Fig. 7 Proposals to explain rapid transfer of markers via periarterial spaces: a the original proposal; b proposed perivascular convection and interstitial diffusion c the glymphatic proposal. In a the blood–brain barrier secretes fluid which flows out of the parenchyma via preferred routes (here the perivascular routes). In b transport in the perivascular spaces is assisted by convective stirring or mixing. In c (see Figure 5 of Iliff et al. [25]) there is preferential inflow via the space between the arterial wall and the pial sheath and preferential outflow via spaces surrounding veins. Red lines represent pial membranes, grey lines the layer of glial end-feet or glia limitans, black arrows are fluxes of markers carried or assisted by convection, green arrows are primarily diffusion. The location of the pial barriers is based on Zhang et al. [23]. The anatomical basis of the perivascular spaces remains controversial (Modified from Figure 9 in [41])