Ion diffusion modified by tortuosity and volume fraction in the extracellular microenvironment of the rat cerebellum.

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Abstract
The validity of the macroscopic laws of ion diffusion was critically examined within the microenvironment of the extracellular space in the rat cerebellum using ion-selective micropipettes and ionophoretic point sources. The concepts of volume averaging, volume fraction (.alpha.) and tortuosity (.lambda.) were defined and shown to be theoretically appropriate for quantifying diffusion in a complex medium such as the brain. Diffusion studies were made with the cations tetramethylammonium and tetraethylammonium and the anions .alpha.-naphthalene sulfonate and hexafluoroarsenate, all of which remained essentially extracellular during the measurements. Diffusion parameters were measured for a period of 50 s and over distances of the order of 0.1 mm. Measurements of the diffusion coefficients of the ions in agar gel gave values that were very close to those derivable from the literature, thus confirming the validity of the method. Measurements in the cerebellum did not reveal any systematic influences of ionophoretic current strength, electrode separation, anisotropy, inhomogeneity, charge discrimination or uptake, within the limits tested. The pooled data from measurements with all the ions gave .alpha. = 0.21 .+-. 0.02 (mean .+-. standard error of mean) and .lambda. = 1.55 .+-. 0.05 (mean .+-. standard error of mean). The extracellular space occupies about 20% of the rat cerebellum and that the diffusion coefficient for small monovalent extracellular ions is reduced by a factor of 2.4 (i.e., .lambda.2) without regard to charge sign. The over-all effect of this is to increase the apparent strength of any ionic source in the cerebellum by a factor of .lambda.2/.alpha., about 12-fold in the present case, and to modify the time course of diffusion. The laws of macroscopic diffusion are closely obeyed in the cerebellum for small ions in the extracellular space, provided that volume fraction and tortuosity are explicitly taken into account. These conclusions may be generally applicable to other brain regions and other diffusing substances.