PMC:6194691 / 230057-237405 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/6194691","sourcedb":"PMC","sourceid":"6194691","source_url":"https://www.ncbi.nlm.nih.gov/pmc/6194691","text":"Appendix E. Blood–brain barrier permeabilities of Na+, K+ and Cl−\nDetermining the permeabilities of the blood–brain barrier for Na+, K+ and Cl− was a major challenge because these ions are transferred between blood and the parenchyma by two routes, directly across the blood–brain barrier and indirectly via CSF. Davson and Welch [417] calculated permeabilities for the blood–brain barrier in rabbits by fitting data for accumulation of tracers in CSF and the parenchyma simultaneously using a simplified, but still complicated, model that allowed for transfers directly between blood and ISF, between blood and CSF and between CSF and ISF. While the model allowed the concentration of tracer in CSF to vary with time, it assumed that there was no variation with position, i.e. that the concentration was the same throughout the ventricles, cisterns and subarachnoid spaces. The model was based on equations that do allow the concentration to vary with position within the parenchyma, but no measurements of the variation were made. Davson and Welch’s approach suffers from the inevitable shortcomings associated with fitting a complicated model to limited data.\nUsing rats, Smith and Rapoport [419] took the more direct experimental approach of measuring the accumulation of tracer within the parenchyma at sites sufficiently far from the choroid plexuses, e.g. the frontal cortex, that, at least initially, entry had to be across the blood–brain barrier. They allowed accumulation to proceed for only 10 min which they reasoned was short enough that they could ignore both backflux from parenchyma to blood and indirect transfer from blood to CSF to parenchyma. One of the arguments that the permeabilities of the blood–brain barrier calculated by Davson and Welch and by Smith and Rapoport are at least reasonable approximations is that these two very different approaches yielded similar answers.\nThere is, however, an apparent difficulty with accepting the values calculated by Smith and Rapoport. Their analysis of the time course of the concentrations within the cortex started with their Eq. 1,40 dcbrx,tdt=PScplasma-PS′cbrx,tVbr+DVbrd2cbrx,tdx2,which is dimensionally inconsistent. In this equation cbr(x,t) is the concentration of tracer in the parenchyma, units dpm g−1; P is the permeability of the blood–brain barrier, units cm s−1; S is the area of the blood–brain barrier, units cm2 g−1; cplasma is the concentration in plasma, units dpm cm−3; Vbr is the volume of distribution of the tracer substance, units cm3 g−1; D is the diffusion constant of the tracer in the extracellular fluid, units cm2 s−1, x is distance from the ventricular surface, units cm; and t is the time, units s. The units of the first two terms on the right hand side, those which describe blood–brain barrier transport, are dpm s−1 g−1, which is the same as for the left hand side, but the units of the third term, which describes diffusion within the cortex, are dpm s−1 cm−3. Terms with different units cannot be added together, thus this equation cannot be correct.\nOn closer inspection of Eq. 40 and the model on which it is based, the conversion factor in the third term, Vbr, is wrong (if the substance is restricted to the extracellular space, Vbr should simply be omitted [553]) but in addition there are more fundamental difficulties. The model is based on at least two unstated assumptions that limit its use: it is assumed that the only movement of ions through the cortex is via diffusion in the extracellular space and that there is no exchange of substance with CSF in the sub-arachnoid spaces. (The first of these shortcomings also compromises the analysis by Davson and Welch [417]). At least for K+ it is clear that movements within cell processes make an important contribution to movements within the cortex, so called spatial buffering (see e.g. [554–556]). As can be seen from Gardner-Medwin’s papers, if the tracer can enter and leave cells on the time scale of the experiments a proper description of the third term on the right hand side of Eq. 40 would be very complicated. The second assumption becomes important if perivascular clearance is comparable to the clearance across the blood–brain barrier (see end of this Appendix).\nAn immediate consequence of the use of Smith and Rapoport’s starting equation is that calculation of the concentrations within the parenchyma cannot be relied upon whenever these concentrations vary with position, as in their Fig. 6, unless the substance in question cannot enter the cells and all positions considered are far from perivascular spaces and the brain surfaces.\nFortunately, Smith and Rapoport designed their experiments in such a way that the calculation of the transfer constants and permeabilities for the blood–brain barrier does not depend on how the model describes diffusion within the parenchyma. Their Eq. 4 for the transfer constant, taken from Fenstermacher and Rapoport [159] yields constants with units cm3 s−1 g−1. Their actual calculations leading to the values in their Table 2 were equivalent to using an equation,41 kbr=cbrT/V¯brain∫0Tcplasmadt,which incorporates a conversion factor between the mass and volume of the brain, V¯brain assumed to be 1 cm3 g−1. In this equation the units of kbr are s−1; cbr(T), units dpm g−1, is the total concentration per gram of tissue; T, units s, is the period of time during which influx occurs; and cplasma is the concentration in plasma, units dpm cm−3. Smith and Rapoport assumed that cplasma was constant so that the integral becomes the product cplasma × T and42 kbr=cbrTcplasmaTV¯brain.\nThe rate of change of the concentration within the brain can be related to the permeability and area of the blood–brain barrier using43 dcbrtdt=PScplasmawhich, using the same assumptions needed for Eq. 42, integrates to44 cbrT=PScplasmaT.\nCombining Eqs. 42 and 4445 P=cbrTcplasmaTS=kbrV¯brainS.\nSmith and Rapoport used S = 140 cm2 g−1 from [557], and a tissue volume per gram, V¯brain = 1 cm3 g−1, leading to the values of P (in cm s−1) quoted in their Table 3. (Eq. 44 shows that the PS product, which is the estimate of the clearance, does not depend on the values assumed for either V¯brain or S. For Na+ PS was 2 × 10−5 cm3 s−1 g−1 = 1.2 µL min−1 g−1. This is similar to estimates of perivascular clearance, ~ 1 µL min−1 g−1 (see Sect. 3.2).\nThe PS product for K+ was [419] 11.3 µL min−1 g−1. This larger value is based on fluxes that were somewhat smaller than those for Na+ but at substantially smaller concentrations, e.g. 4 mM rather than 140 mM. Unlike those for Na+, the fluxes for K+ can be substantially reduced by inhibitors of transporters known to be present in the endothelial cells (reviewed in [4]).\nThe model used by Smith and Rapoport ignores exchange of substance between the parenchyma and CSF in the sub-arachnoid spaces, i.e. it ignores perivascular transport. However, for the same reason that backflux from parenchyma to blood does not alter the initial rate of increase in concentration within the parenchyma, loss to CSF will also not alter the initial rate and thus the calculation of PS. However, once concentrations in parenchyma and CSF increase, net perivascular fluxes for Na+ will be comparable to the net fluxes across the blood–brain barrier and thus cannot be ignored in calculations of the time course.","divisions":[{"label":"title","span":{"begin":0,"end":65}},{"label":"p","span":{"begin":66,"end":1162}},{"label":"p","span":{"begin":1163,"end":1900}},{"label":"p","span":{"begin":1901,"end":3057}},{"label":"label","span":{"begin":2102,"end":2104}},{"label":"p","span":{"begin":3058,"end":4243}},{"label":"p","span":{"begin":4244,"end":4619}},{"label":"p","span":{"begin":4620,"end":5606}},{"label":"label","span":{"begin":5089,"end":5091}},{"label":"label","span":{"begin":5579,"end":5581}},{"label":"p","span":{"begin":5607,"end":5845}},{"label":"label","span":{"begin":5740,"end":5742}},{"label":"label","span":{"begin":5826,"end":5828}},{"label":"p","span":{"begin":5846,"end":5901}},{"label":"label","span":{"begin":5870,"end":5872}},{"label":"p","span":{"begin":5902,"end":6352}},{"label":"p","span":{"begin":6353,"end":6724}}],"tracks":[]}