Biomedical Engineering Reference
In-Depth Information
8.2.2 Current Sources in a Complex Domain
Although a section of an axon or dendrite may be approximated by a straight cable, in reality axons and
dendrites are not straight.Therefore, the Eq. (8.11) is not valid. Furthermore, given the complex tangle of
neurons, the assumption of infinite bath of conductive fluid is not valid either. It is possible to numerically
solve for
φ
e
in a complex domain by building a circuit analog as in Fig. 8.2. Although the circuit is only a
very small portion of a much larger circuit network, it should be clear that we can represent intracellular
and extracellular space by passive resistors and membranes as nonlinear current sources.The advantage of
this arrangement, besides allowing for complex geometries, is that extracellular and intracellular potentials
can be recorded directly at any point (e.g., Node 2). It also naturally allows for the membrane of the cell
to influence currents and potentials in the extracellular space. At the boundaries we can make the simple
assumption that no current may leave, leading to sealed ends as described in Sec. 4.3. To model a 3D
section of neuronal tissue, it is conceptually simple to extend our resistor network into a third dimension.
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0HP
0HP
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Figure 8.2:
Extracellular potentials in a complex network of neurons.
The obvious disadvantage of a circuit network is that it is computationally very slow because
potentials and currents must be computed at
every
point. The more subtle disadvantage is that the
technology does not currently exist to efficiently image the complex web of neurons and directly translate
the image to a circuit model.
8.2.3 The Electroenchephogram (EEG)
From the previous section and Ch. 7 is should be clear that large populations of neurons can generate a
significant extracellular potential that may be detected at some distance.Themore active and synchronized
the neurons, the larger the signal. Of course, any behavior will be greatly averaged but a general idea of
the degree of activity can be determined. At least in principle, we have described precisely the situation in
recording the
electroenchephalogram
or EEG. The EEG is the potential recorded from the surface of the
