Maintenance of brain ISF composition
Some substances in ISF simply need to be expelled, others must be eliminated in a more controlled manner to allow a stable concentration. For most xenobiotics or waste products, the objective is simply to get rid of the substance and keep the extracellular concentration as low as is practical. However, for a number of substances, the objective is to achieve the proper balance between influx, production, consumption and elimination so that their ISF concentrations can be kept within an acceptable range. The objective in this section is to consider how control of ISF concentrations is achieved.
There are several substances whose ISF concentrations must be kept within narrow limits to ensure correct neuronal function. Na+, Cl− and K+ are good examples. Regulation of Na+ and Cl− amounts and concentrations is inextricably linked to the control of extracellular fluid volume and intracranial pressure and is outside the scope of this review (for some discussion see [41]). The control of K+ and HCO3− ISF concentrations was considered in [4]. The following sections consider the general principles and the control of ISF concentrations of CO2 and glucose.

General principles of concentration maintenance: balancing input and output. CO2 as an example
The concentration of a substance can only be maintained at a constant level if its rate of elimination, Relim, is equal to its rate of input, Rin,11 Relim=Rin.
If input exceeds elimination the concentration will increase; if it is less the concentration will decrease. In the face of a given rate of input, be it by influx from outside or local production within the brain, a steady-state can only be achieved if the elimination rate can increase far enough to balance the input (see input Rin2 in Fig. 22a). A steady-state is not possible if elimination is unable to match input (see input at level 2) and under these conditions the concentration will continually increase. Thus it is the relative rates of input and elimination, rather than the rate of input itself that is of primary importance.
Fig. 22 The relation between the rate of elimination of a substance and its concentration. The solid curve in a and line in b show the rate of elimination as a proportion of its possible maximum versus concentration. Possible rates of input are shown as the dashed lines. In a if the rate of input is Rin,1 which is less than the maximum possible rate of elimination, Relim,max, the concentration can be maintained at css. If the rate of input is Rin,2, which exceeds Relim,max, no steady-state is possible and the concentration continually increases. At low concentrations as shown in detail in b the rate of elimination is usually proportional to concentration
The rate of elimination of a substance from the brain parenchyma is determined by its concentration and the ability of the efflux mechanisms to remove the substance. This ability is usually described as the clearance. For a substance eliminated by a single type of transport, the clearance is determined by the number of transporters, the affinity-constant for the substrate and the transporter and the maximum turnover rate. Clearance can be calculated from measurable quantities as12 CL=Relim/c.where Relim is the rate of elimination and c is the concentration of the substance. At sufficiently low concentrations the relation between elimination rate and concentration is linear and the clearance is a constant (see Fig. 22b). At higher concentrations (see Fig. 22a) the relation is no longer linear and the clearance decreases as concentration increases.
The larger the clearance, the higher the rate of elimination possible at any given concentration (see Fig. 23a) and therefore the lower the concentration needed to achieve an elimination rate equal to a particular rate of input, Rin, (see Fig. 23b), i.e.13 c=Rin/CL.
Fig. 23 The relationship between the rates of input and elimination, substrate concentration in ISF and clearance. At steady-state the rate of elimination must equal the rate of input. The horizontal dashed lines show rates of input (R1, R2, R3 and Rin). The clearance, CL, is the slope of the line for the plot of rate of elimination versus concentration. Lines for three values of clearance (CL1, CL2 and CL3) are shown. a To achieve the steady-state concentration, cisf, clearance must be higher to balance the higher rate of input i.e. the rate of input required is proportional to clearance. b For a given rate of input, the steady-state concentration is inversely proportional to CL (compare the three steady state concentrations c1 c2 and c3 achievable for the three clearance values CL1, CL2 and CL3). c For a given clearance the steady-state concentration is proportional to the rate of input. Changes in input need not produce changes in concentration if the clearance can be changed, e.g. for the increase from R1 to R3 shown in a the concentration would be constant if the clearance could be increased from CL1 to CL3
When the clearance is constant, changes in input (R1, R2, R3 in Fig. 23c) lead to proportional changes in steady-state concentration. Such changes in ISF concentration may be fine if the ISF concentration is not critical. Constant clearance avoids the disasters that could occur if the elimination rate could not increase with ISF concentration because then increased rate of input would produce progressively increasing concentration within the parenchyma.
If close control of ISF concentration is required there must either be some means to reduce or prevent changes in input or the clearance must alter. When input is from plasma one way in which changes in input can be made less sensitive to plasma concentration is for the input mechanism to be operating not too far from its maximum rate, i.e. for the substrate concentration in plasma to be well above the Km for the input mechanism. However, the same limitation may apply to efflux as to influx, with the resulting changes in ISF concentration difficult to predict (e.g. for glucose, see Fig. 14 and Appendix D).
If input is determined by production within the parenchyma, closer control in the face of variable input than would be seen for constant clearance must be achieved by altering the mechanisms of elimination to change the clearance. In order for the system to be modified some sort of signal is required ‘to inform’ the elimination system that the input and/or the concentration has changed.
In principle this can be done by feedback control in which increased concentration somehow modifies the mechanism of elimination to increase the clearance, e.g. by recruiting more transporters. To some extent this occurs with CO2. Increased pCO2 is associated with lower pH and stimulation of cerebral blood flow, which washes away the excess CO2 (see Sect. 5.2), i.e. increased pCO2 increases the clearance for CO2. However, feedback control still requires that there be a change in the concentration to stimulate and maintain the process (see Fig. 24).
Fig. 24 Diagram illustrating possible schemes for neurovascular coupling, i.e. regulation of blood flow changes associated with nerve activity. Two forms of control are shown, a simple feedback based on the signal to be regulated, e.g. pCO2, and b feedback plus feed-forward. The feed-forward element, signal2, in b, possibly from astrocytes, allows blood flow to increase with smaller changes in the primary quantity to be regulated, signal1
(Figure reproduced from [4])
Closer control is possible with feed-forward regulation, in which the change in input itself or something closely linked to the input stimulates the change in clearance whether or not the concentration changes. In principle the control could be perfect if somehow a change in input rate could produce proportional change in clearance as indicated in Fig. 23a. It is now clear that increased brain activity, which increases production of CO2, increases blood-flow even without increases in CO2 concentration. This process, called neurovascular coupling [515, 516], is considered in more detail in [4] which can be consulted for further references.
When substrate elimination is limited by transport across the blood–brain barrier rather than by blood-flow, the clearance can be increased by inserting more transporters, by increasing the activity of each transporter, i.e. an increase in the turnover rate or, if the transport isn’t saturated by increasing the affinity of the transporter for the substrate.

Achieving a net flux: glucose as an example
There is regulation of transport across the blood–brain barrier both for glucose and for ions like Na+, K+ or Cl−. Regulation of glucose transport serves primarily to achieve the correct flux to support metabolism whereas regulation of ion transport is important to maintain the correct concentrations in extracellular fluid. The actual glucose concentration in ISF is relatively unimportant so long as it remains well above the Km for hexokinase (0.04–0.05 mM, see Sect. 5.3) but low enough to avoid formation of unwanted glycation products. The requirements for the regulation of the glucose transporter, GLUT1, were considered in detail by Barros et al. [314] and Simpson et al. [315]. Thus this section considers only the principles and the extent to which regulation can be obtained by altering glucose efflux.
GLUT1 transport across the blood–brain barrier must be capable of producing a net flux that is equal to the cerebral metabolic rate for glucose, CMRglc, at all times both at rest and during nervous activity. Furthermore the system must be capable of increasing net flux quickly to match demand. If the net inward flux were not increased, then for a glucose content in brain of 1.3 mM × 0.77 mL g−1 and an increase in glucose consumption rate of 0.65 µmol g−1 min−1 (i.e. to twice resting level, figures for rats), the entire glucose reserve would be consumed in < 2 min.
CMRglc of stimulated nervous tissue isn’t easy to measure, partly because a region large enough to assay is likely to contain both stimulated and unstimulated tissue. Using quantitative autoradiography in rats exposed to monotonic sounds, Cruz et al. [517] were able to see as much as 85% increase in CMRglc in tonotopic bands of the inferior colliculus. Using PET imaging in human subjects viewing a reversing checkerboard pattern, Fox et al. [518] saw 50% increases in the visual cortex. Using measured arterio-venous concentration differences in human volunteers undergoing exhausting cycling or rowing exercise, Quistorff et al. ([353], data from [519]) found more than twofold increases in glucose uptake rate across the blood–brain barrier. (There was also a substantial uptake of lactate). From these and other studies, in order to support nervous activity it must be possible to increase the net flux across the blood–brain barrier by at least twofold within a few minutes.
There are three important steps in the delivery of glucose: arrival in the blood; net transport across the blood–brain barrier; subsequent diffusion to the sites of hexokinase. At rest, the blood flow delivers 5–10 times more glucose than does the net flux across the blood–brain barrier into the parenchyma. As a consequence the glucose concentrations in arterial blood and the capillaries are similar, and increasing blood flow can only produce modest changes in capillary concentration and the net inward flux into the parenchyma. Both diffusion within the parenchyma and transport across astrocyte and neuron membranes have been found to be fast (see Sect. 5.3). Thus the rate-limiting step in delivery of glucose to regions where it is required in the parenchyma is its transfer across the blood–brain barrier.
Increased glucose consumption by cells within the parenchyma will reduce glucose cisf and so reduce glucose efflux, resulting in increased net inward flux. Because the Michaelis–Menten constant, Km, for hexokinase is so low, the concentrations of glucose inside the cells and in ISF can be reduced to values much smaller than that found during times of low nervous activity. The size of this effect can be seen in the data of Betz et al. [327] as described in Appendix D. From that analysis there would be an increase of about 40% in the net inward flux, even if there were no change in transport capacity.22 Decreased glucose efflux is an important part of the response to increased nervous activity but it is not sufficient on its own to support demand [314, 315, 322]. Decreased efflux has the advantage that it occurs rapidly with the increase in glucose demand.
Changes in GLUT1 transporter expression have been documented and reviewed elsewhere [322, 336, 520]. However, such changes are too slow to provide minute to minute changes in response to nervous activity. As discussed by Cura et al. [322] there are two types of changes that may occur quickly (see following), one is recruitment of additional preformed GLUT1 from intracellular stores and the other is an increase in transport rate for the existing GLUT1. Both may be occurring. There are suggestions that these changes may result in large effects, but there is no clear evidence of which if any are important at the blood–brain barrier.
With regard to GLUT1 recruitment to the cell surface, it can be detected not only on the luminal and abluminal membranes but also on vesicle membranes within the cytoplasm of brain endothelial cells [521]. Early studies on recruitment in a number of tissues were reviewed by Carruthers [328]. Subsequently it has been found that activation of AMP protein kinase (AMPK) by AMP when AMP is produced from ATP in response to nerve activity can in turn lead to recruitment to the cell surface. With cell culture systems including brain endothelial cells recruitment in response to AMP can be large, resulting in a two to threefold increase in GLUT1 at the plasma membrane [322, 522, 523].
With regard to modification of GLUT1 transport rate, it is known from studies on red blood cells that GLUT1 can be substantially inhibited by binding of ATP, an effect that is inhibited by AMP. When ATP hydrolysis is stimulated, ATP concentrations decrease and AMP concentrations increase, both of these events acting to release inhibition of GLUT1 [322, 524]. This effect can be large, a four to tenfold increase in glucose transport. Because increased AMP can increase both recruitment and activity of GLUT1 at the cell surface, it is easily imagined that small changes in AMP levels in endothelial cells could increase glucose transport sufficiently to support increased nervous activity.