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 turnover as a driver of brain clearance.

Cerebrospinal fluid (CSF) has historically been considered to function as a sink for brain-derived waste disposal. Recent work suggested that CSF interacts even more intensely with brain tissue than previously recognized, through perivascular spaces that penetrate the brain. Cardiac pulsations, vasomotion, and respiration have been suggested to drive CSF flow in these perivascular spaces, thereby enhancing waste clearance. However, the intrinsic role of CSF production in relation to its distribution volume (turnover) is not an explicit component of recent concepts on brain clearance. Here, we review the work on CSF turnover and volume, focusing on preclinical evidence. Herein, we highlight the use of MRI in establishing CSF-related parameters. We describe the impact of sleep, effect of anesthesia, aging, and hypertension on CSF turnover, and how this relates to brain clearance. Evaluation of the available evidence suggests that CSF turnover is a major determinant in brain clearance. In addition, we propose that several putative drivers of brain clearance, but also conditions associated with impaired clearance, such as aging, may actually relate to altered CSF turnover.

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.

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.

Estimates of the permeability of extra-cellular pathways through the astrocyte endfoot sheath.

BACKGROUND: Astrocyte endfoot processes are believed to cover all micro-vessels in the brain cortex and may play a significant role in fluid and substance transport into and out of the brain parenchyma. Detailed fluid mechanical models of diffusive and advective transport in the brain are promising tools to investigate theories of transport. METHODS: We derive theoretical estimates of astrocyte endfoot sheath permeability for advective and diffusive transport and its variation in microvascular networks from mouse brain cortex. The networks are based on recently published experimental data and generated endfoot patterns are based on Voronoi tessellations of the perivascular surface. We estimate corrections for projection errors in previously published data. RESULTS: We provide structural-functional relationships between vessel radius and resistance that can be directly used in flow and transport simulations. We estimate endfoot sheath filtration coefficients in the range [Formula: see text] to [Formula: see text], diffusion membrane coefficients for small solutes in the range [Formula: see text] to [Formula: see text], and gap area fractions in the range 0.2-0.6%, based on a inter-endfoot gap width of 20 nm. CONCLUSIONS: The astrocyte endfoot sheath surrounding microvessels forms a secondary barrier to extra-cellular transport, separating the extra-cellular space of the parenchyma and the perivascular space outside the endothelial layer. The filtration and membrane diffusion coefficients of the endfoot sheath are estimated to be an order of magnitude lower than those of the extra-cellular matrix while being two orders of magnitude higher than those of the vessel wall.

Human intracranial pulsatility during the cardiac cycle: a computational modelling framework.

BACKGROUND: Today's availability of medical imaging and computational resources set the scene for high-fidelity computational modelling of brain biomechanics. The brain and its environment feature a dynamic and complex interplay between the tissue, blood, cerebrospinal fluid (CSF) and interstitial fluid (ISF). Here, we design a computational platform for modelling and simulation of intracranial dynamics, and assess the models' validity in terms of clinically relevant indicators of brain pulsatility. Focusing on the dynamic interaction between tissue motion and ISF/CSF flow, we treat the pulsatile cerebral blood flow as a prescribed input of the model. METHODS: We develop finite element models of cardiac-induced fully coupled pulsatile CSF flow and tissue motion in the human brain environment. The three-dimensional model geometry is derived from magnetic resonance images (MRI) and features a high level of detail including the brain tissue, the ventricular system, and the cranial subarachnoid space (SAS). We model the brain parenchyma at the organ-scale as an elastic medium permeated by an extracellular fluid network and describe flow of CSF in the SAS and ventricles as viscous fluid movement. Representing vascular expansion during the cardiac cycle, a prescribed pulsatile net blood flow distributed over the brain parenchyma acts as the driver of motion. Additionally, we investigate the effect of model variations on a set of clinically relevant quantities of interest. RESULTS: Our model predicts a complex interplay between the CSF-filled spaces and poroelastic parenchyma in terms of ICP, CSF flow, and parenchymal displacements. Variations in the ICP are dominated by their temporal amplitude, but with small spatial variations in both the CSF-filled spaces and the parenchyma. Induced by ICP differences, we find substantial ventricular and cranial-spinal CSF flow, some flow in the cranial SAS, and small pulsatile ISF velocities in the brain parenchyma. Moreover, the model predicts a funnel-shaped deformation of parenchymal tissue in dorsal direction at the beginning of the cardiac cycle. CONCLUSIONS: Our model accurately depicts the complex interplay of ICP, CSF flow and brain tissue movement and is well-aligned with clinical observations. It offers a qualitative and quantitative platform for detailed investigation of coupled intracranial dynamics and interplay, both under physiological and pathophysiological conditions.

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.

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.

Sleep deprivation impairs molecular clearance from the human brain.

It remains an enigma why human beings spend one-third of their life asleep. Experimental data suggest that sleep is required for clearance of waste products from brain metabolism. This has, however, never been verified in humans. The primary aim of the present study was to examine in vivo whether one night of total sleep deprivation affects molecular clearance from the human brain. Secondarily, we examined whether clearance was affected by subsequent sleep. Multiphase MRI with standardized T1 sequences was performed up to 48 h after intrathecal administration of the contrast agent gadobutrol (0.5 ml of 1 mmol/ml), which served as a tracer molecule. Using FreeSurfer software, we quantified tracer enrichment within 85 brain regions as percentage change from baseline of normalized T1 signals. The cerebral tracer enrichment was compared between two cohorts of individuals; one cohort (n = 7) underwent total sleep deprivation from Day 1 to Day 2 (sleep deprivation group) while an age and gender-matched control group (n = 17; sleep group) was allowed free sleep from Day 1 to Day 2. From Day 2 to 3 all individuals were allowed free sleep. The tracer enriched the brains of the two groups similarly. Sleep deprivation was the sole intervention. One night of sleep deprivation impaired clearance of the tracer substance from most brain regions, including the cerebral cortex, white matter and limbic structures, as demonstrated on the morning of Day 2 after intervention (sleep deprivation/sleep). Moreover, the impaired cerebral clearance in the sleep deprivation group was not compensated by subsequent sleep from Day 2 to 3. The present results provide in vivo evidence that one night of total sleep deprivation impairs molecular clearance from the human brain, and that humans do not catch up on lost sleep.

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.

Intracranial pressure elevation alters CSF clearance pathways.

BACKGROUND: Infusion testing is a common procedure to determine whether shunting will be beneficial in patients with normal pressure hydrocephalus. The method has a well-developed theoretical foundation and corresponding mathematical models that describe the CSF circulation from the choroid plexus to the arachnoid granulations. Here, we investigate to what extent the proposed glymphatic or paravascular pathway (or similar pathways) modifies the results of the traditional mathematical models. METHODS: We used a compartment model to estimate pressure in the subarachnoid space and the paravascular spaces. For the arachnoid granulations, the cribriform plate and the glymphatic circulation, resistances were calculated and used to estimate pressure and flow before and during an infusion test. Finally, different variations to the model were tested to evaluate the sensitivity of selected parameters. RESULTS: At baseline intracranial pressure (ICP), we found a very small paravascular flow directed into the subarachnoid space, while 60% of the fluid left through the arachnoid granulations and 40% left through the cribriform plate. However, during the infusion, 80% of the fluid left through the arachnoid granulations, 20% through the cribriform plate and flow in the PVS was stagnant. Resistance through the glymphatic system was computed to be 2.73 mmHg/(mL/min), considerably lower than other fluid pathways, giving non-realistic ICP during infusion if combined with a lymphatic drainage route. CONCLUSIONS: The relative distribution of CSF flow to different clearance pathways depends on ICP, with the arachnoid granulations as the main contributor to outflow. As such, ICP increase is an important factor that should be addressed when determining the pathways of injected substances in the subarachnoid space. Our results suggest that the glymphatic resistance is too high to allow for pressure driven flow by arterial pulsations and at the same time too small to allow for a direct drainage route from PVS to cervical lymphatics.

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.

Respiratory influence on cerebrospinal fluid flow - a computational study based on long-term intracranial pressure measurements.

Current theories suggest that waste solutes are cleared from the brain via cerebrospinal fluid (CSF) flow, driven by pressure pulsations of possibly both cardiac and respiratory origin. In this study, we explored the importance of respiratory versus cardiac pressure gradients for CSF flow within one of the main conduits of the brain, the cerebral aqueduct. We obtained overnight intracranial pressure measurements from two different locations in 10 idiopathic normal pressure hydrocephalus (iNPH) patients. The resulting pressure gradients were analyzed with respect to cardiac and respiratory frequencies and amplitudes (182,000 cardiac and 48,000 respiratory cycles). Pressure gradients were used to compute CSF flow in simplified and patient-specific models of the aqueduct. The average ratio between cardiac over respiratory flow volume was 0.21 ± 0.09, even though the corresponding ratio between the pressure gradient amplitudes was 2.85 ± 1.06. The cardiac cycle was 0.25 ± 0.04 times the length of the respiratory cycle, allowing the respiratory pressure gradient to build considerable momentum despite its small magnitude. No significant differences in pressure gradient pulsations were found in the sleeping versus awake state. Pressure gradients underlying CSF flow in the cerebral aqueduct are dominated by cardiac pulsations, but induce CSF flow volumes dominated by respiration.