECSC, EEC, EAEC, Brussels and Luxembourg, 1989, pp. 45-64.
19. J. Delforge, A. Syrota, and B. Mazoyer, Identifiability analysis and parameter identification of an in vivo ligand-receptor model from PET data, IEE Trans. Biomed. Eng. 37(7):653-661 (1990).
20. J. Delforge, M. Janier, A. Syrota, C. Crouzel, J.-M. Vallois, J. Cayla, J.-P. Lancon, and B. M. Mazoyer, Noninvasive quantification of muscarinic receptors in vivo with positron emission tomography in the dog heart, Circulation 82(4):1494-1504 (1990).
21. J. Delforge and A. Syrota, Recent developments on modeling of ligand-receptor binding from data obtained by positron emission tomography, Proc. 9th IFAC/IFORS Symp. Identification and System Parameter Estimation, Budapest, 1991, pp. 332-337.
22. V. J. Cunningham, S. P. Hume, G. R. Price, R. G. Ahier, J. E. Cremer, and A. K. P. Jones, Compartmental analysis of diprenorphine binding to opiate receptors in the rat in vivo and its comparison with equilibrium data in vitro, J. Cerebral Blood Flow Metab., 11:1-9 (1991).
23. S. Vajda, H. Rabitz, E. Walter, and Y. Lecourtier, Qualitative and quantitative identifiability analysis of nonlinear chemical kinetic models, Chem. Eng. Commun. 83:191-219 (1989).