Arterial vasodilation drives convective fluid flow in the brain: a poroelastic model

Abstract

The movement of fluid into, through, and out of the brain plays an important role in clearing metabolic waste. However, there is controversy regarding the mechanisms driving fluid movement in the fluid-filled paravascular spaces (PVS), and whether the movement of metabolic waste in the brain extracellular space (ECS) is primarily driven by diffusion or convection. The dilation of penetrating arterioles in the brain in response to increases in neural activity (neurovascular coupling) is an attractive candidate for driving fluid circulation, as it drives deformation of the brain tissue and of the PVS around arteries, resulting in fluid movement. We simulated the effects of vasodilation on fluid movement into and out of the brain ECS using a novel poroelastic model of brain tissue. We found that arteriolar dilations could drive convective flow through the ECS radially outward from the arteriole, and that this flow is sensitive to the dynamics of the dilation. Simulations of sleep-like conditions, with larger vasodilations and increased extracellular volume in the brain showed enhanced movement of fluid from the PVS into the ECS. Our simulations suggest that both sensory-evoked and sleep-related arteriolar dilations can drive convective flow of cerebrospinal fluid not just in the PVS, but also into the ECS through the PVS around arterioles.

Fig. 1

Schematic showing the working of a poroelastic model of the PVS, SAS and the brain tissue. a. Flowchart showing the full range of physics at play between the PVS, SAS, brain tissue, and the ECS that can be simulated by a poroelastic model. The field in green represents the physics that traditional fluid dynamic models capture (cf. [4]. The field light purple (which contains the field in green) represents the physics captured by traditional fluid–structure interaction models (cf. [61]). The model presented in this paper extends the physics captured within the light purple field to also include the physics represented by the arrows outside said field. b. The advantages of using a poroelastic model over a traditional fluid–structure interaction model. In our previous fluid–structure interaction model we only simulated the fluid phase in the PVS and the SAS (shown by black dots). By contrast, with a poroelastic model we can also simulate the elasticity of the connective tissue and, more importantly, the fluid flow and transport through the ECS. These differences mean that a poroelastic model can simulate fluid exchange between the brain parenchyma and other fluid spaces along with the force exchange that can be simulated by a fluid–structure interaction model

Fig. 2

Geometry, boundary conditions and discretization of the model. a. The geometry of the model showing the two domains, with the dimensions and boundary conditions. Solid displacement and fluid velocity were prescribed at the red- and cream-colored surfaces. Pressure-like tractions were prescribed on the green- and blue-colored surfaces. Flow resistance (Robin) boundary conditions were prescribed on the purple-colored surface. Symmetry boundary conditions were prescribed on all other surfaces. b. Tetrahedral mesh used for the finite element model. A fine mesh, with elements of $2\mathrm{\mu }\mathrm{m}$ were used near the regions where no-slip boundary conditions were prescribed and at the interface between the two domains. The mesh size was gradually increased to $10\mathrm{\mu }\mathrm{m}$. c The fluid flow in the SAS at the baseline state, which is a result of the pressure difference applied across the ends (green- and blue-colored surfaces in a)

Fig. 3

The asymmetric waveform of functional hyperemia can drive net directional fluid flow through the PVS. a The radially outward displacement (blue) and velocity (green) of the arteriolar wall for the case of symmetric dilation (top) and asymmetric dilation (bottom). b The time averaged radial Peclet numbers at the PVS-ECS interface as a result of symmetric (top) and (asymmetric) vasodilation. c The pressure and relative fluid velocity in the PVS and the ECS at the times of maximum radially outward and inward arteriolar wall velocity for symmetric (top) and asymmetric (bottom) dilation. The colors show the pressure value in mmHg and the arrows show the magnitude and direction of relative fluid flow. By comparing the ratio of the maximum relative velocity in the PVS and SAS, it can be seen with asymmetric vasodilation more fluid enters the ECS through the PVS than returns into the PVS through the ECS

Fig. 4

Functional hyperemia drives fluid penetration into the brain. a The initial position of particles used for particle tracking simulations. b The waveform of radial displacement of arteriolar displacement for symmetric and asymmetric dilation in the model. The asymmetric dilation waveform represents functional hyperemia. c The distribution of fluid position for 60 s of simulation with symmetric (left) and asymmetric (right) dilation waveform. Asymmetric dilation drives nearly three times (27%) PVS fluid movement into the brain compared to asymmetric dilation (9%). Both symmetric and asymmetric dilation drive similar PVS fluid movement into the SAS (5%). d The particle trajectories of fluid particles shown in (a). Asymmetric dilation moves PVS fluid deeper below the surface into the ECS and moves the fluid further into the brain

Fig. 5

Sleep enhances fluid penetration into brain tissue. a The fluid particle trajectories for 60 s of simulation for the awake state (20% vessel dilation, once every 10 s with ${\zeta }_{R_f}^2=0.2$). b The fluid particle distribution for the awake state simulation. c The PVS fluid distribution at t = 30 s for simulated awake and sleep states, along with the cases where only the dilation and porosity are changed. The increase in porosity increased fluid movement into the ECS without affecting the fluid movement into the SAS, while larger dilations increased fluid movement to both SAS and ECS. d The fluid particle trajectories for 60 s of simulated sleep. The large amplitude vasodilation during sleep, combined with the increased porosity drives PVS fluid penetration into the brain. e The distribution of fluid position for 60 s of simulated sleep. a, b are repeated from the right side of Fig. 4d, c, respectively for better comparison with the sleep state