Table 2.
Summary of Simulations
| 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 | – | 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 |