Figure 3. Anisotropy of the cerebral microvascular network and its fluid conductance.

(A) Flow chart of the fluid conductance simulation. From left to right: original traced data (red for large vessels with radius >5 μm and green for small vessels), applying a pressure profile on the surface of the control volume with a gradient profile and solving the coincide flux equation set for the flow tensor, the annotation rule of the flow tensor, and the sampling dots of the numerical spherical integration. l, perfusing length; P, pressure; Q, fluid flux; R, resistance; μ, viscosity; k, fluid conductance; Δ, changing of the quantity; ·, dot product; ∇, gradient; ∯s, spherical integral; S, spherical surface; n, normal direction; bold font, vector; double top bar, tensor.

(B) Examples illustrating how the structure of the vasculature network affects the flow tensor.

(C–E) Microvessel anisotropy measurement in the isocortex.

(C) Microvessel directionality in cortical layers. Only the dominant direction is displayed for simplicity. Microvessels are colored based on their orientation: magenta for penetrating (P), cyan for anterior-posterior (AP), and yellow for medial-lateral (ML). Shown are examples from the secondary motor cortex (MOs; D) and primary SS barrel field (SSp-bfd; E) cortices. Left: coronal view. Right: sagittal view. The color of individual vessels in the top panel (full-resolution images of the yellow boxed areas in the bottom left panel) represents three directions as in (C). White lines in the top panel denote anatomical annotations from the bottom right. Note the differences in dominant vessel directions based on brain regions and cortical layers.

(F) Fluid conductance results in the cortical flatmap.

(G and H) Relationship between fluid conductance and vessel length density (G) or average radius (H). See Table S7 for full data and abbreviations.