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Hladky SB, Barrand MA. Regulation of brain fluid volumes and pressures: basic principles, intracranial hypertension, ventriculomegaly and hydrocephalus. Fluids Barriers CNS 2024; 21:57. [PMID: 39020364 PMCID: PMC11253534 DOI: 10.1186/s12987-024-00532-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2023] [Accepted: 03/21/2024] [Indexed: 07/19/2024] Open
Abstract
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.
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Affiliation(s)
- Stephen B Hladky
- Department of Pharmacology, Tennis Court Rd, Cambridge, CB2 1PD, UK.
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2
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Cibelli A, Ballesteros-Gomez D, McCutcheon S, Yang GL, Bispo A, Krawchuk M, Piedra G, Spray DC. Astrocytes sense glymphatic-level shear stress through the interaction of sphingosine-1-phosphate with Piezo1. iScience 2024; 27:110069. [PMID: 38868201 PMCID: PMC11167526 DOI: 10.1016/j.isci.2024.110069] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Revised: 04/09/2024] [Accepted: 05/17/2024] [Indexed: 06/14/2024] Open
Abstract
Astrocyte endfeet enwrap brain vasculature, forming a boundary for perivascular glymphatic flow of fluid and solutes along and across the astrocyte endfeet into the brain parenchyma. We evaluated astrocyte sensitivity to shear stress generated by such flow, finding a set point for downstream calcium signaling that is below about 0.1 dyn/cm2. This set point is modulated by albumin levels encountered in cerebrospinal fluid (CSF) under normal conditions and following a blood-brain barrier breach or immune response. The astrocyte mechanosome responsible for the detection of shear stress includes sphingosine-1-phosphate (S1P)-mediated sensitization of the mechanosensor Piezo1. Fluid flow through perivascular channels delimited by vessel wall and astrocyte endfeet thus generates sufficient shear stress to activate astrocytes, thereby potentially controlling vasomotion and parenchymal perfusion. Moreover, S1P receptor signaling establishes a set point for Piezo1 activation that is finely tuned to coincide with CSF albumin levels and to the low shear forces resulting from glymphatic flow.
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Affiliation(s)
- Antonio Cibelli
- Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, USA
| | | | - Sean McCutcheon
- Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, USA
| | - Greta L. Yang
- Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, USA
| | - Ashley Bispo
- Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, USA
| | - Michael Krawchuk
- Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, USA
| | - Giselle Piedra
- Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, USA
| | - David C. Spray
- Department of Neuroscience, Albert Einstein College of Medicine, Bronx, NY 10461, USA
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Boster KAS, Sun J, Shang JK, Kelley DH, Thomas JH. Hydraulic resistance of three-dimensional pial perivascular spaces in the brain. Fluids Barriers CNS 2024; 21:7. [PMID: 38212763 PMCID: PMC10785473 DOI: 10.1186/s12987-023-00505-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2023] [Accepted: 12/15/2023] [Indexed: 01/13/2024] Open
Abstract
BACKGROUND Perivascular spaces (PVSs) carry cerebrospinal fluid (CSF) around the brain, facilitating healthy waste clearance. Measuring those flows in vivo is difficult, and often impossible, because PVSs are small, so accurate modeling is essential for understanding brain clearance. The most important parameter for modeling flow in a PVS is its hydraulic resistance, defined as the ratio of pressure drop to volume flow rate, which depends on its size and shape. In particular, the local resistance per unit length varies along a PVS and depends on variations in the local cross section. METHODS Using segmented, three-dimensional images of pial PVSs in mice, we performed fluid dynamical simulations to calculate the resistance per unit length. We applied extended lubrication theory to elucidate the difference between the calculated resistance and the expected resistance assuming a uniform flow. We tested four different approximation methods, and a novel correction factor to determine how to accurately estimate resistance per unit length with low computational cost. To assess the impact of assuming unidirectional flow, we also considered a circular duct whose cross-sectional area varied sinusoidally along its length. RESULTS We found that modeling a PVS as a series of short ducts with uniform flow, and numerically solving for the flow in each, yields good resistance estimates at low cost. If the second derivative of area with respect to axial location is less than 2, error is typically less than 15%, and can be reduced further with our correction factor. To make estimates with even lower cost, we found that instead of solving for the resistance numerically, the well-known resistance of a circular duct could be scaled by a shape factor. As long as the aspect ratio of the cross section was less than 0.7, the additional error was less than 10%. CONCLUSIONS Neglecting off-axis velocity components underestimates the average resistance, but the error can be reduced with a simple correction factor. These results could increase the accuracy of future models of brain-wide and local CSF flow, enabling better prediction of clearance, for example, as it varies with age, brain state, and pathological conditions.
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Affiliation(s)
- Kimberly A S Boster
- Department of Mechanical Engineering, University of Rochester, Rochester, NY, 14627, USA.
| | - Jiatong Sun
- Department of Mechanical Engineering, University of Rochester, Rochester, NY, 14627, USA
| | - Jessica K Shang
- Department of Mechanical Engineering, University of Rochester, Rochester, NY, 14627, USA
| | - Douglas H Kelley
- Department of Mechanical Engineering, University of Rochester, Rochester, NY, 14627, USA
| | - John H Thomas
- Department of Mechanical Engineering, University of Rochester, Rochester, NY, 14627, USA
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Ballesteros-Gomez D, McCutcheon S, Yang GL, Cibelli A, Bispo A, Krawchuk M, Piedra G, Spray DC. Astrocyte sensitivity to glymphatic shear stress is amplified by albumin and mediated by the interaction of sphingosine 1 phosphate with Piezo1. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.11.06.565884. [PMID: 37986983 PMCID: PMC10659372 DOI: 10.1101/2023.11.06.565884] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2023]
Abstract
Astrocyte endfeet enwrap brain vasculature, forming a boundary for perivascular glymphatic flow of fluid and solutes along and across the astrocyte endfeet into the brain parenchyma. To determine whether astrocytes may sense and respond to the shear forces generated by glymphatic flow, we examined intracellular calcium (Ca 2+ ) changes evoked in astrocytes to brief fluid flow applied in calibrated microfluidic chambers. Shear stresses < 20 dyn/cm 2 failed to evoke Ca 2+ responses in the absence of albumin, but cells responded to shear stress below 1 dyn/cm 2 when as little as 5 μM albumin was present in flow medium. A role for extracellular matrix in mechanotransduction was indicated by reduced sensitivity after degradation of heparan sulfate proteoglycan. Sphingosine-1-phosphate (S1P) amplified shear responses in the absence of albumin, whereas mechanosensitivity was attenuated by the S1P receptor blocker fingolimod. Piezo1 participated in the transduction as revealed by blockade by the spider toxin GsMTX and amplification by the chemical modulator Yoda1, even in absence of albumin or S1P. Our findings that astrocytes are exquisitely sensitive to shear stress and that sensitivity is greatly amplified by albumin concentrations encountered in normal and pathological CSF predict that perivascular astrocytes are responsive to glymphatic shear stress and that responsiveness is augmented by elevated CSF protein. S1P receptor signaling thus establishes a setpoint for Piezo1 activation that is finely tuned to coincide with albumin level in CSF and to the low shear forces resulting from glymphatic flow. Graphical abstract Astrocyte endfoot responds to glymphatic shear stress when albumin is present. Mechanism involves sphingosine-1-phosphate (S1P) binding to its receptor (S1PR), activating phospholipase C (PLC) and thereby sensitizing the response of Piezo1 to flow. Ca 2+ influx triggers Ca 2+ release from intracellular stores and further downstream signaling, thereby modulating parenchymal perfusion. Illustration created using BioRender.com.
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Hussain R, Tithof J, Wang W, Cheetham-West A, Song W, Peng W, Sigurdsson B, Kim D, Sun Q, Peng S, Plá V, Kelley DH, Hirase H, Castorena-Gonzalez JA, Weikop P, Goldman SA, Davis MJ, Nedergaard M. Potentiating glymphatic drainage minimizes post-traumatic cerebral oedema. Nature 2023; 623:992-1000. [PMID: 37968397 PMCID: PMC11216305 DOI: 10.1038/s41586-023-06737-7] [Citation(s) in RCA: 19] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Accepted: 10/10/2023] [Indexed: 11/17/2023]
Abstract
Cerebral oedema is associated with morbidity and mortality after traumatic brain injury (TBI)1. Noradrenaline levels are increased after TBI2-4, and the amplitude of the increase in noradrenaline predicts both the extent of injury5 and the likelihood of mortality6. Glymphatic impairment is both a feature of and a contributor to brain injury7,8, but its relationship with the injury-associated surge in noradrenaline is unclear. Here we report that acute post-traumatic oedema results from a suppression of glymphatic and lymphatic fluid flow that occurs in response to excessive systemic release of noradrenaline. This post-TBI adrenergic storm was associated with reduced contractility of cervical lymphatic vessels, consistent with diminished return of glymphatic and lymphatic fluid to the systemic circulation. Accordingly, pan-adrenergic receptor inhibition normalized central venous pressure and partly restored glymphatic and cervical lymphatic flow in a mouse model of TBI, and these actions led to substantially reduced brain oedema and improved functional outcomes. Furthermore, post-traumatic inhibition of adrenergic signalling boosted lymphatic export of cellular debris from the traumatic lesion, substantially reducing secondary inflammation and accumulation of phosphorylated tau. These observations suggest that targeting the noradrenergic control of central glymphatic flow may offer a therapeutic approach for treating acute TBI.
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Affiliation(s)
- Rashad Hussain
- Center for Translational Neuromedicine, University of Rochester, Rochester, NY, USA.
| | - Jeffrey Tithof
- Department of Mechanical Engineering, University of Rochester, Rochester, NY, USA
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, USA
| | - Wei Wang
- Center for Translational Neuromedicine, University of Rochester, Rochester, NY, USA
| | | | - Wei Song
- Center for Translational Neuromedicine, University of Rochester, Rochester, NY, USA
| | - Weiguo Peng
- Center for Translational Neuromedicine, University of Rochester, Rochester, NY, USA
- Center for Translational Neuromedicine, University of Copenhagen Faculty of Health and Medical Sciences, Copenhagen, Denmark
| | - Björn Sigurdsson
- Center for Translational Neuromedicine, University of Copenhagen Faculty of Health and Medical Sciences, Copenhagen, Denmark
| | - Daehyun Kim
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, USA
| | - Qian Sun
- Center for Translational Neuromedicine, University of Rochester, Rochester, NY, USA
| | - Sisi Peng
- Center for Translational Neuromedicine, University of Rochester, Rochester, NY, USA
| | - Virginia Plá
- Center for Translational Neuromedicine, University of Rochester, Rochester, NY, USA
| | - Douglas H Kelley
- Department of Mechanical Engineering, University of Rochester, Rochester, NY, USA
| | - Hajime Hirase
- Center for Translational Neuromedicine, University of Rochester, Rochester, NY, USA
- Center for Translational Neuromedicine, University of Copenhagen Faculty of Health and Medical Sciences, Copenhagen, Denmark
| | | | - Pia Weikop
- Center for Translational Neuromedicine, University of Copenhagen Faculty of Health and Medical Sciences, Copenhagen, Denmark
| | - Steven A Goldman
- Center for Translational Neuromedicine, University of Rochester, Rochester, NY, USA
- Center for Translational Neuromedicine, University of Copenhagen Faculty of Health and Medical Sciences, Copenhagen, Denmark
| | - Michael J Davis
- Department of Medical Pharmacology and Physiology, School of Medicine, University of Missouri, Columbia, MO, USA
| | - Maiken Nedergaard
- Center for Translational Neuromedicine, University of Rochester, Rochester, NY, USA.
- Center for Translational Neuromedicine, University of Copenhagen Faculty of Health and Medical Sciences, Copenhagen, Denmark.
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Boster KAS, Sun J, Shang JK, Kelley DH, Thomas JH. Hydraulic resistance of three-dimensional pial perivascular spaces in the brain. RESEARCH SQUARE 2023:rs.3.rs-3411983. [PMID: 37886576 PMCID: PMC10602107 DOI: 10.21203/rs.3.rs-3411983/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/28/2023]
Abstract
Background Perivascular spaces (PVSs) carry cerebrospinal fluid (CSF) around the brain, facilitating healthy waste clearance. Measuring those flows in vivo is difficult, and often impossible, because PVSs are small, so accurate modeling is essential for understanding brain clearance. The most important parameter for modeling flow in a PVS is its hydraulic resistance, defined as the ratio of pressure drop to volume flow rate, which depends on its size and shape. In particular, the local resistance per unit length varies along a PVS and depends on variations in the local cross section. Methods Using segmented, three-dimensional images of pial PVSs in mice, we performed fluid dynamical simulations to calculate the resistance per unit length. We applied extended lubrication theory to elucidate the difference between the calculated resistance and the expected resistance assuming a uniform flow. We tested four different approximation methods, and a novel correction factor to determine how to accurately estimate resistance per unit length with low computational cost. To assess the impact of assuming unidirectional flow, we also considered a circular duct whose cross-sectional area varied sinusoidally along its length. Results We found that modeling a PVS as a series of short ducts with uniform flow, and numerically solving for the flow in each, yields good resistance estimates at low cost. If the second derivative of area with respect to axial location is less than 2, error is typically less than 15%, and can be reduced further with our correction factor. To make estimates with even lower cost, we found that instead of solving for the resistance numerically, the well-known resistance of a circular duct could be scaled by a shape factor. As long as the aspect ratio of the cross section was less than 0.7, the additional error was less than 10%. Conclusions Neglecting off-axis velocity components underestimates the average resistance, but the error can be reduced with a simple correction factor. These results could increase the accuracy of future models of brain-wide and local CSF flow, enabling better prediction of clearance, for example, as it varies with age, brain state, and pathological conditions.
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Affiliation(s)
- Kimberly A. S. Boster
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - Jiatong Sun
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - Jessica K. Shang
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - Douglas H. Kelley
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - John H. Thomas
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
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Gan Y, Holstein-Rønsbo S, Nedergaard M, Boster KAS, Thomas JH, Kelley DH. Perivascular pumping of cerebrospinal fluid in the brain with a valve mechanism. J R Soc Interface 2023; 20:20230288. [PMID: 37727070 PMCID: PMC10509587 DOI: 10.1098/rsif.2023.0288] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Accepted: 08/30/2023] [Indexed: 09/21/2023] Open
Abstract
The flow of cerebrospinal fluid (CSF) along perivascular spaces (PVSs) is an important part of the brain's system for clearing metabolic waste. Experiments reveal that arterial motions from cardiac pulsations and functional hyperaemiadrive CSF in the same direction as the blood flow, but the mechanism producing this directionality is unclear. Astrocyte endfeet bound the PVSs of penetrating arteries, separating them from brain extracellular space (ECS) and potentially regulating flow between the two compartments. Here, we present two models, one based on the full equations of fluid dynamics and the other using lumped parameters, in which the astrocyte endfeet function as valves, regulating flow between the PVS and the ECS. In both models, cardiac pulsations drive a net CSF flow consistent with prior experimental observations. Functional hyperaemia, acting with cardiac pulsation, increases the net flow. We also find, in agreement with experiments, a reduced net flow during wakefulness, due to the known decrease in ECS permeability compared to the sleep state. We present in vivo imaging of penetrating arteries in mice, which we use to measure accurately the amplitude of their constrictions and dilations during both cardiac pulsation and functional hyperaemia, an important input for the models. Our models can be used to explore the effects of changes in other input parameters, such as those caused by ageing or disease, as better measurements of these parameters become available.
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Affiliation(s)
- Yiming Gan
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | | | - Maiken Nedergaard
- Center for Translational Neuromedicine, University of Copenhagen, Copenhagen, Denmark
- Center for Translational Neuromedicine and Department of Neuroscience, University of Rochester Medical Center, Rochester, NY 14627, USA
| | - Kimberly A. S. Boster
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - John H. Thomas
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - Douglas H. Kelley
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
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Mukherjee S, Mirzaee M, Tithof J. Quantifying the relationship between spreading depolarization and perivascular cerebrospinal fluid flow. Sci Rep 2023; 13:12405. [PMID: 37524734 PMCID: PMC10390554 DOI: 10.1038/s41598-023-38938-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 07/17/2023] [Indexed: 08/02/2023] Open
Abstract
Recent studies have linked spreading depolarization (SD, an electro-chemical wave in the brain following stroke, migraine, traumatic brain injury, and more) with increase in cerebrospinal fluid (CSF) flow through the perivascular spaces (PVSs, annular channels lining the brain vasculature). We develop a novel computational model that couples SD and CSF flow. We first use high order numerical simulations to solve a system of physiologically realistic reaction-diffusion equations which govern the spatiotemporal dynamics of ions in the extracellular and intracellular spaces of the brain cortex during SD. We then couple the SD wave with a 1D CSF flow model that captures the change in cross-sectional area, pressure, and volume flow rate through the PVSs. The coupling is modelled using an empirical relationship between the excess potassium ion concentration in the extracellular space following SD and the vessel radius. We find that the CSF volumetric flow rate depends intricately on the length and width of the PVS, as well as the vessel radius and the angle of incidence of the SD wave. We derive analytical expressions for pressure and volumetric flow rates of CSF through the PVS for a given SD wave and quantify CSF flow variations when two SD waves collide. Our numerical approach is very general and could be extended in the future to obtain novel, quantitative insights into how CSF flow in the brain couples with slow waves, functional hyperemia, seizures, or externally applied neural stimulations.
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Affiliation(s)
- Saikat Mukherjee
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, 55455, USA.
- Department of Mechanical Engineering, Iowa State University, Ames, IA, 50011, USA.
| | - Mahsa Mirzaee
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, 55455, USA
| | - Jeffrey Tithof
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, 55455, USA
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Raicevic N, Forer JM, Ladrón-de-Guevara A, Du T, Nedergaard M, Kelley DH, Boster K. Sizes and shapes of perivascular spaces surrounding murine pial arteries. Fluids Barriers CNS 2023; 20:56. [PMID: 37461047 PMCID: PMC10351203 DOI: 10.1186/s12987-023-00454-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 06/21/2023] [Indexed: 07/20/2023] Open
Abstract
BACKGROUND Flow of cerebrospinal fluid (CSF) through brain perivascular spaces (PVSs) is essential for the clearance of interstitial metabolic waste products whose accumulation and aggregation is a key mechanism of pathogenesis in many diseases. The PVS geometry has important implications for CSF flow as it affects CSF and solute transport rates. Thus, the size and shape of the perivascular spaces are essential parameters for models of CSF transport in the brain and require accurate quantification. METHODS We segmented two-photon images of pial (surface) PVSs and the adjacent arteries and characterized their sizes and shapes of cross sections from 14 PVS segments in 9 mice. Based on the analysis, we propose an idealized model that approximates the cross-sectional size and shape of pial PVSs, closely matching their area ratios and hydraulic resistances. RESULTS The ratio of PVS-to-vessel area varies widely across the cross sections analyzed. The hydraulic resistance per unit length of the PVS scales with the PVS cross-sectional area, and we found a power-law fit that predicts resistance as a function of the area. Three idealized geometric models were compared to PVSs imaged in vivo, and their accuracy in reproducing hydraulic resistances and PVS-to-vessel area ratios were evaluated. The area ratio was obtained across different cross sections, and we found that the distribution peaks for the original PVS and its closest idealized fit (polynomial fit) were 1.12 and 1.21, respectively. The peak of the hydraulic resistance distribution is [Formula: see text] Pa s/m[Formula: see text] and [Formula: see text] Pa s/m[Formula: see text] for the segmentation and its closest idealized fit, respectively. CONCLUSIONS PVS hydraulic resistance can be reasonably predicted as a function of the PVS area. The proposed polynomial-based fit most closely captures the shape of the PVS with respect to area ratio and hydraulic resistance. Idealized PVS shapes are convenient for modeling, which can be used to better understand how anatomical variations affect clearance and drug transport.
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Affiliation(s)
- Nikola Raicevic
- Department of Mechanical Engineering, University of Rochester, Rochester, USA
| | - Jarod M Forer
- Department of Mechanical Engineering, University of Rochester, Rochester, USA
| | - Antonio Ladrón-de-Guevara
- Center for Translational Neuromedicine and Department of Neuroscience, University of Rochester Medical Center, Rochester, USA
- Department of Biomedical Engineering, University of Rochester, Rochester, USA
| | - Ting Du
- Center for Translational Neuromedicine and Department of Neuroscience, University of Rochester Medical Center, Rochester, USA
- School of Pharmacy, China Medical University, Shenyang, Liaoning, China
| | - Maiken Nedergaard
- Center for Translational Neuromedicine and Department of Neuroscience, University of Rochester Medical Center, Rochester, USA
| | - Douglas H Kelley
- Department of Mechanical Engineering, University of Rochester, Rochester, USA
| | - Kimberly Boster
- Department of Mechanical Engineering, University of Rochester, Rochester, USA.
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Boster KAS, Cai S, Ladrón-de-Guevara A, Sun J, Zheng X, Du T, Thomas JH, Nedergaard M, Karniadakis GE, Kelley DH. Artificial intelligence velocimetry reveals in vivo flow rates, pressure gradients, and shear stresses in murine perivascular flows. Proc Natl Acad Sci U S A 2023; 120:e2217744120. [PMID: 36989300 PMCID: PMC10083563 DOI: 10.1073/pnas.2217744120] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Accepted: 02/15/2023] [Indexed: 03/30/2023] Open
Abstract
Quantifying the flow of cerebrospinal fluid (CSF) is crucial for understanding brain waste clearance and nutrient delivery, as well as edema in pathological conditions such as stroke. However, existing in vivo techniques are limited to sparse velocity measurements in pial perivascular spaces (PVSs) or low-resolution measurements from brain-wide imaging. Additionally, volume flow rate, pressure, and shear stress variation in PVSs are essentially impossible to measure in vivo. Here, we show that artificial intelligence velocimetry (AIV) can integrate sparse velocity measurements with physics-informed neural networks to quantify CSF flow in PVSs. With AIV, we infer three-dimensional (3D), high-resolution velocity, pressure, and shear stress. Validation comes from training with 70% of PTV measurements and demonstrating close agreement with the remaining 30%. A sensitivity analysis on the AIV inputs shows that the uncertainty in AIV inferred quantities due to uncertainties in the PVS boundary locations inherent to in vivo imaging is less than 30%, and the uncertainty from the neural net initialization is less than 1%. In PVSs of N = 4 wild-type mice we find mean flow speed 16.33 ± 11.09 µm/s, volume flow rate 2.22 ± 1.983 × 103 µm3/s, axial pressure gradient ( - 2.75 ± 2.01)×10-4 Pa/µm (-2.07 ± 1.51 mmHg/m), and wall shear stress (3.00 ± 1.45)×10-3 Pa (all mean ± SE). Pressure gradients, flow rates, and resistances agree with prior predictions. AIV infers in vivo PVS flows in remarkable detail, which will improve fluid dynamic models and potentially clarify how CSF flow changes with aging, Alzheimer's disease, and small vessel disease.
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Affiliation(s)
| | - Shengze Cai
- Institute of Cyber-Systems and Control, College of Control Science and Engineering, Zhejiang University, Hangzhou310027, Zhejiang, China
| | - Antonio Ladrón-de-Guevara
- Center for Translational Neuromedicine and Department of Neuroscience, University of Rochester Medical Center, Rochester, NY14627
| | - Jiatong Sun
- Department of Mechanical Engineering, University of Rochester, Rochester, NY14627
| | - Xiaoning Zheng
- Department of Mathematics, College of Information Science and Technology, Jinan University, Guangzhou510632, China
| | - Ting Du
- Center for Translational Neuromedicine and Department of Neuroscience, University of Rochester Medical Center, Rochester, NY14627
- School of Pharmacy, China Medical University, Shenyang, Liaoning110122, China
| | - John H. Thomas
- Department of Mechanical Engineering, University of Rochester, Rochester, NY14627
| | - Maiken Nedergaard
- Center for Translational Neuromedicine and Department of Neuroscience, University of Rochester Medical Center, Rochester, NY14627
| | - George Em Karniadakis
- Division of Applied Mathematics, Brown University, Providence, RI02912
- School of Engineering, Brown University, Providence, RI02912
| | - Douglas H. Kelley
- Department of Mechanical Engineering, University of Rochester, Rochester, NY14627
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Semyachkina-Glushkovskaya OV, Postnov DE, Khorovodov AP, Navolokin NA, Kurthz JHG. Lymphatic Drainage System of the Brain: a New Player in Neuroscience. J EVOL BIOCHEM PHYS+ 2023. [DOI: 10.1134/s0022093023010015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/16/2023]
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12
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Transport in the Brain Extracellular Space: Diffusion, but Which Kind? Int J Mol Sci 2022; 23:ijms232012401. [PMID: 36293258 PMCID: PMC9604357 DOI: 10.3390/ijms232012401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Revised: 10/10/2022] [Accepted: 10/12/2022] [Indexed: 11/17/2022] Open
Abstract
The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the proposed glymphatic hypothesis, which assumes a directed flow of cerebral fluid within the parenchyma, in contrast to the previous notion that diffusion is the main mechanism. However, when discussing the issue of “diffusion or non-diffusion”, much less attention was given to the question that diffusion itself can have a different character. In our opinion, some of the recently published results do not fit into the traditional understanding of diffusion. In this regard, we outline the relevant new theoretical approaches on transport processes in complex random media such as concepts of diffusive diffusivity and time-dependent homogenization, which expands the understanding of the forms of transport of substances based on diffusion.
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Abstract
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.
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Boster KAS, Tithof J, Cook DD, Thomas JH, Kelley DH. Sensitivity analysis on a network model of glymphatic flow. J R Soc Interface 2022; 19:20220257. [PMID: 35642425 PMCID: PMC9156905 DOI: 10.1098/rsif.2022.0257] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 05/05/2022] [Indexed: 12/24/2022] Open
Abstract
Intracranial cerebrospinal and interstitial fluid (ISF) flow and solute transport have important clinical implications, but limited in vivo access to the brain interior leaves gaping holes in human understanding of the nature of these neurophysiological phenomena. Models can address some gaps, but only insofar as model inputs are accurate. We perform a sensitivity analysis using a Monte Carlo approach on a lumped-parameter network model of cerebrospinal and ISF in perivascular and extracellular spaces in the murine brain. We place bounds on model predictions given the uncertainty in input parameters. Péclet numbers for transport in penetrating perivascular spaces (PVSs) and within the parenchyma are separated by at least two orders of magnitude. Low permeability in penetrating PVSs requires unrealistically large driving pressure and/or results in poor perfusion and are deemed unlikely. The model is most sensitive to the permeability of penetrating PVSs, a parameter whose value is largely unknown, highlighting an important direction for future experiments. Until the value of the permeability of penetrating PVSs is more accurately measured, the uncertainty of any model that includes flow in penetrating PVSs is so large that absolute numbers have little meaning and practical application is limited.
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Affiliation(s)
- Kimberly A. S. Boster
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - Jeffrey Tithof
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
| | - Douglas D. Cook
- Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA
| | - John H. Thomas
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - Douglas H. Kelley
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
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Tithof J, Boster KA, Bork PA, Nedergaard M, Thomas JH, Kelley DH. A network model of glymphatic flow under different experimentally-motivated parametric scenarios. iScience 2022; 25:104258. [PMID: 35521514 PMCID: PMC9062681 DOI: 10.1016/j.isci.2022.104258] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2021] [Revised: 02/08/2022] [Accepted: 04/08/2022] [Indexed: 12/04/2022] Open
Abstract
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. We model the CSF pathway as a network of hydraulic resistances Predictions are bracketed by analyzing parametric scenarios for unknown parameters Low-resistance PVSs and high-resistance parenchyma produce realistic flows Astrocyte endfoot gap size is among the important parameters to be measured
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Affiliation(s)
- Jeffrey Tithof
- Department of Mechanical Engineering, University of Rochester, 235 Hopeman Building, Rochester 14627, NY, USA
- Department of Mechanical Engineering, University of Minnesota, 111 Church St SE, Minneapolis 55455, MN, USA
- Corresponding author
| | - Kimberly A.S. Boster
- Department of Mechanical Engineering, University of Rochester, 235 Hopeman Building, Rochester 14627, NY, USA
| | - Peter A.R. Bork
- Center for Translational Neuromedicine, Faculty of Health and Medical Sciences, University of Copenhagen, Blegdamsvej 3B, 2200 Copenhagen N, Copenhagen, Denmark
| | - Maiken Nedergaard
- Center for Translational Neuromedicine, Faculty of Health and Medical Sciences, University of Copenhagen, Blegdamsvej 3B, 2200 Copenhagen N, Copenhagen, Denmark
- Center for Translational Neuromedicine, Department of Neurosurgery, University of Rochester Medical Center, 601 Elmwood Avenue, Rochester 14642, NY, USA
| | - John H. Thomas
- Department of Mechanical Engineering, University of Rochester, 235 Hopeman Building, Rochester 14627, NY, USA
| | - Douglas H. Kelley
- Department of Mechanical Engineering, University of Rochester, 235 Hopeman Building, Rochester 14627, NY, USA
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16
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Abstract
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.
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Affiliation(s)
- Martin Kaag Rasmussen
- Center for Translational Neuromedicine, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
| | - Humberto Mestre
- Center for Translational Neuromedicine, University of Rochester Medical Center, Rochester, New York
| | - Maiken Nedergaard
- Center for Translational Neuromedicine, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark
- Center for Translational Neuromedicine, University of Rochester Medical Center, Rochester, New York
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Hladky SB, Barrand MA. The glymphatic hypothesis: the theory and the evidence. Fluids Barriers CNS 2022; 19:9. [PMID: 35115036 PMCID: PMC8815211 DOI: 10.1186/s12987-021-00282-z] [Citation(s) in RCA: 87] [Impact Index Per Article: 43.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2021] [Accepted: 10/15/2021] [Indexed: 12/13/2022] Open
Abstract
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.
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Affiliation(s)
- Stephen B. Hladky
- Department of Pharmacology, University of Cambridge, Cambridge, CB2 1PD UK
| | - Margery A. Barrand
- Department of Pharmacology, University of Cambridge, Cambridge, CB2 1PD UK
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Wan J, Zhou S, Mea HJ, Guo Y, Ku H, Urbina BM. Emerging Roles of Microfluidics in Brain Research: From Cerebral Fluids Manipulation to Brain-on-a-Chip and Neuroelectronic Devices Engineering. Chem Rev 2022; 122:7142-7181. [PMID: 35080375 DOI: 10.1021/acs.chemrev.1c00480] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Remarkable progress made in the past few decades in brain research enables the manipulation of neuronal activity in single neurons and neural circuits and thus allows the decipherment of relations between nervous systems and behavior. The discovery of glymphatic and lymphatic systems in the brain and the recently unveiled tight relations between the gastrointestinal (GI) tract and the central nervous system (CNS) further revolutionize our understanding of brain structures and functions. Fundamental questions about how neurons conduct two-way communications with the gut to establish the gut-brain axis (GBA) and interact with essential brain components such as glial cells and blood vessels to regulate cerebral blood flow (CBF) and cerebrospinal fluid (CSF) in health and disease, however, remain. Microfluidics with unparalleled advantages in the control of fluids at microscale has emerged recently as an effective approach to address these critical questions in brain research. The dynamics of cerebral fluids (i.e., blood and CSF) and novel in vitro brain-on-a-chip models and microfluidic-integrated multifunctional neuroelectronic devices, for example, have been investigated. This review starts with a critical discussion of the current understanding of several key topics in brain research such as neurovascular coupling (NVC), glymphatic pathway, and GBA and then interrogates a wide range of microfluidic-based approaches that have been developed or can be improved to advance our fundamental understanding of brain functions. Last, emerging technologies for structuring microfluidic devices and their implications and future directions in brain research are discussed.
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Affiliation(s)
- Jiandi Wan
- Department of Chemical Engineering, University of California, Davis, California 95616, United States
| | - Sitong Zhou
- Department of Chemical Engineering, University of California, Davis, California 95616, United States
| | - Hing Jii Mea
- Department of Chemical Engineering, University of California, Davis, California 95616, United States
| | - Yaojun Guo
- Department of Electrical and Computer Engineering, University of California, Davis, California 95616, United States
| | - Hansol Ku
- Department of Electrical and Computer Engineering, University of California, Davis, California 95616, United States
| | - Brianna M Urbina
- Biochemistry, Molecular, Cellular and Developmental Biology Program, University of California, Davis, California 95616, United States
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Ray LA, Pike M, Simon M, Iliff JJ, Heys JJ. Quantitative analysis of macroscopic solute transport in the murine brain. Fluids Barriers CNS 2021; 18:55. [PMID: 34876169 PMCID: PMC8650464 DOI: 10.1186/s12987-021-00290-z] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2021] [Accepted: 11/21/2021] [Indexed: 12/16/2022] Open
Abstract
BACKGROUND Understanding molecular transport in the brain is critical to care and prevention of neurological disease and injury. A key question is whether transport occurs primarily by diffusion, or also by convection or dispersion. Dynamic contrast-enhanced (DCE-MRI) experiments have long reported solute transport in the brain that appears to be faster than diffusion alone, but this transport rate has not been quantified to a physically relevant value that can be compared to known diffusive rates of tracers. METHODS In this work, DCE-MRI experimental data is analyzed using subject-specific finite-element models to quantify transport in different anatomical regions across the whole mouse brain. The set of regional effective diffusivities ([Formula: see text]), a transport parameter combining all mechanisms of transport, that best represent the experimental data are determined and compared to apparent diffusivity ([Formula: see text]), the known rate of diffusion through brain tissue, to draw conclusions about dominant transport mechanisms in each region. RESULTS In the perivascular regions of major arteries, [Formula: see text] for gadoteridol (550 Da) was over 10,000 times greater than [Formula: see text]. In the brain tissue, constituting interstitial space and the perivascular space of smaller blood vessels, [Formula: see text] was 10-25 times greater than [Formula: see text]. CONCLUSIONS The analysis concludes that convection is present throughout the brain. Convection is dominant in the perivascular space of major surface and branching arteries (Pe > 1000) and significant to large molecules (> 1 kDa) in the combined interstitial space and perivascular space of smaller vessels (not resolved by DCE-MRI). Importantly, this work supports perivascular convection along penetrating blood vessels.
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Affiliation(s)
- Lori A Ray
- Department of Chemical and Biological Engineering, Montana State University, Bozeman, USA
| | - Martin Pike
- Advanced Imaging Research Center, Oregon Health and Sciences University, Portland, USA
| | - Matthew Simon
- Department of Anesthesiology and Perioperative Medicine, Oregon Health and Science University, Portland, USA
- Neuroscience Graduate Program, Oregon Health and Science University, Portland, USA
- Denali Therapeutics, San Francisco, USA
| | - Jeffrey J Iliff
- VISN 20 Mental Illness Research, Education and Clinical Center (MIRECC), VA Puget Sound Health Care System, Seattle, USA
- Department of Psychiatry and Behavioral Sciences, University of Washington School of Medicine, Seattle, USA
- Department of Neurology, University of Washington School of Medicine, Seattle, USA
| | - Jeffrey J Heys
- Department of Chemical and Biological Engineering, Montana State University, Bozeman, USA.
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20
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Brain solute transport is more rapid in periarterial than perivenous spaces. Sci Rep 2021; 11:16085. [PMID: 34373476 PMCID: PMC8352970 DOI: 10.1038/s41598-021-95306-x] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2021] [Accepted: 07/23/2021] [Indexed: 11/13/2022] Open
Abstract
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.
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21
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Abstract
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.
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Affiliation(s)
- Douglas H. Kelley
- Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627, USA
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22
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Carr JB, Thomas JH, Liu J, Shang JK. Peristaltic pumping in thin non-axisymmetric annular tubes. JOURNAL OF FLUID MECHANICS 2021; 917:A10. [PMID: 35310826 PMCID: PMC8932954 DOI: 10.1017/jfm.2021.277] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
The two-dimensional laminar flow of a viscous fluid induced by peristalsis due to a moving wall wave has been studied previously for a rectangular channel, a circular tube and a concentric circular annulus. Here, we study peristaltic flow in a non-axisymmetric annular tube: in this case, the flow is three-dimensional, with motions in the azimuthal direction. This type of geometry is motivated by experimental observations of the pulsatile flow of cerebrospinal fluid along perivascular spaces surrounding arteries in the brain, which is at least partially driven by peristaltic pumping due to pulsations of the artery. These annular perivascular spaces are often eccentric and the outer boundary is seldom circular: their cross-sections can be well matched by a simple, adjustable model consisting of an inner circle (the outer wall of the artery) and an outer ellipse (the outer edge of the perivascular space), not necessarily concentric. We use this geometric model as a basis for numerical simulations of peristaltic flow: the adjustability of the model makes it suitable for other applications. We concentrate on the general effects of the non-axisymmetric configuration on the flow and do not attempt to specifically model perivascular pumping. We use a finite-element scheme to compute the flow in the annulus driven by a propagating sinusoidal radial displacement of the inner wall. Unlike the peristaltic flow in a concentric circular annulus, the flow is fully three-dimensional: azimuthal pressure variations drive an oscillatory flow in and out of the narrower gaps, inducing an azimuthal wiggle in the streamlines. We examine the dependence of the flow on the elongation of the outer elliptical wall and the eccentricity of the configuration. We find that the time-averaged volumetric flow is always in the same direction as the peristaltic wave and decreases with increasing ellipticity or eccentricity. The additional shearing motion in the azimuthal direction will increase mixing and enhance Taylor dispersion in these flows, effects that might have practical applications.
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Affiliation(s)
- J. Brennen Carr
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - John H. Thomas
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - Jia Liu
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
| | - Jessica K. Shang
- Department of Mechanical Engineering, University of Rochester, Rochester, NY 14627, USA
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23
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Raghunandan A, Ladron-de-Guevara A, Tithof J, Mestre H, Du T, Nedergaard M, Thomas JH, Kelley DH. Bulk flow of cerebrospinal fluid observed in periarterial spaces is not an artifact of injection. eLife 2021; 10:65958. [PMID: 33687330 PMCID: PMC7979157 DOI: 10.7554/elife.65958] [Citation(s) in RCA: 35] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2020] [Accepted: 03/08/2021] [Indexed: 12/24/2022] Open
Abstract
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.
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Affiliation(s)
- Aditya Raghunandan
- Department of Mechanical Engineering, University of Rochester, Rochester, United States
| | - Antonio Ladron-de-Guevara
- Center for Translational Neuromedicine, University of Rochester Medical Center, Rochester, United States
| | - Jeffrey Tithof
- Department of Mechanical Engineering, University of Rochester, Rochester, United States.,Department of Mechanical Engineering, University of Minnesota, Minneapolis, United States
| | - Humberto Mestre
- Center for Translational Neuromedicine, University of Rochester Medical Center, Rochester, United States
| | - Ting Du
- Center for Translational Neuromedicine, University of Rochester Medical Center, Rochester, United States
| | - Maiken Nedergaard
- Center for Translational Neuromedicine, University of Rochester Medical Center, Rochester, United States.,Center for Translational Neuromedicine, University of Copenhagen, Rochester, United States
| | - John H Thomas
- Department of Mechanical Engineering, University of Rochester, Rochester, United States
| | - Douglas H Kelley
- Department of Mechanical Engineering, University of Rochester, Rochester, United States
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24
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Troyetsky DE, Tithof J, Thomas JH, Kelley DH. Dispersion as a waste-clearance mechanism in flow through penetrating perivascular spaces in the brain. Sci Rep 2021; 11:4595. [PMID: 33633194 PMCID: PMC7907360 DOI: 10.1038/s41598-021-83951-1] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2020] [Accepted: 02/10/2021] [Indexed: 01/31/2023] Open
Abstract
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.
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Affiliation(s)
- Daniel E Troyetsky
- Department of Mechanical Engineering, University of Rochester, Rochester, 14627, NY, USA
| | - Jeffrey Tithof
- Department of Mechanical Engineering, University of Rochester, Rochester, 14627, NY, USA
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, 55455, MN, USA
| | - John H Thomas
- Department of Mechanical Engineering, University of Rochester, Rochester, 14627, NY, USA
| | - Douglas H Kelley
- Department of Mechanical Engineering, University of Rochester, Rochester, 14627, NY, USA.
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25
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Faghih MM, Keith Sharp M. Mechanisms of tracer transport in cerebral perivascular spaces. J Biomech 2021; 118:110278. [PMID: 33548658 DOI: 10.1016/j.jbiomech.2021.110278] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2021] [Accepted: 01/16/2021] [Indexed: 02/09/2023]
Abstract
Tracers infused into the brain appear to be transported along channels surrounding cerebral blood vessels. Bulk fluid flow has been hypothesized in paravascular "glymphatic" channels (outer space between the pial membrane and astrocyte endfeet), as well as in the periarterial space (inner space between smooth muscle cells). The plausibility of net flow in these channels due to steady and oscillatory pressures is reviewed, as is that of transport by oscillatory shear-enhanced dispersion in the absence of net flow. Models including 1D branching networks of annular channels and an expanded compartmental model for humans both predict that flow driven by physiologic steady pressure differences is unlikely in both periarterial and paraarterial spaces, whether the spaces are open or filled with porous media. One exception is that a small additional steady pressure difference could drive paraarterial flow if the space is open. The potential that the tracer injection itself could present such a pressure difference is outlined. Oscillatory (peristaltic) wall motion alone has been found to be insufficient to drive significant forward flow. However, a number of hypothesized mechanisms that have yet to be experimentally verified in the brain may create directional flow in combination with wall motion. Shear-augmented dispersion due to oscillatory pressure in channels with a range of porosity has been modeled analytically. Enhancement of axial dispersion is small for periarterial channels. In open paraarterial channels, dispersion enhancement with optimal lateral mixing is large enough that it may explain observed tracer transport without net forward fluid flow.
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Affiliation(s)
- Mohammad M Faghih
- Department of Mechanical Engineering, University of Louisville Louisville, KY 40292, United States
| | - M Keith Sharp
- Department of Mechanical Engineering, University of Louisville Louisville, KY 40292, United States.
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