Estimating the permeability of brain tissue through CFD simulations of flow in realistic geometries

Cerebrospinal fluid enters the brain tissue where it mixes with the interstitial fluid in the extracellular space (ECS, i.e., the space between cells). This process leads to the clearance of metabolic waste products, whose accumulation contributes to neurological diseases such as Alzheimer's. Hence, understanding the role of fluid flow in maintaining brain health is of critical importance, but fluid flow within the brain tissue cannot be directly measured, leaving many open questions. Brain tissue can be modelled as a porous medium with flow described by Darcy's law, but the permeability is not well characterized, with different estimates spanning several orders of magnitude, which introduces significant uncertainty in any attempts to model the flow. In this study, we estimate the permeability of brain tissue using computational fluid dynamics simulations of flow through a realistic three-dimensional ECS geometry derived from publicly available data. We solved for the speeds resulting from an imposed pressure drop in Stokes flow since ECS flow is characterized by very low Reynolds numbers (estimated to be on the order of 10-7) and then calculated the permeability using Darcy's law. ECS volume fraction (ratio of the ECS volume to total volume) is known to vary between sleep and wakefulness, so we quantified how permeability varies with ECS volume fraction, providing insight into the corresponding variation in flow dynamics. We also quantified the degree of anisotropy in ECS permeability, which has implications for modeling.