There may be an alternative explanation. The higher observed density of dextran or Aβ within the extracellular spaces of the smooth muscle layer than in the interstitial spaces of the parenchyma [102] might suggest that it binds, reversibly, to some component of the extracellular matrix in the layer. There is in fact good evidence for interaction of the Aβ peptides with some components [505, 506]. If the high concentrations within the basement membranes of the layer reflect binding rather than some form of impermeant sheath, then it is not clear whether Aβ and the dextrans reach the sites of the binding by moving parallel to the vessel wall or by traversing it (see Fig. 21). If the latter, movements parallel to the vessel would be occurring via an extramural route that might have a much lower resistance to flow. Transverse movement has been observed for both horseradish peroxidase and 3H-leucine with large cerebral arteries [507], and no additional impermeant layer is known to exist around smaller arteries inside the parenchyma [98]. There is at present no compelling evidence to decide between the intramural and extramural routes for movement parallel to the vessels. Fig. 21 Putative routes for periarterial efflux. In the intramural proposal solutes move parallel to the vessel wall along the basement membranes of the smooth muscle layer, shown as blue trajectories. In the extramural proposal movements of solutes parallel to the vessel occur primarily in a perivascular space with lower resistance to flow. They also move in and out of the wall by a combination of diffusion and convection, shown as the red trajectories. As discussed in Sect. 3.1 the nature of the extramural pathway is still controversial including whether it is a space one side or the other of the pial cells or alternatively the pial and glial basement membranes themselves. endo endothelium, s.m smooth muscle, BM basement membrane. Pial cells and pial basement membrane(s) are shown together because they are very thin