  Local field potentials (LFPs) are routinely measured experimentally in brain
tissue, and exhibit strong low-pass frequency filtering properties, with high
frequencies (such as action potentials) being visible only at very short
distances ($\approx$10~$\mu m$) from the recording electrode. Understanding
this filtering is crucial to relate LFP signals with neuronal activity, but not
much is known about the exact mechanisms underlying this low-pass filtering. In
this paper, we investigate a possible biophysical mechanism for the low-pass
filtering properties of LFPs. We investigate the propagation of electric fields
and its frequency dependence close to the current source, i.e. at length scales
in the order of average interneuronal distance. We take into account the
presence of a high density of cellular membranes around current sources, such
as glial cells. By considering them as passive cells, we show that under the
influence of the electric source field, they respond by polarisation, i.e.,
creation of an induced field. Because of the finite velocity of ionic charge
movement, this polarization will not be instantaneous. Consequently, the
induced electric field will be frequency-dependent, and much reduced for high
frequencies. Our model establishes that with respect to frequency attenuation
properties, this situation is analogous to an equivalent RC-circuit, or better
a system of coupled RC-circuits. We present a number of numerical simulations
of induced electric field for biologically realistic values of parameters, and
show this frequency filtering effect as well as the attenuation of
extracellular potentials with distance. We suggest that induced electric fields
in passive cells surrounding neurons is the physical origin of frequency
filtering properties of LFPs.
