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

Are brain displacements and pressures within the parenchyma induced by surface pressure differences? A computational modelling study

The intracranial pressure is implicated in many homeostatic processes in the brain and is a fundamental parameter in several diseases such as e.g. idiopathic normal pressure hydrocephalus. The presence of a small but persistent pulsatile intracranial pulsatile transmantle pressure gradient (on the order of a few mmHg/m at peak) has recently been demonstrated in hydrocephalus subjects. A key question is whether pulsatile intracranial pressure and displacements can be induced by a small pressure gradient originating from the brain surface alone. In this study, we model the brain parenchyma as either a linearly elastic or a poroelastic medium, and impose a pulsatile pressure gradient acting between the ventricular and the pial surfaces but no additional external forces. Using this high-resolution physics-based model, we use in vivo pulsatile pressure gradients from subjects with idiopathic normal pressure hydrocephalus to compute parenchyma displacement, volume change, fluid pressure, and fluid flux. The resulting displacement field is pulsatile and in qualitatively and quantitatively good agreement with the literature, both with elastic and poroelastic models. However, the pulsatile forces on the boundaries are not sufficient for pressure pulse propagation through the brain parenchyma. Our results suggest that pressure differences at the brain surface, originating e.g. from pulsating arteries surrounding the brain, are not alone sufficient to drive interstitial fluid flow within the brain parenchyma and that potential pressure gradients found within the parenchyma rather arise from a large portion of the blood vessel network, including smaller blood vessels within the brain parenchyma itself.

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.

Neural activity induces strongly coupled electro-chemo-mechanical interactions and fluid flow in astrocyte networks and extracellular space-A computational study

The complex interplay between chemical, electrical, and mechanical factors is fundamental to the function and homeostasis of the brain, but the effect of electrochemical gradients on brain interstitial fluid flow, solute transport, and clearance remains poorly quantified. Here, via in-silico experiments based on biophysical modeling, we estimate water movement across astrocyte cell membranes, within astrocyte networks, and within the extracellular space (ECS) induced by neuronal activity, and quantify the relative role of different forces (osmotic, hydrostatic, and electrical) on transport and fluid flow under such conditions. We find that neuronal activity alone may induce intracellular fluid velocities in astrocyte networks of up to 14μm/min, and fluid velocities in the ECS of similar magnitude. These velocities are dominated by an osmotic contribution in the intracellular compartment; without it, the estimated fluid velocities drop by a factor of ×34-45. Further, the compartmental fluid flow has a pronounced effect on transport: advection accelerates ionic transport within astrocytic networks by a factor of ×1-5 compared to diffusion alone.

Disentangling the impact of cerebrospinal fluid formation and neuronal activity on solute clearance from the brain

BACKGROUND

Despite recent attention, pathways and mechanisms of fluid transposition in the brain are still a matter of intense discussion and driving forces underlying waste clearance in the brain remain elusive. Consensus exists that net solute transport is a prerequisite for efficient clearance. The individual impact of neuronal activity and cerebrospinal fluid (CSF) formation, which both vary with brain state and anesthesia, remain unclear.

METHODS

To separate conditions with high and low neuronal activity and high and low CSF formation, different anesthetic regimens in naive rat were established, using Isoflurane (ISO), Medetomidine (MED), acetazolamide or combinations thereof. With dynamic contrast-enhanced MRI, after application of low molecular weight contrast agent (CA) Gadobutrol to cisterna magna, tracer distribution was monitored as surrogate for solute clearance. Simultaneous fiber-based Ca²⁺-recordings informed about the state of neuronal activity under different anesthetic regimen. T2-weighted MRI and diffusion-weighted MRI (DWI) provided size of subarachnoidal space and aqueductal flow as surrogates for CSF formation. Finally, a pathway and mechanism-independent two-compartment model was introduced to provide a measure of efficiency for solute clearance from the brain.

RESULTS

Anatomical imaging, DWI and Ca²⁺-recordings confirmed that conditions with distinct levels of neuronal activity and CSF formation were achieved. A sleep-resembling condition, with reduced neuronal activity and enhanced CSF formation was achieved using ISO+MED and an awake-like condition with high neuronal activity using MED alone. CA distribution in the brain correlated with the rate of CSF formation. The cortical brain state had major influence on tracer diffusion. Under conditions with low neuronal activity, higher diffusivity suggested enlargement of extracellular space, facilitating a deeper permeation of solutes into brain parenchyma. Under conditions with high neuronal activity, diffusion of solutes into parenchyma was hindered and clearance along paravascular pathways facilitated. Exclusively based on the measured time signal curves, the two-compartment model provided net exchange ratios, which were significantly larger for the sleep-resembling condition than for the awake-like condition.

CONCLUSIONS

Efficiency of solute clearance in brain changes with alterations in both state of neuronal activity and CSF formation. Our clearance pathway and mechanism agnostic kinetic model informs about net solute transport, solely based on the measured time signal curves. This rather simplifying approach largely accords with preclinical and clinical findings.

Fluid dynamics in aging-related dementias

Recent human and animal model experimental studies revealed novel pathways for fluid movement, immune cell trafficking and metabolic waste clearance in CNS. These studies raise the intriguing possibility that the newly discovered pathways, including the glymphatic system, lymphatic meningeal vessels and skull-brain communication channels, are impaired in aging and neurovascular and neurodegenerative diseases associated with dementia, including Alzheimer's disease (AD) and AD-related dementia. We provide an overview of the glymphatic and dural meningeal lymphatic systems, review current methods and approaches used to study glymphatic flow in humans and animals, and discuss current evidence and controversies related to its role in CNS flow homeostasis under physiological and pathophysiological conditions. Non-invasive imaging approaches are needed to fully understand the mechanisms and pathways driving fluid movement in CNS and their roles across lifespan including healthy aging and aging-related dementia.

Multi-compartmental model of glymphatic clearance of solutes in brain tissue

The glymphatic system is the subject of numerous pieces of research in biology. Mathematical modelling plays a considerable role in this field since it can indicate the possible physical effects of this system and validate the biologists' hypotheses. The available mathematical models that describe the system at the scale of the brain (i.e. the macroscopic scale) are often solely based on the diffusion equation and do not consider the fine structures formed by the perivascular spaces. We therefore propose a mathematical model representing the time and space evolution of a mixture flowing through multiple compartments of the brain. We adopt a macroscopic point of view in which the compartments are all present at any point in space. The equations system is composed of two coupled equations for each compartment: One equation for the pressure of a fluid and one for the mass concentration of a solute. The fluid and solute can move from one compartment to another according to certain membrane conditions modelled by transfer functions. We propose to apply this new modelling framework to the clearance of 14C-inulin from the rat brain.

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.

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

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

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.

Fluid transport in the brain

The brain harbors a unique ability to, figuratively speaking, shift its gears. During wakefulness, the brain is geared fully toward processing information and behaving, while homeostatic functions predominate during sleep. The blood-brain barrier establishes a stable environment that is optimal for neuronal function, yet the barrier imposes a physiological problem; transcapillary filtration that forms extracellular fluid in other organs is reduced to a minimum in brain. Consequently, the brain depends on a special fluid [the cerebrospinal fluid (CSF)] that is flushed into brain along the unique perivascular spaces created by astrocytic vascular endfeet. We describe this pathway, coined the term glymphatic system, based on its dependency on astrocytic vascular endfeet and their adluminal expression of aquaporin-4 water channels facing toward CSF-filled perivascular spaces. Glymphatic clearance of potentially harmful metabolic or protein waste products, such as amyloid-β, is primarily active during sleep, when its physiological drivers, the cardiac cycle, respiration, and slow vasomotion, together efficiently propel CSF inflow along periarterial spaces. The brain's extracellular space contains an abundance of proteoglycans and hyaluronan, which provide a low-resistance hydraulic conduit that rapidly can expand and shrink during the sleep-wake cycle. We describe this unique fluid system of the brain, which meets the brain's requisites to maintain homeostasis similar to peripheral organs, considering the blood-brain-barrier and the paths for formation and egress of the CSF.

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.

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.

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.

On the Sensitivity Analysis of Porous Finite Element Models for Cerebral Perfusion Estimation

Computational physiological models are promising tools to enhance the design of clinical trials and to assist in decision making. Organ-scale haemodynamic models are gaining popularity to evaluate perfusion in a virtual environment both in healthy and diseased patients. Recently, the principles of verification, validation, and uncertainty quantification of such physiological models have been laid down to ensure safe applications of engineering software in the medical device industry. The present study sets out to establish guidelines for the usage of a three-dimensional steady state porous cerebral perfusion model of the human brain following principles detailed in the verification and validation (V&V 40) standard of the American Society of Mechanical Engineers. The model relies on the finite element method and has been developed specifically to estimate how brain perfusion is altered in ischaemic stroke patients before, during, and after treatments. Simulations are compared with exact analytical solutions and a thorough sensitivity analysis is presented covering every numerical and physiological model parameter. The results suggest that such porous models can approximate blood pressure and perfusion distributions reliably even on a coarse grid with first order elements. On the other hand, higher order elements are essential to mitigate errors in volumetric blood flow rate estimation through cortical surface regions. Matching the volumetric flow rate corresponding to major cerebral arteries is identified as a validation milestone. It is found that inlet velocity boundary conditions are hard to obtain and that constant pressure inlet boundary conditions are feasible alternatives. A one-dimensional model is presented which can serve as a computationally inexpensive replacement of the three-dimensional brain model to ease parameter optimisation, sensitivity analyses and uncertainty quantification. The findings of the present study can be generalised to organ-scale porous perfusion models. The results increase the applicability of computational tools regarding treatment development for stroke and other cerebrovascular conditions.

Harnessing cerebrospinal fluid circulation for drug delivery to brain tissues

Initially thought to be useful only to reach tissues in the immediate vicinity of the CSF circulatory system, CSF circulation is now increasingly viewed as a viable pathway to deliver certain therapeutics deeper into brain tissues. There is emerging evidence that this goal is achievable in the case of large therapeutic proteins, provided conditions are met that are described herein. We show how fluid dynamic modeling helps predict infusion rate and duration to overcome high CSF turnover. We posit that despite model limitations and controversies, fluid dynamic models, pharmacokinetic models, preclinical testing, and a qualitative understanding of the glymphatic system circulation can be used to estimate drug penetration in brain tissues. Lastly, in addition to highlighting landmark scientific and medical literature, we provide practical advice on formulation development, device selection, and pharmacokinetic modeling. Our review of clinical studies suggests a growing interest for intra-CSF delivery, particularly for targeted proteins.

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.

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.

Exploring neurodegenerative disorders using a novel integrated model of cerebral transport: Initial results

The neurovascular unit (NVU) underlines the complex and symbiotic relationship between brain cells and the cerebral vasculature, and dictates the need to consider both neurodegenerative and cerebrovascular diseases under the same mechanistic umbrella. Importantly, unlike peripheral organs, the brain was thought not to contain a dedicated lymphatics system. The glymphatic system concept (a portmanteau of glia and lymphatic) has further emphasized the importance of cerebrospinal fluid transport and emphasized its role as a mechanism for waste removal from the central nervous system. In this work, we outline a novel multiporoelastic solver which is embedded within a high precision, subject specific workflow that allows for the co-existence of a multitude of interconnected compartments with varying properties (multiple-network poroelastic theory, or MPET), that allow for the physiologically accurate representation of perfused brain tissue. This novel numerical template is based on a six-compartment MPET system (6-MPET) and is implemented through an in-house finite element code. The latter utilises the specificity of a high throughput imaging pipeline (which has been extended to incorporate the regional variation of mechanical properties) and blood flow variability model developed as part of the VPH-DARE@IT research platform. To exemplify the capability of this large-scale consolidated pipeline, a cognitively healthy subject is used to acquire novel, biomechanistically inspired biomarkers relating to primary and derivative variables of the 6-MPET system. These biomarkers are shown to capture the sophisticated nature of the NVU and the glymphatic system, paving the way for a potential route in deconvoluting the complexity associated with the likely interdependence of neurodegenerative and cerebrovascular diseases. The present study is the first, to the best of our knowledge, that casts and implements the 6-MPET equations in a 3D anatomically accurate brain geometry.

This was the year that was: brain barriers and brain fluid research in 2019

This editorial highlights advances in brain barrier and brain fluid research published in 2019, as well as addressing current controversies and pressing needs. Topics include recent advances related to: the cerebral endothelium and the neurovascular unit; the choroid plexus, arachnoid membrane; cerebrospinal fluid and the glymphatic hypothesis; the impact of disease states on brain barriers and brain fluids; drug delivery to the brain; and translation of preclinical data to the clinic. This editorial also mourns the loss of two important figures in the field, Malcolm B. Segal and Edward G. Stopa.

The Glymphatic System: A Review of the Challenges in Visualizing its Structure and Function with MR Imaging

The central nervous system (CNS) was previously thought to be the only organ system lacking lymphatic vessels to remove waste products from the interstitial space. Recently, based on the results from animal experiments, the glymphatic system was hypothesized. In this hypothesis, cerebrospinal fluid (CSF) enters the periarterial spaces, enters the interstitial space of the brain parenchyma via aquaporin-4 (AQP4) channels in the astrocyte end feet, and then exits through the perivenous space, thereby clearing waste products. From the perivenous space, the interstitial fluid drains into the subarachnoid space and meningeal lymphatics of the parasagittal dura. It has been reported that the glymphatic system is particularly active during sleep. Impairment of glymphatic system function might be a cause of various neurodegenerative diseases such as Alzheimer’s disease, normal pressure hydrocephalus, glaucoma, and others. Meningeal lymphatics regulate immunity in the CNS. Many researchers have attempted to visualize the function and structure of the glymphatic system and meningeal lymphatics in vivo using MR imaging. In this review, we aim to summarize these in vivo MR imaging studies and discuss the significance, current limitations, and future directions. We also discuss the significance of the perivenous cyst formation along the superior sagittal sinus, which is recently discovered in the downstream of the glymphatic system.

Fluid Flow and Mass Transport in Brain Tissue

Despite its small size, the brain consumes 25% of the body’s energy, generating its own weight in potentially toxic proteins and biological debris each year. The brain is also the only organ lacking lymph vessels to assist in removal of interstitial waste. Over the past 50 years, a picture has been developing of the brain’s unique waste removal system. Experimental observations show cerebrospinal fluid, which surrounds the brain, enters the brain along discrete pathways, crosses a barrier into the spaces between brain cells, and flushes the tissue, carrying wastes to routes exiting the brain. Dysfunction of this cerebral waste clearance system has been demonstrated in Alzheimer’s disease, traumatic brain injury, diabetes, and stroke. The activity of the system is observed to increase during sleep. In addition to waste clearance, this circuit of flow may also deliver nutrients and neurotransmitters. Here, we review the relevant literature with a focus on transport processes, especially the potential role of diffusion and advective flows.