Phase offset between arterial pulsations and subarachnoid space pressure fluctuations are unlikely to drive periarterial cerebrospinal fluid flow

Abstract

Circulation of fluid through the central nervous system maintains fluid homeostasis and is involved in solute clearance. The glymphatic system is hypothesised to facilitate waste clearance in the brain, with inflow via periarterial spaces, bulk flow through the parenchyma, and outflow via perivenous spaces. The driving force for this mechanism is unknown. Previous modelling in the spinal cord suggests that timing offsets between arterial and subarachnoid space pressure pulses can enable net inflow in perivascular spaces (PVS). This study adapted the spinal pulse offset mechanism to the brain and simulated movement of tracer particles used in experiments. Both bulk flow and diffusive movement of tracer were simulated. Intracranial pressure pulses were applied to one end of a 300-μm-long perivascular space combined with a moving arterial wall simulating arterial pulsations. The simulations indicate the pulse offset mechanism can enable net inflow via PVS; however, it is unknown whether the temporal offset required is physiologically realistic. Increasing the positive component of the ICP (intracranial pressure) pulse increased net flow. Tracer particles driven by bulk flow reached the outlet of the PVS with a net speed of ~ 16 μm/s when the permeability was two orders of magnitude higher than values in the literature. These particles were unable to penetrate into the parenchyma in the absence of diffusion. Dispersion dominated tracer movement in the parenchyma. Further research is required to reconcile discrepancies between these results, and both experimental and computational studies.

Appendices

Appendix 1

There is some controversy in the literature as to whether there is a meaningful mean pressure difference between the ventricles and SAS or between the SAS and parenchyma. However, as fluid flows from one to the other at various points in the cardiac cycle, there is clearly a dynamic pressure difference during the cardiac cycle.

As stated in the main text in Sect. 1 ‘The impetus for investigating the pulse offset mechanism was that both the PVS associated with the artery and PVS associated with the venule might be connected to the cranial SAS’ (Hannocks et al. 2018; Mastorakos and McGavern 2019). Therefore, it seems unlikely that the pressures where they join the SAS would differ significantly. Figure

Fig. 10

Schematic of an artery-vein pair with a parenchymal section between them. Both these vessels are connected to approximately the same region of the SAS. If this assumption is correct, then there would be no significant pressure difference between the periarterial and perivenous spaces. Blue arrows indicate possible flow directions

10 illustrates this point.

It is due to both above-mentioned factors that the pulse offset mechanism was developed under a zero-net pressure condition where the modelled pressure is the difference between the SAS and parenchyma. To create this pressure input for the model, data from Kasprowicz et al. (2016) (Fig.

Fig. 11

Pressure and displacement boundary conditions. a Averaged ICP trace from b (triangles) converted from mmHg to Pa for use in Ansys CFX. Fourier series fit of the data (line). b Original SAS ICP pressure recording modified for the results in a and c (Kasprowicz et al. 2016). (c) Pressure pulse curve applied to the SAS (magnitude of P = 133 Pa = 1 mmHg). Area is the same above and below the curve resulting in no net pressure applied to the system over the course of 1 cycle

11). This recording was used as it showed three distinct pulses over a time scale of seconds, in humans. While the pressure recordings are slightly noisy, this was softened by taking the average of the three traces. This was done primarily to obtain a shape for the SAS ICP based on human in vivo results. The averaged result is shown in Fig. 11b along with a Fourier series fit used to further reduce the noise.

The mean of the SAS pressure from Kasprowicz et al. is ~ 27 mmHg and the initial assumption of our model is that there is no net pressure in the modelled region. Therefore, the curve in Fig. 11a is shifted to a mean of zero; the PVS outlet is also set to 0 mmHg (effectively 27 mmHg). Thus, the curve in Fig. 2b was shifted to have a mean of 0 mmHg. This ensured that the cyclic pressure added no net pressure to the system per cycle, the area above and below the curve summed to zero. The pressure was scaled to 1 mmHg based on the findings of Stephensen et al. (2002) and Penn and Linninger (2009), which show that the pressure difference between the SAS and venules, parenchyma and venules do not exceed ~ 1 mmHg leading to a further assumption that the magnitude of the pressure difference between the SAS and parenchyma would also not exceed this value. It must be stated that the results of Stephensen et al. are from humans and Penn et al. are from dog experiments.

Appendix 2

2.1 Permeability calculation

Permeability of the astrocyte end-foot layer was calculated for a single end-foot using Darcy’s law in the absence of gravitational forces. This was further multiplied by the number of end-feet in the simulated area:

$${\rm{Q}} = \frac{{\upkappa {\rm{A}}\left( {\Delta {\rm{P}}} \right)}}{{\upmu}\rm{L}}$$

where

$${\rm{Q}} = {\rm{volumetric flow rate through AQP}}4\,{\rm{multipled by the number of AQP}}4\,{\rm{in an endfoot}}$$

${\rm{Volumetric flow rate of a single AQP}}4 = 35 \times 10^{{ - 14}} {\rm{cm}}^{3} {\rm{s}}^{{ - 1}}\,$ (Yang and Verkman 1997) $= 3.5 \times 10^{{ - 19}}\, {\rm{m}}^{3} {\rm{s}}^{{ - 1}}$

No. of AQP4 channels per end-foot = 78 000 (Nagelhus et al. 1998) ${\rm{giving Q}} = 3.5 \times 10^{{ - 19}} \, {\rm{m}}^{3} {\rm{s}}^{{ - 1}} \times 78000 = 1.53 \times 10^{{ - 12}} {\rm{m}}^{3} {\rm{s}}^{{ - 1}}$

$$\kappa = {\rm{permeability in m}}^{2}$$

$A = {\rm{area \, of \, an \, end \,foot}} = 78\,{\upmu} {\rm{m}}^{2}$ (Asgari et al. 2015) $= 7.8 \times 10^{{ - 11}}\, {\rm{m}}^{2}$

${{\Delta }}P = 1\,{\rm{mmHg}} = 133.322\,{\rm{Pa}}$(Penn and Linninger 2009; Stephensen et al. 2002)

$$\mu = {\rm{~dynamic~viscosity~of~CSF}} = 0.8 \times 10^{{ - 3}} {\rm{~Pa}}.{\rm{s}}$$

L = depth of the end-feet layer $= 1{\rm{~}} \times {\rm{~}}10^{{ - 6}} {\rm{~m~}}$ (Mathiisen et al. 2010).

The area of the astrocyte layer is 300 µm (length) × 8.72 µm (width) = 2616 µm² and the area of an end-foot is 78 µm².

$\therefore$ 2616/78 = 34 is the number of end-feet modelled in the astrocyte region.

$${\rm{Rearranging~for~}}\kappa {\rm{~}}$$

$$\kappa = ~\frac{{Q\mu L}}{{A\left( {\Delta P} \right)}}34 = 7.3 \times 10^{{ - 14}} ~{\rm{m}}^{2} ~$$