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.

Author Summary

For a very long time, the measurement of the large scale potentials produced by the brain from outside of the head, using electroencephalography and magnetoencephalography, and from inside the head, using electrocorticography, has fixated on changes in specific rhythms and frequency ranges. This fixation presupposes physiologic changes where neuronal populations synchronously oscillate at specific timescales. Here, we demonstrate that there are phenomena which obey a broadband, power-law form extending across the entire frequency domain, with no special timescale. It is shown that, with local brain activity, there is an increase in power across all frequencies, and the power-law shape is conserved. Furthermore, we illustrate through simple simulation how fluctuations in this phenomenon may be linked to increases and decreases in “noise-like” patterns of activity in neuronal populations. Although power-laws have been postulated to exist in background electrical brain activity, the view that local activity can be captured by fluctuations in a broadband power-law in the power spectrum of electric potential timeseries represents a fundamentally new way of thinking about changes in the electric potential produced by the brain, and provides insight into what types of neuronal processes might produce these potentials.