Mechanisms driving perivascular solute efflux
Diffusion is not adequate for perivascular influx because substances added to CSF are found deep in the parenchyma much too quickly for diffusion over the distance involved, a millimeter or more [25, 68, 69, 84]. Similarly diffusion cannot account for efflux from parenchyma to CSF of substances like polyethylene glycol and dextran [126, 127], serum albumin [83], mannitol [25] or inulin [62, 128]. Thus alternative mechanisms have been proposed (see Fig. 7).
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])
Proposal 1 The first proposal (Fig. 7a) was that secretion of fluid by the blood–brain barrier provides a small pressure gradient for outflow of ISF along preferential routes (see [83, 126, 127, 129, 130]). These routes could be perivascular spaces or the extracellular spaces parallel to the axons in nerve fibre tracts. When this proposal was put forward more than 30 years ago (see e.g. [83]) it was believed that the half-life for clearance of marker solutes by outflow was of the order of 12 h. However, all of these early studies were performed on animals anaesthetized using barbiturates. Using either conscious animals or those anaesthetized with ketamine/zylazine or halothane, the half-lives are much shorter, 2–4 h [25, 62, 85, 131]. Perivascular efflux of solutes is considerably faster than envisaged by Cserr and coworkers. It should also be pointed out that Proposal 1 does not and was never intended to provide any explanation for the rapid influx of solutes. In Proposal 1 (and in Proposal 3, see below) the solutes are swept out of the parenchyma by the flow through the perivascular system. Estimates of the flow rate required to eliminate substances at the observed rates can be calculated from their clearances1 CLperivascular=rateofelimination/cisfand the assumption that the concentration of the solute is the same in ISF and the outflow. Then because elimination is by outflow2 rateofelimination=rateofoutflow×concentration in outflowand substituting that into the definition of clearance,3 CLperivascular=rateofoutflow×concentration in outflow/cisf,which, because the concentration in the outflow is the same as cisf, becomes4 CLperivascular=rateofoutflow.
From the known volume of distribution of suitable substances such as inulin or sucrose, 200 µL g−1, and the range of their half lives, 2–4 h, and the relation between clearance, half-life and volume of distribution, CL = 0.69 VD/t1/2, the clearances and thus the required flow rates are in the range 0.6–1.2 µL g−1 min−1. For a human with a 1400 g brain this is 1.2–2.4 L day−1. Even the bottom of this range is somewhat more than twice the rate of production of CSF. There is no other reason to suspect that there is a rate of secretion of fluid across the blood–brain barrier that exceeds the rate of fluid secretion by the choroid plexuses (see Section 4.1 in [4]). The rate of fluid secretion across the blood–brain barrier is very unlikely to be this large and is almost certain to be insufficient to account for perivascular clearance of solutes.
Proposal 2 (Fig. 7b) The second suggestion, recently revived, is that convection in the perivascular spaces, arterial and possibly venous, leads to convective mixing of the fluid in the spaces allowing relatively rapid movements of solutes both inwards and outwards [41, 78, 82, 96, 132]. Such mixing probably presupposes that perivascular spaces are compressible. Convective mixing is perhaps better called dispersion [78]. Papisov [133] and Asgari et al. [134] discuss a similar effect in the spinal cord allowing transport of solutes down their concentration gradients against the direction of net flow of CSF and at rates much greater than allowed by diffusion. In this proposal diffusion is taken to be adequate to explain movements within the interstitial spaces in the parenchyma because the distances involved are sufficiently short (see Sect. 3.2.1).
In this proposal (and in Proposal 3, see below), an important part of the mechanism is thought to be convection in spaces whose dimensions are changed by periodic compression resulting from the changes in blood pressure during the cardiac cycle [13, 25, 70, 82, 96, 132]. The length of space around a cortical vessel that is compressed at one time is as long as the vessel [78, 82]. Bradbury et al. [82] were of the opinion that periodic compression and reexpansion of this space “would cause to-and-fro movement of fluid in and out of the brain” such that “A basis would be provided for substances in solution or suspension to be moved either out of or into the brain depending on the relative concentration in subarachnoid CSF.” Another variation on this theme may be possible if there are layers of differing compressibility, both connected via relatively low resistance pathways to the brain surface.
Back-and-forth convective movements in perivascular spaces would only be apparent using techniques with both good spatial resolution and time resolution better than a fraction of a second. Such movements have been observed in perivascular spaces very close to the cortical surface using india ink [84] and in the periarterial spaces at the cortical surfaces using microspheres [108]. But with techniques now available for viewing, if perivascular spaces exist that allow convective back and forth movements, all that would be seen within the parenchyma would be accelerated movement down the concentration gradient regardless of its direction, i.e. the periarterial influxes and effluxes that have been observed.
Proposal 3 (Fig. 7c) The third proposal, the glymphatic hypothesis [25, 109, 135–137], asserts.There is an inward flow of CSF along periarterial spaces;
The flow is driven across the layer of astrocyte endfeet into the parenchyma aided by the presence of Aqp4 in the endfeet;
The flow propels the waste products of metabolism into the perivenous space again crossing the layer of endfeet, presumably again aided by the presence of Aqp4;
The flow exits the parenchyma by the perivenous route and reaches lymphatic vessels in the neck.
As indicated when considering Proposal 1, a flow of ~ 0.6 µL g−1 min−1 or more would be required to remove the efflux markers at the observed rate. For a 1400 g brain, that is c. 1.2 L day−1 roughly twice the generally accepted rate of CSF production. Thus even if the rest of this proposal is correct, either the glymphatic flow does not direct ISF out of the brain directly to lymphatic vessels or the rate of CSF production is greater than is generally accepted.
The earlier evidence for and against the glymphatic hypothesis was discussed in [41] where it was argued that while a recirculation of CSF could explain influx and efflux of substances much faster than by simple diffusion, it did not explain either the observed outward movements of solutes along arteries [70, 71, 82, 83, 87, 130] or the observed continuation of rapid inward periarterial movement of large solutes when the proposed glymphatic circulation was interrupted at the level of the astrocyte endfeet by global knockout of Aqp4 [25].
Proposal 4 (not shown in Fig. 7) The most recent proposal [101] is that vasomotion, waxing and waning contraction of the smooth muscle fibres in the arterial wall, propels fluid towards the brain surface along the basement membranes of the vessel wall. This proposal does not seek to explain the rapid influx of markers along arterial walls, possibly by a different pathway.

Is movement within the parenchyma determined by diffusion or by flow from periarterial to perivenular spaces?
It is unclear how the flow required for the glymphatic hypothesis to be correct, at least 0.6 µL g−1 min−1 (see Proposal 3 above), could be driven through the parenchyma. Jin et al. [77] and Holter et al. [80] have calculated fluid flows within the parenchyma using, respectively, 2-D and 3-D models of the geometry and dimensions of the interstitial spaces. Jin et al. concluded that “little or no advective solute transport is predicted to occur with physiological paravascular pressure differences” taken to be < 5 mmHg. (Strictly advection corresponds to flow while convection includes both flow and diffusion). Furthermore they concluded that the water permeability of the endfeet membrane facing the microvessels, i.e. the membrane containing Aqp4, could have little direct effect on water flow into the parenchyma.7 Jin et al. assumed that the ISF between the cells behaves as a free fluid with the viscosity of water. If instead ISF in the interstitial spaces in the brain has properties similar to those of extracellular fluid in tissues in the rest of the body (see [138, 139], discussion in [41] and,8 the pressure required for flow would be much larger than that calculated by Jin et al. making bulk flow (advection) even less likely (compare [140]).
Holter et al. [80] have investigated what they consider to be a more realistic model of the parenchyma than that evaluated by Jin et al. One aspect is undeniably more realistic, it treats movement in three dimensions rather than two. It is also asserted that treating the obstacles to flow as being much smaller and more numerous than in Jin et al’s simulation produces a more faithful result. Jin et al. used barriers sized like cell bodies, while Holter et al. have adopted the smaller objects used in Kinney’s construction of the extracellular space [141], which allows for cell bodies and processes. (Smaller objects may be analogous to the increased resistance to flow resulting from macromolecules dissolved in peripheral extracellular fluid, see Footnote 8). Holter et al. conclude that flow makes a much smaller contribution than calculated by Jin et al. However, while Jin et al. treat the entrance and exit of fluid across the endfoot layers explicitly, this is missing from the treatment given by Holter et al. Given that the conclusion is “no flow” in both studies this difference between them may be of no consequence.
It should be noted that neither Jin et al. [77] nor Holter et al. [80] have considered flow along the basement membranes surrounding capillaries presumably because the total area available for such flow is less than for flow via the interstitial spaces (and flow along basement membranes wasn’t considered in the glymphatic hypothesis). Asgari et al. [73] assumed that the resistance to flow of the basement membranes would be the same as for slabs of ®Matrigel of the same dimensions, and on this basis concluded that flow via basement membranes would be less than through the interstitium (compare the discussion in [16]).
That flow through the parenchyma is not needed to explain the delivery of solutes to perivascular spaces was suggested by the results obtained using integrative optical imaging (see e.g. [24, 76, 142, 143]). That technique showed that in apparently isotropic regions of brain the spread of fluorescent indicators appears symmetrical over distances of at least 100 µm from a point source (for examples see [24]), indicating that molecules within ISF can reach perivascular spaces in any direction and in good time by diffusion with no evidence for preferential movement towards either arterioles or venules. However, that technique was applied using a water immersion microscope objective after opening the skull and dura to allow access [142]. The open skull and dura may have perturbed flow in the parenchyma. (There is good evidence that cisternal puncture changes flow in the basal cisterns and subarachnoid spaces [25, 89]). Symmetrical spread has now been convincingly confirmed in a systematic study using both direct observation through a cranial window after injection of fluorescently labelled dextrans and recovery from photobleaching [79]. However, it should be noted that the window was glazed after dye injection and hence only shortly before observations were made.
Smith et al. [79] have also found (1) that the dependence of the rate of movements within the parenchyma on the size of the solute is close to that expected if the movement occurs by diffusion; (2) that, in contrast to the report of Iliff et al. [25], the amounts of solutes entering the parenchyma are similar in Aqp4+/+ and Aqp4−/− mice; and (3) that local movement of solutes in the parenchyma is not impaired just after cardiorespiratory arrest. They conclude that “these results do not support glymphatic, convective solute transport in brain parenchyma.” In reply to point (2) a group of researchers have posted an un-refereed summary of their experience that comparing three different Aqp4 knockout transgenic lines, including the cell line used by Smith et al. [79], Aqp4 does support “fluid and solute transport and efflux in brain in accordance with the glymphatic system model” [144]. The role of Aqp4 is discussed further in [140].
Pizzo et al. [16] have looked at the distribution of IgG and much smaller single domain antibodies after cisternal infusion. They found that the antibodies rapidly enter the perivascular spaces of blood vessels of all sizes be they arteries, veins or capillaries. The distribution within the parenchyma was as expected for diffusion including the differences between the profiles for different sizes of fluorescent marker. Further discussion supporting the importance of diffusion over bulk flow in the extracellular spaces of the parenchyma can be found in [40]. Perivascular solute movements are considered further in Sect. 5.7.1.2.

Is there a glymphatic circulation?
The answer depends partly on what one means by glymphatic circulation. If the meaning is “Convective glymphatic fluxes of CSF and ISF propel the waste products of neuron metabolism into the paravenous space” [136], then the answer is almost certainly no (compare [40, 140], though it should be noted that [54, 137] still argue in favour of the original glymphatic hypothesis). However, if glymphatic circulation is taken to mean only that there is a net inward periarterial flow, a net outward perivenous flow, and some connection between them, then the answer still isn’t known with any certainty. The results discussed above [24, 76, 79, 142, 143] provide powerful experimental support for the widely held view that a glymphatic circulation is not needed to explain solute movements over the short distances that are important in the parenchyma. Furthermore the calculations of Asgari et al. [73, 78], Jin et al. [77] and Holter et al. [80] (see also Footnote 8) suggest that flow through the interstitial spaces of grey matter or along the basement membranes of microvessels in the parenchyma is negligible. However, it is not yet clear that the available experimental results exclude the possibility that there is a net flow between the perivascular spaces of arterioles and venules that is large enough to complete a recirculation pathway inwards from CSF via periarterial routes and back to CSF via perivenous routes.9 If that flow exists it could be important for transport of solutes over the relatively large distances encountered along the perivascular spaces (see e.g. [76]) while still being negligible relative to diffusion for transport over the relatively short distances within the parenchyma. Interestingly this scenario was proposed recently by Coles et al. [1] (see also Iliff et al. [145]) based on detailed consideration of the evidence available even before publication of the results in [16, 79].
While there have now been hundreds of references to the glymphatic mechanism, almost all of these treat it as accepted dogma and do not test the assumptions or the evidence on which it is based. At present it would be better to refer to perivascular elimination and delivery of substances without prejudice to the mechanism(s) by which these are achieved.