Fig 1.
To study the mechanisms behind perivascular fluid flow, we extracted an image-based bifurcating arterial geometry (A) and generated a computational model of a surrounding perivascular space (B) subjected to different forces: arterial wall deformations (red arrows), systemic pressure variations (blue arrows) and rigid motions (black arrows) (C) to predict the induced CSF flow and pressure (D). Scale bar: 0.05 mm.
Table 1.
Summary of computational models of pial surface PVS flow represented by the time-dependent Stokes equations over a moving domain.
Fig 2.
Overview of the computational mesh generation.
A) The artery geometry was extracted from the Aneurisk dataset repository [38] (case id C0075) and clipped. B) The domain center line was computed using VMTK, and subsequently used to define the extruded PVS. The color indicates the distance from the center line to the vessel wall. A finite element mesh was generated of the full geometry (including both the artery and the PVS) (C), before the outer PVS mesh (D) was extracted for simulations.
Fig 3.
Top panel: Snapshots of CSF velocity and pressure at the time of peak velocity (or t = 0.048 s) for models A–D. Pressure is shown everywhere with opacity, while velocity profiles are shown for given slices along the PVS (A, B) or as streamlines (C, D). A) With arterial wall deformations as the only driving force, pressure reaches a maximum close to the bifurcation, and velocity is stagnant at this point in space. As the artery expands, fluid flows in different directions within the PVS, always out of the domain, and velocities increase towards the inlet and outlet of the PVS. B) Adding a static pressure gradient of 1.46 mmHg/m (0.195 Pa/mm) results in higher peak velocities and less backflow, but oscillations due to arterial pulsations are still prominent. The pressure increases, but flow patterns are visually similar to (A). Differences can be seen in magnitude of flow at the inlets and outlets. C) A sinusoidally varying pressure gradient did not change the general flow pattern seen in (A, B) with parallel streamlines. D) Rigid motion of the artery caused less orderly CSF flow with more complex streamline patterns. E) Detailed flow patterns of the movement around bifurcations from (A). Slow flow close to the bifurcation is observed. F) Time profiles of the average normal velocity at the inlet for the four different models are similar, but differ in somewhat in shape during diastole. Negative values here correspond to flow downwards (in the direction of the net blood flow), while positive values correspond to flow upwards. G) Close-up on F) demonstrating that peak velocities are nearly identical for each model. H) Position plots of particles at the inlet indicating net flow only when a static pressure gradient is included. Net flow velocity at the inlet was 28μm/s.
Fig 4.
A) Streamlines (colored by velocity magnitude) during systole for model A, with arterial expansion as the only driver for PVS flow. Flow is slower in the central parts of the geometry and increase towards the inlets/outlets. Due to the low Reynolds number, there are no recurrent patterns of flow in or around the bifurcation. Note that the streamlines seem to originate out from the arterial wall as a response to the expansion of the artery. B) Velocity distribution in a slice close to the bifurcation reveals bidirectional flow. Bidirectional flow suggests possibilities for recirculation regions and circular flow patterns, but this was not observed in the streamlines shown in A). C) Streamlines during diastole. Streamlines are nearly identical during diastole and systole because of the low Reynolds numbers. D) Velocity distribution during diastole in the same slice as in B) shows reversal of flow direction and lower velocity magnitudes compared to systole.
Fig 5.
PVS flow predictions at a reduced arterial frequency and non-zero static pressure gradients compared with experimentally observed microsphere paths.
A) Extraction of rigid arterial motions and three sample microspheres (p1, p2, p3) from experimental reports by Mestre et al [2]. (Figure based on images adapted from [2, S2 Movie] (CC BY 4.0)). Red arrows illustrate the rigid motion of the vessel with a peak amplitude of ≈ 6μm. B) Position (relative to each starting point) over time of model particles suspended at the PVS inlet and left outlet (2.2 Hz, static pressure gradient of 1.46 mmHg/m) compared to microsphere paths.
Fig 6.
Compliance and resistance change flow characteristics, but not net flow.
A) Peak pressure occurs at the outlets during systole when accounting for compliance and resistance downstream. B) The pressure is similar at each outlet, but differ in time of peak and peak value. At the inlet, the pressure is always close to 0. C) Fluid velocity at the inlet and outlets. Compliance and resistance at the outlets restrict flow over these boundaries. The inflow velocity is more than four times larger than the outflow velocities. Peak velocity occurs earlier at the outlets than at the inlet, as the pressure at the outlets increase as fluid starts to move out. Net flow is still negligible (net flow velocity <0.2μm/s).
Fig 7.
PVS model length modulates velocity.
A) The average normal velocity at the inlet in idealized PVS models increases with increasing model length. B) Position of a particle moving with the velocity at the inlet. Net flow velocities (in parenthesis for each model length in the legend) are small compared to the large average normal velocity amplitudes, but can reach up to 7 μm/s for the longer models (100 mm). C) Schematic of the idealized axisymmetric model. For long wavelengths, the displacement is almost uniform along the PVS. Increased PVS length will thus increase velocity at the model ends as more fluid needs to escape the domain.