Hydraulic resistance of three-dimensional pial perivascular spaces in the brain.

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.

Hydraulic resistance of three-dimensional pial perivascular spaces in the brain.

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.

Perivascular pumping in the mouse brain: Improved boundary conditions reconcile theory, simulation, and experiment.

Cerebrospinal fluid (CSF) flows through the perivascular spaces (PVSs) surrounding cerebral arteries. Revealing the mechanisms driving that flow could bring improved understanding of brain waste transport and insights for disorders including Alzheimer's disease and stroke. In vivo velocity measurements of CSF in surface PVSs in mice have been used to argue that flow is driven primarily by the pulsatile motion of artery walls - perivascular pumping. However, fluid dynamics theory and simulation have predicted that perivascular pumping produces flows differing from in vivo observations starkly, particularly in the phase and relative amplitude of flow oscillation. We show that coupling theoretical and simulated flows to more realistic end boundary conditions, using resistance and compliance values measured in mice instead of using periodic boundaries, results in velocities that match observations more closely in phase and relative amplitude of oscillation, while preserving the existing agreement in mean flow speed. This quantitative agreement among theory, simulation, and in vivo measurement further supports the idea that perivascular pumping is an important CSF driver in physiological conditions.

Peristaltic pumping in thin non-axisymmetric annular tubes.

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.

Patient-Specific Multiscale Modeling of the Assisted Bidirectional Glenn.

BACKGROUND: First-stage palliation of neonates with single-ventricle physiology is associated with poor outcomes and challenging clinical management. Prior computational modeling and in vitro experiments introduced the assisted bidirectional Glenn (ABG), which increased pulmonary flow and oxygenation over the bidirectional Glenn (BDG) and the systemic-to-pulmonary shunt in idealized models. In this study, we demonstrate that the ABG achieves similar performance in patient-specific models and assess the influence of varying shunt geometry. METHODS: In a small cohort of single-ventricle prestage 2 patients, we constructed three-dimensional in silico models and tuned lumped parameter networks to match clinical measurements. Each model was modified to produce virtual BDG and ABG surgeries. We simulated the hemodynamics of the stage 1 procedure, BDG, and ABG by using multiscale computational modeling, coupling a finite-element flow solver to the lumped parameter network. Two levels of pulmonary vascular resistances (PVRs) were investigated: baseline (low) PVR of the patients and doubled (high) PVR. The shunt nozzle diameter, anastomosis location, and shape were also manipulated. RESULTS: The ABG increased the pulmonary flow rate and pressure by 15% to 20%, which was accompanied by a rise in superior vena caval pressure (2 to 3 mm Hg) at both PVR values. Pulmonary flow rate and superior vena caval pressures were most sensitive to the shunt nozzle diameter. CONCLUSIONS: Patient-specific ABG performance was similar to prior idealized simulations and experiments, with good performance at lower PVR values in the range of measured clinical data. Larger shunt outlet diameters and lower PVR led to improved ABG performance.