Fractal properties of arterial trees are analysed using the cascade model of turbulence theory. It is shown that the branching process leads to a non-uniform structure at the micro-level meaning that blood supply to the tissue varies in space. From the model it is concluded that, depending on the branching parameter, vessels of a specific size contribute dominantly to the blood supply of tissue. The corresponding tissue elements form a dense set in the tissue. Furthermore, if blood flow in vessels can get obstructed with some probability, the above set of tissue elements may not be dense anymore. Then there is the risk that, spread out over the tissue, nutrient and gas exchange fall short.