Peristaltic pumping in thin non-axisymmetric annular tubes

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

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

The directional flow generated by peristalsis in perivascular networks-Theoretical and numerical reduced-order descriptions

Directional fluid flow in perivascular spaces surrounding cerebral arteries is hypothesized to play a key role in brain solute transport and clearance. While various drivers for a pulsatile flow, such as cardiac or respiratory pulsations, are well quantified, the question remains as to which mechanisms could induce a directional flow within physiological regimes. To address this question, we develop theoretical and numerical reduced-order models to quantify the directional (net) flow induceable by peristaltic pumping in periarterial networks. Each periarterial element is modeled as a slender annular space bounded internally by a circular tube supporting a periodic traveling (peristaltic) wave. Under reasonable assumptions of a small Reynolds number flow, small radii, and small-amplitude peristaltic waves, we use lubrication theory and regular perturbation methods to derive theoretical expressions for the directional net flow and pressure distribution in the perivascular network. The reduced model is used to derive closed-form analytical expressions for the net flow for simple network configurations of interest, including single elements, two elements in tandem, and a three element bifurcation, with results compared with numerical predictions. In particular, we provide a computable theoretical estimate of the net flow induced by peristaltic motion in perivascular networks as a function of physiological parameters, notably, wave length, frequency, amplitude, and perivascular dimensions. Quantifying the maximal net flow for specific physiological regimes, we find that vasomotion may induce net pial periarterial flow velocities on the order of a few to tens of μ m/s and that sleep-related changes in vasomotion pulsatility may drive a threefold flow increase.

Perivascular pumping of cerebrospinal fluid in the brain with a valve mechanism

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.

Quantifying the relationship between spreading depolarization and perivascular cerebrospinal fluid flow

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.

Image Analysis Techniques for In Vivo Quantification of Cerebrospinal Fluid Flow

Over the last decade, there has been a tremendously increased interest in understanding the neurophysiology of cerebrospinal fluid (CSF) flow, which plays a crucial role in clearing metabolic waste from the brain. This growing interest was largely initiated by two significant discoveries: the glymphatic system (a pathway for solute exchange between interstitial fluid deep within the brain and the CSF surrounding the brain) and meningeal lymphatic vessels (lymphatic vessels in the layer of tissue surrounding the brain that drain CSF). These two CSF systems work in unison, and their disruption has been implicated in several neurological disorders including Alzheimer's disease, stoke, and traumatic brain injury. Here, we present experimental techniques for in vivo quantification of CSF flow via direct imaging of fluorescent microspheres injected into the CSF. We discuss detailed image processing methods, including registration and masking of stagnant particles, to improve the quality of measurements. We provide guidance for quantifying CSF flow through particle tracking and offer tips for optimizing the process. Additionally, we describe techniques for measuring changes in arterial diameter, which is an hypothesized CSF pumping mechanism. Finally, we outline how these same techniques can be applied to cervical lymphatic vessels, which collect fluid downstream from meningeal lymphatic vessels. We anticipate that these fluid mechanical techniques will prove valuable for future quantitative studies aimed at understanding mechanisms of CSF transport and disruption, as well as for other complex biophysical systems.

The glymphatic system: Current understanding and modeling

We review theoretical and numerical models of the glymphatic system, which circulates cerebrospinal fluid and interstitial fluid around the brain, facilitating solute transport. Models enable hypothesis development and predictions of transport, with clinical applications including drug delivery, stroke, cardiac arrest, and neurodegenerative disorders like Alzheimer's disease. We sort existing models into broad categories by anatomical function: Perivascular flow, transport in brain parenchyma, interfaces to perivascular spaces, efflux routes, and links to neuronal activity. Needs and opportunities for future work are highlighted wherever possible; new models, expanded models, and novel experiments to inform models could all have tremendous value for advancing the field.

A one-dimensional model for the pulsating flow of cerebrospinal fluid in the spinal canal

The monitoring of intracranial pressure (ICP) fluctuations, which is needed in the context of a number of neurological diseases, requires the insertion of pressure sensors, an invasive procedure with considerable risk factors. Intracranial pressure fluctuations drive the wave-like pulsatile motion of cerebrospinal fluid (CSF) along the compliant spinal canal. Systematically derived simplified models relating the ICP fluctuations with the resulting CSF flow rate can be useful in enabling indirect evaluations of the former from non-invasive magnetic resonance imaging (MRI) measurements of the latter. As a preliminary step in enabling these predictive efforts, a model is developed here for the pulsating viscous motion of CSF in the spinal canal, assumed to be a linearly elastic compliant tube of slowly varying section, with a Darcy pressure-loss term included to model the fluid resistance introduced by the trabeculae, which are thin collagen-reinforced columns that form a web-like structure stretching across the spinal canal. Use of Fourier-series expansions enables predictions of CSF flow rate for realistic anharmonic ICP fluctuations. The flow rate predicted using a representative ICP waveform together with a realistic canal anatomy is seen to compare favourably with in vivo phase-contrast MRI measurements at multiple sections along the spinal canal. The results indicate that the proposed model, involving a limited number of parameters, can serve as a basis for future quantitative analyses targeting predictions of ICP temporal fluctuations based on MRI measurements of spinal-canal anatomy and CSF flow rate.

Emerging Roles of Microfluidics in Brain Research: From Cerebral Fluids Manipulation to Brain-on-a-Chip and Neuroelectronic Devices Engineering

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.

Dispersion as a waste-clearance mechanism in flow through penetrating perivascular spaces in the brain

Accumulation of metabolic wastes in the brain is correlated with several neurodegenerative disorders, including Alzheimer's disease. Waste transport and clearance occur via dispersion, the combined effect of diffusion and advection by flow of fluid. We examine the relative contributions of diffusion and advection in the perivascular spaces (PVSs) that surround penetrating cortical blood vessels and are filled with cerebrospinal fluid (CSF). To do so, we adapt prior analytic predictions of dispersion to the context of PVSs. We also perform advection-diffusion simulations in PVS-like geometries with parameters relevant to transport of amyloid-[Formula: see text] (associated with Alzheimer's) in a variety of flows, motivated by in vivo measurements. Specifically, we examine solute transport in steady and unsteady Poiseuille flows in an open (not porous) concentric circular annulus. We find that a purely oscillatory flow enhances dispersion only weakly and does not produce significant transport, whereas a steady flow component, even if slow, clears waste more effectively.