Experimental and mathematical analysis of in vitro Pitavastatin hepatic uptake across species.

1. To investigate the non-linear kinetics of in vitro hepatocyte uptake across species, the OATP substrate Pitavastatin was used as a probe. 2. Experiments were conducted at AstraZeneca (Alderley Park, Macclesfield) using freshly isolated rat, dog and human hepatocytes, utilising the "oil spin" methodology described by Hassen et al. (1996). Very few mechanistic models have previously been used to characterise the uptake process. 3. Here two candidate pharmacokinetic non-linear compartmental models are proposed. Both models have been shown to be structurally identifiable and distinghishable previously, which establishes that all unknown parameters could be identified from the experimental observations available and that input/output relationships for both the candidate models were structurally different. 4. A kinetic modelling software package, FACSIMILE (MCPA Software, Faringdon, UK), was used to obtain numerical solutions for the system equations and for parameter estimation. Model fits gave good agreement with the in vitro data and suggest the current widely accepted assumption that the rate of diffusion across the hepatocyte cell membrane is the same at both 4 °C and 37 °C is not valid, at least for Pitavastatin. Although this finding has already been proposed, this is the first time it is comprehensively debunked using statistical testing.

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

In 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.

Compartmental modelling of the pharmacokinetics of a breast cancer resistance protein.

A mathematical model for the pharmacokinetics of Hoechst 33342 following administration into a culture medium containing a population of transfected cells (HEK293 hBCRP) with a potent breast cancer resistance protein inhibitor, Fumitremorgin C (FTC), present is described. FTC is reported to almost completely annul resistance mediated by BCRP in vitro. This non-linear compartmental model has seven macroscopic sub-units, with 14 rate parameters. It describes the relationship between the concentration of Hoechst 33342 and FTC, initially spiked in the medium, and the observed change in fluorescence due to Hoechst 33342 binding to DNA. Structural identifiability analysis has been performed using two methods, one based on the similarity transformation/exhaustive modelling approach and the other based on the differential algebra approach. The analyses demonstrated that all models derived are uniquely identifiable for the experiments/observations available. A kinetic modelling software package, namely FACSIMILE (MPCA Software, UK), was used for parameter fitting and to obtain numerical solutions for the system equations. Model fits gave very good agreement with in vitro data provided by AstraZeneca across a variety of experimental scenarios.