Perivascular pumping in the mouse brain: Improved boundary conditions reconcile theory, simulation, and experiment

Gaps in the wall of a perivascular space act as valves to produce a directed flow of cerebrospinal fluid: a hoop-stress model

The flow of cerebrospinal fluid (CSF) along perivascular spaces (PVSs) is an important part of the brain's system for clearing metabolic waste. Astrocyte endfeet bound the PVSs of penetrating arteries, separating them from brain extracellular space. Gaps between astrocyte endfeet might provide a low-resistance pathway for fluid transport across the wall. Recent studies suggest that the astrocyte endfeet function as valves that rectify the CSF flow, producing the net flow observed in pial PVSs by changing the size of the gaps in response to pressure changes. In this study, we quantify this rectification based on three features of the PVSs: the quasi-circular geometry, the deformable endfoot wall, and the pressure oscillation inside. We provide an analytical model, based on the thin-shell hoop-stress approximation, and predict a pumping efficiency of about 0.4, which would contribute significantly to the observed flow. When we add the flow resistance of the extracellular space (ECS) to the model, we find an increased net flow during sleep, due to the known increase in ECS porosity (decreased flow resistance) compared to that in the awake state. We corroborate our analytical model with three-dimensional fluid-solid interaction simulations.

Spontaneous vasomotion propagates along pial arterioles in the awake mouse brain like stimulus-evoked vascular reactivity

Sensory stimulation evokes a local, vasodilation-mediated blood flow increase to the activated brain region, which is referred to as functional hyperemia. Spontaneous vasomotion is a change in arteriolar diameter that occurs without sensory stimulation, at low frequency (∼0.1 Hz). These vessel diameter changes are a driving force for perivascular soluble waste clearance, the failure of which has been implicated in neurodegenerative disease. Stimulus-evoked vascular reactivity is known to propagate along penetrating arterioles to pial arterioles, but it is unclear whether spontaneous vasomotion propagates similarly. We therefore imaged both stimulus-evoked and spontaneous changes in pial arteriole diameter in awake, head-fixed mice with 2-photon microscopy. By cross-correlating different regions of interest (ROIs) along the length of imaged arterioles, we assessed vasomotion propagation. We found that both during rest and during visual stimulation, one-third of the arterioles showed significant propagation (i.e., a wave), with a median (interquartile range) wave speed of 405 (323) µm/s at rest and 345 (177) µm/s during stimulation. In a second group of mice, with GCaMP expression in their vascular smooth muscle cells, we also found spontaneous propagation of calcium signaling along pial arterioles. In summary, we demonstrate that spontaneous vasomotion propagates along pial arterioles like stimulus-evoked vascular reactivity.

Pulsatile cerebral paraarterial flow by peristalsis, pressure and directional resistance

BACKGROUND

A glymphatic system has been proposed that comprises flow that enters along cerebral paraarterial channels between the artery wall and the surrounding glial layer, continues through the parenchyma, and then exits along similar paravenous channels. The mechanism driving flow through this system is unclear. The pulsatile (oscillatory plus mean) flow measured in the space surrounding the middle cerebral artery (MCA) suggests that peristalsis created by intravascular blood pressure pulses is a candidate for the paraarterial flow in the subarachnoid spaces. However, peristalsis is ineffective in driving significant mean flow when the amplitude of channel wall motion is small, as has been observed in the MCA artery wall. In this paper, peristalsis in combination with two additional mechanisms, a longitudinal pressure gradient and directional flow resistance, is evaluated to match the measured MCA paraarterial oscillatory and mean flows.

METHODS

Two analytical models are used that simplify the paraarterial branched network to a long continuous channel with a traveling wave in order to maximize the potential effect of peristalsis on the mean flow. The two models have parallel-plate and annulus geometries, respectively, with and without an added longitudinal pressure gradient. The effect of directional flow resistors was also evaluated for the parallel-plate geometry.

RESULTS

For these models, the measured amplitude of arterial wall motion is too large to cause the small measured amplitude of oscillatory velocity, indicating that the outer wall must also move. At a combined motion matching the measured oscillatory velocity, peristalsis is incapable of driving enough mean flow. Directional flow resistance elements augment the mean flow, but not enough to provide a match. With a steady longitudinal pressure gradient, both oscillatory and mean flows can be matched to the measurements.

CONCLUSIONS

These results suggest that peristalsis drives the oscillatory flow in the subarachnoid paraarterial space, but is incapable of driving the mean flow. The effect of directional flow resistors is insufficient to produce a match, but a small longitudinal pressure gradient is capable of creating the mean flow. Additional experiments are needed to confirm whether the outer wall also moves, as well as to validate the pressure gradient.

Investigating molecular transport in the human brain from MRI with physics-informed neural networks

In recent years, a plethora of methods combining neural networks and partial differential equations have been developed. A widely known example are physics-informed neural networks, which solve problems involving partial differential equations by training a neural network. We apply physics-informed neural networks and the finite element method to estimate the diffusion coefficient governing the long term spread of molecules in the human brain from magnetic resonance images. Synthetic testcases are created to demonstrate that the standard formulation of the physics-informed neural network faces challenges with noisy measurements in our application. Our numerical results demonstrate that the residual of the partial differential equation after training needs to be small for accurate parameter recovery. To achieve this, we tune the weights and the norms used in the loss function and use residual based adaptive refinement of training points. We find that the diffusion coefficient estimated from magnetic resonance images with physics-informed neural networks becomes consistent with results from a finite element based approach when the residuum after training becomes small. The observations presented here are an important first step towards solving inverse problems on cohorts of patients in a semi-automated fashion with physics-informed neural networks.