Finding identifiable parameter combinations in nonlinear ODE models and the rational reparameterization of their input-output equations

Mathematical Biosciences

Volumn 233, Issue 1, 2011, Pages 19-31

  Meshkat, Nicolette ^a   Anderson, Chris ^a   DiStefano, Joseph J ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Engineering IV   (United States)

Author keywords

Differential algebra; Gr bner Basis; Identifiability; Reparameterization

Indexed keywords

COMPUTING SOLUTIONS; DIFFERENTIAL ALGEBRAS; DYNAMIC SYSTEM MODELS; IDENTIFIABILITY; INFINITE NUMBERS; INPUT-OUTPUT; INPUT-OUTPUT DATA; PARAMETER COMBINATION; REPARAMETERIZATION; STRUCTURAL IDENTIFIABILITY;

ALGORITHMS; NONLINEAR EQUATIONS;

PARAMETER ESTIMATION;

ALGORITHM; INPUT-OUTPUT ANALYSIS; NONLINEARITY; NUMERICAL MODEL; PARAMETERIZATION;

ALGORITHM; ARTICLE; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; PROBLEM SOLVING; QUANTITATIVE ANALYSIS;

ALGORITHMS; HIV INFECTIONS; HUMANS; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; MODELS, THEORETICAL; NONLINEAR DYNAMICS; T-LYMPHOCYTES;

EID: 79961127728     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2011.06.001     Document Type: Article

References (20)

1. Evans N.D., Chappell M.J. Extensions to a procedure for generating locally identifiable reparameterisations of unidentifiable systems. Math. Biosci. 2000, 168:137.
2. Gunn R.N., Chappell M.J., Cunningham V.J. Reparameterisation of unidentifiable systems using the Taylor series approach. Proceedings of the Third IFAC Symposium on Modelling and Control in Biomedical Systems 1997, 247. Pergamon, Oxford. D.A. Linkens, E. Carson (Eds.).
3. Pohjanpalo H. System identifiability based on the power series expansion of the solution. Math. Biosci. 1978, 41:21.
4. Chappell M.J., Gunn R.N. A procedure for generating locally identifiable reparameterisations of unidentifiable non-linear systems by the similarity transformation approach. Math. Biosci. 1998, 148:21.
5. Denis-Vidal L., Joly-Blanchard G., Noiret C. Some effective approaches to check the identifiability of uncontrolled nonlinear systems. Math. Comput. Simulat. 2001, 57:35.
6. Boulier F. Differential elimination and biological modelling. Radon Series Comput. Appl. Math. 2007, 2:111.
7. Meshkat N., Eisenberg M., DiStefano J.J. An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner Bases. Math. Biosci. 2009, 222:61.
8. M.P. Saccomani, S. Audoly, G. Bellu, L. D'Angiò, A new differential algebra algorithm to test identifiability of nonlinear systems with given initial conditions, in: Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida, USA, 2001, pp. 3108-3113.
9. DiStefano J.J., Cobelli C. On parameter and structural identifiability: Nonunique observability/reconstructibility for identifiable systems, other ambiguities, and new definitions. IEEE Trans. Automat. Control 1980, 25-4:830.
10. Ljung L., Glad T. On global identifiability for arbitrary model parameterization. Automatica 1994, 30-2:265.
11. F. Ollivier, Le problème de l'identifiabilité structurelle globale: étude théoritique, méthodes effectives et bornes de complexité, Ph.D. Thesis, Ecole Polytechnique, 1990.
12. F. Ollivier, Identifiabilité des systèmes, Technical Report 97-04, GAGE, Ecole Polytechnique, 1997, pp. 43-54.
13. Bellu G., Saccomani M.P., Audoly S., D'Angiò L. DAISY: a new software tool to test global identifiability of biological and physiological systems. Comput. Methods Programs Biomedicine 2007, 88:52.
14. Saccomani M.P., Audoly S., D'Angiò L. Parameter identifiability of nonlinear systems: the role of initial conditions. Automatica 2003, 39:619.
15. Margaria G., Riccomagno E., Chappell M.J., Wynn H.P. Differential algebra methods for the study of the structural identifiability of rational function state-space models in the biosciences. Math. Biosci. 2001, 174:1.
16. Cox D., Little J., O'Shea D. Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra 2007, Springer. third ed.
17. Shannon D., Sweedler M. Using Gröbner Bases to determine algebra membership, split surjective algebra homomorphisms and determine birational equivalence. J. Symb. Comput. 1988, 6(2-3):267.
18. Ueno K. An Introduction to Algebraic Geometry 1995, American Mathematical Society.
19. Shafarevich I. Basic Algebraic Geometry 1 1988, Springer-Verlag. second ed.
20. Miao H., Xia X., Perelson A.S., Wu H. On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics. SIAM Rev. 2011, 53(1):3.