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Fig. 2 | Fluids and Barriers of the CNS

Fig. 2

From: Functional hyperemia drives fluid exchange in the paravascular space

Fig. 2

Modeling fluid flows and induced pressures while ignoring brain deformability. Note the geometry is depicted with an unequal aspect ratio in the radial (r) and axial (z) directions for viewing convenience. a Geometry of the PVS in in our model. The outer wall of the arteriole is shown in dark orange and the boundary of the brain parenchyma is shown in pink. The dashed line represents the centerline of the arteriole. The inset shows the imposed heartbeat-driven pulsations in arteriolar radius (± 0.5% of mean radius [16], Ri) at 10 Hz, the heartrate of an un-anesthetized mouse. The pulse wave travels at 1 m per second along the arteriolar wall, into the brain [57, 58] (blue arrow). The flow through the SAS and the brain parenchyma was modelled by flow resistances (shown in blue and magenta respectively). In (b) and (c) a cross section of the PVS is shown together with the surrounding arteriolar wall (on the left) and brain tissue (on the right). b Plot of the fluid velocity induced in the PVS by the arteriolar pulsation. Contour showing the axial velocity (velocity in the z-direction) in a cross-section of the PVS. The colors indicate the direction and magnitude of flow. Fluid velocity vectors (arrows) are provided to help the reader interpret the flow direction from the colors. Heartbeat pulsations drive negligible unidirectional flow with a mean flow speed(-[vz]) of 5.5 × 10−4 µm/s. To make the arteriolar wall movements clearly visible, we scaled the displacements by a factor of 10 in post-processing. c Fluid pressure in the PVS corresponding to the flow shown in (b). Pressure changes due to fluid flow in the PVS reach several mmHg. These pressures will deform the soft brain tissue, which has a shear modulus of 1–8 kPa [63, 144] (8–60 mmHg). The dotted line shows the estimated deformation in the brain tissue (shear modulus 4 kPa–Kirchhoff/De Saint–Venant elasticity with Poisson ratio of 0.45) from the pressure shown in the figure. Under these assumptions, the deformations in the brain tissue are 60 times bigger (3.59 µm) in magnitude compared the peak of heartbeat driven pulsations (0.06 µm—shown on inset in (a)). Therefore, the deformability of brain tissue cannot be neglected

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