Models commonly used in neural signal analysis

VARX model of the brain:

A) Block diagram of 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) is unobserved intrinsic “random” brain activity. B) Example of input stimulus features x(t). C) Single channel examples of neural signal y(t). D) Examples of moving-average response filters B. E) Effect size R for the “connections” captured by auro-regresive filters A.

Connectivity of stimulated neural mass model for the whole brain, and estimated VARX model.

A) True structural connectivity used to simulate neural activity using a neural mass model with the neurolib python toolbox. 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 A matrix of the VARX model on the simulated data. C) Comparison of true and VARX estimate of connectivity. D) Absolute value of the sparse-inverse functional connectivity (estimated using graphical lasso 47).

Spurious intrinsic connectivity in A is removed when modeling the effect of exogenous input with B.

Comparison of VARX model with and without inputs. A) p-values for each connection in A for VARX model with inputs on one subject (Pat_1); B) for VARX model without inputs; C) difference. Both models are fit to the same data. D) Difference of fraction of significant recurrent connections between VARX models with and without inputs. E) Mean difference in R over all electrodes between VARX models with and without inputs. Each point is a subject. Dashed line is the median across subjects. F) Difference between the VARX models with different input combinations and the VARX model without inputs. Red line shows mean across patients, black lines the 95% confidence interval. Negative values indicate a decrease in connectivity strength when exogenous input is accounted for.

Recurrent connectivity A during movies does not detectably differ from rest.

Effect size R for each connection in A. A) VARX model of 5 minutes of LFP recordings during movie watching, with sound envelope, fixation onsets and film cuts as input features. B) VARX model during resting fixation with fixation onset as input feature. C) Difference in the number of significant connections (p<.0001) between movie and rest. D) Difference in mean effect size across all channels between movie and rest. Dots represent subjects, dashed line the median across subjects. Axial view of significant connections in E) the movie task, F) resting state, and G) the difference between movies and resting state. Dots show the location of contacts in MNI space. Lines show significant connections between contacts. For plotting purposes connections in the upper triangle are plotted and asymmetries ignored. Only channels with p-values < 0.001 in both conditions are plotted.

Impulse response models.

A) Immediate responses B to fixation onset are weaker and shorter than B) the overall system response H. Significant responses of select channels in for one example patient. C) Power and D) mean length of responses in significant channels for all patients. Each line is a patient. Channels with the strongest responses are shown in panels A&B. Responses to fixation onset in all significant channels, as well as auditory envelope and film cuts are shown in Figure S9.

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 subjects, contrasting responsive vs non-responsive channels.

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

A) Difference of s R − R T howing 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 hierarchy.