Modeling brain extracellular space from diffusion data

The extracellular space (ECS) of the brain is a thin region surrounding each cell that is filled with a medium resembling cerebrospinal fluid and an unknown amount of extracellular matrix. The ECS is difficult to study but diffusion measurements based on a point-source diffusion paradigm have begun to reveal the complex structure of this region. Despite the complexity, a modified version of Fick’s classical diffusion equation incorporating parameters for volume fraction and tortuosity has been shown to be valid. Using real-time iontophoresis and the small molecule tetramethylammonium, the volume fraction of typical brain tissue has been determined to be 0.2, i.e. 20% of the brain is ECS and the typical tortuosity is 1.6, which means that a small molecule has an effective diffusion coefficient that is 2.6 less than in free solution. Monte Carlo modeling, however, shows that a simple ensemble of convex cells, each surrounded by a uniform ECS cannot generate a tortuosity greater than 1.225. Further modeling suggests that the discrepancy between experiments and theory may be accounted for by the existence of dead-space microdomains in the ECS; a viscous extracellular matrix might also play a role. Diffusion measurements with integrative optical imaging of fluorescent macromolecules and quantum dots show that tortuosity is increased with macromolecular size and analysis based on the theory of restricted diffusion in pores suggests that the width of the ECS is in the range 38-64 nm.