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 |