Macroscopic models of local field potentials and the apparent
1/f noise in brain activity.
Claude Bedard and Alain Destexhe.
Biophysical Journal 96: 2589-2603, 2009.
The power spectrum of local field potentials (LFPs) has been reported
to scale as the inverse of the frequency, but the origin of this "1/f
noise" is at present unclear. Macroscopic measurements in cortical
tissue demonstrated that electric conductivity (as well as
permittivity) is frequency dependent, while other measurements failed
to evidence any dependence on frequency. In the present paper, we
propose a model of the genesis of LFPs which accounts for the above
data and contradictions. Starting from first principles (Maxwell
equations), we introduce a macroscopic formalism in which macroscopic
measurements are naturally incorporated, and also examine different
physical causes for the frequency dependence. We suggest that ionic
diffusion primes over electric field effects, and is responsible for
the frequency dependence. This explains the contradictory
observations, and also reproduces the 1/f power spectral structure of
LFPs, as well as more complex frequency scaling. Finally, we suggest
a measurement method to reveal the frequency dependence of current
propagation in biological tissue, and which could be used to directly
test the predictions of the present formalism.
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