Biomedical Engineering Reference
In-Depth Information
1.10 Neural Networks, Cell Assemblies, and Field Theoretic
Descriptions
The physiological origins of the source dynamics
P
(
r
,
t
) are poorly understood. Neu-
ral network models are able to produce oscillatory behavior that may appear super-
ficially similar to an EEG; however, network models typically depend on many
parameters that lack a physiological basis. Furthermore, the multiple mechanisms
by which neurons interact may not fit naturally into network models. Any network
description must be scale dependent so, for example, macroscopic network ele-
ments (centimeter scale) are themselves complex systems containing smaller
(
mesoscopic
, millimeter-scale) network elements. The mesoscopic elements are, in
turn, composed of still smaller scale elements [22]. Partly for these reasons,
neuroscientists often prefer the term
cell assemblies
, originating with the pioneering
work of Donald Hebb [23] in 1949. This label denotes a diffuse cell group capable
of acting briefly as a single structure, for example, one or more cortical dipole layers
that may be functionally connected. We may reasonably postulate cooperative
activity within cell assemblies without explicitly specifying interaction mechanisms.
Brain processes may involve the formation of cell assemblies at multiple spatial
scales [24-26]. Such neuron groups may produce a wide range of local delays and
associated characteristic (or resonant) frequencies [4]. Network models can incor-
porate some physiologically realistic features; however, field descriptions of brain
dynamics may be required to fill the dual role of modeling dynamic behavior and
making contact with macroscopic EEG data. In this context, the word
field
refers to
mathematical functions expressing, for example, the mesoscopic source function
P
(
r
,
t
) or perhaps the numbers of active synapses in each mesoscopic tissue volume.
In the view adopted here, cell assemblies are pictured as embedded within synaptic
and action potential fields [2, 4, 18-20, 25, 27, 28].
We tentatively view the small alpha dipole layers implied by Figure 1.8 as
embedded in the standing wave field implied by Figure 1.7. Electric and magnetic
fields (EEGs and MEGs) provide large-scale, short-time measures of the modula-
tions of synaptic and action potential fields around their background levels. These
synaptic fields are analogous to common physical fields, for example, sound waves,
which are short-time modulations of pressure about background levels. These
short-time modulations of synaptic activity are distinguished from long-timescale
(seconds
to
minutes)
modulations
of
brain
chemistry
controlled
by
neuromodulators.
1.11
Phase Locking
Cell assemblies that form and dissolve on roughly 100-ms timescales in the brain are
believed to underlie cognitive processing. They may develop simultaneously at mul-
tiple spatial scales, but only vary large scales are observable with scalp recordings.
Laplacian measures apply to somewhat smaller spatial structures than potentials,
but they are still very large scale compared to intracranial recordings. If cell assem-
blies are indeed responsible for cognition, one may reasonably expect to observe
correlations between EEG phase locking and mental or behavioral activity at some
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