A model of anomalous extracellular diffusion: source location matters

Brain extracellular space (ECS) serves as a transportation channel for biologically significant molecules but the diffusion-mediated transport through the ECS is hindered by its geometrically complex structure. We proposed that the hindrance originated in large part from the presence of dead space microdomains which can transiently retain diffusing molecules [1]. Such pocket-like structures, e.g., those formed by astrocytic wrappings, result in three consecutive diffusion regimes [2]. Following a brief and rapid free diffusion after release, an anomalous diffusion phase gradually reduces the diffusion rate until the bulk hindered normal diffusion is reached. The anomalous diffusion thus facilitates a smooth transition between two normal diffusion regimes. We have shown that when the diffusion source is placed in the well-connected compartment outside of any pockets, the anomalous phase can be described as subdiffusion characterized by its anomalous exponent dw > 2 [2]. Here, we examine the effect of the instantaneous point source placement, inside or outside of the deadend pockets, on the transiently anomalous diffusion phase.