Origin of the apparent tissue conductivity in the molecular and granular layers of the in vitro turtle cerebellum and the interpretation of current source-density analysis

1. We determined the origin of the apparent tissue conductivity (σ(a)) of the turtle cerebellum in vitro. 2. Application of a current with a known current density (J) along the longitudinal axis of a conductivity cell produced an electric field in the cerebellum suspended in the cell. The measured electric field (E) perpendicular to the cerebellar surface indicated a significant inhomogeneity in σ(a) (= J/E) with a major discontinuity between the molecular layer (0.25 ± 0.05 S/m, mean ± SD) and granular layers (0.15 ± 0.03 S/m) (n = 39). 3. This inhomogeneity was more pronounced after anoxic depolarization. The value of σ(a) decreased to 0.11 ± 0.03 and 0.040 ± 0.008 S/m in the molecular and granular layers, respectively. The ratio of σ(a)s in the two layers increased from 1.67 in the normoxic condition to 2.75 after anoxic depolarization. 4. This difference in σ(a) across the two layers was present within the range of frequencies (DC to 10 kHz) studied where the phase of σ(a) was small (less than ± 2°) and therefore σ(a) was ohmic. 5. The inhomogeneity in σ(a) was in part due to an inhomogeneity in the extracellular conductivity (σ(e)) as determined from the extracellular diffusion of ionophoresed tetramethylammonium. Like σ(a), the value of σ(e) was also higher in the molecular layer (0.165 S/m) than in the granular layer (0.097 S/m). The inhomogeneity in σ(e) was due to a smaller tortuosity and a larger extracellular volume fraction in the molecular layer compared with the granular layer. 6. σ(a) was, however, consistently higher, by ~50%, than σ(e). A core conductor model of the cerebellum indicated that these discrepancies between σ(a) and σ(e) were attributable to additional conductivity produced by a passage of the longitudinal applied current through the intracellular space of Purkinje cells and ependymal glial cells, with the glial compartment playing the dominant role. Cells with a long process and a short space constant such as the ependymal glia evidently enhance the effective 'extracellular' conductivity by serving as intracellular conduits for the applied current. The result implies that the effective σ(e) may be larger than σ(e) for neuronally generated currents in the turtle cerebellum because the space constant for Purkinje cells is several times greater than that for the ependymal glia and consequently Purkinje cell-generated currents travel over a long distance relative to the space constant of glial cells. 7. Some implications of the inhomogeneity were examined by comparing the depth profiles of the current source density (CSD) estimated for various conductivity profiles. The CSD profile for the inhomogeneous case, using the measured profile of σ(a), did not differ qualitatively from that for the homogeneous case using the average of measured σ(a)s, suggesting that the CSD analysis may provide a qualitatively accurate picture of actual CSD profiles even if one uses a homogeneous approximation for the actual conductivity. However, quantitatively the CSD profiles were different in the two cases, demonstrating importance of measurements of the conductivity profile for rigorous analyses of CSD.