Physiological Foundations of Quantitative EEG Analysis - Quantitative EEG Analysis Methods and Clinical Applications - page 6

This difference partly accounts for the strong emphasis on thalamocortical interac-
tions (versus corticocortical interactions), especially in physiology literature empha-
sizing animal experiments. Neocortical neurons within each cerebral hemisphere are
connected by short intracortical fibers with axon lengths mostly less than 1 mm, in
addition to 10 10 corticocortical fibers. Cross hemisphere interactions occur by
means of about 10 8 callosal axons through the corpus callosum and several smaller
structures connecting the two brain halves.
Action potentials evoked by external stimuli reach the cerebral cortex in less
than 20 ms, and monosynaptic transmission times across the entire cortex are about
30 ms. By contrast, consciousness of external events may take 300 to 500 ms to
develop [7]. This finding suggests that consciousness of external events requires
multiple feedback signals between remote cortical and subcortical regions. It also
implies that substantial functional integration and, by implication, EEG phase lock-
ing may be an important metric of cognition [8].

1.4 Brain Sources

The relationship between scalp potential and brain sources in an isotropic (but gen-
erally inhomogeneous) volume conductor may be expressed concisely by the follow-
ing form of Poisson's equation:

[ ]

() ( ) ()

∇⋅ σ r ∇ Φ r , t =− s r , t (1.3)

( r ) is the
electrical conductivity of tissue (brain, skull, scalp, and so forth), and s ( r , t )
(

Here ∇ is the usual vector operator indicating three spatial derivatives, σ

A/mm 3 ) is the neural tissue current source function. A similar equation governs
anisotropic tissue; however, the paucity of data on tensor conductivity limits its
application to electroencephalography. Figure 1.3 represents a general volume con-
ductor; source current s ( r , t ) is generated within the inner circles. In the brain, s ( r , t )
dynamic behavior is determined by poorly understood and generally nonlinear

μ

F

∂Φ
∂ n

Φ S or

S

σ ( r

s () r,

Figure 1.3 The outer ellipse represents the surface of a general volume conductor; the circles indi-
cate regions where current sources s ( r , t ) are generated. The forward problem is well posed if all
sources are known, and if either potential

∂
∂

n

⎛
⎜

⎞
⎟

Φ S or its normal derivative is known over the entire

S

surface. In EEG applications, current flow into the surrounding air space and into the neck region is
assumed to be zero, that is, the boundary condition

∂
∂

n

⎛
⎜

⎞
⎟ ≈

0 is adopted. In high-resolution EEGs,

s

the potential on some inner surface (dashed line indicating dura or cortex) is estimated from the mea-
sured outer surface potential Φ S .