Models commonly used in neural signal analysis

VARX model of the brain:

A) Block diagram of the VARX model. y(t) represents observable neural activity in different brain areas, x(t) are observable features of a continuous sensory stimulus, A represent the recurrent connections within and between brain areas (intrinsic effect), and B captures the transduction of the sensory stimuli into neural activity and transmission to different brain areas (extrinsic effect). The diagonal term in A captures recurrent feedback within a brain area. Finally, e(t) captures unobserved “random” brain activity, which leads to intrinsic variability. B) Example of input stimulus features x(t). C) Example of neural signal y(t) recorded at a single location in the brain. We analyze local field potentials (LFP) and broad-band high frequency activity (BHA) in separate analyses. D) Examples of filters B for individual feed-forward connections between an extrinsic input and a specific recording location in the brain. E) Effect size R for the recurrent connections captured by auto-regressive filters A.

Structural connectivity of stimulated neural mass model for the whole brain, and estimated recurrent connectivity in VARX model.

A) True structural connectivity C used to simulate neural activity using a neural mass model with the neurolib python toolbox. Structural connectivity is based on diffusion tensor imaging data between 80 brain areas (called Cmat in neurolib). Here showing the square root of the “Cmat’’ matrix for better visibility of small connectivity values. B) Effect size estimate R for the recurrent connectivity matrix A of the VARX model on the simulated data. The diagonal in R is omitted as it is also missing in the structural connectivity Cmat. C) Comparison of true and VARX estimate of connectivity. D) Absolute value of the sparse-inverse functional connectivity (estimated using graphical lasso 48).

Spurious recurrent connectivity in A is removed when modeling the effect of extrinsic input with. B.

Comparison of VARX model with and without inputs. A) log p-values for each connection in A for a VARX model without inputs on one patient (Pat_1); B) for a VARX model with inputs; C) difference of logp for VAX model without minus with inputs (panel A - B). Both models are fit to the same data. D) Thresholding panels A and B at p<0.0001 gives a fraction of significant connections. Here we show the fraction of significant channels for models with and without input. Each line is a patient with color indicating increase or decrease. E) Mean R over all channels for VARX models with and without inputs. Values in D) and E) have been normalized to models without input. F) Change in R values when successively adding inputs to the VARX model. Black line shows mean across patients, shaded gray area the standard error of the mean. Stars indicate features that further reduce effect size over the previously added feature with statistical significance (Wilcoxon rank sum test p<0.05). Negative values indicate a decrease in connectivity strength when the extrinsic inputs are accounted for. Results for BHA are shown in Fig. S5.

Recurrent connectivity during movies is decreased compared to rest.

Effect size R for each connection in A of one patient (Pat_7) for A) a VARX model during resting fixation with fixation onset as input feature. B) The same with a VARX model of LFP recordings during movie watching, with the following input features: sound envelope, acoustic edges, fixation onsets, fixation novelty, motion and film cuts. C) Fraction of significant connections (p<0.0001) for movies and rest. D) Mean effect size across all channels for movies and rest. Each line is a patient, with color indicating a numerical increase or decrease. For the movie conditions, we averaged across four different 5 min movie segments. E) Axial view of significant connections in resting state. Black dots show the location of contacts in MNI space. Lines show significant connections between contacts (p<0.001) colored in red according to effect size R. For plotting purposes connections in the upper triangle are plotted and asymmetries ignored. F) The same for the movie task, and G) the difference between movies and resting state, showing both increases or decreases for specific connections. Differences between BHA recurrent connectivity A during movies and resting-state are shown in Figure S7.

Impulse response models.

A) Feed-forward responses B to fixation onset are weaker and shorter than B) the overall system response H. Impulse response models for fixation onset in channels with significant responses for one example patient. C) Power and D) mean length of responses in significant channels for all patients. Each line is a patient. Responses to fixation onset in all significant channels, as well as auditory envelope and film cuts are shown in Figure S10.

For BHA, relative power of innovation vs signal drops during movies as compared to rest in responsive channels.

A) Effect size R for extrinsic effect B in all channels for 3 input features (scene cuts, fixation onset, sound envelope). In this example 15 electrodes had significant responses to one of the three inputs (Bonferroni corrected at p<0.01). B) Change in relative power of innovation (dB(innovation power / signal power), then subtracting movie - rest). C) Change in relative power of innovation in a simulation of a VARX model with gain adaptation. Here we are using the A and B filters that were estimated on BHA on the example from panel A and B. D) Median of power ratio change across all patients, contrasting responsive vs non-responsive channels.

Recurrent connectivity of LFP is directed from sensory to higher-order areas.

A) Difference of R − RT showing asymmetric directed effects. Dashed lines indicate regions of interest in the Desikan-Killiany atlas. B) Mean directionality across patients and T1w/T2w ratio are averaged in parcels of the Desikan-Killiany atlas. C) Mean directionality is correlated with cortical hierarchy, estimated with the T1w/T2w ratio. Each dot represents a parcel in the Desikan-Kiliany atlas with error-bars indicating error of the mean across patients with channels in that parcel. The datapoint on the top left is the transverse temporal gyrus. Note that the x-axis has been flipped to show areas higher on the cortical hierarchy on the right. T1w/T2w ratio and cortical hierarchy have an inverse relationship.