Contribution of dead-space microdomains to tortuosity of brain extracellular space

The extracellular space (ECS) of the brain is a major channel for intercellular communication, nutrient and metabolite trafficking, and drug delivery. The dominant transport mechanism is diffusion, which is governed by two structural parameters, tortuosity and volume fraction. Tortuosity (lambda) represents the hindrance imposed on the diffusing molecules by the tissue in comparison with an obstacle-free medium, while volume fraction (alpha) is the proportion of tissue volume occupied by the ECS. Diffusion of small ECS markers can be exploited to measure lambda and alpha. In healthy brain tissue, lambda is about 1.6 but increases to 1.9-2.0 in pathologies that involve cellular swelling. Previously it was thought that lambda could be explained by the circumnavigation of diffusing molecules around cells. Numerical models of assemblies of convex cells, however, give an upper limit of about 1.23 for lambda. Therefore, additional factors must be responsible for lambda in brain. In principle, two mechanisms could account for the measured value: a more complex ECS geometry or an extracellular macromolecular matrix. Here we review recent work in ischemic tissue suggesting concave geometrical formations, dead-space microdomains, as a major determinant of extracellular tortuosity. A theoretical model of lambda based on diffusion dwell times supports this hypothesis and predicts that, in ischemia, dead spaces occupy approximately 60% of ECS volume fraction leaving only approximately 40% for well-connected channels. It is further proposed that dead spaces are present in healthy brain tissue where they constitute about 40% of alpha. The presence of dead-space microdomains in the ECS implies microscopic heterogeneity of extracellular channels with fundamental implications for molecular transport in brain.