Functional connectivity of fractal and oscillatory cortical activity is distinct

Electrophysiological signals of cortical population activity contain oscillatory and fractal (1/frequency) components. However, the relationship between these components is unclear. To address this, we investigated human resting-state MEG recordings. We applied combined source-analysis, signal orthogonalization and irregular-resampling autospectral analysis (IRASA) to separate oscillatory and fractal components of the MEG signals at the cortical source-level. We then compared the spatial correlation structure of fractal and oscillatory components across the human cortex. We found that these correlation structures differed, which suggests different mechanisms underlying fractal and oscillatory population signal components.


Introduction
Neuronal population activity, as measured with EEG, MEG or LFPs, can be separated into oscillatory and the fractal components. While oscillations have been implicated in various functions (Buzsáki & Draguhn, 2004), it is not until recently that the broadband, or 1/frequency, part of the spectrum became itself a focus of study (He, 2014). Broadband activity has been related to neural noise (Voytek, Kramer, Case, Lepage, Tempesta, Knight & Gazzaley, 2015), selforganized criticality, long range temporal correlations, and excitation-inhibition balance. However, it remains unclear how oscillatory and fractal signal components are related.
To address this, we systematically compared the functional connectivity, i.e. spatial correlation structure, of fractal and oscillatory components of human cortical population activity using restingstate MEG recordings.

Methods
We analyzed data from 112 healthy subjects recorded either at the MEG Center, Tuebingen or as part of the Human Connectome Project (HCP).
Clean data was high-pass filtered at 0.1 Hz using a 4th order Butterworth filter. We removed line noise artifacts and resampled the data to 1000 Hz.
We used linearly constrained minimum variance (LCMV) beamforming (Van Veen, van Drongelen, Yuchtman & Suzuki, 1997) to project the sensorlevel MEG data into source space using a singleshell head-model leadfield (Nolte, 2003) based on each individual subject's MRI. We analyzed the source-level data in nonoverlapping 3 s sliding windows. For each timewindow and source-location, we applied timedomain orthogonalization to discount volume conduction effects (Hipp, Hawellek, Corbetta, Siegel & Engel, 2012). We then performed irregularresampling auto-spectral analysis (IRASA) (Wen & Liu, 2016) on the orthogonalized signal to split the signal into oscillatory and fractal components. To assess functional connectivity, we took the logarithm of oscillatory and fractal power spectra and binned them into logarithmically spaced bins. (Hipp, Hawellek, Corbetta, Siegel & Engel, 2012). Then, we computed the Pearson correlation between each pair of orthogonalized seeds.
To compare the correlation structures of fractal and oscillatory components, we performed a correlation with attenuation correction (Siems, Pape, Hipp, & Siegel, 2016). Attenuation correction takes into account each signal's reliability (SNR) and computes correlations corrected for finite SNR.

Results
We source-reconstructed cortical activity from the MEG, discounted volume conduction by means of signal orthogonalization and separated fractal and oscillatory components using IRASA. We fitted and compared different signal models of the fractal power spectra. From the tested models, the optimal model (minimum AIC) included a knee at 15 Hz and included the (non-flat) shape of the power spectrum during empty-room MEG measurements (Bedard, Gomes, Bal & Destexhe, 2017;Dehghani, Bédard, Cash, Halgren, & Destexhe, 2010).
We then computed the attenuation corrected correlation between the brain-wide correlation patterns of oscillatory and fractal signal components (Figure 1). Across the entire investigated frequency range, attenuation corrected correlations were substantially larger than 0 but significantly smaller than 1. Thus, the functional connectivity patterns of oscillatory and fractal components were distinct. At 5.5 Hz the difference between connectivity patterns was most pronounced. For frequencies around 10 Hz and 64 Hz connectivity patterns were most similar.

Conclusions
Our results show that fractal and oscillatory signal components provide different information about the temporal correlation, i.e. functional connectivity, of different cortical regions. This raises the question, which processes may be reflected by the functional connectivity of fractal signal components?
Broadband activity is correlated with neuronal firing rates in intracortical recordings. Thus, the connectivity patterns of fractal activity measured with MEG may provide a window into the spatial structure of co-fluctuations of broadband or spiking activity.

Independent
of the specific underlying mechanisms, the observed differences in connectivity patterns of oscillatory and fractal activity indicate that oscillatory and fractal signals components are, at least partially, independent. This suggests different neuronal mechanisms underlying fractal and oscillatory components of human cortical population signals. Figure 1: Attenuation corrected correlation between cortex-wide correlation patterns of fractal and oscillatory neuronal activity: a) Attenuation corrected and non-corrected correlation between correlation patterns of fractal and oscillatory activity , b) inter-subject reliabilities of correlation patterns of fractal and oscillatory activity, c), proportion of reliable patterns. Shaded regions in a) and b) indicate 5-95% and 25-75% percentiles across the cortex.