Potentiating glymphatic drainage minimizes post-traumatic cerebral oedema

Cerebral oedema is associated with morbidity and mortality after traumatic brain injury (TBI)1. Noradrenaline levels are increased after TBI2-4, and the amplitude of the increase in noradrenaline predicts both the extent of injury5 and the likelihood of mortality6. Glymphatic impairment is both a feature of and a contributor to brain injury7,8, but its relationship with the injury-associated surge in noradrenaline is unclear. Here we report that acute post-traumatic oedema results from a suppression of glymphatic and lymphatic fluid flow that occurs in response to excessive systemic release of noradrenaline. This post-TBI adrenergic storm was associated with reduced contractility of cervical lymphatic vessels, consistent with diminished return of glymphatic and lymphatic fluid to the systemic circulation. Accordingly, pan-adrenergic receptor inhibition normalized central venous pressure and partly restored glymphatic and cervical lymphatic flow in a mouse model of TBI, and these actions led to substantially reduced brain oedema and improved functional outcomes. Furthermore, post-traumatic inhibition of adrenergic signalling boosted lymphatic export of cellular debris from the traumatic lesion, substantially reducing secondary inflammation and accumulation of phosphorylated tau. These observations suggest that targeting the noradrenergic control of central glymphatic flow may offer a therapeutic approach for treating acute TBI.

Lumped parameter liver simulation to predict acute haemodynamic alterations following partial resections

Partial liver resections are routinely performed in living donor liver transplantation and to debulk tumours in liver malignancies, but surgical decisions on vessel reconstruction for adequate inflow and outflow are challenging. Pre-operative evaluation is often limited to radiological imaging, which fails to account for post-resection haemodynamic alterations. Substantial evidence suggests post-surgical increase in local volume flow rate enhances shear stress, signalling hepatic regeneration, but excessive shear stress has been postulated to result in small for size syndrome and liver failure. Predicting haemodynamic alterations throughout the liver is particularly challenging due to the dendritic architecture of the vasculature, spanning several orders of magnitude in diameter. Therefore, we developed a mathematical lumped parameter model with realistic heterogeneities capturing inflow/outflow of the human liver to simulate acute perfusion alterations following surgical resection. Our model is parametrized using clinical measurements, relies on a single free parameter and accurately captures established perfusion characteristics. We quantify acute changes in volume flow rate, flow speed and wall shear stress following variable, realistic liver resections and make comparisons with the intact liver. Our numerical model runs in minutes and can be adapted to patient-specific anatomy, providing a novel computational tool aimed at assisting pre- and intra-operative surgical decisions for liver resections.

Quantifying the relationship between spreading depolarization and perivascular cerebrospinal fluid flow

Recent studies have linked spreading depolarization (SD, an electro-chemical wave in the brain following stroke, migraine, traumatic brain injury, and more) with increase in cerebrospinal fluid (CSF) flow through the perivascular spaces (PVSs, annular channels lining the brain vasculature). We develop a novel computational model that couples SD and CSF flow. We first use high order numerical simulations to solve a system of physiologically realistic reaction-diffusion equations which govern the spatiotemporal dynamics of ions in the extracellular and intracellular spaces of the brain cortex during SD. We then couple the SD wave with a 1D CSF flow model that captures the change in cross-sectional area, pressure, and volume flow rate through the PVSs. The coupling is modelled using an empirical relationship between the excess potassium ion concentration in the extracellular space following SD and the vessel radius. We find that the CSF volumetric flow rate depends intricately on the length and width of the PVS, as well as the vessel radius and the angle of incidence of the SD wave. We derive analytical expressions for pressure and volumetric flow rates of CSF through the PVS for a given SD wave and quantify CSF flow variations when two SD waves collide. Our numerical approach is very general and could be extended in the future to obtain novel, quantitative insights into how CSF flow in the brain couples with slow waves, functional hyperemia, seizures, or externally applied neural stimulations.

Image Analysis Techniques for In Vivo Quantification of Cerebrospinal Fluid Flow

Over the last decade, there has been a tremendously increased interest in understanding the neurophysiology of cerebrospinal fluid (CSF) flow, which plays a crucial role in clearing metabolic waste from the brain. This growing interest was largely initiated by two significant discoveries: the glymphatic system (a pathway for solute exchange between interstitial fluid deep within the brain and the CSF surrounding the brain) and meningeal lymphatic vessels (lymphatic vessels in the layer of tissue surrounding the brain that drain CSF). These two CSF systems work in unison, and their disruption has been implicated in several neurological disorders including Alzheimer's disease, stoke, and traumatic brain injury. Here, we present experimental techniques for in vivo quantification of CSF flow via direct imaging of fluorescent microspheres injected into the CSF. We discuss detailed image processing methods, including registration and masking of stagnant particles, to improve the quality of measurements. We provide guidance for quantifying CSF flow through particle tracking and offer tips for optimizing the process. Additionally, we describe techniques for measuring changes in arterial diameter, which is an hypothesized CSF pumping mechanism. Finally, we outline how these same techniques can be applied to cervical lymphatic vessels, which collect fluid downstream from meningeal lymphatic vessels. We anticipate that these fluid mechanical techniques will prove valuable for future quantitative studies aimed at understanding mechanisms of CSF transport and disruption, as well as for other complex biophysical systems.

Sensitivity analysis on a network model of glymphatic flow

Intracranial cerebrospinal and interstitial fluid (ISF) flow and solute transport have important clinical implications, but limited in vivo access to the brain interior leaves gaping holes in human understanding of the nature of these neurophysiological phenomena. Models can address some gaps, but only insofar as model inputs are accurate. We perform a sensitivity analysis using a Monte Carlo approach on a lumped-parameter network model of cerebrospinal and ISF in perivascular and extracellular spaces in the murine brain. We place bounds on model predictions given the uncertainty in input parameters. Péclet numbers for transport in penetrating perivascular spaces (PVSs) and within the parenchyma are separated by at least two orders of magnitude. Low permeability in penetrating PVSs requires unrealistically large driving pressure and/or results in poor perfusion and are deemed unlikely. The model is most sensitive to the permeability of penetrating PVSs, a parameter whose value is largely unknown, highlighting an important direction for future experiments. Until the value of the permeability of penetrating PVSs is more accurately measured, the uncertainty of any model that includes flow in penetrating PVSs is so large that absolute numbers have little meaning and practical application is limited.

A network model of glymphatic flow under different experimentally-motivated parametric scenarios

Flow of cerebrospinal fluid (CSF) through perivascular spaces (PVSs) in the brain delivers nutrients, clears metabolic waste, and causes edema formation. Brain-wide imaging cannot resolve PVSs, and high-resolution methods cannot access deep tissue. However, theoretical models provide valuable insight. We model the CSF pathway as a network of hydraulic resistances, using published parameter values. A few parameters (permeability of PVSs and the parenchyma, and dimensions of PVSs and astrocyte endfoot gaps) have wide uncertainties, so we focus on the limits of their ranges by analyzing different parametric scenarios. We identify low-resistance PVSs and high-resistance parenchyma as the only scenario that satisfies three essential criteria: that the flow be driven by a small pressure drop, exhibit good CSF perfusion throughout the cortex, and exhibit a substantial increase in flow during sleep. Our results point to the most important parameters, such as astrocyte endfoot gap dimensions, to be measured in future experiments.

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We model the CSF pathway as a network of hydraulic resistances

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Predictions are bracketed by analyzing parametric scenarios for unknown parameters

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Low-resistance PVSs and high-resistance parenchyma produce realistic flows

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Astrocyte endfoot gap size is among the important parameters to be measured

Model of glymphatic clearance of aggregating proteins from the brain interstitium

A growing body of evidence suggests that cerebrospinal fluid circulates through the brain to sweep away high-molecular-weight solutes. Multiple studies demonstrate that flow through this pathway, often referred to as the glymphatic system, is most active during sleep. We numerically model the clearance of amyloid-β (a high-molecular-weight protein connected to Alzheimer's disease) from the brain interstitium by combined diffusion and glymphatic advection. We first compare the clearance for a range of different flow conditions and quantify the relation between the clearance rates and Péclet number Pe. We then simulate protein buildup using a reaction-advection-diffusion equation based on the Smoluchowski aggregation scheme and quantify the buildup for different Pe. We find that for flows with Pe≳1, the rate of accumulation of heavy aggregates decreases exponentially with Pe. We finally explore the effect of the sleep-wake cycle by incorporating a variation in the flow speed motivated by experimental measurements. We find that periods of sleep lead to better clearance of intermediate protein aggregates and deter the buildup of large aggregates in the brain. In a conservative estimate, for Pe≈1, we find a 32% reduction in the buildup rate of heavier protein aggregates compared to purely diffusive clearance.

Cerebrospinal fluid is a significant fluid source for anoxic cerebral oedema

Cerebral edema develops after anoxic brain injury. In two models of asphyxial and asystolic cardiac arrest without resuscitation, we found that edema develops shortly after anoxia secondary to terminal depolarizations and the abnormal entry of cerebrospinal fluid (CSF). Edema severity correlated with the availability of CSF with the age-dependent increase in CSF volume worsening the severity of edema. Edema was identified primarily in brain regions bordering CSF compartments in mice and humans. The degree of ex vivo tissue swelling was predicted by an osmotic model suggesting that anoxic brain tissue possesses a high intrinsic osmotic potential. This osmotic process was temperature-dependent, proposing an additional mechanism for the beneficial effect of therapeutic hypothermia. These observations show that CSF is a primary source of edema fluid in anoxic brain. This novel insight offers a mechanistic basis for the future development of alternative strategies to prevent cerebral edema formation after cardiac arrest.

Endothelial cell apicobasal polarity coordinates distinct responses to luminally versus abluminally delivered TNF-α in a microvascular mimetic

Endothelial cells (ECs) are an active component of the immune system and interact directly with inflammatory cytokines. While ECs are known to be polarized cells, the potential role of apicobasal polarity in response to inflammatory mediators has been scarcely studied. Acute inflammation is vital in maintaining healthy tissue in response to infection; however, chronic inflammation can lead to the production of systemic inflammatory cytokines and deregulated leukocyte trafficking, even in the absence of a local infection. Elevated levels of cytokines in circulation underlie the pathogenesis of sepsis, the leading cause of intensive care death. Because ECs constitute a key barrier between circulation (luminal interface) and tissue (abluminal interface), we hypothesize that ECs respond differentially to inflammatory challenge originating in the tissue versus circulation as in local and systemic inflammation, respectively. To begin this investigation, we stimulated ECs abluminally and luminally with the inflammatory cytokine tumor necrosis factor alpha (TNF-α) to mimic a key feature of local and systemic inflammation, respectively, in a microvascular mimetic (μSiM-MVM). Polarized IL-8 secretion and polymorphonuclear neutrophil (PMN) transmigration were quantified to characterize the EC response to luminal versus abluminal TNF-α. We observed that ECs uniformly secrete IL-8 in response to abluminal TNF-α and is followed by PMN transmigration. The response to abluminal treatment was coupled with the formation of ICAM-1-rich membrane ruffles on the apical surface of ECs. In contrast, luminally stimulated ECs secreted five times more IL-8 into the luminal compartment than the abluminal compartment and sequestered PMNs on the apical EC surface. Our results identify clear differences in the response of ECs to TNF-α originating from the abluminal versus luminal side of a monolayer for the first time and may provide novel insight into future inflammatory disease intervention strategies.

Bulk flow of cerebrospinal fluid observed in periarterial spaces is not an artifact of injection

Cerebrospinal fluid (CSF) flowing through periarterial spaces is integral to the brain’s mechanism for clearing metabolic waste products. Experiments that track tracer particles injected into the cisterna magna (CM) of mouse brains have shown evidence of pulsatile CSF flow in perivascular spaces surrounding pial arteries, with a bulk flow in the same direction as blood flow. However, the driving mechanism remains elusive. Several studies have suggested that the bulk flow might be an artifact, driven by the injection itself. Here, we address this hypothesis with new in vivo experiments where tracer particles are injected into the CM using a dual-syringe system, with simultaneous injection and withdrawal of equal amounts of fluid. This method produces no net increase in CSF volume and no significant increase in intracranial pressure. Yet, particle-tracking reveals flows that are consistent in all respects with the flows observed in earlier experiments with single-syringe injection.

Dispersion as a waste-clearance mechanism in flow through penetrating perivascular spaces in the brain

Accumulation of metabolic wastes in the brain is correlated with several neurodegenerative disorders, including Alzheimer's disease. Waste transport and clearance occur via dispersion, the combined effect of diffusion and advection by flow of fluid. We examine the relative contributions of diffusion and advection in the perivascular spaces (PVSs) that surround penetrating cortical blood vessels and are filled with cerebrospinal fluid (CSF). To do so, we adapt prior analytic predictions of dispersion to the context of PVSs. We also perform advection-diffusion simulations in PVS-like geometries with parameters relevant to transport of amyloid-[Formula: see text] (associated with Alzheimer's) in a variety of flows, motivated by in vivo measurements. 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 enhances dispersion only weakly and does not produce significant transport, whereas a steady flow component, even if slow, clears waste more effectively.

Surface periarterial spaces of the mouse brain are open, not porous

Fluid-dynamic models of the flow of cerebrospinal fluid in the brain have treated the perivascular spaces either as open (without internal solid obstacles) or as porous. Here, we present experimental evidence that pial (surface) periarterial spaces in mice are essentially open. (1) Paths of particles in the perivascular spaces 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 are 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.

Cerebrospinal fluid influx drives acute ischemic tissue swelling

Stroke affects millions each year. Poststroke brain edema predicts the severity of eventual stroke damage, yet our concept of how edema develops is incomplete and treatment options remain limited. In early stages, fluid accumulation occurs owing to a net gain of ions, widely thought to enter from the vascular compartment. Here, we used magnetic resonance imaging, radiolabeled tracers, and multiphoton imaging in rodents to show instead that cerebrospinal fluid surrounding the brain enters the tissue within minutes of an ischemic insult along perivascular flow channels. This process was initiated by ischemic spreading depolarizations along with subsequent vasoconstriction, which in turn enlarged the perivascular spaces and doubled glymphatic inflow speeds. Thus, our understanding of poststroke edema needs to be revised, and these findings could provide a conceptual basis for development of alternative treatment strategies.

Hydraulic resistance of periarterial spaces in the brain

Background

Periarterial spaces (PASs) are annular channels that surround arteries in the brain and contain cerebrospinal fluid (CSF): a flow of CSF in these channels is thought to be an important part of the brain’s system for clearing metabolic wastes. In vivo observations reveal that they are not concentric, circular annuli, however: the outer boundaries are often oblate, and the arteries that form the inner boundaries are often offset from the central axis.

Methods

We model PAS cross-sections as circles surrounded by ellipses and vary the radii of the circles, major and minor axes of the ellipses, and two-dimensional eccentricities of the circles with respect to the ellipses. For each shape, we solve the governing Navier–Stokes equation to determine the velocity profile for steady laminar flow and then compute the corresponding hydraulic resistance.

Results

We find that the observed shapes of PASs have lower hydraulic resistance than concentric, circular annuli of the same size, and therefore allow faster, more efficient flow of cerebrospinal fluid. We find that the minimum hydraulic resistance (and therefore maximum flow rate) for a given PAS cross-sectional area occurs when the ellipse is elongated and intersects the circle, dividing the PAS into two lobes, as is common around pial arteries. We also find that if both the inner and outer boundaries are nearly circular, the minimum hydraulic resistance occurs when the eccentricity is large, as is common around penetrating arteries.

Conclusions

The concentric circular annulus assumed in recent studies is not a good model of the shape of actual PASs observed in vivo, and it greatly overestimates the hydraulic resistance of the PAS. Our parameterization can be used to incorporate more realistic resistances into hydraulic network models of flow of cerebrospinal fluid in the brain. Our results demonstrate that actual shapes observed in vivo are nearly optimal, in the sense of offering the least hydraulic resistance. This optimization may well represent an evolutionary adaptation that maximizes clearance of metabolic waste from the brain.

Flow of cerebrospinal fluid is driven by arterial pulsations and is reduced in hypertension

Flow of cerebrospinal fluid (CSF) through perivascular spaces (PVSs) in the brain is important for clearance of metabolic waste. Arterial pulsations are thought to drive flow, but this has never been quantitatively shown. We used particle tracking to quantify CSF flow velocities in PVSs of live mice. CSF flow is pulsatile and driven primarily by the cardiac cycle. The speed of the arterial wall matches that of the CSF, suggesting arterial wall motion is the principal driving mechanism, via a process known as perivascular pumping. Increasing blood pressure leaves the artery diameter unchanged but changes the pulsations of the arterial wall, increasing backflow and thereby reducing net flow in the PVS. Perfusion-fixation alters the normal flow direction and causes a 10-fold reduction in PVS size. We conclude that particle tracking velocimetry enables the study of CSF flow in unprecedented detail and that studying the PVS in vivo avoids fixation artifacts.

Transcranial optical imaging reveals a pathway for optimizing the delivery of immunotherapeutics to the brain

Despite the initial promise of immunotherapy for CNS disease, multiple recent clinical trials have failed. This may be due in part to characteristically low penetration of antibodies to cerebrospinal fluid (CSF) and brain parenchyma, resulting in poor target engagement. We here utilized transcranial macroscopic imaging to noninvasively evaluate in vivo delivery pathways of CSF fluorescent tracers. Tracers in CSF proved to be distributed through a brain-wide network of periarterial spaces, previously denoted as the glymphatic system. CSF tracer entry was enhanced approximately 3-fold by increasing plasma osmolality without disruption of the blood-brain barrier. Further, plasma hyperosmolality overrode the inhibition of glymphatic transport that characterizes the awake state and reversed glymphatic suppression in a mouse model of Alzheimer's disease. Plasma hyperosmolality enhanced the delivery of an amyloid-β (Aβ) antibody, obtaining a 5-fold increase in antibody binding to Aβ plaques. Thus, manipulation of glymphatic activity may represent a novel strategy for improving penetration of therapeutic antibodies to the CNS.

Unstable equilibria and invariant manifolds in quasi-two-dimensional Kolmogorov-like flow

Recent studies suggest that unstable, nonchaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role of unstable equilibrium solutions and their invariant manifolds in a weakly turbulent, electromagnetically driven, shallow fluid layer. Identifying instants when turbulent evolution slows down, we compute 31 unstable equilibria of a realistic two-dimensional model of the flow. We establish the dynamical relevance of these unstable equilibria by showing that they are closely visited by the turbulent flow. We also establish the dynamical relevance of unstable manifolds by verifying that they are shadowed by turbulent trajectories departing from the neighborhoods of unstable equilibria over large distances in state space.

Optimal stretching in the reacting wake of a bluff body

We experimentally study spreading of the Belousov-Zhabotinsky reaction behind a bluff body in a laminar flow. Locations of reacted regions (i.e., regions with high product concentration) correlate with a moderate range of Lagrangian stretching and that range is close to the range of optimal stretching previously observed in topologically different flows [T. D. Nevins and D. H. Kelley, Phys. Rev. Lett. 117, 164502 (2016)]. The previous work found optimal stretching in a closed, vortex dominated flow, but this article uses an open flow and only a small area of appreciable vorticity. We hypothesize that optimal stretching is common in advection-reaction-diffusion systems with an excitation threshold, including excitable and bistable systems, and that the optimal range depends on reaction chemistry and not on flow shape or characteristic speed. Our results may also give insight into plankton blooms behind islands in ocean currents.

Forecasting Fluid Flows Using the Geometry of Turbulence

The existence and dynamical role of particular unstable solutions (exact coherent structures) of the Navier-Stokes equation is revealed in laboratory studies of weak turbulence in a thin, electromagnetically driven fluid layer. We find that the dynamics exhibit clear signatures of numerous unstable equilibrium solutions, which are computed using a combination of flow measurements from the experiment and fully resolved numerical simulations. We demonstrate the dynamical importance of these solutions by showing that turbulent flows visit their state space neighborhoods repeatedly. Furthermore, we find that the unstable manifold associated with one such unstable equilibrium predicts the evolution of turbulent flow in both experiment and simulation for a considerable period of time.

Chaos in fermionic many-body systems and the metal-insulator transition

We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix scaffolding ensemble (ScE) that mimics this transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body system is much less sparse than ScE.