Substituting for E in Eq. 2 provides a (vector) measure of J based on voltage, but still does not represent the point current generators in Eq. 1. However, a subsequent divergence operation (i.e., spatial differentiation to quantify the divergence of current flow at each point) transforms the vector field J into a scalar current source density (CSD), or Im following the nomenclature of Nicholson and Freeman (1975): Eq. 3Im=∇·(σ(-∇Φ)) where the subscript m is used to indicate that the current is injected into the extracellular medium across the cell membranes (m) of neurons within the tissue. If tissue impedance may further be considered to be spatially invariant (or approximately so), the tensor σ may be replaced by scalar constant σ to yield the scalar relationship: Eq. 4Im=-σ∇2Φ
