Simulated power spectral density (PSD) of background electrocorticogram (ECoG)

Abstract

The ECoG background activity of cerebral cortex in states of rest and slow wave sleep resembles broadband noise. The power spectral density (PSD) then may often conform to a power-law distribution: a straight line in coordinates of log power vs. log frequency. The exponent, x, of the distribution, 1/f(x), ranges between 2 and 4. These findings are explained with a model of the neural source of the background activity in mutual excitation among pyramidal cells. The dendritic response of a population of interactive excitatory neurons to an impulse input is a rapid exponential rise and a slow exponential decay, which can be fitted with the sum of two exponential terms. When that function is convolved as the kernel with pulses from a Poisson process and summed, the resulting "brown" or "black noise conforms to the ECoG time series and the PSD in rest and sleep. The PSD slope is dependent on the rate of rise. The variation in the observed slope is attributed to variation in the level of the background activity that is homeostatically regulated by the refractory periods of the excitatory neurons. Departures in behavior from rest and sleep to action are accompanied by local peaks in the PSD, which manifest emergent nonrandom structure in the ECoG, and which prevent reliable estimation of the 1/f(x) exponents in active states. We conclude that the resting ECoG truly is low-dimensional noise, and that the resting state is an optimal starting point for defining and measuring both artifactual and physiological structures emergent in the activated ECoG.

Vortices in brain activity: Their mechanism and significance for perception

“…The similarity held for differing pass bandwidths and center frequencies and equally for brown and black noises with various slopes (Freeman & Zhai, 2009) for human, cat and rabbit ECoG.…”

“…The important generalization is that the spectra of the mesoscopic rest ECoG are continuous and power-law for all slopes between −2 and −4 (Freeman & Zhai, 2009). The implied selfsimilarity has been confirmed over the spectral ranges of clinical interest: theta, alpha, beta, and gamma (Freeman, 2007a;Freeman, O'Nuillain, & Rodriguez, 2008).…”

“…Upon active engagement with the environment, peaks emerge above the powerlaw level (Freeman, 2006(Freeman, , 2007aFreeman & Zhai, 2009), curve fitting by linear regression with the criterion of least squares residuals indicates a slope shallower than −2, but with excessive residuals (Freeman, 2009b). proportional to the bandwidth in Hz by a factor of 0.641 (Sect. 3.8., page 90, equation 3.8-3.15 in Rice (1945)).…”

“…The distributions of the logarithm of analytic power were calculated from a 17 s continuous record from 64 electrodes at 2 ms intervals (B) for comparison with 64 simulated independent time series. The pass band was in the low gamma range (Freeman & Zhai, 2009). Spikes less than the inferred threshold are referred to as null spikes.…”

“…The impulse response is adequately simulated with the sum of two exponential terms, one for the rise rate and the other for the decay rate, thus neglecting higher order poles. The rise rate determines the slope of the PSD, and the decay rate determines the break frequency, below which the spectrum tends to be flat (Freeman & Zhai, 2009). Excitatory input drives cortex above its self-regulated set point that determines the background level.…”