The manner in which both inert and metabolised substances distribute into the liver was studied in both conscious and anaesthetised dogs by means of the multiple indicator dilution technique. The major aim of the study was to see whether the two vascular inputs of the liver, the hepatic artery and the portal vein, perfuse regions of the liver which are different in terms of vascular anatomy and substrate uptake and metabolism. This was carried out by injecting solutes into these two vessels and measuring their distribution and metabolism. The first series of experiments examined the intrahepatic distribution of four inert tracers: 51Cr-labelled red blood cells; 125I-alburnin; 14C sucrose and 3H-water in conscious dogs. The results were interpreted according to transit-time analysis and by the flow-limited model of Goresky (1963). The fact that the albumin and sucrose curves could be fitted to the flow-limited model confirmed that the endothelial lining of the sinusoids is extremely permeable, even to large molecules such as proteins. The uptake of these substances by the liver is, therefore, in keeping with their rate of delivery by the blood, hence the term "flow-limited". The volume of distribution of the tracers was found to increase with hepatic blood flow with the exception of the cellular water volume. There appeared to be no route-dependent difference in these volumes, except for the extravascular volume of distribution of sucrose, which was greater following arterial injection.The outflow profiles of tritiated water could not be fitted to the Goresky flow-limited model (1963) in some experiments, suggesting that the distribution of water in the liver was not flow-limited. Because water uptake is known to be flow-limited in organs much less permeable than the liver, this observation was of considerable interest. The resolution of this paradox forms the second part of the thesis. The outflow curves were re-analysed with a model of axial diffusion. The outflow profiles predicted by this model were found to depend largely on how the sinusoids are assumed to contribute to the heterogeneity of the transit times of injected tracers. Close fits of the profiles were achieved when the transit-time heterogeneity was assumed to be due to a distribution of sinusoidal flows or by extra-sinusoidal dispersion of the bolus. The average diffusion coefficient of water in the liver derived from this modelling was in agreement with literature estimates, providing support for the hypothesis that the anomalous behaviour of water visible at low flows is due to axial diffusion.The possibility that axial tissue diffusion could be an important factor in determining the elimination of drugs by the liver was investigated by the construction of a diffusion model of steady-state hepatic elimination. The data from several published studies were fitted successfully with this model which predicts that the fraction of a highly-extracted and diffusible drug which escapes removal by the liver (hepatic availability) will be almost flow-independent. The on-going paradox as to why the well-stirred model is more successful in predicting blood levels of lipophilic compounds than more physiologic models is likely to be due to the neglect of axial tissue diffusion in the latter models.The investigation of the route-dependence of the elimination of substrates by the liver was continued in the third part of the thesis. The endogenous substrates, galactose, leucine and palmitate were studied with the multiple indicator dilution technique in anaesthetised dogs. In general, no route differences were observed for the extraction fraction of these compounds when corrected for the total hepatic blood flow. The ratio of influx to efflux appeared to be also independent of route. The elimination of palmitate was almost two-fold greater in females than in males. The volumes of distribution of inert tracers were route-independent and the previous finding that the extravascular space of distribution of sucrose is greater following arterial injection was not confirmed in these experiments. However, the sinusoidal blood volume measured following arterial injection appeared to increase faster with hepatic blood flow than that following with portal injection.The work carried out in this thesis identified some of the shortcomings of the kinetic model of Goresky. The well-established problem of distortion of the bolus by extra-sinusoidal dispersion (Goresky and Silverman, 1964; Luxon and Forker, 1982) was demonstrated to be problematic, particularly following arterial injection. This is likely to be due to the large variety of possible anatomical routes of arterial input into the liver. Choosing a "perfect" reference for the leucine experiments proved difficult as leucine appeared to have an extravascular volume of distribution between those of sucrose and albumin. Selection of the "perfect" reference is likely to be problem for the analysis of other substrates when the kinetic model of Goresky is used. For this reason, the effect of choosing a poor reference was explored in the final section of the thesis. With the use of simulation, the selection of the reference was shown to have a large impact on the recovered values of the elimination parameters. However, it was demonstrated that this problem can be rectified by solving for the "perfect" reference, even in the presence of experimental noise. The leucine data were reanalysed successfully using this modified Goresky model, demonstrating the applicability of the approach.In general, the multiple indicator dilution technique, although having certain limitations, is shown to be a powerful tool in probing the structure and function of vascular organs. In the case of the liver, localised specialisation of the parenchyma as a result of selective perfusion by one of the blood inputs (portal vein or hepatic artery) was not detected. Although it is possible that this may have been due to the selection of inappropriate substrates, it is more likely that route differences in substrate elimination are not significant present because of the dynamic nature of the perfusion heterogeneity. The demonstration of axial tissue diffusion and of the significant effect of hepatic blood flow on sinusoidal blood volume are likely to cause a fundamental rethinking of the appropriate ways of modelling hepatic elimination.