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 lambda; 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, lambda can equal or exceed the typical experimental value of about 1.6. The simulations further revealed that lambda is relatively independent of cavity shape and the number of cavities per cell. It mainly depends on the total ECS volume fraction alpha, the cavity volume fraction alpha(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 lambda to alpha, alpha(c), and an empirical exit factor beta that correlated with the ease with which a molecule could leave a cavity and its vicinity.