Session P03: Biological Fluid Dynamics: Physiological Lymphatic and CSF Flows

Role of Valve Spacing and Vessel Contraction Wavelength on Lymphatic Pumping Performance

The lymphatic system plays an important role in body's homeostasis through transport of lymph, fatty acid, and immune cells within an extensive network of lymphatic valves and vessels. These system of valves and vessels allow unidirectional pumping overall without any centralized pump against adverse pressure gradient, but many aspects of lymphatic  operation, especially the role of lymphatic valves, are less understood. Our work aims to explore some of these areas through fully coupled 3D fluid-structure interaction computational model to understand the effect of lymphatic valve spacing and vessel contraction wavelength on pumping performance. Our results suggest that flow rate and pumping efficiency can have a drastic difference depending on whether the valve spacing matches with vessel contraction wavelength while increased valve density from smaller valve spacing cause increase in work done by the vessel to account for increased viscous loss. Overall, our work investigates many unexplored regions of lymphatic operation and brings a greater understanding in the role that lymphatic valves play in overall pumping performance.   

Simulations of Cervical Lymphatic Vessels to Quantify Optimal Intrinsic Pumping

The lymphatic system maintains extracellular fluid levels in the body while removing metabolic waste products and cellular debris. Reduced flow through cervical lymphatic vessels (CLVs; located in the neck) has recently been implicated in several neurological disorders including traumatic brain injury, stroke, and Alzheimer’s disease. Our research aims to simulate fluid flow through CLVs of rodents, which provides one of the primary routes through which fluid leaves the skull. Recent experimental measurements demonstrate that contractions of vessel segments (i.e. intrinsic pumping), along with the presence of valves, provide the primary driving mechanism for CLVs. To capture the strong nonlinearities of the valves and elastic properties of the lymphangion walls, we adapt a lumped parameter model of the lymphatic system that was introduced by Bertram et al. (Biomech Model Mechanobiol 2014). We investigate how the net flow rate changes as we vary the number of lymphangions, contraction frequency, and contraction phase shift for adjacent lymphangions. We identify the optimal parameter ranges that maximize fluid flow through CLVs. These results provide important insight into brain health and potential mechanisms of neurological disorders.    

Sensitivity Analysis of a Hydraulic Network Model of Glymphatic Flow

Flow of cerebrospinal fluid and extracellular fluid in the brain interior has significant implications for waste clearance and drug and nutrient delivery. However, limited in vivo access to the brain interior leaves gaping holes in human understanding and has led to debate on the nature of these flows. We developed a lumped-parameter network model representing the glymphatic system, based on available experimental measurements. Of the 23 parameters in the model, 11 are difficult to measure directly and have considerable uncertainty associated with them. We performed a sensitivity analysis using a Monte Carlo approach to determine how the model parameters affect quantities of interest, including total model hydraulic resistance, flow distribution, and parenchymal perfusion. The sensitivity analysis revealed that total model resistance is most sensitive to the permeability of penetrating perivascular spaces, which can motivate future experimental efforts. The input parameter space was reduced based on the range of parameters that require an unrealistically large driving pressure. Model features that are known or hypothesized to change with arousal state were varied to determine which parameters have the greatest potential to regulate glymphatic flow.     

Hydraulic resistance model for interstitial fluid flow in the brain

Flow of interstitial fluid between the perivascular spaces around penetrating blood vessels in the brain tissue called the parenchyma is thought to be an important part of the brain's glymphatic system for waste clearance. Due to the difficulty of making measurements in the parenchyma, fluid-dynamic models are employed to better understand this flow. We used an analytical solution for Darcy flow in a porous medium with line sources (representing arterioles) and line sinks (representing venules) to model the flow and hydraulic resistance for various arrangements of the vessels. Other models use a 1:1 ratio of arterioles to venules, but experimental data suggest that humans have a 2:1 ratio and mice have a 1:3 ratio. We find that the resistances produced by these ratios are significantly different, implying that a simple dipole is not an appropriate model of the flow. We calculated flows and resistances based on experimental measurements of the locations of arterioles and venules in rodent and primate brains. We also created idealized arrangements that maximize intervessel spacing, thus minimizing the resistance and required driving pressure, which can be used to estimate the resistance in the absence of data of the locations of the penetrating vessels.   

Flow in porous media as a model for transport of interstitial fluid in the brain.

There is emerging evidence that the vasculatue of the brain dictates the drainage of beta-amyloid proteins and interstitial fluid. One of the pathways to clear these proteins out of the brain is along arterial walls. This flow occurs along the tunica media of the arteries and arterioles that consists mainly of smooth muscle cells and extracellular matrix. Recent studies suggest that ultraslow frequency oscillations resulting from contractile activity of smooth muscle cells in the tunica media play an important role in the drainage of fluids and solutes. These oscillations in the microvasculature are independent of the neuronal activity. In our earlier work, deformations of the arterial wall boundaries due to heart pulses were theorized to drive the interstitial fluid flow. In our current work, we investigate the role of forward propagating arterial pulsations and reverse low-frequency smooth muscle contraction waves on the flow transport along the arterial walls. We created a mathematical model that accounts for the porosity dynamics of the periarterial basement membrane space. We report phase diagrams that identify combinations of the parameters of these waves that induce either forward or reverse flows in these periarterial channels.    

A 1-D Pulse Wave Model Coupling Arterial and Perivascular Flow

In vivo measurements of cerebrospinal fluid in the perivascular spaces (PVSs) of the brain—annular channels surrounding the cerebral arteries—suggest that flow is driven by waves propagating along the arterial wall. Here, we present a one-dimensional pulse wave propagation model for flow and pressure that couples the arterial and perivascular networks. The model first simulates pulsatile blood flow through a vascular network terminated with Windkessel lumped parameter models. The arterial area deformation wave is then coupled to a PVS network model. This approach simplifies the fluid-structure interaction and allows the investigation of flow and pressure in PVSs in parts of the brain that are not experimentally accessible. To our knowledge, there is currently no other computational model of perivascular flow that can account for the evolution in the arterial wave through bifurcations or explicitly includes the effects of arterial material properties on perivascular flow.   

Neural activity increases cerebrospinal fluid influx and waste removal in the glymphatic system

The flow of cerebrospinal fluid (CSF) fluid through perivascular spaces (PVSs) is an essential part of the glymphatic system, which promotes metabolic waste clearance in the brain. Neuronal activation leads to vessel dilation, increased blood flow, and an increase in local consumption of energy and production of metabolites. Because neural activity is linked to the production of metabolic waste, we examined whether neuronal activation induced by whisker stimulation also increases glymphatic fluid transport and thereby boosts the removal of metabolic waste. We studied fluid flow in the brains of anesthetized mice using a two-photon microscope, dye visualization, and particle tracking. We found that whisker stimulation increases blood flow and CSF inflow. Particle tracking showed that vessel dilation decreases the CSF downstream velocity but also increases outward flow away from the dilating arterial wall. Increased CSF tracer accumulation and later clearance were noted within the activated hemisphere compared with the opposite hemisphere, demonstrating that neural activity increases glymphatic influx and waste removal. In comparison, laser-induced constriction of the vessel in transgenic mice revealed that  pure vessel constriction in the absence of neural activation does also increase the CSF volumetric flow and drives backflow in downstream regions.   

One-dimensional simulations enable study of cerebrospinal fluid flow in branching perivascular spaces

The glymphatic system efficiently removes metabolic wastes, such as amyloid$-\beta$, from the brain by utilizing cerebrospinal fluid (CSF) flow through perivascular spaces (PVSs), annular pathways surrounding cortical arteries and veins. Neurodegenerative diseases such as Alzheimer's are connected to reduction in fluid transport and accumulation of amyloid$-\beta$ in the brain. A leading hypothesis suggests arterial pulsations drive CSF flow through PVSs via peristalsis. Some prior numerical simulations refute this idea, but they solely employ small arterial segments with no bifurcations. Our work utilizes 1D modeling to investigate flow in complex branching geometries without excessive computational cost. By employing realistic values for geometry of brain vasculature and arterial pulsations, we quantify peristaltic transport in complex, branching networks and explore how changing peristalsis wave parameters might alter fluid flow in such geometries.   

Phase contrast MRI characterization and mathematical modeling of the cerebrospinal fluid dynamics along the spinal canal

Phase contrast (PC) MRI flow measurements in 6 healthy adult subjects are used to quantify the motion of the cerebrospinal fluid (CSF) along the spinal canal. Measurements are taken at multiple locations in the cervical, thoracic, and lumbar regions, thereby enabling a complete characterization of the oscillatory axial flow. The results are used to inform a one-dimensional description for the wave dynamics incorporating a linear elastic model for the spinal-canal compliance as well as the effect of flow resistance due to microanatomical features. The analysis provides increased understanding of the connection between the intracranial pressure fluctuations and the resulting CSF pulsating flow.   

In-vitro characterization of the motion of the cerebrospinal fluid in the spinal canal

The work studies the motion of the cerebrospinal fluid (CSF) in the spinal canal (SAS), driven by intracranial pressure fluctuations with angular frequency ω. These fluctuations induces a displacement of the CSF of tidal volume very small compared with the total volume in the SAS (△V/V ∼ ε << 1). To that aim, in-vitro experiments of the dispersion of a solute have been conducted in a simplified facility to characterize the effects of the canal geometry and the Womersley number (α). The experimental results show that the flow configuration changes as α varies. Thus, the flow moves upwards along the narrowest sections of the canal for small values of α, while it starts moving downwards as α increases. Furthermore, it is also reported the formation of recirculating cells when the eccentricity varies along the canal. These experimental results are in good agreement with previous analytical and numerical predictions.   

In-vivo experiments on respiratory-driven spinal CSF flow

In recent years, respiration has been postulated as a major driving mechanism for the flow of cerebrospinal fluid (CSF) in the spinal canal. Previous studies have employed real-time phase-contrast magnetic resonance imaging (MRI) to investigate forced and extreme breathing maneuvers. The present work reports respiratory-gated MRI measurements of CSF flow in the spinal canal under normal, controlled breathing. Six different vertebral levels were considered for a set of healthy subjects. Results show cranial/caudal motion during inspiration/expiration, with large flow rates and stroke volumes at the lumbar and lower thoracic regions, where respiration-driven flow rates appear to be higher than previously reported cardiac-driven rates, the latter being dominant in the upper cervical region. Although significant differences are found between different subjects, the results suggest that the respiratory cycle should be accounted for in the full characterization of spinal CSF flow and associated transport rates.   

Floquet stability analysis of a two-layer oscillatory flow near a flexible wall as a model to study the flow induced in syringomyelia cavities

Syringomyelia is a disorder characterized by the accumulation of fluid in the spinal cord, forming macroscopic fluid-filled cavities, called syrinxes, the growth of which can lead to progressive neurological damage. It is widely accepted that both the hydrodynamics of the cerebrospinal fluid in the spinal subarachnoid space and the motion of the fluid inside the syringomyelia cavities play an important role in their formation and growth. In the present work we are concerned with the coupling between the motion in these two fluid layers, enabled by the flexible nature of the spinal-cord nervous tissue that separates them. In particular, we have studied a simplified model problem involving the Floquet stability analysis of the oscillatory flow of two layers of fluid separated by an initially undeformed flexible wall. The results of the analysis show that, for a given amount of (linear) coupling between the pressure difference across the wall and the wall deformation, there exists a critical value of the Reynolds number above which the flow becomes unstable to perturbations that are synchronous with the basic oscillatory state.