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Table 2 Summary of Simulations

From: Functional hyperemia drives fluid exchange in the paravascular space

Figure Brain model Fluid permeability (m2) Arteriolar wall movement Mean downstream speed (µm/s) PVS fluid exchanged with SAS Conclusion
2 Non-compliant 2 × 10−14 Heartbeat ∆Rmax = 0.06 µm 5.5 × 10−4 Expected brain deformation, 3.59 µm > pulsation amplitude, 0.06 µm
3 SVK, µs = 4 kPa (compressible) 2 × 10−14 Heartbeat ∆Rmax = 0.06 µm 2.6 × 10−3 0.21% No appreciable fluid exchange
4 SVK, µs = 4 kPa (compressible) 2 × 10−14 Hyperemia ∆Rmax = 1.8 µm 0.12 49.46% Appreciable fluid exchange by hyperemia
5b SVK, µs = 1–8 kPa 2 × 10−14 Heartbeat/Hyperemia ∆Rmax = 0.06/1.8 µm Heartbeat 0.09–0.29%
Hyperemia
26.96–59.55%
Fluid exchange of hyperemia ≈ 200 × fluid exchange of heartbeat
5c SVK, µs = 4 kPa 2 × 10−14
PVS width = 3-9 µm
Heartbeat/Hyperemia ∆Rmax = 0.06/1.8 µm Heartbeat 0.08–0.21%
Hyperemia
17.88–49.46%
Fluid exchange of hyperemia ≈ 200 × fluid exchange of heartbeat
5d SVK, µs = 4 kPa 2 × 10−15 –7 × 10−13
&
∞ (Navier–Stokes)
Heartbeat/Hyperemia ∆Rmax = 0.06/1.8 µm Heartbeat 0.06–1.37%
Hyperemia
17.85–70.55%
Fluid exchange of hyperemia ≈ 200 × fluid exchange of heartbeat
5 h SVK, µs = 4 kPa 2 ×  × 10−14 ∆Rmax = 0.24 µm Frequency, f = 0.05-10 Hz \(Q_{f} = 2.33f^{ - 0.57}\) Fluid exchange is inversely related to frequency of arteriolar wall movement
S1 Non-compliant ∞ (Navier–Stokes) Heartbeat ∆Rmax = 0.06 µm 1.8 × 10−3 Expected brain deformation, 0.08 µm > pulsation amplitude, 0.06 µm
S2 Non-compliant 2x10−14
No SAS/parenchyma flow resistances
Heartbeat ∆Rmax = 0.06 µm 2.6 × 10−3 Expected brain deformation, 0.71 µm > pulsation amplitude, 0.06 µm
S3 Non-compliant 2 × 10−14
Arteriole length = 100 mm
Heartbeat ∆Rmax = 0.06 µm 143.2 Flow accompanied by 200,000 mmHg pressure changes
S4 Neo-Hookean, µs = 4 kPa (incompressible) 2 × 10−14 Heartbea ∆Rmax = 0.06 µm 1.1 × 10−4 0.18% No appreciable fluid exchange
S5 SVK, µs = 4 kPa (compressible) 2 × 10−14
SAS geometry explicitly modeled
Heartbeat ∆Rmax = 0.06 µm 2.6 × 10−3 0.23% No appreciable fluid exchange
S6 SVK, µs = 4 kPa (compressible) 2 × 10−14 Hyperemia ∆Rmax = 1.8 µm 0.12 49.46% Tissue displacement has a typical waveform
S7 Neo-Hookean, µs = 4 kPa (Incompressible) 2 × 10−14 Hyperemia ∆Rmax = 1.8 µm 0.13 50.92% Appreciable fluid exchange
S8 SVK, µs = 4 kPa (compressible) 2 × 10−14
SAS geometry explicitly modeled
Hyperemia ∆Rmax = 1.8 µm 0.12 49.66% Appreciable fluid exchange