A transport model for the blood-brain barrier

The blood-brain barrier (BBB) has unique structures in order to protect the central nervous system (CNS). In addition to the tight junction of the brain blood microvessel, there is a uniform and narrow matrix-like basement membrane layer (30-40 nm) sandwiched between the vessel wall and the astrocyte processes ensheathing the cerebral microvessel. To understand the mechanism by which these structural components modulate permeability of the BBB, we developed a new mathematical model for water and solute transport across BBB. The flows in the cleft of the tight junction and in the slit between astrocyte process end feet were approximated by a Hele-Shaw channel flow while the fiber matrix layer at the luminal surface of the vessel was modeled as a Darcy medium and that in the basal lamina as a Brinkman medium. The solute transport through the BBB region was considered as a pure diffusion process. The predicted hydraulic conductivitv (L_p) is 7.2 times 10^-9cm/s/cmH₂O and the predicted solute permeability (P) for sodium fluorescein (NaF, MW = 376) is 6.3 times 10^-6 cm Is for the BBB in the pia mater at the surface of the CNS. The resistance from the basement membrane and astrocytes accounts for ~7 folds and ~4 folds of those from the vessel wall components for L_p and P^NaF, respectively. Our results suggest that they are components modulate permeability of the BBB to water and solutes through mathematical modeling. significant contributors permeability.