Estimates of the permeability of extra-cellular pathways through the astrocyte endfoot sheath

Abstract

Abstract Background Astrocyte endfoot processes are believed to cover all micro-vessels in the brain cortex and may play a significant role in fluid and substance transport into and out of the brain parenchyma. Detailed fluid mechanical models of diffusive and advective transport in the brain are promising tools to investigate theories of transport. Methods We derive theoretical estimates of astrocyte endfoot sheath permeability for advective and diffusive transport and its variation in microvascular networks from mouse brain cortex. The networks are based on recently published experimental data and generated endfoot patterns are based on Voronoi tessellations of the perivascular surface. We estimate corrections for projection errors in previously published data. Results We provide structural-functional relationships between vessel radius and resistance that can be directly used in flow and transport simulations. We estimate endfoot sheath filtration coefficients in the range $$L_p=2\times 10^{-11}\,\hbox {m}\,\hbox {Pa}^{-1}\,\hbox {s}^{-1}$$ L p = 2 × 10 - 11 m Pa - 1 s - 1 to $$3\times 10^{-10} \,\hbox {m}\,\hbox {Pa}^{-1}\,\hbox {s}^{-1}$$ 3 × 10 - 10 m Pa - 1 s - 1 , diffusion membrane coefficients for small solutes in the range $$C_M= 5 \times 10^{2}\,\hbox {m}^{-1}$$ C M = 5 × 10 2 m - 1 to $$6\times 10^{3}\,\hbox {m}^{-1}$$ 6 × 10 3 m - 1 , and gap area fractions in the range 0.2–0.6%, based on a inter-endfoot gap width of 20 nm. Conclusions The astrocyte endfoot sheath surrounding microvessels forms a secondary barrier to extra-cellular transport, separating the extra-cellular space of the parenchyma and the perivascular space outside the endothelial layer. The filtration and membrane diffusion coefficients of the endfoot sheath are estimated to be an order of magnitude lower than those of the extra-cellular matrix while being two orders of magnitude higher than those of the vessel wall.