Session H02: Biological Fluid Dynamics: Physiological Lymphatic and CSF Flows (5:45pm - 6:30pm CST)

Surface periarterial spaces in the mouse brain are open, not porous.

Fluid-dynamic models of the flow of cerebrospinal fluid (CSF) in the brain have treated the perivascular spaces either as open (without internal solid obstacles) or as porous. We present experimental evidence that surface periarterial spaces in mice are essentially open: (1) Paths of particles in the PVS are smooth, as expected for viscous flow in an open vessel, not diffusive, as expected for flow in a porous medium. (2) Time-averaged velocity profiles in periarterial spaces agree closely with theoretical profiles for viscous flow in realistic models, but not with the nearly uniform profiles expected for porous medium. Because these spaces are open, they have much lower hydraulic resistance than if they were porous. To demonstrate, we compute hydraulic resistance for realistic periarterial spaces, both open and porous, and show that the resistance of the porous spaces is greater, typically by a factor of a hundred or more. The open nature of these periarterial spaces allows significantly greater flow rates and more efficient removal of metabolic waste products.   

A 2D microfluidic model of CSF motion in periarterial spaces of the brain

We have developed microfluidic devices to serve as two-dimensional models of periarterial spaces in the human brain. Using particle tracking velocimetry, we analyzed flow induced by a peristaltic wave in a frequency range representative of human heartbeats. We found that the induced flow moved in the same direction on average as the peristaltic wave. However, the induced flow oscillated forward and backward during each pulsation. We have found a power law relationship between the root-mean-square (RMS) velocity of the induced flow and the driving frequency.~ We have also developed detailed characterizations of the fluid motion at each frequency by creating phase plots of the oscillatory motion and analyzing the velocity distributions and their moments. Our observation that induced flow oscillated but moved in the same direction as the peristaltic wave on average was consistent with previous models of peristalsis. We concluded that the peristaltic wave along a flexible membrane induced fluid motion that was similar to what has been observed during \textit{in vivo }experiments, and that the induced mean and RMS velocities decreased as the frequency increased.   

A porous media model of transport in the brain interstitium

Material transport in the interstitial spaces of the mammalian brain is important for neuromodulation and clearance of waste products such as amyloid $\beta$, which is linked to Alzheimer's disease. However, the exact nature of the transport mechanism remains unclear. We use high-order numerical simulations to quantify advective and diffusive transport in the brain interstitium. To this end, we use a porous media model to understand the volume-averaged fluid flow between the perivascular spaces of the penetrating arterioles and venules in the brain interstitium. We solve the governing equations of fluid flow in a porous media along with a coupled advection-diffusion equation using experimentally observed parameters. We then quantify the relative importance of advective and diffusive transport in the brain interstitium, highlighting the differences between these two distinct transport mechanisms. Our numerical approach is quite general and it would be straightforward in the future to explore the coupled dynamics of advection-diffusion transport and spreading depolarization in the brain which is associated with events such as stroke, migraine and traumatic brain injury.   

Multi-Slice 2D MR Flow Imaging to Improve Signal-to-Noise Ratio and Velocity Noise in Assessment of Cerebrospinal Fluid Flow

Flow-encoding MRI techniques have been increasingly applied to quantitatively and qualitatively assess changes in cerebrospinal fluid (CSF) flow dynamics in various neurological conditions, such as Chiari I malformation, hydrocephalus, and syringomyelia/hydromyelia. Conventional flow-encoding MRI strategies have been hampered by low signal-to-noise ratio (SNR) and high velocity noise due to the long T1 relaxation time of CSF and the typical short repetition times (TR) of phase-contrast MRI (PC-MRI). We propose a strategy for a multi-slice 3-directional 2D PC-MRI sequence that increases the TR for each slice. To ensure a longer TR acquisition, slice encoding was designed to be interleaved with each cardiac cycle. The results of the phantom scan with water (T1 \textasciitilde 3000ms) demonstrated that the proposed strategy provided 140{\%} increase of SNR and 33-47{\%} decrease of velocity noise, when compared to corresponding 2D and 4D flow MRI acquisitions.   

A model for the oscillatory flow in the cerebral aqueduct

The transmantle pressure (TMP) (the pressure difference between the lateral ventricles of the brain and the cranial subarachnoid space) has been reasoned to play a key role in the development of some neurogenerative diseases, such as idiopathic Normal Pressure Hydrocephalus (iNPH). Direct measurement of this quantity requires very accurate simultaneous readings from two separate high-resolution pressure sensors implanted in the brain, an invasive procedure with considerable health risk factors. Despite considerable past efforts, there still is an unmet demand to develop non-invasive techniques capable of calculating the temporal variation of the TMP along the cardiac cycle. We present a simplified model to indirectly calculate the TMP from phase contrast MRI velocity measurements of the cerebrospinal fluid (CSF) in the cerebral aqueduct connecting the third and fourth brain ventricles. We further apply this non-invasive method to human subjects with ages ranging from 25 to 92 years showing that the TMP monotonically increases with age.   

Modeling fluid transport in a contracting lymphatic vessel

The lymphatic system plays a crucial role for the body by transporting interstitial fluid, fatty acid, and immune cells. This is achieved through networks of valved contracting vessels called lymphangions that circulate fluid without central pump and against adverse condition. Despite a large medical importance to understand this process, research on lymphatic pumping has been limited, especially on lymphatic valves. In this work, we develop a fully coupled 3D fluid-structure interaction model to investigate how different valve and vessel properties such as contraction frequency, contraction amplitude, and valve elastic properties affect the pumping against an adverse pressure gradient. Our results suggest that the valve's ability to effectively reduce backflow under different flow conditions is the determining factor in overall pumping performance of lymphatic system. We show that lymphatic valves increase net flow when compared with vessels without valves at the cost of increased viscous losses. Furthermore, at certain conditions valves can diminish the pumping performance, suggesting potential implications to lymphatic pathologies.   

Does injection in the cisterna magna drive fluid flow into the brain?

According to the glymphatic hypothesis, fluid enters the brain and clears neuronal waste products, such as amyloid-$\beta $, from deep within the brain tissue. Failure to clear such waste products can lead to large amyloid deposits in the brain -- the diagnostic signature of Alzheimer's disease. The pulsatile convective influx of cerebrospinal fluid (CSF) through narrow perivascular spaces surrounding the brain's vasculature is integral to this clearance mechanism. Experiments that inject tracer particles in the cisterna magna have shown evidence that CSF flow is driven by arterial pulsation. Yet, this notion remains controversial as the tracer injection process could also drive flow by increasing intercranial pressure. Here, we present results quantifying the glymphatic influx from experiments that combine in vivo imaging and particle tracking. We utilize a dual syringe system with simultaneous injection and withdrawal of fluid from the cisterna magna. The net change in intercranial pressure is negligible, but tracers are still found to be actively pumped into the brain. Furthermore, we show that mean flow speeds and flow characteristics observed across injection methods are consistent, bolstering the hypothesis that arterial pulsation is the primary driver of flow into the brain.   

One-dimensional Simulations Enable Study of Cerebrospinal Fluid Flow in Complex Perivascular Space Geometries

Removal of brain's protein wastes such as amyloid-\begin{align*}\beta \end{align*} is facilitated by cerebrospinal fluid (CSF) transport in perivascular spaces (PVSs), which are annular channels surrounding blood vessels. Buildup of amyloid-\begin{align*}\beta \end{align*} in the brain is connected to neurological disorders such as Alzheimer's disease. Here, we derive and solve the one-dimensional (1D) Navier-Stokes equation to study CSF flow in PVSs. 1D modeling let us simulate complex geometries that are not computationally feasible in higher- dimensional simulations. We model PVSs as an annulus filled with CSF and impermeable walls. Two cases are considered: 1) a straight annulus with a finite length, 2) an annulus bifurcating into two smaller but identical branches. In both cases, the outer radius of the annulus is fixed while inner radius changes periodically in time to model arterial pulsations, which are hypothesized to drive CSF through PVSs. We utilize both a sinusoidal function and a realistic waveform obtained from in vivo experiments. This approach will enable new insights into peristalsis in complicated geometries, expanding our knowledge of the brain's waste removal system and paving the way for new understanding of the mechanisms leading to neurological diseases.   

Buoyancy Effects on Intrathecal Drug Dispersion

This study investigates the transport of drugs delivered by direct injection into the cerebrospinal fluid (CSF) in the spinal subarachnoid space. CSF motion is caused by pressure oscillations induced by the cardiac and respiratory cycles. The resulting oscillatory velocity is known to have a time-averaged Lagrangian component, the sum of steady-streaming and Stokes drift velocities, which largely determines the drug dispersion rate along the canal. Although the relative density differences between the drug and the CSF are typically very small--on the order of 1/1000 for drugs diluted with water and 1/100 for drugs diluted with dextrose--the associated Richardson numbers are shown to be of order unity, so that the resulting buoyancy-induced velocities are comparable to those of steady streaming. As a consequence, the slow time-averaged Lagrangian motion of the CSF is strongly coupled with the transport of the drug, resulting in a slowly evolving steady-streaming problem which can be treated with two-time scale methods. The theoretical analysis produces a nonlinear transport equation that is solved numerically for several Richardson numbers, representing the dispersion of drugs that are slightly more dense or slightly less dense than the CSF.   

An idealized hydraulic network model for predicting cerebrospinal fluid transport throughout perivascular spaces in the brain

Recent advances in experimental techniques have enabled direct measurement of cerebrospinal fluid (CSF) flow through perivascular spaces (PVSs) near the surface of the brain. These PVSs are annular channels surrounding blood vessels in the brain which compose part of the glymphatic system, a waste removal pathway demonstrated to play an important role in Alzheimer’s disease, stroke, and more. Currently, technical challenges prevent high-resolution measurements of CSF flow far below the surface of the brain. Hence, we have developed a hydraulic network model to estimate CSF transport throughout the interconnected PVSs. This model is based on the hydraulic analog of Ohm's law and utilizes an idealized geometry based on prior quantification of vasculature topology in the brain. We use this model to compute the approximate pressure gradients necessary to drive the flows observed experimentally, and we estimate the flow speeds, Reynolds number, and P\'eclet number throughout the PVS network, including regions where experimental measurements are currently not feasible. Our results generate testable hypotheses, some of which may be confirmed with existing technology and others that require further advancement of measurement techniques.   

Dispersion as a waste clearance mechanism in pressure-driven flow through open penetrating perivascular spaces

Determining the relative contributions of advection and diffusion in transporting metabolic waste products in perivascular spaces (PVSs) is an important step in understanding the brain's system for removal of these waste products, failure of which may lead to neurological diseases such as Alzheimer's. Experiments have measured flow properties in PVSs around pial (surface) arteries through the use of tracer particles, but little is known about flows in the PVSs around arteries that penetrate deeper into the brain. Some recent publications have claimed that a purely oscillatory flow will lead to transport that is substantially faster than diffusion in these spaces, precluding any need for bulk flow. We evaluate the plausibility of these claims by utilizing analytical solutions and numerical simulations based on physically relevant parameters to quantify the transport of a solute (amyloid-beta) in a penetrating PVS. Specifically, we examine solute transport in steady and unsteady Poiseuille flows in an open (not porous) concentric circular annulus. We find that a purely oscillatory flow only weakly enhances dispersion and does not produce significant transport, whereas a steady (bulk) component of flow, even if slow, is much more effective as a clearance mechanism.