W

Here, the three integral signs indicate integration over a small, local volume W of tissue, where dW(w) is the tissue volume element. s(r0, w, t) is the local volume source current (mA/mm3) near membrane surfaces inside a tissue volume with vector location r0. w is the vector location of sources within dW(w) as indicated in Fig. 5. The current dipole moment per unit volume P(r', t) in a conductive medium is fully analogous to charge polarization in a dielectric (insulator). Macroscopic tissue volumes satisfy the condition of electro-neutrality at EEG frequencies. That is, current consists of movement of positive and negative ions in opposite directions, but the total charge in any mesoscopic tissue volume is essentially zero. Cortical morphology is characterized by its columnar structure with pyramidal cell axons aligned normal to the local cortical surface. Because of this layered structure, the volume elements dW(w) may be viewed as cortical columns with height e2-5 mm, as shown in Fig. 5. For purposes of describing scalp potentials, the choice of basic cortical column diameter is somewhat arbitrary. Anything between the cortical minicolumn (e0.03 mm) and macrocolumn scales (e 1 mm) may be used to describe scalp potentials.

The microsources s(r', w, t) are generally mixed positive and negative due to local inhibitory and excitatory synapses, respectively. In addition to these active sources, the s(r', w, t) include passive membrane (return) current required for current conservation. Dipole moment per unit volume P(r', t) has units of current density (mA/m2). For the idealized case of sources of one sign confined to a superficial cortical layer and sources of opposite sign confined to a deep layer, P(r0, t) is approximately the diffuse current density across the column. This corresponds to superficial inhibitory synapses and deep excitatory synapses, for example. However, more generally, column source strength P(r0, t) is reduced as excitatory and inhibitory synapses overlap along column axes.

Increased membrane capacity tends to confine the microsources s(r', w, t) within each column to produce smaller effective pole separations—that is, smaller strengths P(r', t). However, capacitive effects at macroscopic scales are negligible in normal EEG frequency bands. Also, tissue conductivity is only very weakly dependent on frequency. As a result of these two properties, a single dipole source implanted in the brain generates a time dependence of scalp potential that is identical (except for amplitude attenuation) to that of the source. Amplitude attenuation is independent of source frequency in the EEG range if the sources are equally distributed in location. The selective attenuation of different EEG frequency bands occurs as an indirect result of distinct spatial distributions of the sources.

Human neocortical sources may be viewed as forming a large dipole sheet (or layer) of perhaps

1500-3000 cm2 over which the function P(r', t) varies continuously with cortical location r0, measured in and out of cortical folds. In limiting cases, this dipole layer might consist of only a few discrete regions where P(r', t) is large, consisting of localized or focal sources. However, more generally, P(r0, t) is distributed over the entire folded surface. The question of whether P(r', t) is distributed or localized in particular brain states is often controversial. The averaging of EPs over trials substantially alters the nature of this issue. Such time averaging strongly biases EPs toward (trial-to-trial) time stationary sources (e.g., sources confined to primary sensory cortex).

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