Dispersion in porous media in oscillatory flow between flat plates: applications to intrathecal, periarterial and paraarterial solute transport in the central nervous system

Flow in temporally and spatially varying porous media: a model for transport of interstitial fluid in the brain

Flow in a porous medium can be driven by the deformations of the boundaries of the porous domain. Such boundary deformations locally change the volume fraction accessible by the fluid, creating non-uniform porosity and permeability throughout the medium. In this work, we construct a deformation-driven porous medium transport model with spatially and temporally varying porosity and permeability that are dependent on the boundary deformations imposed on the medium. We use this model to study the transport of interstitial fluid along the basement membranes in the arterial walls of the brain. The basement membrane is modeled as a deforming annular porous channel with the compressible pore space filled with an incompressible, Newtonian fluid. The role of a forward propagating peristaltic heart pulse wave and a reverse smooth muscle contraction wave on the flow within the basement membranes is investigated. Our results identify combinations of wave amplitudes that can induce either forward or reverse transport along these transport pathways in the brain. The magnitude and direction of fluid transport predicted by our model can help in understanding the clearance of fluids and solutes along the Intramural Periarterial Drainage route and the pathology of cerebral amyloid angiopathy.

Impact of thermodynamical rotational flow of cerebrospinal fluid in the presence of elasticity

OBJECTIVE

To explore the experimental justification of cerebrospinal fluid (CSF) amplitude and elastic fluctuations of ventricles, we extend our previous computational study to models with rotational flow and suitable boundary conditions. In the present study, we include an elastic effect due to the interaction with the thermal solutal model which accounts for CSF motion which flows rotationally due to hydrocephalus flows within the spinal canal.

METHODS

Using an analytical pertubation method, we have attempted a new model to justify CSF flow movement using the influences of wall temperature difference.

RESULTS

This paper presents results from a computational study of the biomechanics of hydrocephalus, with special emphasis on a reassessment of the parenchymal elastic module. CSF amplitude in hydrocephalus patients is 2.7 times greater than that of normal subjects.

CONCLUSIONS

This finding suggests a non-linear mechanical system to present the hydrocephalic condition using a numerical model. The results can be useful to relieve the complexities in the mechanism of hydrocephalus and can shed light to support clinically for a convincing simulation.

A novel method to quantify perivascular space enlargement near the syrinx in a rodent model of post-traumatic syringomyelia

Posttraumatic syringomyelia (PTS) is an enigmatic condition characterized by the development of fluid-filled cysts (syrinxes) within the spinal cord. Perivascular spaces (PVS) are a critical component of fluid transport within the central nervous system (CNS), with dilated PVSs variably implicated in the pathogenesis of syringomyelia. The extent and spatial distribution of dilated PVSs in syringomyelia, however, remains unclear. This study aims to develop a method to assess PVS dimensions across multiple spinal cord segments in rats with PTS. Syrinxes were induced in two Sprague-Dawley rats at C6/7 with computer-controlled motorized spinal cord impaction; two control rats underwent sham laminectomies. Spinal cord segments were obtained at C4, C6 and C8, cleared via tissue clearing protocols, stained with immunofluorescent antibodies and imaged under confocal microscopy. Qualitative and quantitative analyses of PVS size were performed. Arteriolar PVSs were enlarged in the perisyringeal region of the spinal cord, compared to the control cord. No PVS enlargement was observed above or below the syrinx. These results confirm previous incidental findings of enlarged PVSs in the perisyringeal region, providing new insights into PVS dimensions across multiple spinal segments, and providing a novel method for quantifying spinal cord perivascular space size distributions.

Cerebrospinal fluid-contacting neurons: multimodal cells with diverse roles in the CNS

The cerebrospinal fluid (CSF) is a complex solution that circulates around the CNS, and whose composition changes as a function of an animal's physiological state. Ciliated neurons that are bathed in the CSF - and thus referred to as CSF-contacting neurons (CSF-cNs) - are unusual polymodal interoceptive neurons. As chemoreceptors, CSF-cNs respond to variations in pH and osmolarity and to bacterial metabolites in the CSF. Their activation during infections of the CNS results in secretion of compounds to enhance host survival. As mechanosensory neurons, CSF-cNs operate together with an extracellular proteinaceous polymer known as the Reissner fibre to detect compression during spinal curvature. Once activated, CSF-cNs inhibit motor neurons, premotor excitatory neurons and command neurons to enhance movement speed and stabilize posture. At longer timescales, CSF-cNs instruct morphogenesis throughout life via the release of neuropeptides that act over long distances on skeletal muscle. Finally, recent evidence suggests that mouse CSF-cNs may act as neural stem cells in the spinal cord, inspiring new paths of investigation for repair after injury.

Human brain solute transport quantified by glymphatic MRI-informed biophysics during sleep and sleep deprivation

Whether you are reading, running or sleeping, your brain and its fluid environment continuously interacts to distribute nutrients and clear metabolic waste. Yet, the precise mechanisms for solute transport within the human brain have remained hard to quantify using imaging techniques alone. From multi-modal human brain MRI data sets in sleeping and sleep-deprived subjects, we identify and quantify CSF tracer transport parameters using forward and inverse subject-specific computational modelling. Our findings support the notion that extracellular diffusion alone is not sufficient as a brain-wide tracer transport mechanism. Instead, we show that human MRI observations align well with transport by either by an effective diffusion coefficent 3.5[Formula: see text] that of extracellular diffusion in combination with local clearance rates corresponding to a tracer half-life of up to 5 h, or by extracellular diffusion augmented by advection with brain-wide average flow speeds on the order of 1-9 [Formula: see text]m/min. Reduced advection fully explains reduced tracer clearance after sleep-deprivation, supporting the role of sleep and sleep deprivation on human brain clearance.

Astrocyte endfeet may theoretically act as valves to convert pressure oscillations to glymphatic flow

The glymphatic system of cerebrospinal fluid transport through the perivascular spaces of the brain has been implicated in metabolic waste clearance, neurodegenerative diseases and in acute neurological disorders such as stroke and cardiac arrest. In other biological low-pressure fluid pathways such as in veins and the peripheral lymphatic system, valves play an important role in ensuring the flow direction. Though fluid pressure is low in the glymphatic system and directed bulk flow has been measured in pial and penetrating perivascular spaces, no valves have yet been identified. Valves, which asymmetrically favour forward flow to backward flow, would imply that the considerable oscillations in blood and ventricle volumes seen in magnetic resonance imaging could cause directed bulk flow. Here, we propose that astrocyte endfeet may act as such valves using a simple elastic mechanism. We combine a recent fluid mechanical model of viscous flow between elastic plates with recent measurements of in vivo elasticity of the brain to predict order of magnitude flow-characteristics of the valve. The modelled endfeet are effective at allowing forward while preventing backward flow.

Multi-scale analysis of concentration distribution in unsteady Couette–Poiseuille flows through a porous channel

A multiple-scale perturbation analysis is presented to analyse the two-dimensional concentration distribution of passive contaminant released in an incompressible viscous fluid flowing between two parallel plates filled with a porous medium. The flow is driven by the combined effect of the upper plate oscillation in its own plane moving with a constant velocity, and the periodic pressure gradient. Mei’s homogenization technique is used to find the concentration distribution up to third order, complemented with the dispersion coefficients for four different situations, namely, steady, pulsatile, oscillatory and the combined effect of all these. We observe that when the flow is under the combined effect of wall oscillation and pressure pulsation, then the respective frequency (Womersley number) and amplitude parameters oppose each other while influencing the dispersion coefficient. Our analysis reveals that for a fixed amplitude of oscillation and pulsation, the frequency of pressure pulsation has a stronger effect on the dispersion coefficient compared with the wall oscillation. On the other hand, when the Womersley number is kept fixed, amplitude of the wall oscillation dominates the pressure pulsation. This behaviour is more prominent for higher values of the Darcy number. The transverse concentration distribution and its dependency on porous medium parameters are also discussed in detail.

CSF circulation and dispersion yield rapid clearance from intracranial compartments

In this paper, we used a computational model to estimate the clearance of a tracer driven by the circulation of cerebrospinal fluid (CSF) produced in the choroid plexus (CP) located within the lateral ventricles. CSF was assumed to exit the subarachnoid space (SAS) via different outflow routes such as the parasagittal dura, cribriform plate, and/or meningeal lymphatics. We also modelled a reverse case where fluid was produced within the spinal canal and absorbed in the choroid plexus in line with observations on certain iNPH patients. No directional interstitial fluid flow was assumed within the brain parenchyma. Tracers were injected into the foramen magnum. The models demonstrate that convection in the subarachnoid space yields rapid clearance from both the SAS and the brain interstitial fluid and can speed up intracranial clearance from years, as would be the case for purely diffusive transport, to days.

The glymphatic system: Current understanding and modeling

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.

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

Arterial vasodilation drives convective fluid flow in the brain: a poroelastic model

The movement of fluid into, through, and out of the brain plays an important role in clearing metabolic waste. However, there is controversy regarding the mechanisms driving fluid movement in the fluid-filled paravascular spaces (PVS), and whether the movement of metabolic waste in the brain extracellular space (ECS) is primarily driven by diffusion or convection. The dilation of penetrating arterioles in the brain in response to increases in neural activity (neurovascular coupling) is an attractive candidate for driving fluid circulation, as it drives deformation of the brain tissue and of the PVS around arteries, resulting in fluid movement. We simulated the effects of vasodilation on fluid movement into and out of the brain ECS using a novel poroelastic model of brain tissue. We found that arteriolar dilations could drive convective flow through the ECS radially outward from the arteriole, and that this flow is sensitive to the dynamics of the dilation. Simulations of sleep-like conditions, with larger vasodilations and increased extracellular volume in the brain showed enhanced movement of fluid from the PVS into the ECS. Our simulations suggest that both sensory-evoked and sleep-related arteriolar dilations can drive convective flow of cerebrospinal fluid not just in the PVS, but also into the ECS through the PVS around arterioles.

The glymphatic hypothesis: the theory and the evidence

The glymphatic hypothesis proposes a mechanism for extravascular transport into and out of the brain of hydrophilic solutes unable to cross the blood-brain barrier. It suggests that there is a circulation of fluid carrying solutes inwards via periarterial routes, through the interstitium and outwards via perivenous routes. This review critically analyses the evidence surrounding the mechanisms involved in each of these stages. There is good evidence that both influx and efflux of solutes occur along periarterial routes but no evidence that the principal route of outflow is perivenous. Furthermore, periarterial inflow of fluid is unlikely to be adequate to provide the outflow that would be needed to account for solute efflux. A tenet of the hypothesis is that flow sweeps solutes through the parenchyma. However, the velocity of any possible circulatory flow within the interstitium is too small compared to diffusion to provide effective solute movement. By comparison the earlier classical hypothesis describing extravascular transport proposed fluid entry into the parenchyma across the blood-brain barrier, solute movements within the parenchyma by diffusion, and solute efflux partly by diffusion near brain surfaces and partly carried by flow along "preferred routes" including perivascular spaces, white matter tracts and subependymal spaces. It did not suggest fluid entry via periarterial routes. Evidence is still incomplete concerning the routes and fate of solutes leaving the brain. A large proportion of the solutes eliminated from the parenchyma go to lymph nodes before reaching blood but the proportions delivered directly to lymph or indirectly via CSF which then enters lymph are as yet unclear. In addition, still not understood is why and how the absence of AQP4 which is normally highly expressed on glial endfeet lining periarterial and perivenous routes reduces rates of solute elimination from the parenchyma and of solute delivery to it from remote sites of injection. Neither the glymphatic hypothesis nor the earlier classical hypothesis adequately explain how solutes and fluid move into, through and out of the brain parenchyma. Features of a more complete description are discussed. All aspects of extravascular transport require further study.

Effect of Ventricular Elasticity Due to Congenital Hydrocephalus

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Congenital hydrocephalusis is an asymmetric and unusual cerebrospinal fluid flow during fetal development. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. This paper presents a mathematical model to establish the effects of ventricular elasticity through a porous channel. The current model is good enough for immediate use by a neurosurgeon. The mathematical model is likely to be a powerful tool for the better treatment of hydrocephalus and other brain biomechanics. The non-linear dimensionless governing equations are solved using a perturbation technique, and the outcome is portrayed graphically with the aid of MATLAB.

Brain solute transport is more rapid in periarterial than perivenous spaces

Fluid flow in perivascular spaces is recognized as a key component underlying brain transport and clearance. An important open question is how and to what extent differences in vessel type or geometry affect perivascular fluid flow and transport. Using computational modelling in both idealized and image-based geometries, we study and compare fluid flow and solute transport in pial (surface) periarterial and perivenous spaces. Our findings demonstrate that differences in geometry between arterial and venous pial perivascular spaces (PVSs) lead to higher net CSF flow, more rapid tracer transport and earlier arrival times of injected tracers in periarterial spaces compared to perivenous spaces. These findings can explain the experimentally observed rapid appearance of tracers around arteries, and the delayed appearance around veins without the need of a circulation through the parenchyma, but rather by direct transport along the PVSs.

Phase offset between arterial pulsations and subarachnoid space pressure fluctuations are unlikely to drive periarterial cerebrospinal fluid flow

Circulation of fluid through the central nervous system maintains fluid homeostasis and is involved in solute clearance. The glymphatic system is hypothesised to facilitate waste clearance in the brain, with inflow via periarterial spaces, bulk flow through the parenchyma, and outflow via perivenous spaces. The driving force for this mechanism is unknown. Previous modelling in the spinal cord suggests that timing offsets between arterial and subarachnoid space pressure pulses can enable net inflow in perivascular spaces (PVS). This study adapted the spinal pulse offset mechanism to the brain and simulated movement of tracer particles used in experiments. Both bulk flow and diffusive movement of tracer were simulated. Intracranial pressure pulses were applied to one end of a 300-μm-long perivascular space combined with a moving arterial wall simulating arterial pulsations. The simulations indicate the pulse offset mechanism can enable net inflow via PVS; however, it is unknown whether the temporal offset required is physiologically realistic. Increasing the positive component of the ICP (intracranial pressure) pulse increased net flow. Tracer particles driven by bulk flow reached the outlet of the PVS with a net speed of ~ 16 μm/s when the permeability was two orders of magnitude higher than values in the literature. These particles were unable to penetrate into the parenchyma in the absence of diffusion. Dispersion dominated tracer movement in the parenchyma. Further research is required to reconcile discrepancies between these results, and both experimental and computational studies.

Brain cerebrospinal fluid 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.

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.

Fast uncertainty quantification of tracer distribution in the brain interstitial fluid with multilevel and quasi Monte Carlo

Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty-from uncertain input parameters to uncertain output quantities-in high resolution mathematical models of brain physiology. Advanced Monte Carlo methods such as quasi Monte Carlo (QMC) and multilevel Monte Carlo (MLMC) have the potential to dramatically improve upon standard Monte Carlo (MC) methods, but their applicability and performance in biomedical applications is underexplored. In this paper, we design and apply QMC and MLMC methods to quantify uncertainty in a convection-diffusion model of tracer transport within the brain. We show that QMC outperforms standard MC simulations when the number of random inputs is small. MLMC considerably outperforms both QMC and standard MC methods and should therefore be preferred for brain transport models.

The mechanisms behind perivascular fluid flow

Flow of cerebrospinal fluid (CSF) in perivascular spaces (PVS) is one of the key concepts involved in theories concerning clearance from the brain. Experimental studies have demonstrated both net and oscillatory movement of microspheres in PVS (Mestre et al. (2018), Bedussi et al. (2018)). The oscillatory particle movement has a clear cardiac component, while the mechanisms involved in net movement remain disputed. Using computational fluid dynamics, we computed the CSF velocity and pressure in a PVS surrounding a cerebral artery subject to different forces, representing arterial wall expansion, systemic CSF pressure changes and rigid motions of the artery. The arterial wall expansion generated velocity amplitudes of 60-260 μm/s, which is in the upper range of previously observed values. In the absence of a static pressure gradient, predicted net flow velocities were small (<0.5 μm/s), though reaching up to 7 μm/s for non-physiological PVS lengths. In realistic geometries, a static systemic pressure increase of physiologically plausible magnitude was sufficient to induce net flow velocities of 20-30 μm/s. Moreover, rigid motions of the artery added to the complexity of flow patterns in the PVS. Our study demonstrates that the combination of arterial wall expansion, rigid motions and a static CSF pressure gradient generates net and oscillatory PVS flow, quantitatively comparable with experimental findings. The static CSF pressure gradient required for net flow is small, suggesting that its origin is yet to be determined.

The myodural bridge of the American alligator (Alligator mississippiensis) alters CSF flow

Disorders of the volume, pressure or circulation of the cerebrospinal fluid (CSF) lead to disease states in both newborns and adults; despite this significance, there is uncertainty regarding the basic mechanics of the CSF. The suboccipital muscles connect to the dura surrounding the spinal cord, forming a complex termed the 'myodural bridge'. This study tests the hypothesis that the myodural bridge functions to alter the CSF circulation. The suboccipital muscles of American alligators were surgically exposed and electrically stimulated simultaneously with direct recordings of CSF pressure and flow. Contraction of the suboccipital muscles significantly changed both CSF flow and pressure. By demonstrating another influence on CSF circulation and pulsatility, the present study increases our understanding of the mechanics underlying the movement of the CSF.

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.

Functional hyperemia drives fluid exchange in the paravascular space

The brain lacks a conventional lymphatic system to remove metabolic waste. It has been proposed that directional fluid movement through the arteriolar paravascular space (PVS) promotes metabolite clearance. We performed simulations to examine if arteriolar pulsations and dilations can drive directional CSF flow in the PVS and found that arteriolar wall movements do not drive directional CSF flow. We propose an alternative method of metabolite clearance from the PVS, namely fluid exchange between the PVS and the subarachnoid space (SAS). In simulations with compliant brain tissue, arteriolar pulsations did not drive appreciable fluid exchange between the PVS and the SAS. However, when the arteriole dilated, as seen during functional hyperemia, there was a marked exchange of fluid. Simulations suggest that functional hyperemia may serve to increase metabolite clearance from the PVS. We measured blood vessels and brain tissue displacement simultaneously in awake, head-fixed mice using two-photon microscopy. These measurements showed that brain deforms in response to pressure changes in PVS, consistent with our simulations. Our results show that the deformability of the brain tissue needs to be accounted for when studying fluid flow and metabolite transport.

Arterial pulsations drive oscillatory flow of CSF but not directional pumping

The brain lacks a traditional lymphatic system for metabolite clearance. The existence of a "glymphatic system" where metabolites are removed from the brain's extracellular space by convective exchange between interstitial fluid (ISF) and cerebrospinal fluid (CSF) along the paravascular spaces (PVS) around cerebral blood vessels has been controversial. While recent work has shown clear evidence of directional flow of CSF in the PVS in anesthetized mice, the driving force for the observed fluid flow remains elusive. The heartbeat-driven peristaltic pulsation of arteries has been proposed as a probable driver of directed CSF flow. In this study, we use rigorous fluid dynamic simulations to provide a physical interpretation for peristaltic pumping of fluids. Our simulations match the experimental results and show that arterial pulsations only drive oscillatory motion of CSF in the PVS. The observed directional CSF flow can be explained by naturally occurring and/or experimenter-generated pressure differences.

In vitro and numerical simulation of blood removal from cerebrospinal fluid: comparison of lumbar drain to Neurapheresis therapy

BACKGROUND

Blood removal from cerebrospinal fluid (CSF) in post-subarachnoid hemorrhage patients may reduce the risk of related secondary brain injury. We formulated a computational fluid dynamics (CFD) model to investigate the impact of a dual-lumen catheter-based CSF filtration system, called Neurapheresis™ therapy, on blood removal from CSF compared to lumbar drain.

METHODS

A subject-specific multiphase CFD model of CSF system-wide solute transport was constructed based on MRI measurements. The Neurapheresis catheter geometry was added to the model within the spinal subarachnoid space (SAS). Neurapheresis flow aspiration and return rate was 2.0 and 1.8 mL/min, versus 0.2 mL/min drainage for lumbar drain. Blood was modeled as a bulk fluid phase within CSF with a 10% initial tracer concentration and identical viscosity and density as CSF. Subject-specific oscillatory CSF flow was applied at the model inlet. The dura and spinal cord geometry were considered to be stationary. Spatial-temporal tracer concentration was quantified based on time-average steady-streaming velocities throughout the domain under Neurapheresis therapy and lumbar drain. To help verify CFD results, an optically clear in vitro CSF model was constructed with fluorescein used as a blood surrogate. Quantitative comparison of numerical and in vitro results was performed by linear regression of spatial-temporal tracer concentration over 24-h.

RESULTS

After 24-h, tracer concentration was reduced to 4.9% under Neurapheresis therapy compared to 6.5% under lumbar drain. Tracer clearance was most rapid between the catheter aspiration and return ports. Neurapheresis therapy was found to have a greater impact on steady-streaming compared to lumbar drain. Steady-streaming in the cranial SAS was ~ 50× smaller than in the spinal SAS for both cases. CFD results were strongly correlated with the in vitro spatial-temporal tracer concentration under Neurapheresis therapy (R² = 0.89 with + 2.13% and - 1.93% tracer concentration confidence interval).

CONCLUSION

A subject-specific CFD model of CSF system-wide solute transport was used to investigate the impact of Neurapheresis therapy on tracer removal from CSF compared to lumbar drain over a 24-h period. Neurapheresis therapy was found to substantially increase tracer clearance compared to lumbar drain. The multiphase CFD results were verified by in vitro fluorescein tracer experiments.

Optimal Mass Transport with Lagrangian Workflow Reveals Advective and Diffusion Driven Solute Transport in the Glymphatic System

The glymphatic system (GS) hypothesis states that advective driven cerebrospinal fluid (CSF) influx from the perivascular spaces into the interstitial fluid space rapidly transport solutes and clear waste from brain. However, the presence of advection in neuropil is contested and solutes are claimed to be transported by diffusion only. To address this controversy, we implemented a regularized version of the optimal mass transport (rOMT) problem, wherein the advection/diffusion equation is the only a priori assumption required. rOMT analysis with a Lagrangian perspective of GS transport revealed that solute speed was faster in CSF compared to grey and white matter. Further, rOMT analysis also demonstrated 2-fold differences in regional solute speed within the brain. Collectively, these results imply that advective transport dominates in CSF while diffusion and advection both contribute to GS transport in parenchyma. In a rat model of cerebral small vessel disease (cSVD), solute transport in the perivascular spaces (PVS) and PVS-to-tissue transfer was slower compared to normal rats. Thus, the analytical framework of rOMT provides novel insights in the local dynamics of GS transport that may have implications for neurodegenerative diseases. Future studies should apply the rOMT analysis approach to confirm GS transport reductions in humans with cSVD.

Non-invasive MRI quantification of cerebrospinal fluid dynamics in amyotrophic lateral sclerosis patients

Background

Developing novel therapeutic agents to treat amyotrophic lateral sclerosis (ALS) has been difficult due to multifactorial pathophysiologic processes at work. Intrathecal drug administration shows promise due to close proximity of cerebrospinal fluid (CSF) to affected tissues. Development of effective intrathecal pharmaceuticals will rely on accurate models of how drugs are dispersed in the CSF. Therefore, a method to quantify these dynamics and a characterization of differences across disease states is needed.

Methods

Complete intrathecal 3D CSF geometry and CSF flow velocities at six axial locations in the spinal canal were collected by T2-weighted and phase-contrast MRI, respectively. Scans were completed for eight people with ALS and ten healthy controls. Manual segmentation of the spinal subarachnoid space was performed and coupled with an interpolated model of CSF flow within the spinal canal. Geometric and hydrodynamic parameters were then generated at 1 mm slice intervals along the entire spine. Temporal analysis of the waveform spectral content and feature points was also completed.

Results

Comparison of ALS and control groups revealed a reduction in CSF flow magnitude and increased flow propagation velocities in the ALS cohort. Other differences in spectral harmonic content and geometric comparisons may support an overall decrease in intrathecal compliance in the ALS group. Notably, there was a high degree of variability between cases, with one ALS patient displaying nearly zero CSF flow along the entire spinal canal.

Conclusion

While our sample size limits statistical confidence about the differences observed in this study, it was possible to measure and quantify inter-individual and cohort variability in a non-invasive manner. Our study also shows the potential for MRI based measurements of CSF geometry and flow to provide information about  the hydrodynamic environment of the spinal subarachnoid space. These dynamics may be studied further to understand the behavior of CSF solute transport in healthy and diseased states.

Fluid dynamics of cerebrospinal fluid flow in perivascular spaces

The flow of cerebrospinal fluid along perivascular spaces (PVSs) is an important part of the brain's system for delivering nutrients and eliminating metabolic waste products (such as amyloid-β); it also offers a pathway for the delivery of therapeutic drugs to the brain parenchyma. Recent experimental results have resolved several important questions about this flow, setting the stage for advances in our understanding of its fluid dynamics. This review summarizes the new experimental evidence and provides a critical evaluation of previous fluid-dynamic models of flows in PVSs. The review also discusses some basic fluid-dynamic concepts relevant to these flows, including the combined effects of diffusion and advection in clearing solutes from the brain.

Uncertainty quantification of parenchymal tracer distribution using random diffusion and convective velocity fields

Background

Influx and clearance of substances in the brain parenchyma occur by a combination of diffusion and convection, but the relative importance of these mechanisms is unclear. Accurate modeling of tracer distributions in the brain relies on parameters that are partially unknown and with literature values varying by several orders of magnitude. In this work, we rigorously quantified the variability of tracer distribution in the brain resulting from uncertainty in diffusion and convection model parameters.

Methods

Using the convection–diffusion–reaction equation, we simulated tracer distribution in the brain parenchyma after intrathecal injection. Several models were tested to assess the uncertainty both in type of diffusion and velocity fields and also the importance of their magnitude. Our results were compared with experimental MRI results of tracer enhancement.

Results

In models of pure diffusion, the expected amount of tracer in the gray matter reached peak value after 15 h, while the white matter did not reach peak within 24 h with high likelihood. Models of the glymphatic system were similar qualitatively to the models of pure diffusion with respect to expected time to peak but displayed less variability. However, the expected time to peak was reduced to 11 h when an additional directionality was prescribed for the glymphatic circulation. In a model including drainage directly from the brain parenchyma, time to peak occured after 6–8 h for the gray matter.

Conclusion

Even when uncertainties are taken into account, we find that diffusion alone is not sufficient to explain transport of tracer deep into the white matter as seen in experimental data. A glymphatic velocity field may increase transport if a large-scale directional structure is included in the glymphatic circulation.

Transition to turbulence in an oscillatory flow through stenosis

Onset of flow transition in a sinusoidally oscillating flow through a rigid, constant area circular pipe with a smooth sinusoidal obstruction in the center of the pipe is studied by performing direct numerical simulations, with resolutions close to the Kolmogorov microscales. The studied pipe is stenosed in the center with a 75% reduction in area in two distinct configurations-one that is symmetric to the axis of the parent pipe and the other that is offset by 0.05 diameters to introduce an eccentricity, which disturbs the flow thereby triggering the onset of flow transition. The critical Reynolds number at which the flow transitions to turbulence for a zero-mean oscillatory flow through a stenosis is shown to be nearly tripled in comparison with studies of pulsating unidirectional flow through the same stenosis. The onset of transition is further explored with three different flow pulsation frequencies resulting in a total of 90 simulations conducted on a supercomputer. It is found that the critical Reynolds number at which the oscillatory flow transitions is not affected by the pulsation frequencies. The locations of flow breakdown and re-stabilization post-stenosis are, however, respectively shifted closer to the stenosis throat with increasing pulsation frequencies. The results show that oscillatory physiological flows, while more stable, exhibit fluctuations due to geometric complexity and have implications in studies of dispersion and solute transport in the cerebrospinal fluid flow and understanding of pathological conditions.

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.