Nicholson (1973) derived a CSD implementation for recordings through laminated tissue (e.g., cerebellar or cerebral cortex). The derivation posits an arbitrary closed surface area bounding a volume of tissue that contains neuronal core conductors, each characterized by transmembrane currents reflecting neuronal polarization due to resting- and activity-related processes. Eq. 4 therefore defines Im as the volume-dependent CSD that it “smoothed out” over the volume implicit in the divergence operation. In the case of an orthogonal penetration through laminated tissue, and assuming sufficient radial invariance (i.e., isopotential lines are radial to the recording axis in the region sampled), current flows normal to the lamination, suggesting a one-dimensional model obeying: Eq. 5Φ(xl)=∫0CG(xl,z)Im(z)dz where xl is the depth orthogonal to the uniform generator, depth C encompasses all active generators, and G is a weighting function relating the geometry and impedance of the tissue to the recording site. This one-dimensional model may be interpreted as a spatial convolution integral (Nicholson, 1973), and expresses a simplified forward solution for reconstructing laminar field potential profiles represented by the CSD.1
