title: A graphical method for practical and informative identifiability analyses of physiological models: a case study of insulin kinetics and sensitivity.
abstract: BACKGROUND
  Derivative based a-priori structural identifiability analyses of mathematical models can offer valuable insight into the identifiability of model parameters. However, these analyses are only capable of a binary confirmation of the mathematical distinction of parameters and a positive outcome can begin to lose relevance when measurement error is introduced. This article presents an integral based method that allows the observation of the identifiability of models with two-parameters in the presence of assay error.
  
  
  METHODS
  The method measures the distinction of the integral formulations of the parameter coefficients at the proposed sampling times. It can thus predict the susceptibility of the parameters to the effects of measurement error. The method is tested in-silico with Monte Carlo analyses of a number of insulin sensitivity test applications.
  
  
  RESULTS
  The method successfully captured the analogous nature of identifiability observed in Monte Carlo analyses of a number of cases including protocol alterations, parameter changes and differences in participant behaviour. However, due to the numerical nature of the analyses, prediction was not perfect in all cases.
  
  
  CONCLUSIONS
  Thus although the current method has valuable and significant capabilities in terms of study or test protocol design, additional developments would further strengthen the predictive capability of the method. Finally, the method captures the experimental reality that sampling error and timing can negate assumed parameter identifiability and that identifiability is a continuous rather than discrete phenomenon.
authors: Centre for Bioengineering, Department of Mechanical Engineering, University of Canterbury, New Zealand, Private Bag 4800, Christchurch, New Zealand. paul.docherty@pg.canterbury.ac.nz
authors: Paul D
authors: PD
authors: Docherty
authors: J Geoffrey
authors: JG
authors: Chase
authors: Thomas F
authors: TF
authors: Lotz
authors: Thomas
authors: T
authors: Desaive
references: IEEE Trans Biomed Eng. 2001 Jan;48(1):55-65
references: 11235592
references: Am J Physiol. 1999 Jun;276(6):E1171-93
references: 10362630
references: Metabolism. 2004 Oct;53(10):1349-54
references: 15375793
references: IEEE Trans Biomed Eng. 1998 Jan;45(1):36-47
references: 9444838
references: Comput Methods Programs Biomed. 2007 Oct;88(1):52-61
references: 17707944
references: Am J Physiol. 1979 Jun;236(6):E667-77
references: 443421
references: Bioinformatics. 2009 Aug 1;25(15):1923-9
references: 19505944
references: Math Biosci. 2003 Jul;184(1):53-67
references: 12788233
references: IEEE Trans Biomed Eng. 2009 Sep;56(9):2156-66
references: 19380266
references: Comput Methods Programs Biomed. 2008 Mar;89(3):215-25
references: 18242418
references: Curr Opin Biotechnol. 2011 Feb;22(1):109-16
references: 20970318
references: J Diabetes Sci Technol. 2010 Nov 01;4(6):1408-23
references: 21129337
references: Am J Physiol. 1999 Sep;277(3):E481-8
references: 10484360
references: Comput Methods Programs Biomed. 2011 Nov;104(2):120-34
references: 20851494
references: Am J Physiol Endocrinol Metab. 2002 Mar;282(3):E564-73
references: 11832358
references: Open Med Inform J. 2009 Dec 02;3:65-76
references: 20148062
references: J Clin Endocrinol Metab. 2000 Jul;85(7):2504-8
references: 10902801
references: Diabetes. 1994 Jul;43(7):890-6
references: 8013753
references: Dan Med Bull. 1990 Apr;37(2):143-53
references: 2188802
references: Am J Physiol. 1999 Jan;276(1):E151-4
references: 9886961
references: Comput Methods Programs Biomed. 2005 Mar;77(3):259-70
references: 15721654
references: Diabetes. 1992 Mar;41(3):368-77
references: 1551497