We analyzed the relationship between LFP and CSD signals based on theoretical arguments described below (Nunez and Srinivasan, 2006). Electrophysiological studies usually assume moment-by-moment quasi-stationarity (Plosney and Heppner 1967) and spatial uniformity of conductivity σ (Logothetis et al., 2007). Then the relationship between spatial distributions of electrical potential Φ(r→) and charges q(r→) is described by the Poisson's differential equation σ∇2Φ(r→)=−q(r→) (Nunez and Srinivasan, 2006). The spatial second derivative of electrical potential describes the presence or absence of local charges or current densities. The equation underlies the idea to use the numerical differentiation of LFP to estimate CSD (Mitzdorf, 1985). In the macaque, auditory field potential of the order of 100 μV in auditory cortex attenuates to the order of 1 μV above the dura or at the scalp where were tens of millimeters away (Legatt et al., 1986). Within the auditory cortex, distances between the cortical layers that generate LFPs are less than a millimeter. These conditions approximate a simple boundary condition Φ(∞) = 0, and the solution of Poisson's equation is well known as, Φ(r→)=14πσ∫q(r→−r→′)∣r→−r→′∣dr→′.
