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Conventional ‘well-stirred’ extrapolation methodology using intrinsic metabolic clearance data from rat liver microsomes poorly predicts in vivo clearance for approximately half of drug discovery compounds. The aim of this present study was to gain a more detailed understanding of the hepatobiliary disposition pathways which influence drug clearance. A set of 77 new chemical entities (NCEs), demonstrating a range of physicochemical properties and in vitro-in vivo clearance correlations (IVIVC), were employed to explore relationships between hepatobiliary disposition pathways in rat and physicochemical, structural and molecular properties of the NCEs. Primary rat hepatocytes with >80% cell viability were successfully isolated from male Han Wistar rats and used to establish in vitro models of drug uptake and biliary efflux. Preliminary studies with cultured primary rat hepatocytes indicated that uptake of d8-taurocholic acid and pitavastatin was time, concentration and temperature dependent. Initial studies with sandwich cultured primary rat hepatocytes demonstrated that cellular accumulation and biliary efflux of [3H]-Taurocholic acid was time and concentration dependent. These in vitro rat hepatocyte models were then used to investigate drug uptake and biliary efflux for all NCEs. In general, NCEs with high (passive) permeability showed better IVIVC and a lower incidence of active uptake and biliary efflux compared to NCEs with lower permeability, suggesting permeability is a key property influencing hepatobiliary drug disposition in rat. Preliminary in silico models analysing structural and molecular descriptors of substrates of active transport in rat hepatocytes were developed and indicated modest potential to highlight clearance pathways beyond hepatic metabolism but further follow up work with larger, more diverse compound sets is warranted to gain confidence in these models. Extended clearance models were investigated to estimate the effect of hepatic transporters on clearance and to predict the overall hepatic clearance of the NCEs. None of these models resulted in a 1 to 1 correlation but in general, improvements in clearance predictions were made when drug transport processes were accounted for. In vivo excretion studies using bile duct cannulated rats demonstrated that NCEs with high permeability and good IVIVC were not directly eliminated in bile or urine as unchanged drug, whereas NCEs with lower permeability and poor IVIVC (> 3-fold under predicted) were all directly eliminated unchanged indicating key drivers of clearance beyond metabolism. In conclusion these investigations confirmed a role for hepatic transporters in clearance but the complex nature of active transport mechanisms and a lack of robust in vitro tools create challenges in the quantitative prediction of hepatobiliary clearance. However, one of the key findings from this research, which is highly applicable in early drug discovery, was to identify the existence of disposition permeability relationships. These can be anticipated by observing physicochemical parameters of NCEs in conjunction with conventional IVIVC, since NCEs that are not highly permeable, possess some hydrophobic characteristics, and which are poor substrates of cytochrome P450 enzymes are more likely to be good substrates of transporters and be directly eliminated in bile and/or urine. The present study focused on exploring hepatobiliary disposition pathways using rat as the investigative species. Whilst there is no guarantee that pathways relevant to rat will be similar to other preclinical species or even humans, an early diagnosis of dominant clearance pathways can guide a more efficient use of the ADME-PK toolbox.

Philosophiae Doctor - PhD / Fitted operator finite difference methods (FOFDMs) for singularly perturbed problems have been explored for the last three decades. The construction of these numerical schemes is based on introducing a fitting factor along with the diffusion coefficient or by using principles of the non-standard finite difference methods. The FOFDMs based on the latter idea, are easy to construct and they are extendible to solve partial differential equations (PDEs) and their systems. Noting this flexible feature of the FOFDMs, this thesis deals with extension of these methods to solve interior layer problems, something that was still outstanding. The idea is then extended to solve singularly perturbed time-dependent PDEs whose solutions possess interior layers. The second aspect of this work is to improve accuracy of these approximation methods via methods like Richardson extrapolation. Having met these three objectives, we then extended our approach to solve singularly perturbed two-point boundary value problems with variable diffusion coefficients and analogous time-dependent PDEs. Careful analyses followed by extensive numerical simulations supporting theoretical findings are presented where necessary.