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In this thesis, theoretical models of fluid flows close to arterial walls are studied. There are two main areas of study: (i) Flow near an oscillating stagnation point. The existence of a stagnation point which oscillates in position as well as in strength has been observed at certain sites prone to occlusive arterial disease. The two oscillations can interact non-linearly, altering the mean shear stress distribution on the wall. The problem is studied analytically and numerically in two and three dimensions, where in the three-dimensional case the basic stagnation-point flow is axisymmetric. In the physiologically relevant regime, it is found that the positional oscillations break the symmetry of the system, shifting the point of lowest mean wall shear stress away from the centre of these oscillations. The mass transport properties of such a flow are also studied by calculating particle trajectories and mass fluxes. (ii) Flow over an isolated obstacle on a plane wall. The vascular endothelium is a monolayer of cells lining the arterial walls. The endothelial cells convert mechanical forces into biological responses and a dysfunction of this natural process is one of the many proposed mechanisms for the initiation of atherosclerosis. The endothelium is a non-uniform surface with crests at the cellular nuclei and troughs at junctions between cells. A model for a single endothelial nucleus raised above the cellular monolayer is considered here. The time- and length-scales are such that the local fluid behaviour is dominated by viscous forces and the steady Stokes equations are applicable. These equations are solved numerically by a boundary element collocation method and the total force on a variety of nuclear shapes is calculated. Further away from the nucleus, but still on a cellular length-scale, weak inertia effects are introduced. Fourier transform methods are then used to obtain a closed form solution for the pressures and stresses on the wall, which are investigated by asymptotic methods.

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The prototypic heparan sulfate (HS)-dependent angiogenic cytokine is FGF-2. Here we present the first in vivo study of size fractionated heparin oligosaccharides in 3 models of angiogenesis that are progressively less dependent on FGF-2. We developed the modified hollow fibre assay, a novel model for quantifying angiogenesis in vivo. We tested the ability of size defined oligosaccharides (dp 6-14) to inhibit FGF-2 in a sponge model of angiogenesis, where the process can be driven by a defined angiogenic molecule. Sponges were implanted subcutaneously and injected with FGF2 100 ng/day and oligosaccharides (20 mglkg/day). After 14 days the sponges were excised and the microvessel density (MVD) measured. Octasaccharides were the most potent species, reducing MVD to levels below those observed in saline treated implants. In a second experiment HEC-FGF2 human endometrial cancer cells that over-express FGF-2 were implanted in a hollow fibre placed subcutaneously in vivo. Oligosaccharides were administered at 20 mglkg/day for 2 weeks and the data again showed that octasaccharides significantly reduced MVD around the fiber. In a more complex model, where angiogenesis was induced by a broad spectrum of growth factors including VEGF, we implanted H460 lung carcinoma cells in hollow fibers and treated the animals with oligosaccharides at 20mglkg/day over three weeks. The data showed that octasaccharides were able to reduce the microvessel density to the level of angiogenesis present in empty hollow fibres. Preliminary investigation of 6-0-desulfated heparins showed that these also had anti-angiogenic activity. In summary, we have shown that heparin octasaccharides have antiangiogenic activity in vivo in several models of variable dependence on FGF-2. We have now embarked on a synthetic programme to produce and investigate oligosaccharides with predefined sulfation patterns and cytokine specificities as FGF inhibitors.