Power-Law Scaling in the Brain Surface Electric Potential

Abstract

Recent studies have identified broadband phenomena in the electric potentials produced by the brain. We report the finding of power-law scaling in these signals using subdural electrocorticographic recordings from the surface of human cortex. The power spectral density (PSD) of the electric potential has the power-law form from 80 to 500 Hz. This scaling index, , is conserved across subjects, area in the cortex, and local neural activity levels. The shape of the PSD does not change with increases in local cortical activity, but the amplitude, , increases. We observe a “knee” in the spectra at , implying the existence of a characteristic time scale . Below , we explore two-power-law forms of the PSD, and demonstrate that there are activity-related fluctuations in the amplitude of a power-law process lying beneath the rhythms. Finally, we illustrate through simulation how, small-scale, simplified neuronal models could lead to these power-law observations. This suggests a new paradigm of non-oscillatory “asynchronous,” scale-free, changes in cortical potentials, corresponding to changes in mean population-averaged firing rate, to complement the prevalent “synchronous” rhythm-based paradigm.

Neurophysiologic correlates of fMRI in human motor cortex

“…1, 2, and 5), consistent with previous studies [Crone et al, 1998a;Leuthardt et al, 2007;Miller et al, 2007;Miller et al, 2009b]. This high frequency spectral power change has been shown to correlate directly with firing rate [Manning et al, 2009;Miller et al, 2009a;Whittingstall and Logothetis, 2009], and has been demonstrated to reflect broadspectral change across all frequencies Miller et al, 2009b]. Previous studies examined the relationship between spectral power change and BOLD change within a specific region [Logothetis et al, 2001;Maier et al, 2008;Mukamel et al, 2005;Niessing et al, 2005].…”

“…S2). A power law (constantÁf Àv ) was fit to the power spectrum from the rest period for each electrode and the power was normalized (by element-wise division at each frequency) with respect to this power law [Miller et al, 2009a]. Peaks in the normalized power spectrum, i.e., where the first derivative was 0, were detected for each electrode.…”

“…Power decreases in low frequency sensorimotor rhythms are distributed over larger areas of cortex [Crone et al, 1998b;Miller et al, 2007]. These spectral changes are associated with different processes: broadband power change is associated with local neuronal processing [Manning et al, 2009;Miller et al, 2009a], whereas low frequency oscillations reflect an aspect of subcortical-cortical interaction [Brown, 2003;Feige et al, 2005;Pfurtscheller and Lopes da Silva, 1999;Schnitzler et al, 2006]. Functional MRI BOLD change has also been compared with electrocortial stimulation mapping, and has been shown to be adequately sensitive but less specific in predicting electrocortical stimulation sites [Pouratian et al, 2002;Rutten et al, 2002].…”

BOLD Consistently Matches Electrophysiology in Human Sensorimotor Cortex at Increasing Movement Rates: A Combined 7T fMRI and ECoG Study on Neurovascular Coupling

“…The ECoG HFB power shows considerable decline in neuronal activity after the initial movement for the movement rates X1 Hz for both M1 and S1. 17 As broadband HFB power changes have been linked to neuronal population firing rate, [19][20][21] the observed decline in the ECoG HFB power at higher movement rates in this study could suggest that, after movement initiation, fewer motor cortex neurons have to fire or firing rates may possibly decline when multiple similar movements are made at a fast rate. 17 Including this subject-specific drop in neuronal activity as a weighting function in a BOLD fMRI prediction model, we obtained a close match with the measured BOLD data from the same cortical regions in the same subjects ( Figures 6A and 6B).…”

“…18 Importantly, the ECoG electrode grids employed here allowed for a spatial resolution that is on the same order as our fMRI measurements. Studies have shown that power in higher frequencies (440 Hz) correlates well with neuronal firing rates [19][20][21] and also with BOLD signal change. 22,23 The ECoG high-frequency broadband power thus provided a direct measure of electrical activity in confined neuronal ensembles, which we compared with BOLD fMRI measurements.…”