Resolving Scale-Dependent Diffusivity in the Brain Extracellular Space

Abstract

Transport through the brain extracellular space has traditionally been summarized by effective diffusion coefficients measured over specific observation ranges. Whether local mobility remains predictive as the same molecule explores larger distances remains unresolved. Here, we track individual ultrashort carbon nanotubes in three dimensions within living hippocampal tissue, following their motion from nanometre to micrometre scales. Using freely diffusing nanotubes in water as an experimental reference, we resolve trajectory-specific crossover lengths beyond which instantaneous diffusivity decreases, with slice-level medians of 0.67 $\hat{I}¼$m in the pyramidal layer and 0.52 $\hat{I}¼$m in the radiatum. The pyramidal layer combines higher short-time diffusivity with an approximately twofold larger post-crossover restriction exponent than the radiatum ($\vartheta$ = 0.77 versus 0.38). This decoupling of local mobility from larger-scale exploration is incompatible with a scale-independent rescaling of transport, showing that effective extracellular diffusivity must be interpreted relative to the scale of exploration.

11 pages, 5 Figures, Supplementary information including 4 Figures and 2 Tables