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Cerebrospinal fluid (CSF) flow is crucial for clearing metabolic waste from the brain, a process whose dysregulation is linked to neurodegenerative diseases like Alzheimer's. Traditional approaches like particle tracking velocimetry (PTV) are limited by their reliance on single-plane two-dimensional measurements, which fail to capture the complex dynamics of CSF flow fully. To overcome these limitations, we employ artificial intelligence velocimetry (AIV) to reconstruct three-dimensional velocities, infer pressure and wall shear stress and quantify flow rates. Given the experimental nature of the data and inherent variability in biological systems, robust uncertainty quantification (UQ) is essential. Towards this end, we have modified the baseline AIV architecture to address aleatoric uncertainty caused by noisy experimental data, enhancing our measurement refinement capabilities. We also implement UQ for the model and epistemic uncertainties arising from the governing equations and network representation. Towards this end, we test multiple governing laws, representation models and initializations. Our approach not only advances the accuracy of CSF flow quantification but also can be adapted to other applications that use physics-informed machine learning to reconstruct fields from experimental data, providing a versatile tool for inverse problems., Competing Interests: We declare we have no competing interests., (© 2024 The Author(s).)

Cervical lymphatic vessels (cLVs) have been shown to drain solutes and cerebrospinal fluid (CSF) from the brain. However, their hydrodynamical properties have never been evaluated in vivo. Here, we developed two-photon optical imaging with particle tracking in vivo of CSF tracers (2P-OPTIC) in superficial and deep cLVs of mice, characterizing their flow and showing that the major driver is intrinsic pumping by contraction of the lymphatic vessel wall. Moreover, contraction frequency and flow velocity were reduced in aged mice, which coincided with a reduction in smooth muscle actin expression. Slowed flow in aged mice was rescued using topical application of prostaglandin F 2α , a prostanoid that increases smooth muscle contractility, which restored lymphatic function in aged mice and enhanced central nervous system clearance. We show that cLVs are important regulators of CSF drainage and that restoring their function is an effective therapy for improving clearance in aging., (© 2024. The Author(s), under exclusive licence to Springer Nature America, Inc.)

Brain waste is largely cleared via diffusion and advection in cerebrospinal fluid (CSF). CSF flows through a pathway referred to as the glymphatic system, which is also being targeted for delivering drugs to the brain. Despite the importance of solute transport, no brain-wide models for predicting clearance and delivery through perivascular pathways and adjacent parenchyma existed. We devised such a model by upgrading an existing model of CSF flow in the mouse brain to additionally solve advection-diffusion equations, thereby estimating solute transport. We simulated steady-state transport of 3 kDa dextran injected proximal to the perivascular space (PVS) of the middle cerebral artery, mimicking in vivo experiments. We performed a sensitivity analysis of 11 biological properties of PVSs and brain parenchyma by repeatedly simulating solute transport with varying parameter values. Parameter combinations that led to a large total pressure gradient, poor CSF perfusion or a steep solute gradient were deemed unrealistic. Solute concentrations in parenchyma were most sensitive to changes in pial PVS size, as this parameter linearly affects volume flow rates. We also found that realistic transport requires both highly permeable penetrating PVSs and high-resistance parenchyma. This study highlights the potential of brain-wide models to provide insights into solute transport processes.

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.

Background: Perivascular spaces (PVSs) carry cerebrospinal fluid (CSF) around the brain, facilitating healthy waste clearance. Measuring those flows in vivo is difficult, and often impossible, because PVSs are small, so accurate modeling is essential for understanding brain clearance. The most important parameter for modeling flow in a PVS is its hydraulic resistance, defined as the ratio of pressure drop to volume flow rate, which depends on its size and shape. In particular, the local resistance per unit length varies along a PVS and depends on variations in the local cross section., Methods: Using segmented, three-dimensional images of pial PVSs in mice, we performed fluid dynamical simulations to calculate the resistance per unit length. We applied extended lubrication theory to elucidate the difference between the calculated resistance and the expected resistance assuming a uniform flow. We tested four different approximation methods, and a novel correction factor to determine how to accurately estimate resistance per unit length with low computational cost. To assess the impact of assuming unidirectional flow, we also considered a circular duct whose cross-sectional area varied sinusoidally along its length., Results: We found that modeling a PVS as a series of short ducts with uniform flow, and numerically solving for the flow in each, yields good resistance estimates at low cost. If the second derivative of area with respect to axial location is less than 2, error is typically less than 15%, and can be reduced further with our correction factor. To make estimates with even lower cost, we found that instead of solving for the resistance numerically, the well-known resistance of a circular duct could be scaled by a shape factor. As long as the aspect ratio of the cross section was less than 0.7, the additional error was less than 10%., Conclusions: Neglecting off-axis velocity components underestimates the average resistance, but the error can be reduced with a simple correction factor. These results could increase the accuracy of future models of brain-wide and local CSF flow, enabling better prediction of clearance, for example, as it varies with age, brain state, and pathological conditions., (© 2024. The Author(s).)

Over the past 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 drains CSF). These two CSF systems work in unison, and their disruption has been implicated in several neurological disorders including Alzheimer's disease, stroke, 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., Competing Interests: Conflict of Interest The authors have no competing interests to declare that are relevant to the content of this article.

Cerebral oedema is associated with morbidity and mortality after traumatic brain injury (TBI) 1 . Noradrenaline levels are increased after TBI 2-4 , and the amplitude of the increase in noradrenaline predicts both the extent of injury 5 and the likelihood of mortality 6 . Glymphatic impairment is both a feature of and a contributor to brain injury 7,8 , 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., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

Background: Perivascular spaces (PVSs) carry cerebrospinal fluid (CSF) around the brain, facilitating healthy waste clearance. Measuring those flows in vivo is difficult, and often impossible, because PVSs are small, so accurate modeling is essential for understanding brain clearance. The most important parameter for modeling flow in a PVS is its hydraulic resistance, defined as the ratio of pressure drop to volume flow rate, which depends on its size and shape. In particular, the local resistance per unit length varies along a PVS and depends on variations in the local cross section., Methods: Using segmented, three-dimensional images of pial PVSs in mice, we performed fluid dynamical simulations to calculate the resistance per unit length. We applied extended lubrication theory to elucidate the difference between the calculated resistance and the expected resistance assuming a uniform flow. We tested four different approximation methods, and a novel correction factor to determine how to accurately estimate resistance per unit length with low computational cost. To assess the impact of assuming unidirectional flow, we also considered a circular duct whose cross-sectional area varied sinusoidally along its length., Results: We found that modeling a PVS as a series of short ducts with uniform flow, and numerically solving for the flow in each, yields good resistance estimates at low cost. If the second derivative of area with respect to axial location is less than 2, error is typically less than 15%, and can be reduced further with our correction factor. To make estimates with even lower cost, we found that instead of solving for the resistance numerically, the well-known resistance of a circular duct could be scaled by a shape factor. As long as the aspect ratio of the cross section was less than 0.7, the additional error was less than 10%., Conclusions: Neglecting off-axis velocity components underestimates the average resistance, but the error can be reduced with a simple correction factor. These results could increase the accuracy of future models of brain-wide and local CSF flow, enabling better prediction of clearance, for example, as it varies with age, brain state, and pathological conditions., Competing Interests: Competing interests The authors declare that they have no competing interests.

The flow of cerebrospinal fluid (CSF) along perivascular spaces (PVSs) is an important part of the brain's system for clearing metabolic waste. Experiments reveal that arterial motions from cardiac pulsations and functional hyperaemiadrive CSF in the same direction as the blood flow, but the mechanism producing this directionality is unclear. Astrocyte endfeet bound the PVSs of penetrating arteries, separating them from brain extracellular space (ECS) and potentially regulating flow between the two compartments. Here, we present two models, one based on the full equations of fluid dynamics and the other using lumped parameters, in which the astrocyte endfeet function as valves, regulating flow between the PVS and the ECS. In both models, cardiac pulsations drive a net CSF flow consistent with prior experimental observations. Functional hyperaemia, acting with cardiac pulsation, increases the net flow. We also find, in agreement with experiments, a reduced net flow during wakefulness, due to the known decrease in ECS permeability compared to the sleep state. We present in vivo imaging of penetrating arteries in mice, which we use to measure accurately the amplitude of their constrictions and dilations during both cardiac pulsation and functional hyperaemia, an important input for the models. Our models can be used to explore the effects of changes in other input parameters, such as those caused by ageing or disease, as better measurements of these parameters become available.

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.

Background: Flow of cerebrospinal fluid (CSF) through brain perivascular spaces (PVSs) is essential for the clearance of interstitial metabolic waste products whose accumulation and aggregation is a key mechanism of pathogenesis in many diseases. The PVS geometry has important implications for CSF flow as it affects CSF and solute transport rates. Thus, the size and shape of the perivascular spaces are essential parameters for models of CSF transport in the brain and require accurate quantification., Methods: We segmented two-photon images of pial (surface) PVSs and the adjacent arteries and characterized their sizes and shapes of cross sections from 14 PVS segments in 9 mice. Based on the analysis, we propose an idealized model that approximates the cross-sectional size and shape of pial PVSs, closely matching their area ratios and hydraulic resistances., Results: The ratio of PVS-to-vessel area varies widely across the cross sections analyzed. The hydraulic resistance per unit length of the PVS scales with the PVS cross-sectional area, and we found a power-law fit that predicts resistance as a function of the area. Three idealized geometric models were compared to PVSs imaged in vivo, and their accuracy in reproducing hydraulic resistances and PVS-to-vessel area ratios were evaluated. The area ratio was obtained across different cross sections, and we found that the distribution peaks for the original PVS and its closest idealized fit (polynomial fit) were 1.12 and 1.21, respectively. The peak of the hydraulic resistance distribution is [Formula: see text] Pa  s/m[Formula: see text] and [Formula: see text] Pa s/m[Formula: see text] for the segmentation and its closest idealized fit, respectively., Conclusions: PVS hydraulic resistance can be reasonably predicted as a function of the PVS area. The proposed polynomial-based fit most closely captures the shape of the PVS with respect to area ratio and hydraulic resistance. Idealized PVS shapes are convenient for modeling, which can be used to better understand how anatomical variations affect clearance and drug transport., (© 2023. The Author(s).)

Functional hyperemia, also known as neurovascular coupling, is a phenomenon that occurs when neural activity increases local cerebral blood flow. Because all biological activity produces metabolic waste, we here sought to investigate the relationship between functional hyperemia and waste clearance via the glymphatic system. The analysis showed that whisker stimulation increased both glymphatic influx and clearance in the mouse somatosensory cortex with a 1.6-fold increase in periarterial cerebrospinal fluid (CSF) influx velocity in the activated hemisphere. Particle tracking velocimetry revealed a direct coupling between arterial dilation/constriction and periarterial CSF flow velocity. Optogenetic manipulation of vascular smooth muscle cells enhanced glymphatic influx in the absence of neural activation. We propose that impedance pumping allows arterial pulsatility to drive CSF in the same direction as blood flow, and we present a simulation that supports this idea. Thus, functional hyperemia boosts not only the supply of metabolites but also the removal of metabolic waste., (© 2023. The Author(s), under exclusive licence to Springer Nature America, Inc.)

Quantifying the flow of cerebrospinal fluid (CSF) is crucial for understanding brain waste clearance and nutrient delivery, as well as edema in pathological conditions such as stroke. However, existing in vivo techniques are limited to sparse velocity measurements in pial perivascular spaces (PVSs) or low-resolution measurements from brain-wide imaging. Additionally, volume flow rate, pressure, and shear stress variation in PVSs are essentially impossible to measure in vivo. Here, we show that artificial intelligence velocimetry (AIV) can integrate sparse velocity measurements with physics-informed neural networks to quantify CSF flow in PVSs. With AIV, we infer three-dimensional (3D), high-resolution velocity, pressure, and shear stress. Validation comes from training with 70% of PTV measurements and demonstrating close agreement with the remaining 30%. A sensitivity analysis on the AIV inputs shows that the uncertainty in AIV inferred quantities due to uncertainties in the PVS boundary locations inherent to in vivo imaging is less than 30%, and the uncertainty from the neural net initialization is less than 1%. In PVSs of N = 4 wild-type mice we find mean flow speed 16.33 ± 11.09 µm/s, volume flow rate 2.22 ± 1.983 × 10 3 µm 3 /s, axial pressure gradient ( - 2.75 ± 2.01)×10 -4 Pa/µm (-2.07 ± 1.51 mmHg/m), and wall shear stress (3.00 ± 1.45)×10 -3 Pa (all mean ± SE). Pressure gradients, flow rates, and resistances agree with prior predictions. AIV infers in vivo PVS flows in remarkable detail, which will improve fluid dynamic models and potentially clarify how CSF flow changes with aging, Alzheimer's disease, and small vessel disease.

Background: Flow of cerebrospinal fluid (CSF) through brain perivascular spaces (PVSs) is essential for the clearance of interstitial metabolic waste products whose accumulation and aggregation is a key mechanism of pathogenesis in many diseases. The PVS geometry has important implications for CSF flow as it affects CSF and solute transport rates. Thus, the size and shape of the perivascular spaces are essential parameters for models of CSF transport in the brain and require accurate quantification. Methods: We segmented two-photon images of pial (surface) PVSs and the adjacent arteries and characterized their sizes and shapes of thousands of cross sections from 14 PVS segments in 9 mice. Based on the analysis, we propose an idealized model that approximates the cross-sectional size and shape of pial PVSs, closely matching their area ratios and hydraulic resistances. Results: PVS size only approximately scales with vessel size, and the ratio of PVS-to-vessel area varies widely across the thousands of cross sections analyzed. The hydraulic resistance per unit length of the PVS scales with the PVS cross-sectional area, and we found a power-law fit that predicts resistance as a function of the area. Three idealized geometric models were compared to PVSs imaged in vivo, and their accuracy in reproducing hydraulic resistances and PVS-to-vessel area ratios were evaluated. The area ratio was obtained across thousands of different cross sections, and we found that the distribution peaks for the original PVS and its closest idealized fit (polynomial fit) were 1.12 and 1.21, respectively. The peak of the hydraulic resistance distribution is 1.73 x 10 15 Pa-s/m 5 and 1.44 x 10 15 Pa-s/m 5 for the segmentation and its closest idealized fit, respectively. Conclusions: Brief summary and potential implicationsPVS hydraulic resistance can be reasonably predicted as a function of the PVS area. The proposed polynomial-based fit most closely captures the shape of the PVS with respect to area ratio and hydraulic resistance. Idealized PVS shapes are convenient for modeling, which can be used to better understand how anatomical variations affect clearance and drug delivery transport.

In this study, we leverage geometry-induced asymmetries to rectify oscillatory flows and induce net directional transport of fluid in a looped network. We demonstrate this valveless rectification phenomenon in an experimental apparatus that consists of an acrylic flow chamber with a deformable wall connected to a syringe pump via a T-junction. Here, oscillatory flows were forced by the syringe pump. We found that the asymmetries that existed in the geometric configuration of the looped channel could be exploited to generate net directional flow and that this geometric configuration is key in determining the directionality. By varying the pumping parameters in the system, we determined a relationship between the frequency and stroke length of the forcing syringe pump and the resulting directional flow in the loop. Using an analytical model and flow computations, we posit how asymmetric flow separation occurring at the T-junction could explain the observed flows.

Circulation of cerebrospinal fluid and interstitial fluid around the central nervous system and through the brain transports not only those water-like fluids but also any solutes they carry, including nutrients, drugs, and metabolic wastes. Passing through brain tissue primarily during sleep, this circulation has implications for neurodegenerative disorders including Alzheimer's disease, for tissue damage during stroke and cardiac arrest, and for flow-related disorders such as hydrocephalus and syringomyelia. Recent experimental results reveal several features of this flow, but other aspects are not fully understood, including its driving mechanisms. We review the experimental evidence and theoretical modeling of cerebrospinal fluid flow, including the roles of advection and diffusion in transporting solutes. We discuss both local, detailed fluid-dynamic models of specific components of the system and global hydraulic models of the overall network of flow paths.

In this study, we present a novel, bioinspired experimental apparatus, its construction, data acquisition methodology, and validation for the study of peristaltic flows. The apparatus consists of a series of stepper motor actuators, which deflect a deformable membrane to produce peristaltic flows. We show that this apparatus design has significant advantages over previous designs that have been used to study peristaltic flows by offering a much wider range of modeling capabilities. Comparisons between the capabilities of our apparatus and previous ones show our apparatus spanning a larger range of wavelength λ , wave speed c , amplitude A , and waveform (i.e. the apparatus is not constrained to nondispersive waves or to a sinusoidal shape). This large parameter range makes the apparatus a useful tool for biomimetic experimental modeling, particularly for systems that have complex waveforms, such as peristaltic flows in perivascular vessels, arteries, the cochlea, and the urethra. We provide details on the experimental design and construction for ease of reconstruction to the reader. The apparatus capabilities are validated for a large parameter range by comparing experimental measurements to analytic results from (Ibanez et al 2021 Phys. Rev. Fluids 6 103101) for high Reynolds number ( Re  > 1) and (Jaffrin and Shapiro 1971 Annu. Rev. Fluid Mech. 3 3-37) for low Reynolds number ( Re  < 1) applications. We show that the apparatus is useful for biophysical peristaltic studies and has potential applications in other types of studies., (© 2022 IOP Publishing Ltd.)

Glymphatic fluid transport eliminates metabolic waste from the brain including amyloid-β, yet the methodology for studying efflux remains rudimentary. Here, we develop a method to evaluate glymphatic real-time clearance. Efflux of Direct Blue 53 (DB53, also T-1824 or Evans Blue) injected into the striatum is quantified by imaging the DB53 signal in the vascular compartment, where it is retained due to its high affinity to albumin. The DB53 signal is detectable as early as 15 min after injection and the efflux kinetics are sharply reduced in mice lacking the water channel aquaporin 4 (AQP4). Pharmacokinetic modeling reveal that DB53 efflux is consistent with the existence of two efflux paths, one with fast kinetics (T 1/2  = 50 min) and another with slow kinetics (T 1/2  = 240 min), in wild-type mice. This in vivo methodology will aid in defining the physiological variables that drive efflux, as well as the impact of brain states or disorders on clearance kinetics., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2022. Published by Elsevier Inc.)

We review theoretical and numerical models of the glymphatic system, which circulates cerebrospinal fluid and interstitial fluid around the brain, facilitating solute transport. Models enable hypothesis development and predictions of transport, with clinical applications including drug delivery, stroke, cardiac arrest, and neurodegenerative disorders like Alzheimer's disease. We sort existing models into broad categories by anatomical function: Perivascular flow, transport in brain parenchyma, interfaces to perivascular spaces, efflux routes, and links to neuronal activity. Needs and opportunities for future work are highlighted wherever possible; new models, expanded models, and novel experiments to inform models could all have tremendous value for advancing the field., Competing Interests: We declare no conflicts of interest., (© 2022 The Author(s).)

Cerebrospinal fluid (CSF) flows through the perivascular spaces (PVSs) surrounding cerebral arteries. Revealing the mechanisms driving that flow could bring improved understanding of brain waste transport and insights for disorders including Alzheimer's disease and stroke. In vivo velocity measurements of CSF in surface PVSs in mice have been used to argue that flow is driven primarily by the pulsatile motion of artery walls - perivascular pumping. However, fluid dynamics theory and simulation have predicted that perivascular pumping produces flows differing from in vivo observations starkly, particularly in the phase and relative amplitude of flow oscillation. We show that coupling theoretical and simulated flows to more realistic end boundary conditions, using resistance and compliance values measured in mice instead of using periodic boundaries, results in velocities that match observations more closely in phase and relative amplitude of oscillation, while preserving the existing agreement in mean flow speed. This quantitative agreement among theory, simulation, and in vivo measurement further supports the idea that perivascular pumping is an important CSF driver in physiological conditions., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

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.

Cerebral oedema develops after anoxic brain injury. In two models of asphyxial and asystolic cardiac arrest without resuscitation, we found that oedema develops shortly after anoxia secondary to terminal depolarizations and the abnormal entry of CSF. Oedema severity correlated with the availability of CSF with the age-dependent increase in CSF volume worsening the severity of oedema. Oedema 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 oedema fluid in anoxic brain. This novel insight offers a mechanistic basis for the future development of alternative strategies to prevent cerebral oedema formation after cardiac arrest., (© The Author(s) (2021). Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved. For permissions, please email: journals.permissions@oup.com.)

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., Competing Interests: The authors declare no competing interests., (© 2022 The Author(s).)

Metabolic wastes may be cleared from the brain by the flow of interstitial fluid (ISF) through extracellular spaces in the parenchyma, as proposed in the glymphatic model. Owing to the difficulty of obtaining experimental measurements, fluid-dynamic models are employed to better understand parenchymal flow. Here we use an analytical solution for Darcy flow in a porous medium with line sources (representing penetrating arterioles) and line sinks (representing ascending venules) to model the flow and calculate the hydraulic resistance as a function of parenchymal permeability and ISF viscosity for various arrangements of the vessels. We calculate how the resistance varies with experimentally determined arrangements of arterioles and venules in mouse and primate brains. Based on experimental measurements of the relative numbers of arterioles and venules and their spacing, we propose idealized configurations for mouse and primate brains, consisting of regularly repeating patterns of arterioles and venules with even spacing. We explore how the number of vessels, vessel density, arteriole-to-venule ratio, and arteriole and venule distribution affect the hydraulic resistance. Quantifying how the geometry affects the resistance of brain parenchyma could help future modelling efforts characterize and predict brain waste clearance, with relevance to diseases such as Alzheimer's and Parkinson's.

Peristaltic flows occur when fluid in a channel is driven by periodic, traveling wall deformations, as in industrial peristaltic pumps, urethras, stomachs, and cochleae. Peristaltic flows often vary periodically at every point in space but nonetheless cause net transport and mixing of solutes because of Lagrangian (Stokes) drift. Direct numerical simulation can predict peristaltic flows but is computationally expensive, particularly for determining functional relationships between drive parameters and transport or mixing. We present a simple analytic model of peristaltic flow that expresses flow velocity and drift velocity in terms of deformation speed and amplitude. The model extends beyond prior studies by allowing arbitrary wave forms via Fourier series. To validate our analytic model, we present experiments and simulations; both closely match the analytic model over a range of deformation speeds and amplitudes. We demonstrate the applicability of the model by quantifying variations in the thickness of the reflux region (where fluid drifts opposite the direction of travel of deformations) and by modeling mixing in the cochlea, which is promoted by peristaltic flow.

Cerebrospinal fluid flows around and into the brain, driven by intricate mechanisms, with profound implications for human health. According to the glymphatic hypothesis, in physiological conditions, cerebrospinal fluid flows primarily during sleep and serves to remove metabolic wastes like the amyloid-beta and tau proteins whose accumulation is believed to cause Alzheimer's disease. This paper reviews one research team's recent in vivo experiments and theoretical studies to better understand the fluid dynamics of brain cerebrospinal fluid flow. Driving mechanisms are considered, particularly arterial pulsation. Flow correlates closely with artery motion and changes when artery motion is manipulated. Though there are discrepancies between in vivo observations and predictions from simulations and theoretical studies of the mechanism, realistic boundary conditions bring closer agreement. Vessel shapes are considered, and have elongation that minimizes their hydraulic resistance, perhaps through evolutionary optimization. The pathological condition of stroke is considered. Much tissue damage after stroke is caused by swelling, and there is now strong evidence that early swelling is caused not by fluid from blood, as is commonly thought, but by cerebrospinal fluid. Finally, drug delivery is considered, and demonstrations show the glymphatic system could quickly deliver drugs across the blood-brain barrier. The paper closes with a discussion of future opportunities in the fast-changing field of brain fluid dynamics.

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., Competing Interests: AR, AL, JT, HM, TD, MN, JT, DK No competing interests declared, (© 2021, Raghunandan et al.)

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.

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., (© The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.)

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.

The cochlea is filled with two lymphatic fluids. Homeostasis of the cochlear fluids is essential for healthy hearing. The sensory epithelium called the organ of Corti separates the two fluids. Corti fluid space, extracellular fluid space within the organ of Corti, looks like a slender micro-tube. Substantial potassium ions are constantly released into the Corti fluid by sensory receptor cells. Excess potassium ions in the Corti fluid are resorbed by supporting cells to maintain fluid homeostasis. Through computational simulations, we investigated fluid mixing within the Corti fluid space. Two assumptions were made: first, there exists a longitudinal gradient of potassium ion concentration; second, outer hair cell motility causes organ of Corti deformations that alter the cross-sectional area of the Corti fluid space. We hypothesized that mechanical agitations can accelerate longitudinal mixing of Corti fluid. Corti fluid motion was determined by solving the Navier-Stokes equations incorporating nonlinear advection term. Advection-diffusion equation determined the mixing dynamics. Simulating traveling boundary waves, we found that advection and diffusion caused comparable mixing when the wave amplitude and speed were 25 nm and 7 m/s, respectively. Higher-amplitude and faster waves caused stronger advection. When physiological traveling waves corresponding to 70 dB sound pressure level at 9 kHz were simulated, advection speed was as large as 1 mm/s in the region basal to the peak responding location. Such physiological agitation accelerated longitudinal mixing by more than an order of magnitude, compared to pure diffusion. Our results suggest that fluid motion due to outer hair cell motility can help maintain longitudinal homeostasis of the Corti fluid.

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., (Copyright © 2020 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

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.

The glymphatic system is a highly polarized cerebrospinal fluid (CSF) transport system that facilitates the clearance of neurotoxic molecules through a brain-wide network of perivascular pathways. Herein we have mapped the development of the glymphatic system in mice. Perivascular CSF transport first emerges in hippocampus in newborn mice, and a mature glymphatic system is established in the cortex at 2 weeks of age. Formation of astrocytic endfeet and polarized expression of aquaporin 4 (AQP4) consistently coincided with the appearance of perivascular CSF transport. Deficiency of platelet-derived growth factor B (PDGF-B) function in the PDGF retention motif knockout mouse line Pdgfb ret/ret suppressed the development of the glymphatic system, whose functions remained suppressed in adulthood compared with wild-type mice. These experiments map the natural development of the glymphatic system in mice and define a critical role of PDGF-B in the development of perivascular CSF transport., (Copyright © 2019 The Authors. Published by Elsevier Inc. All rights reserved.)

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.

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.

In advection-reaction-diffusion systems, the spreading of a reactive scalar can be significantly influenced by the flow field in which it grows. In systems with sharp boundaries between reacted and unreacted regions, motion of the reaction fronts that lie at those boundaries can quantify spreading. Here, we present an algorithm for measuring the velocity of reaction fronts in the presence of flow, expanding previous work on tracking reaction fronts without flow. The algorithm provides localized measurements of front speed and can distinguish its two components: one from chemical dynamics and another from the underlying flow. We validate that the algorithm returns the expected front velocity components in two simulations and then show that in complex experimental flows, the measured front velocity maps fronts from one time step to the next self-consistently. Finally, we observe a variation of the chemical speed with flow speed in a variety of experiments with different time scales and length scales.

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.

An online consultation tool, the Sexually Transmitted Diseases Clinical Consultation Network is a new resource for sexually transmitted disease clinicians and clinic managers. An initial evaluation shows that most requests (29%) were from medical doctors, followed by nurse practitioners (22%). Syphilis queries comprised 39% of consults followed by gonorrhea (12%) and chlamydia (11%).

We present an algorithm for measuring the speed and thickness of reaction fronts, and from those quantities, the diffusivity and the reaction rate of the active chemical species. This front-tracking algorithm provides local measurements suitable for statistics and requires only a sequence of concentration fields. Though our eventual goal is front tracking in advection-reaction-diffusion, here we demonstrate the algorithm in reaction-diffusion. We test the algorithm with validation data in which front speed and thickness are prescribed, as well as simulation results in which diffusivity and reaction rate are prescribed. In all tests, measurements closely match true values. We apply the algorithm to laboratory experiments using the Belousov-Zhabotinsky reaction, producing speed, diffusivity, and reaction rate measurements that are statistically more robust than in prior studies. Finally, we use thickness measurements to quantify the concentration profile of chemical waves in the reaction.

We investigate growth of the excitable Belousov-Zhabotinsky reaction in chaotic, time-varying flows. In slow flows, reacted regions tend to lie near vortex edges, whereas fast flows restrict reacted regions to vortex cores. We show that reacted regions travel toward vortex centers faster as flow speed increases, but nonreactive scalars do not. For either slow or fast flows, reaction is promoted by the same optimal range of the local advective stretching, but stronger stretching causes reaction blowout and can hinder reaction from spreading. We hypothesize that optimal stretching and blowout occur in many advection-diffusion-reaction systems, perhaps creating ecological niches for phytoplankton in the ocean.

A growing number of electrochemical technologies depend on fluid flow, and often that fluid is opaque. Measuring the flow of an opaque fluid is inherently more difficult than measuring the flow of a transparent fluid, since optical methods are not applicable. Ultrasound can be used to measure the velocity of an opaque fluid, not only at isolated points, but at hundreds or thousands of points arrayed along lines, with good temporal resolution. When applied to a liquid metal electrode, ultrasound velocimetry involves additional challenges: high temperature, chemical activity, and electrical conductivity. Here we describe the experimental apparatus and methods that overcome these challenges and allow the measurement of flow in a liquid metal electrode, as it conducts current, at operating temperature. Temperature is regulated within ±2 °C using a Proportional-Integral-Derivative (PID) controller that powers a custom-built furnace. Chemical activity is managed by choosing vessel materials carefully and enclosing the experimental setup in an argon-filled glovebox. Finally, unintended electrical paths are carefully prevented. An automated system logs control settings and experimental measurements, using hardware trigger signals to synchronize devices. This apparatus and these methods can produce measurements that are impossible with other techniques, and allow optimization and control of electrochemical technologies like liquid metal batteries.

Collective animal behaviour is often modeled by systems of agents that interact via effective social forces, including short-range repulsion and long-range attraction. We search for evidence of such effective forces by studying laboratory swarms of the flying midge Chironomus riparius. Using multi-camera stereoimaging and particle-tracking techniques, we record three-dimensional trajectories for all the individuals in the swarm. Acceleration measurements show a clear short-range repulsion, which we confirm by considering the spatial statistics of the midges, but no conclusive long-range interactions. Measurements of the mean free path of the insects also suggest that individuals are on average very weakly coupled, but that they are also tightly bound to the swarm itself. Our results therefore suggest that some attractive interaction maintains cohesion of the swarms, but that this interaction is not as simple as an attraction to nearest neighbours.

Using filter-space techniques, we study the scale-to-scale transport of energy in a quasi-two-dimensional, weakly turbulent fluid flow averaged along the trajectories of fluid elements. We find that although the spatial mean of this Lagrangian-averaged flux is nearly unchanged from its Eulerian counterpart, the spatial structure of the scale-to-scale energy flux changes significantly. In particular, its features appear to correlate with the positions of Lagrangian coherent structures (LCS's). We show that the LCS's tend to lie at zeros of the scale-to-scale flux, and therefore that the LCS's separate regions that have qualitatively different dynamics. Since LCS's are also known to be impenetrable barriers to advection and mixing, we therefore find that the fluid on either side of an LCS is both kinematically and dynamically distinct. Our results extend the utility of LCS's by making clear the role they play in the flow dynamics in addition to the kinematics.

Although understanding the collective migration of cells, such as that seen in epithelial sheets, is essential for understanding diseases such as metastatic cancer, this motion is not yet as well characterized as individual cell migration. Here we adapt quantitative metrics used to characterize the flow and deformation of soft matter to contrast different types of motion within a migrating sheet of cells. Using a Finite-Time Lyapunov Exponent (FTLE) analysis, we find that - in spite of large fluctuations - the flow field of an epithelial cell sheet is not chaotic. Stretching of a sheet of cells (i.e., positive FTLE) is localized at the leading edge of migration and increases when the cells are more highly stimulated. By decomposing the motion of the cells into affine and non-affine components using the metric D 2 min , we quantify local plastic rearrangements and describe the motion of a group of cells in a novel way. We find an increase in plastic rearrangements with increasing cell densities, whereas inanimate systems tend to exhibit less non-affine rearrangements with increasing density.

Collective animal behaviour occurs at nearly every biological size scale, from single-celled organisms to the largest animals on earth. It has long been known that models with simple interaction rules can reproduce qualitative features of this complex behaviour. But determining whether these models accurately capture the biology requires data from real animals, which has historically been difficult to obtain. Here, we report three-dimensional, time-resolved measurements of the positions, velocities, and accelerations of individual insects in laboratory swarms of the midge Chironomus riparius. Even though the swarms do not show an overall polarisation, we find statistical evidence for local clusters of correlated motion. We also show that the swarms display an effective large-scale potential that keeps individuals bound together, and we characterize the shape of this potential. Our results provide quantitative data against which the emergent characteristics of animal aggregation models can be benchmarked.

Using high-resolution particle tracking velocimetry, we study the effects of the forcing geometry on the statistics of an electromagnetically stirred thin-layer flow. We consider two forcing arrangements: one that produces a lattice of vortices as a base flow, and one that produces an array of shear bands. We find that the vortex flow drives stronger fluctuating kinetic energy while the shear-band flow leads to more intense fluctuating velocity gradients. We explain our results by considering the spectral flow of energy in the system. Our results have implications for the design of two-dimensional flow experiments.