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

Simulating the impact of tumor mechanical forces on glymphatic networks in the brain parenchyma

The brain glymphatic system is currently being explored in the context of many neurological disorders and diseases, including traumatic brain injury, Alzheimer's disease, and ischemic stroke. However, little is known about the impact of brain tumors on glymphatic function. Mechanical forces generated during tumor development and growth may be responsible for compromised glymphatic transport pathways, reducing waste clearance and cerebrospinal fluid (CSF) transport in the brain parenchyma. One such force is solid stress, i.e., growth-induced forces from cell hyperproliferation and excess matrix deposition. Because there are no prior studies assessing the impact of tumor-derived solid stress on glymphatic system structure and performance in the brain parenchyma, this study serves to fill an important gap in the field. We adapted a previously developed Electrical Analog Model using MATLAB Simulink for glymphatic transport coupled with Finite Element Analysis for tumor mechanical stresses and strains in COMSOL. This allowed simulation of the impact of tumor mechanical force generation on fluid transport within brain parenchymal glymphatic units-which include perivascular spaces, astrocytic networks, interstitial spaces, and capillary basement membranes. We conducted a parametric analysis to compare the contributions of tumor size, tumor proximity, and ratio of glymphatic subunits to the stress and strain experienced by the glymphatic unit and corresponding reduction in flow rate of CSF. Mechanical stresses intensify with proximity to the tumor and increasing tumor size, highlighting the vulnerability of nearby glymphatic units to tumor-derived forces. Our stress and strain profiles reveal compressive deformation of these surrounding glymphatics and demonstrate that varying the relative contributions of astrocytes vs. interstitial spaces impact the resulting glymphatic structure significantly under tumor mechanical forces. Increased tumor size and proximity caused increased stress and strain across all glymphatic subunits, as does decreased astrocyte composition. Indeed, our model reveals an inverse correlation between extent of astrocyte contribution to the composition of the glymphatic unit and the resulting mechanical stress. This increased mechanical strain across the glymphatic unit decreases the venous efflux rate of CSF, dependent on the degree of strain and the specific glymphatic subunit of interest. For example, a 20% mechanical strain on capillary basement membranes does not significantly decrease venous efflux (2% decrease in flow rates), while the same magnitude of strain on astrocyte networks and interstitial spaces decreases efflux flow rates by 7% and 22%, respectively. Our simulations reveal that solid stress from growing brain tumors directly reduces glymphatic fluid transport, independently from biochemical effects from cancer cells. Understanding these pathophysiological implications is crucial for developing targeted interventions aimed at restoring effective waste clearance mechanisms in the brain. This study opens potential avenues for future experimental research in brain tumor-related glymphatic dysfunction.

Regulation of brain fluid volumes and pressures: basic principles, intracranial hypertension, ventriculomegaly and hydrocephalus

The principles of cerebrospinal fluid (CSF) production, circulation and outflow and regulation of fluid volumes and pressures in the normal brain are summarised. Abnormalities in these aspects in intracranial hypertension, ventriculomegaly and hydrocephalus are discussed. The brain parenchyma has a cellular framework with interstitial fluid (ISF) in the intervening spaces. Framework stress and interstitial fluid pressure (ISFP) combined provide the total stress which, after allowing for gravity, normally equals intracerebral pressure (ICP) with gradients of total stress too small to measure. Fluid pressure may differ from ICP in the parenchyma and collapsed subarachnoid spaces when the parenchyma presses against the meninges. Fluid pressure gradients determine fluid movements. In adults, restricting CSF outflow from subarachnoid spaces produces intracranial hypertension which, when CSF volumes change very little, is called idiopathic intracranial hypertension (iIH). Raised ICP in iIH is accompanied by increased venous sinus pressure, though which is cause and which effect is unclear. In infants with growing skulls, restriction in outflow leads to increased head and CSF volumes. In adults, ventriculomegaly can arise due to cerebral atrophy or, in hydrocephalus, to obstructions to intracranial CSF flow. In non-communicating hydrocephalus, flow through or out of the ventricles is somehow obstructed, whereas in communicating hydrocephalus, the obstruction is somewhere between the cisterna magna and cranial sites of outflow. When normal outflow routes are obstructed, continued CSF production in the ventricles may be partially balanced by outflow through the parenchyma via an oedematous periventricular layer and perivascular spaces. In adults, secondary hydrocephalus with raised ICP results from obvious obstructions to flow. By contrast, with the more subtly obstructed flow seen in normal pressure hydrocephalus (NPH), fluid pressure must be reduced elsewhere, e.g. in some subarachnoid spaces. In idiopathic NPH, where ventriculomegaly is accompanied by gait disturbance, dementia and/or urinary incontinence, the functional deficits can sometimes be reversed by shunting or third ventriculostomy. Parenchymal shrinkage is irreversible in late stage hydrocephalus with cellular framework loss but may not occur in early stages, whether by exclusion of fluid or otherwise. Further studies that are needed to explain the development of hydrocephalus are outlined.

Simulating the Impact of Tumor Mechanical Forces on Glymphatic Networks in the Brain Parenchyma

Background

The brain glymphatic system is currently being explored in the context of many neurological disorders and diseases, including traumatic brain injury, Alzheimer's disease, and ischemic stroke. However, little is known about the impact of brain tumors on glymphatic function. Mechanical forces generated during tumor development and growth may be responsible for compromised glymphatic transport pathways, reducing waste clearance and cerebrospinal fluid (CSF) transport in the brain parenchyma. One such force is solid stress, i.e., growth-induced forces from cell hyperproliferation and excess matrix deposition. Because there are no prior studies assessing the impact of tumor-derived solid stress on glymphatic system structure and performance in the brain parenchyma, this study serves to fill an important gap in the field.

Methods

We adapted a previously developed Electrical Analog Model using MATLAB Simulink for glymphatic transport coupled with Finite Element Analysis for tumor mechanical stresses and strains in COMSOL. This allowed simulation of the impact of tumor mechanical force generation on fluid transport within brain parenchymal glymphatic units - which include paravascular spaces, astrocytic networks, interstitial spaces, and capillary basement membranes. We conducted a parametric analysis to compare the contributions of tumor size, tumor proximity, and ratio of glymphatic subunits to the stress and strain experienced by the glymphatic unit and corresponding reduction in flow rate of CSF.

Results

Mechanical stresses intensify with proximity to the tumor and increasing tumor size, highlighting the vulnerability of nearby glymphatic units to tumor-derived forces. Our stress and strain profiles reveal compressive deformation of these surrounding glymphatics and demonstrate that varying the relative contributions of astrocytes vs. interstitial spaces impact the resulting glymphatic structure significantly under tumor mechanical forces. Increased tumor size and proximity caused increased stress and strain across all glymphatic subunits, as does decreased astrocyte composition. Indeed, our model reveals an inverse correlation between extent of astrocyte contribution to the composition of the glymphatic unit and the resulting mechanical stress. This increased mechanical strain across the glymphatic unit decreases the venous efflux rate of CSF, dependent on the degree of strain and the specific glymphatic subunit of interest. For example, a 20% mechanical strain on capillary basement membranes does not significantly decrease venous efflux (2% decrease in flow rates), while the same magnitude of strain on astrocyte networks and interstitial spaces decreases efflux flow rates by 7% and 22%, respectively.

Conclusion

Our simulations reveal that solid stress from brain tumors directly reduces glymphatic fluid transport, independently from biochemical effects from cancer cells. Understanding these pathophysiological implications is crucial for developing targeted interventions aimed at restoring effective waste clearance mechanisms in the brain.This study opens potential avenues for future experimental research in brain tumor-related glymphatic dysfunction.

Modeling of brain efflux: Constraints of brain surfaces

Fluid efflux from the brain plays an important role in solute waste clearance. Current experimental approaches provide little spatial information, and data collection is limited due to short duration or low frequency of sampling. One approach shows tracer efflux to be independent of molecular size, indicating bulk flow, yet also decelerating like simple membrane diffusion. In an apparent contradiction to this report, other studies point to tracer efflux acceleration. We here develop a one-dimensional advection-diffusion model to gain insight into brain efflux principles. The model is characterized by nine physiological constants and three efflux parameters for which we quantify prior uncertainty. Using Bayes' rule and the two efflux studies, we validate the model and calculate data-informed parameter distributions. The apparent contradictions in the efflux studies are resolved by brain surface boundaries being bottlenecks for efflux. To critically test the model, a custom MRI efflux assay measuring solute dispersion in tissue and release to cerebrospinal fluid was employed. The model passed the test with tissue bulk flow velocities in the range 60 to 190 [Formula: see text]m/h. Dimensional analysis identified three principal determinants of efflux, highlighting brain surfaces as a restricting factor for metabolite solute clearance.

Gaps in the wall of a perivascular space act as valves to produce a directed flow of cerebrospinal fluid: a hoop-stress model

The flow of cerebrospinal fluid (CSF) along perivascular spaces (PVSs) is an important part of the brain's system for clearing metabolic waste. Astrocyte endfeet bound the PVSs of penetrating arteries, separating them from brain extracellular space. Gaps between astrocyte endfeet might provide a low-resistance pathway for fluid transport across the wall. Recent studies suggest that the astrocyte endfeet function as valves that rectify the CSF flow, producing the net flow observed in pial PVSs by changing the size of the gaps in response to pressure changes. In this study, we quantify this rectification based on three features of the PVSs: the quasi-circular geometry, the deformable endfoot wall, and the pressure oscillation inside. We provide an analytical model, based on the thin-shell hoop-stress approximation, and predict a pumping efficiency of about 0.4, which would contribute significantly to the observed flow. When we add the flow resistance of the extracellular space (ECS) to the model, we find an increased net flow during sleep, due to the known increase in ECS porosity (decreased flow resistance) compared to that in the awake state. We corroborate our analytical model with three-dimensional fluid-solid interaction simulations.

Circadian Mechanisms in Brain Fluid Biology

The brain is a complex organ, fundamentally changing across the day to perform basic functions like sleep, thought, and regulating whole-body physiology. This requires a complex symphony of nutrients, hormones, ions, neurotransmitters and more to be properly distributed across the brain to maintain homeostasis throughout 24 hours. These solutes are distributed both by the blood and by cerebrospinal fluid. Cerebrospinal fluid contents are distinct from the general circulation because of regulation at brain barriers including the choroid plexus, glymphatic system, and blood-brain barrier. In this review, we discuss the overlapping circadian (≈24-hour) rhythms in brain fluid biology and at the brain barriers. Our goal is for the reader to gain both a fundamental understanding of brain barriers alongside an understanding of the interactions between these fluids and the circadian timing system. Ultimately, this review will provide new insight into how alterations in these finely tuned clocks may lead to pathology.

Analysis of potassium ion diffusion from neurons to capillaries: Effects of astrocyte endfeet geometry

Neurovascular coupling (NVC) refers to a local increase in cerebral blood flow in response to increased neuronal activity. Mechanisms of communication between neurons and blood vessels remain unclear. Astrocyte endfeet almost completely cover cerebral capillaries, suggesting that astrocytes play a role in NVC by releasing vasoactive substances near capillaries. An alternative hypothesis is that direct diffusion through the extracellular space of potassium ions (K+ ) released by neurons contributes to NVC. Here, the goal is to determine whether astrocyte endfeet present a barrier to K+ diffusion from neurons to capillaries. Two simplified 2D geometries of extracellular space, clefts between endfeet, and perivascular space are used: (i) a source 1 μm from a capillary; (ii) a neuron 15 μm from a capillary. K+ release is modelled as a step increase in [K+ ] at the outer boundary of the extracellular space. The time-dependent diffusion equation is solved numerically. In the first geometry, perivascular [K+ ] approaches its final value within 0.05 s. Decreasing endfeet cleft width or increasing perivascular space width slows the rise in [K+ ]. In the second geometry, the increase in perivascular [K+ ] occurs within 0.5 s and is insensitive to changes in cleft width or perivascular space width. Predicted levels of perivascular [K+ ] are sufficient to cause vasodilation, and the rise time is within the time for flow increase in NVC. These results suggest that direct diffusion of K+ through the extracellular space is a possible NVC signalling mechanism.