Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake

Abstract

a b s t r a c tIn this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available.

Structural Identifiability of Dynamic Systems Biology Models

“…We applied the proposed methodology to a number of published models of varying size and complexity [19, 27–32], some of which have been recently used to benchmark identifiability analysis methods [10, 19, 20]. The main features of the models are summarized in Table 2, and schematic diagrams are shown in Figs 2–4.…”

“…Furthermore, the results obtained for the rational counterpart are not necessarily valid for the original non-rational model in the case of unidentifiability [18]. Recent studies [9, 10, 19–21] show that, in general, the choice of a structural identifiability method involves trade-offs between generality of the application, computational cost, and level of detail of the results. In conclusion, there is currently a lack of structural identifiability methods of the sufficient generality and robustness to be applied to nonlinear models of general form and realistic size [21, 22].…”

“…Some of them are non-rational systems exhibiting Hill kinetics, that is, with expressions containing terms of the form k 1 x n /( k 2 + x n ), such as the Goodwin model of transcriptional repression [27], the mitogen-activated protein kinase (MAPK) signalling cascade [28], and the genetic network that controls the circadian clock in Arabidopsis thaliana [29]. Other models analysed here include drug uptake into hepatocytes [19], NF- κ B [30] and JAK/STAT [31] signalling pathways, and the central carbon metabolism of Chinese hamster ovary cells [32]. These case studies include models whose identifiability had not been previously determined, and for some of them we found unidentifiabilities that had not been reported before.…”

Structural Identifiability of Equivalent Circuit Models for Li-Ion Batteries

“…If equating the monomials of these functions produces only one solution for the unknown parameters, then the system is SGI. In terms of run time and memory utilisation, the univariate polynomial algorithm in Maple 2010 is the most efficient algorithm out of all the approaches described [54]. However, it can still be very memory-intensive, particularly if the model equations contain complicated nonlinear terms [54] (see Section 2).…”

“…The Rosenfeld-Gröbner algorithm in Maple 2010 can be very memory-intensive, particularly if the model equations contain complicated nonlinear terms. See [54] for examples of where this approach fails to yield results for nonlinear models, as there is not enough memory available for Maple 2010 to perform the required symbolic calculations.…”