Cell cavities increase tortuosity in brain extracellular space

Brain extracellular space (ECS) forms hindered pathways for molecular diffusion in chemical signaling and drug delivery. Hindrance is quantified by the tortuosity λ; the tortuosity obtained from simulations using uniformly spaced convex cells is significantly lower than that measured experimentally. To attempt to account for the difference in results, this study employed a variety of ECS models based on an array of cubic cells containing open rectangular cavities that provided the ECS with dead-space microdomains. Monte Carlo simulations demonstrated that, in such ECS models, λ can equal or exceed the typical experimental value of about 1.6. The simulations further revealed that λ is relatively independent of cavity shape and the number of cavities per cell. It mainly depends on the total ECS volume fraction α, the cavity volume fraction αc, and whether the cavity is located at the center of a cell face or formed at the junction of multiple cells. To describe the results from the different ECS models, an expression was obtained that related λ to α, αc, and an empirical exit factor β that correlated with the ease with which a molecule could leave a cavity and its vicinity.