Arterial pulsations and transmantle pressure synergetically drive glymphatic flow

Abstract

Clearance of waste material from the brain by the glymphatic system results from net flow of cerebrospinal fluid (CSF) through perivascular spaces surrounding veins and arteries. In periarterial spaces, this bulk flow is directed from the cranial subarachnoid space towards the brain's interior. The precise pumping mechanism explaining this net inflow remains unclear. While in vivo experiments have shown that the pulsatile motion in periarterial spaces is synchronized with arterial pulsations, peristalsis alone has been deemed insufficient to explain bulk flow. In this study we examine an alternative mechanism based on the interaction between arterial pulsations and fluctuations in transmantle pressure. Previously studied using pressure data from a hydrocephalus patient, this mechanism is analyzed here in healthy subjects using in vivo flow measurements obtained via phase-contrast magnetic resonance imaging. Arterial pulsations are derived from flow-rate measurements of arterial blood entering the cranial cavity, while transmantle-pressure fluctuations are computed using measurements of CSF flow in the cerebral aqueduct. The two synchronized waveforms are integrated into a canonical multi-branch model of the periarterial spaces, yielding a closed-form expression for the bulk flow. The results confirm that the dynamic interactions between arterial pulsations and transmantle pressure are sufficient to generate a positive inflow along periarterial spaces.

Fig. 1

Sketches of the cranial CSF spaces and plots of their cyclic flow patterns. (a) Representation of the brain and the primary sites of CSF. (b) PVS connecting the cranial SAS with the interior of the brain. Two schematics are included to visualize the dynamic interaction between arterial pulsations and transmantle pressure fluctuations. On the left, resistance to CSF efflux towards the SAS () increases during arterial systole. On the right, CSF inflow towards the brain’s interior () is facilitated during diastole. (c) Representation of the ventricular system, with indication of the cerebral aqueduct that connects the third and fourth ventricle. (d, e) Simultaneous in vivo MRI measurements in four healthy volunteers of (d) arterial blood flow at the C2 level entering the cranial vault (sum of the flow rates in the two vertebral and the two internal carotid arteries), and (e) CSF flow rate in the aqueduct measured from the third to the fourth ventricle.

Fig. 2

Model of the multi-branched periarterial network. (a) Schematic representation of a perivascular tree with an end-to-end length , where each path connecting the cerebral subarachnoid space (SAS) to the brain’s interior undergoes bifurcations. (b) Model of the -th element of the network. (c) Values of the parameter , which measures the effect of the multi-branched model on bulk flow, obtained for different ratios as a function of the number of bifurcations . (d) Variation of the cycle-averaged dimensionless resistance with for .

Fig. 3

Computed results for each of the four subjects (S1, S2, S3, S4) using the parameters m,, cm, , , and . (a) Normalized arterial wall displacement adapted from Bilston et al.. (b) Computed transmantle pressure for the four subjects, corresponding to the aqueductal flow rate measurements shown in Fig. 1e. Both (a) and (b) are synchronized with the heartbeat, with indicating a small phase offset. (c) Results for , showing the evolution with time of the PVS entrance flow rate (left) and subject-specific values of the bulk flow rate () and apparent pressure difference () (right). In all cases, as revealed in the schematic inset, is greater than , the latter denoting the cycle-averaged transmantle pressure. (d) Variation of bulk flows calculated in (c) as a function of the phase shift , with a table showing, for each subject, the ranges of where bulk inflow of CSF occurs (i.e. ).

Fig. 4

Effectiveness of the pumping mechanism within the physiologically relevant range using pressure data from subject S2. (a) Evolution of the apparent pressure difference, , with varying amplitudes of arterial deformations, . The three curves, in different shades of blue, correspond to the ratios , 2.0, and 3.0. A red horizontal line represents the mean transmantle pressure, . (b) The value of , as a function of , that results in zero bulk flow (i.e., ), with the three points corresponding to the inset in (a).

Fig. 5

The variation of the bulk flow rate with the dimensionless downstream resistance as obtained from (39) for three different values of . The analysis is based on pressure data from subject S2 using the parameters m, cm, , , and . Circle markers indicate, for each the estimated resistance associated with the presence of pericapillary elements at the downstream end of the perivascular network.

Fig. 6

Validation of our model using data and results from Martinac et al.. (a) Arterial pulsations and transmantle pressure used by Martinac et al., adapted from Bilston et al. and Kasprowicz et al., respectively. (b) Comparison of the variation with of the bulk flow rate (normalized to give a unity peak-to-peak amplitude) determined by Martinac et al. (green bars) with that evaluated using Eq. (25) for the waveforms shown here with , and .