Structural identifiability and indistinguishability of compartmental models

Bibliography

• Nestorov I. Whole body pharmacokinetic models. Clin Pharmacokinetics 2003;42:883-908
   PubMed Web of Science ®Google Scholar
• Bellman R, strm KJ. On structural identifiability. Math Biosci 1970;7:329-39
   Google Scholar
• Eisenfeld J. On identifiability of the impulse-response in compartmental systems. Math Biosci 1979;47:15-33
   Web of Science ®Google Scholar
• Brown RF. Role of identifiability in validation of compartmental models. Math Comput Simulation 1982;24:483-6
   Web of Science ®Google Scholar
• Cobelli C, Saccomani MP. Letter to the editor: unappreciation of a priori identifiability in software packages causes ambiguities in numerical estimates. Am J Physiol, Endocrinol Metab 1990;258:E1058-9
   Google Scholar
• Slob W, Janssenn PHM, van den Hof JM. Structural Identifiability of PBPK Models: practical consequences for modelling strategies and study designs. Crit Rev Toxicol 1997;27(2):261-72
   PubMed Web of Science ®Google Scholar
• Walter E, Le Cardinal G, Bertrand P. On the identifiability of linear state systems. Math Biosci 1976;31:131-76
   Web of Science ®Google Scholar
• Milanese M, Molino GP. Structural identifiability of compartmental models and pathophysiological information from the kinetics of drugs. Math Biosci 1975;26:175-90
   Google Scholar
• Margaria G, Riccomagno E, White LJ. Structural identifiability analysis of some highly structured families of statespace models using differential algebra. J Math Biol 2004;49:433-54
   PubMed Web of Science ®Google Scholar
• Hart CM, Mulholland RJ. Structural identifiability of compartment systems based upon measurements of accumulated tracer in closed pools. Math Biosci 1979;47:239-253
   Web of Science ®Google Scholar
• Eisenfeld J. New techniques for structural identifiability for large linear and nonlinear compartmental systems. Math Comput Simulation 1982;24:494-501
   Web of Science ®Google Scholar
• Delforge J. On local identifiability of linear systems. Math Biosci 1984;70:1-37
   Web of Science ®Google Scholar
• Audoly S, D'Angio L. On the identifiability of linear compartmental systems: a revisited transfer function approach based on topological principles. Math Biosci 1983;66:201-28
   Web of Science ®Google Scholar
• Chappell MJ, Godfrey KR, Vajda S. Global identifiability of the parameters of nonlinear systems with specified inputs: a comparison of methods. Math Biosci 1990;102:41-73
   PubMed Web of Science ®Google Scholar
• Chapman MJ, Godfrey KR, Chappell MJ, Evans NJ. Structural identifiability of a class of nonlinear compartmental systems using linear/nonlinear splitting and symbolic computation. Math Biosci 2003;183:1-14
   PubMed Web of Science ®Google Scholar
• Denis-Vidal L, Joly-Blanchard G. Equivalence and identifiability analysis of uncontrolled nonlinear dynamical systems. Automatica 2004;40:287-292
   Web of Science ®Google Scholar
• Evans ND, Errington RJ, Shelley M, et al. A mathematical model for the in vitro kinetics of the anti cancer agent topotecan. Math Biosci 2004;189:185-217
   PubMed Web of Science ®Google Scholar
• Ljung L, Glad T. On global identifiability of arbitrary model parameterisations. Automatica 1994;30:265-76
   Web of Science ®Google Scholar
• Saccomani MP, Audoly S, D'Angio L. Parameter identifiability of nonlinear systems: the role of initial conditions. Automatica 2003;39:619-32
   Web of Science ®Google Scholar
• Margaria G, Riccomagno E, Chappell MJ, Wynn HP. Differential algebra methods for the study of the structural identifiability of rational function state-space models in the biosciences. Math Biosci 2001;74:1-26
   Google Scholar
• Godfrey KR, Jones RP, Brown RF, Norton JP. Factors affecting the identifiability of compartmental models. Automatica 1982;18:285-93
   Web of Science ®Google Scholar
• Saccomani MP, Cobelli C. A minimal input-output configuration for a priori identifiability of a compartmental model of leucine metabolism. IEEE Trans Biomed Eng 1993;40:797-803
   PubMed Web of Science ®Google Scholar
• Walter E. Identifiability of state space models. Lecture notes in biomathematics, Vol. 46. Springer, Berlin, Germany; 1982
   Google Scholar
• Jacquez JA. Compartmental analysis in biology and medicine. Biomedware, Ann Arbor, Michigan, U.S.A; 1996
   Google Scholar
• Yates JWT, Arundel PA. On the volume of distribution at steady-state and its relationship with two compartment models. J Pharm Sci 2008a;97:111-22
   PubMed Web of Science ®Google Scholar
• Vaugham DP. On the transformation of compartmental systems and the indeterminancy of the volume of distribution. J Pharm Sci 1989;78:1045-150
   PubMed Web of Science ®Google Scholar
• Evans ND, Godfrey KR, Chapman MJ, et al. An identifiability analysis of a parent-metabolite pharmacokinetic model for ivabradine. J Pharmacokinet Pharmacodyn 2001;28:93-105
   PubMed Web of Science ®Google Scholar
• Gibaldi M, Perrier D. Pharmacokinetics. Marcel Dekker, Inc. New York; 1982
   Google Scholar
• Pohjanpalo H. System identifiability based on the power series expansion of the solution. Math Biosci 1978;41:21-33
   Web of Science ®Google Scholar
• Margaria G, Riccomagno E, Chappell MJ, Wynn HP. Differential algebra methods for the study of the structural identifiability of rational function state-space models. Math Biosci 2001;174:1-26
   PubMed Web of Science ®Google Scholar
• Denis-Vidal L, Joly-Blanchard G, Noiret C. Some effective approaches to check the identifiability of uncontrolled nonlinear systems. Math Comput Simulation 2001;57:35-44
   Web of Science ®Google Scholar
• Chappell MJ, Gunn RN. A procedure for generating locally identifiable reparameterisations of unidentifiable nonlinear systems by the similarity transformation approach. Math Biosci 1998;148:21-41
   PubMed Web of Science ®Google Scholar
• Cobelli C, Distefano JJ, Ruggeri A. Minimal sampling schedules for identification of dynamic models of metabolic systems of clinical interest: case studies for two liver function tests. Math Biosci 1983;63:173-186
   Web of Science ®Google Scholar
• Gueorguieva I, Aarons L, Ogungbenro K, et al. Optimal design for multivariate response pharmacokinetic model. J Pharmacokinet Pharmacodyn 2006;33:97-124
   PubMed Web of Science ®Google Scholar
• Pronzato L, Walter E. Robust experimental design via maximin optimization. Math Biosci 1988;89:161-76
   Web of Science ®Google Scholar
• Bellu G, Saccomani MP, Audoly S, D'Angio L. DAISY: a new software tool to test global identifiability of biological systems. Comput Methods Program Biomed 2007;52-61
   PubMed Web of Science ®Google Scholar
• Audoly S, D'Angio L, Saccomani MP, Cobelli C. Global identifiability of linear compartmental models a computer algebra algorithm. IEEE Trans Biomed Eng 1998;45:36-47
   PubMed Web of Science ®Google Scholar
• Yates JWT. Structural Identifiability of Physiologically Based Pharmacokinetic Models. J. Pharmacokinetics Pharmacodynamics;33:421-439
   PubMed Web of Science ®Google Scholar