Markers for perivascular transport clearly have perivascular pathways for entry and exit from the parenchyma, but there is controversy as to whether efflux, influx or both occur along arteries and/or veins (for discussion see [16, 39, 41, 52, 72]). Efflux along arteries has been seen in many studies (e.g. [70, 82–88]) with substances even reaching the large arteries near the circle of Willis [82], and influx has also been seen in many studies [15, 16, 25, 69, 71, 79, 84, 88–92]. Evidence of influx along some vessels was obtained as early as 1960 [93]. Perivenous influx [16] and efflux [25, 69, 84, 94] have been reported. Efflux along unspecified blood vessels has also been seen [79]. The available evidence suggests that both influx and efflux occur along both arteries and veins [41, 78, 95] either via common pathways or separately along parallel pathways [88, 95] (see Proposal 2 below). In Fig. 5 movements are shown as occurring in both directions along both.