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 α c , 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 , α c , and an empirical exit factor β that correlated with the ease with which a molecule could leave a cavity and its vicinity.