Changes in diffusion through the brain extracellular space.
ECS (extracellular space) works as the microenvironment of brain cells. Diffusion through ECS may be described through an effective diffusion coefficient, D (e), which in turn depends on ECS porosity, epsilon, and tortuosity, T. In the present research, diffusion data together with epsilon and T were collected from the specialized literature and analysed to seek a correlation of T versus epsilon. On the basis of D (e) data, upper and lower T boundaries were defined and related to topologically 'dense' and 'loose' cell arrangement. A possible range for T variation was obtained for ECS, with epsilon ranging from 0.05 to 0.6. A tortuosity index ( n ) in the form of T and epsilon logarithmic ratio was introduced. This index may be adopted for recalculation of T or epsilon if only one of these parameters is known. As a result of data analysis and modelling, it was concluded that, upon different external conditions, for instance oxygen depletion, the ECS porosity decreases and cells (presumably through membrane rearrangements) adjust the void space to keep the diffusion within a defined range, which gives the living tissue the ability to maintain the diffusion level up to two or more times higher than in conventional granular bed packing. Thus, even with a dramatic ECS decrease, the cellular system is still able to support a given diffusion by decreasing the value of T. The obtained results clearly show the existence of three data clusters: a region of normal brain functioning, both for young and adult brains, for values of epsilon comprised between 0.15 and 0.30, and two regions of abnormal brain behaviour to the left and to the right of the normal region, corresponding to different states (aging, tumours, anoxia, brain death, etc.). The present approach allows defining the optimal range of epsilon and T to assure the best ECS diffusion efficiency for a specified macromolecule. This might be important in brain clinical treatment.