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Table 1 Average parameters computed for two microvascular networks

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

Symbol

MVN1

MVN2

Unit

Description

\(S_C\)

\(8.5\times 10^{-6}\)

\(1.2\times 10^{-5}\)

\(\hbox {m}^{2}\)

endfoot sheath surface area (C)

\(S_A\)

\(3.2\times 10^{-7}\)

\(7.5\times 10^{-7}\)

\(\hbox {m}^{2}\)

endfoot sheath surface area (A)

\(S_V\)

\(2.6\times 10^{-7}\)

\(4.6\times 10^{-7}\)

\(\hbox {m}^{2}\)

endfoot sheath surface area (V)

S

\(9.1\times 10^{-6}\)

\(1.3\times 10^{-5}\)

\(\hbox {m}^{2}\)

endfoot sheath surface area (all)

V

\(5.5\times 10^{-10}\)

\(6.9\times 10^{-10}\)

\(\hbox {m}^{-3}\)

total sample volume (bounding box)

\(\zeta\)

\(2.8\times 10^{-2}\)

\(3.4\times 10^{-2}\)

–

volume fraction vessel (outer)

\(\zeta ^L\)

\(1.0\times 10^{-2}\)

\(1.2\times 10^{-2}\)

–

volume fraction vessel (lumen)

S/V

\(1.7\times 10^{4}\)

\(1.9\times 10^{4}\)

\(\hbox {m}^{2}\hbox {m}^{-3}\)

surface to volume ratio (outer surface)

\(S^{L}/V\)

\(1.0\times 10^{4}\)

\(1.2\times 10^{4}\)

\(\hbox {m}^{2}\hbox {m}^{-3}\)

surface to volume ratio (lumen surface)

  1. MVN1 and MVN2 are networks extracted from the mouse cortex [19]. Capillaries (C) are defined as vessels with \(r_{\textrm{v}} < 3.0\,\upmu \hbox {m}\). Venous (V) and arterial (A) vessel segments (\(r_{\textrm{v}} \ge 3.0\,\upmu \hbox {m}\)) are distinguished by local blood pressure (see Methods). Pial vessels are excluded from the analysis. Outer surface refers to the endfoot sheath surface. The surface area is computed on the basis of circular cross-secitons and estimated \(r_{\textrm{o}}\) (outer radius including endfoot sheath, see Methods). Surfaces and volumes are based on the assumption of cylindrical segments with radius \(r_{\textrm{v}}\) (lumen, L) or \(r_{\textrm{o}}\)