Macroscopic resting-state brain dynamics are best described by linear models

It is typically assumed that large networks of neurons exhibit a large repertoire of nonlinear behaviours. Here we challenge this assumption by leveraging mathematical models derived from measurements of local field potentials via intracranial electroencephalography and of whole-brain blood-oxygen-level-dependent brain activity via functional magnetic resonance imaging. We used state-of-the-art linear and nonlinear families of models to describe spontaneous resting-state activity of 700 participants in the Human Connectome Project and 122 participants in the Restoring Active Memory project. We found that linear autoregressive models provide the best fit across both data types and three performance metrics: predictive power, computational complexity and the extent of the residual dynamics unexplained by the model. To explain this observation, we show that microscopic nonlinear dynamics can be counteracted or masked by four factors associated with macroscopic dynamics: averaging over space and over time, which are inherent to aggregated macroscopic brain activity, and observation noise and limited data samples, which stem from technological limitations. We therefore argue that easier-to-interpret linear models can faithfully describe macroscopic brain dynamics during resting-state conditions.


Statistics
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Data analysis
Custom MATLAB software, executed in MATLAB R2018a, was used for data pre-processing and for all analyses in the manuscript.All the MATLAB code used for pre-processing and data analysis are publicly available on Github at https://github.com/enozari/rest-system-id.A few publicly available MATLAB packages were also used within this custom code, as described in the README file in the Github repository.
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We only used data from publicly available and well-cited datasets (HCP and RAM).Participants were recruited as described in the respective dataset descriptions.

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The HCP experiments were carried out by the WU-Minn consortium and its adherence to ethical standards was approved by the Internal Review Board of the respective institutions.Explicit informed consent was acquired from all participants involved in the study.
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Sample size 700 participants in the fMRI analysis, 122 participants in the iEEG analysis.These sample sizes were the maximum available from either dataset, and were far more than statistically needed (as indicated in the comparison p-value tables in Figs.2,3, where almost all p-values fall below 1e-20 for iEEG and 1e-40 for fMRI).
Data exclusions fMRI data: we removed participants from further analysis if any of their four resting scans had excessively large head motion, defined by having frames with greater than 0.2 mm frame-wise displacement or a derivative root mean square (DVARS) above 75.Also, participants listed in [Elam, "Hcp data release updates: Known issues and planned fixes", 2020] under ``3T Functional Preprocessing Error of all 3T RL fMRI runs in 25 Subjects" or ``Subjects without Field Maps for Structural scans" were removed.
iEEG data: For all participants, we rejected noisy channels that were either (i) marked as noisy in the RAM dataset notes, (ii) had a line length greater then three times the mean, (iii) had z-scored kurtosis greater than 1.5, or (iv) had a z-scored power-spectral density dissimilarity measure greater than 1.5.The dissimilarity measure used was the average of one minus the Spearman's rank correlation with all channels.
All exclusion criteria are minimal and were pre-established.

Replication
Cross-validation was used so that the performance of all included models was tested on data not seen during training.
Randomization No group allocation was performed or was applicable.All models were applied to all the data segments given the computational nature of the study, so no randomization was performed.

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No group allocation was performed or was applicable.Blinding was therefore not applicable.
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