A model for the blood–brain barrier permeability to water and small solutes

The blood–brain barrier (BBB) has unique structures in order to protect the central nervous system. In addition to the tight junction of the microvessel endothelium, there is a uniform and narrow matrix-like basement membrane (BM) sandwiched between the vessel wall and the astrocyte foot processes ensheathing the cerebral microvessel. To understand the mechanism by which these structural components modulate permeability of the BBB, we developed a mathematical model for water and solute transport across the BBB. The fluid flow in the cleft regions of the BBB were approximated by the Poiseuille flow while those in the endothelial surface glycocalyx layer (SGL) and BM were approximated by the Darcy and Brinkman flows, respectively. Diffusion equations in each region were solved for the solute transport. The anatomical parameters were obtained from electron microscopy studies in the literature. Our model predicts that compared to the peripheral microvessels with endothelium only, the BM and the wrapping astrocytes can reduce hydraulic conductivity (Lp) of the BBB and the permeability to sodium fluorescein (PNaF) by up to 6-fold when the fiber density in the BM is the same as that in the SGL. Even when the SGL and the tight junctions of the endothelium are compromised, the BM and astrocyte foot processes can still maintain the low Lp and PNaF of the BBB. Our model predictions indicate that the BM and astrocytes of the BBB provide a great protection to the CNS under both physiological and pathological conditions.