Sheet and void porous media models for brain interstitial space.

The interstitial space (ISS) component of brain extracellular space resembles an unconsolidated porous medium. Previous analysis of the diffusion of small molecules in this domain shows that the typical porosity is 0.2 and typical tortuosity 1.6. An ensemble of cubic cells separated by uniform sheets of ISS cannot generate the measured tortuosity, even if some of the tortuosity value is attributed to interstitial viscosity, so more complex models are needed. Here two models are analysed: the corner cubic void (CCV) and the edge tunnel void (ETV). Both models incorporate dead spaces formed from local expansions of the ISS to increase geometrical tortuosity. Using Monte Carlo simulation of diffusion it is found that in the range of normal porosities, the square of the tortuosity is a linear function of the ratio of void to sheet volumes for the CCV model and this model can generate the experimentally observed tortuosities. For abnormally high porosities, however, the linear relation fails. The ETV model shows a quartic functional relation and can only generate the observed tortuosity if interstitial viscosity is present. The CCV model is used to analyse the recently described changes in porosity between asleep and awake brain states.