Power-Law Scaling in the Brain Surface Electric Potential

By Kai J. Miller, L. Sorensen, Jeffrey G. Ojemann, M. Nijs. PLoS Comput. Biol., 2009

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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.

Subfields: Cognitive Neuroscience

View Paper: https://www.semanticscholar.org/paper/9cd7051c17f524d3e15f088f2c594246d4dad493

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In Cognitive Neuroscience

Citations in the corpus

Criticality in the brain: A synthesis of neurobiology, models and cognition. (2017, background): “…criticality based on the observation of power law scaling in empirical data should be made with caution, particularly if the scaling extends for less than two orders of magnitude or the slope of the power law is steep (Miller et al., 2009) – i.e. the scaling exponent a is greater than 2.5.”
Oscillations and the basal ganglia: Motor control and beyond (2013, neutral): “, 2012), is the product of multiple, dynamic, phase-coupled neuronal clusters spanning this broad frequency range, or reflects the brief and asynchronous burst of activity hypothesized to be an LFP correlate of population firing (Manning et al., 2009; Miller et al., 2009; Ray and Maunsell, 2010).”
Being Critical of Criticality in the Brain (2012, background): “Avalanche dynamics also have been reported in human brain oscillations (Poil et al., 2008) and there are several reports of power law scaling (Miller et al., 2009) even though these are not necessarily attributed to avalanches.”
Emergent complex neural dynamics (2010, background): “[24] Miller KJ, Sorensen LB, Ojemann JG, den Nijs M.”
Construct validation of a DCM for resting state fMRI (2015, neutral): “We note that for the human EEG, this is generally not the case – above 10 Hz, γ = 2.5 and above 70 Hz γ is usually greater than 3.5 – which is consistent with a Poisson process (see Bedard et al., 2006; Miller et al., 2009).”
Age-Related Changes in 1/f Neural Electrophysiological Noise (2015, background): “This is important given that taskrelated increases in neural activity result in an overall increase, an upward shift, in the broadband and high gamma PSD (Manning et al., 2009; Miller et al., 2009b).”
Review of the BCI Competition IV (2012, methodology): “When captured, this broadband feature has been be a robust correlate of ﬁnger movement at individual sites in motor cortex (Miller et al., 2009b; Figures 26 and 30 ).”
Inferring Synaptic Excitation/Inhibition Balance from Field Potentials (2016, neutral): “We ask: can changes in the ratio of excitatory to inhibitory synapse density be captured by changes in PSD slope, measured along the depth of CA1?”
Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition. (2014, background): “It has been well described that the power spectral density of recordings from the brain follows a 1/f ̨ distribution, where ̨ is a positive scalar (Bedard et al., 2006; Miller et al., 2009).”
Self-organized criticality as a fundamental property of neural systems (2014, background): “Imaging data suggests furthermore power-law noise because activity ﬂuc-tuations (e.g., EEG Novikov et al., 1997, ECoG Miller et al., 2009) and correlation ﬂuctuations (e.g., EEG and MEG Linkenkaer-Hansen et al., 2001, fMRI and MEG Kitzbichler et al., 2009) follow power-laws.”
Untangling cross-frequency coupling in neuroscience (2014, positive): “The latter can be estimated by subtracting from the real power spectrum the power spectrum of baseline or a fit of the background power spectrum [38].”
The temporal structures and functional significance of scale-free brain activity (2010, positive): “Miller et al. (2009a) described an overall shift of power spectrum in >25 Hz range during a hand motor task, without any significant change in the power-law exponent.”
Revealing neuronal function through microelectrode array recordings (2015, positive): “Moreover, the frequency spectra observed in LFP and EEG (Pritchard, 1992; Freeman et al., 2003; Bédard et al., 2006a; Buzsaki, 2006; Bédard and Destexhe, 2009; Miller et al., 2009; Milstein et al., 2009) led to uncertainties regarding the role of extracellular space in frequency dependent ﬁltering.”