Brain pulsations enhance cerebrospinal fluid flow in perivascular spaces

TL;DR

This work develops a lubrication-theory framework to quantify how brain pulsations and pulsatile arterial-wall motion drive cerebrospinal fluid flow in brain perivascular spaces. By nondimensionalizing the axisymmetric, thin-film problem and solving a pressure-boundary-value problem over a cardiac cycle, the authors show that brain pulsations magnify net axial CSF transport, yielding physiologically relevant mean flows and velocities. The findings suggest brain pulsations are a significant factor in glymphatic clearance, with implications for aging, PVS dilation, and neurodegenerative risk, and identify directions for in-vivo validation and model extensions that incorporate aging and AQP4-channel effects.

Abstract

A novel approach is adopted to model cerebrospinal fluid (CSF) flow in human perivascular spaces (PVSs) surrounding brain-penetrating arteries. It is proposed that the outer PVS boundary oscillates due to brain pulsations and the arterial wall motion is driven by a blood pressure wave. Lubrication theory is employed to derive a mathematical model for the CSF flow, which is then solved numerically. A parametric analysis is undertaken to investigate the effect of the brain pulsations, which shows that pulsations magnify the net axial CSF flows created by the arterial wall motion. The findings suggest that net axial CSF flows are almost entirely positive (deeper into the brain), with arterial wall motion highly dependent on PVS-penetrating artery configurations. Given the glymphatic hypothesis, the findings support the clinical practice of treating dilated PVS as indicators of an increased likelihood of neurodegenerative conditions, such as dementia.

Figures (8)

• Figure 1: The geometry of PVS-penetrating artery anatomy being studied is illustrated. The wall of the penetrating artery (shown in deep red) constitutes the inner boundary of the PVS and moves in two dimensions in accordance with functions $\eta^* \left( z^*, t^* \right)$ and $\xi^* \left( z^*, t^* \right)$ as a result of a cardiac driven blood pressure wave. The outer PVS boundary moves in accordance with the function $\kappa^* \left( t^* \right)$ as a result of brain pulsations. CSF moves within the PVS and is shown in blue. The neutral radius of the artery is $a$ with a wall thickness of $h$ and the mean PVS thickness is $b$.
• Figure 2: Panels (a) and (b) show the dimensionless radial displacement, $\eta(z,t)$, and the dimensionless axial displacement, $\xi(z,t)$, respectively, plotted against the dimensionless axial length ($z$) at five time points spanning the cardiac cycle. These results correspond to the baseline parameter values outlined in Table \ref{['tab: parms']}. In all cases, displacements are shown over a distance significantly greater than the length of the artery used in the baseline model, $L/\lambda \approx 0.12$. Panel (c) shows the maximum dimensionless displacements along the axial length and over a cardiac cycle as a function of the Young's modulus. Panel (d) presents the variation of the wavelength, $\lambda$ (blue solid line), and attenuation length, $z_a$ (black dashed line), with respect to the Young's modulus. Panel (e) displays the maximum dimensionless displacements of $\eta(z,t)$ and $\xi(z,t)$ along the axial length and over a cardiac cycle as a function of a large pathological range of the arterial wall thickness, $h$.
• Figure 3: Dimensionless flow rates calculated using the baseline parameter values outlined in Table I. Panel (a) shows the instantaneous flow rate $Q(z,t)$ plotted against the dimensionless length $(z)$ at five points spanning the cardiac cycle and with no brain oscillations, $K/b=0$. Panels (b) and (c) show the averaged flow rate $\overline{Q}(t)$, Eq. \ref{['eq: average z flow rate']}, with and without arterial axial deformations, respectively. In both cases, different brain oscillation amplitudes are considered. Panel (d) shows the mean flow rate $\langle Q\rangle$, Eq. \ref{['eq: mean flow rate']}, as a function of the amplitude of the brain tissue oscillations, $K/b$. The dashed line corresponds to the case with no arterial axial deformations.
• Figure 4: Dimensionless mean axial CSF flow rate, $\langle Q\rangle$, as a function of (a) heart rate, $\left( hrate \right)$, (b) blood pressure wave amplitude, $\left( B \right)$, (c) arterial radii, $\left( R_a \right)$, and (d) arterial wall’s Young’s modulus ($E$). In all cases, different brain oscillation amplitudes are considered: $K/b = 0$ (solid black line), $0.2$ (dotted blue line), $0.4$ (dashed purple line), and $0.6$ (dashdotted red line).
• Figure 5: (a) Dimensionless mean axial CSF flow rates, $\langle Q\rangle$, as a function of arterial wall thickness $\left( h \right)$. Panel (a) shows results for the clinically normal range. Panel (b) shows that the mean axial CSF flow rate falls off steeply as the arterial wall thickness $\left( h \right)$ moves outside the clinically normal range, which is depicted by the grey band. In all cases, different brain oscillation amplitudes are considered: $K/b = 0$ (solid black line), $0.2$ (dotted blue line), $0.4$ (dashed purple line), and $0.6$ (dashdotted red line). When no brain pulsations are included relatively very small negative flow rates are observed, as shown in the semi-log plot of the inset of panel (b).