S. Y. A. Cheung, I. Gueorguieva and L. Aarons
School of Pharmacy and Pharmaceutical Sciences, The University of Manchester
Objectives: It is essential to establish the importance and raise the awareness of structural identifiability analysis [1] of system models as the prerequisite for population PK/PD experimental design. The analysis should be performed prior to the planned experiment to identify whether the internal structure includes assumed unknown pathways and parameters values that can be uniquely globally determined by input-output experiments. A locally identifiable model is one that consists of a finite set of parameter values, which indicates there is a finite set of estimated parameters. An unidentifiable model consists of infinite sets of parameters values and is not suitable for system identification in which the proposed model would require modification such as reparametrization or redesign of the intended experiments. These concepts are demonstrated through the investigation of the structural identifiability analysis of two linear models: a semi-physiologically based drug-metabolite model of dextromethorphan (DEX) and dextrorphan (DOR) [2] and a whole body physiologically based pharmacokinetic model (WBPBPK) of diazepam [3].
Methods: The exhaustive modelling or similarity transformation approach [4] was chosen from other existing methods [1] to use for the structural identifiability analysis for both linear systems due to its robustness and the efficiency in handling a large number of input-output measurements. The models also underwent controllability and observability checks to verify the complete controllability and observability of the models when using the similarity transformation approach. Analysis was carried out on variant models with different model structure assumptions to ratify the dependence of model assumptions in relation to the identifiability results. The similarity transformation approach was carried out using the symbolic calculation software, MATHEMATICA.
Results: The result of the semi-physiologically based model studies shows the impact of modification and simplification of the model in relation to the level of structural identifiability. The structural identifiability of the WBPBPK model was ascertained. The cases where hepatic intrinsic clearance was known and unknown a priori were considered.
Conclusions: The prior consideration of the structural identifiability is shown to be an important part of PK/PD experimental design lead to an understanding of the relationship between input-output experiments and the internal structure of the proposed model. This allows development of the model before any actual experiment is carried out.
References:
[1] Godfrey, K. R. and DiStefano III., J. J., Identifiability of model parameters. In E. Walter, editor, Identifiability of parametric models, pp.1-20, Oxford, 1987. Pergamon Press.
[2] Moghadamnia, A. A. et al., Physiologically based modelling of inhibition of metabolism and assessment of the relative potency of drug and metabolite: dextromethorphan vs. dextrorphan using quinidine inhibition, British Journal of Clinical Pharmacology, Vol. 56, pp. 57-67, 2003.
[3] Gueorguieva, I., et al., Fuzzy simulation of pharmacokinetic models: case study of whole body physiologically based model of whole body physiologically based model of diazepam, Journal of Pharmacokinetics and Pharmacodynamics, Vol. 31, pp. 185-212, 2004.
[4] Evans, N. D. et al., An Identifiability of a Parent-Metabolite Pharmacokinetic Model for Ivabradine, Journal of Pharmacokinetics and Pharmacodynamics, Vol. 28, pp. 93-105, 2001.
Reference: PAGE 14 (2005) Abstr 724 [www.page-meeting.org/?abstract=724]
Poster: poster