Fig 1.
Whole-brain imaging data, computational model of large-scale brain dynamics, and schematic of analysis.
(A) An example of white matter streamlines reconstructed from diffusion imaging and tractography of a human brain. (B) Noninvasive magnetic resonance imaging scans of human brain anatomy are used to segment the cortex and subcortex into 82 regions. (C) Adjacency matrix for a group-averaged structural brain network. Individual brain areas are represented as network nodes, and normalized white matter streamline counts between region pairs are represented as weighted network edges. (D) Matrix of Euclidean distances between the centers of mass of all region pairs. (E) Left: Structural brain network representation; location of gray circles correspond to region centers of mass, and teal lines show the strongest 20% of interareal connections, with line thickness proportional to connection strength. The two encircled nodes correspond to an unperturbed region j and an excited region i in the large-scale brain network, with the perturbed region indicated by the yellow lightning bolt. Right: Schematic of the computational model of large-scale brain dynamics. The activity of a given brain region j is modeled as a Wilson-Cowan neural mass, composed of interacting populations of excitatory E and inhibitory I neurons. Neural masses are then coupled through their excitatory pools according to the structure of the anatomical brain network. A perturbation to region i (pictorially represented with the lightning bolt) is modeled as an increase in its excitatory input from PE → PE + ΔPE. (F) The computational model generates oscillatory time-series of neural population activity for each brain region. These time-series can then be analyzed in Fourier space to determine relevant frequency bands for further analysis. After filtering time-series within the same frequency band of interest, functional interactions between brain region pairs are determined by extracting phase variables from each region’s filtered activity via the Hilbert transform, and then computing the phase-locking value to assess the consistency of phase relations over time and trials.
Table 1.
Parameter values for the large-scale Wilson-Cowan neural mass model and for the numerical simulations.
Table 2.
List of computed measures.
Fig 2.
Long-range coupling strength C and background drive modulate firing rates and oscillation frequencies at baseline.
(A) The time- and network-averaged population firing rate as a function of C and
(units are arbitrary). (B) The network-averaged peak frequency of regional activity 〈fpeak〉 as a function of C and
. (C) A segment of the activity of one brain area and (D) the corresponding power spectra of the same area at the working point denoted by the red dot in panels A and B (
, C = 2.5). (E) A segment of the activity of one brain area and (F) the corresponding power spectra of the same area at the working point denoted by the orange dot in panels A and B (
, C = 2.5). (G) A segment of the activity of one brain area and (H) the corresponding power spectra of the same area at the working point denoted by the yellow dot in panels A and B (
, C = 2.5).
Fig 3.
Long-range coupling strength C and background drive modulate network phase-coherence and relationships between structural and functional connectivity at baseline.
(A) The global order parameter ρglobal vs. , for different fixed values of C. Error bars are estimated from 100 bootstrap samples of the simulations at each coupling and background drive, and correspond to ± one standard deviation of the bootstrap disribution of ρglobal. (B) The difference between the global and local order parameters, ρglobal − ρlocal, vs.
, for different fixed values of C. Error bars are estimated from 100 bootstrap samples of the simulations at each coupling and background drive, and correspond to ± one standard deviation of the bootstrap distribution of ρglobal − ρlocal. (C) Region-by-region PLV matrices for various values of
at fixed C = 2.5. The boxed matrices correspond to the red, orange, and yellow working points in Fig 2 and in panels A and B of this figure. (D) The Spearman correlation rs between structural node strength sstruc and functional node strength sfunc vs.
at fixed C = 2.5. Empty circles indicate that the correlation was not statistically significant at the p = 0.05 level. The arrows mark three different working points—WP1, WP2, and WP3 (which correspond to the red, orange, and yellow dots/boxes in this figure)—that will be studied in detail.
Fig 4.
Regional excitation causes local and downstream changes to brain areas’ power spectra in different frequency bands at WP1.
(A) Schematic of a brain network depicting the stimulated site i in brightest red. The black arrows point to two other regions j and k that lie at progressively further topological distances from the perturbed area in the structural network. In this figure, regions i, j, and k correspond to brain areas 1 (R–Lateral Orbitofrontal), 4 (R–Medial Orbitofrontal), and 10 (R–Precentral), respectively. (B) Left: A segment of region i’s activity time-course in the baseline condition. Right: A segment of region i’s activity time-course when it is stimulated. (C) Power spectra of area i and two other downstream regions j and k. In all three panels, the lighter curves correspond to the baseline condition, and the darker curves correspond to the state in which i is driven with additional input. The gray vertical lines indicate the peak frequency of region i in the excited condition. (D) Histogram of the shift in peak frequency
induced by stimulating unit i, plotted over all choices of the perturbed area. (E) Distribution of peak frequencies of all units in the baseline condition
(light gray) and distribution of the peak frequency units acquire when directly excited
(dark gray). (F) Average power spectra 〈psd〉j≠i over all units j ≠ i at baseline (light gray) and when unit i is perturbed with additional input (dark gray). (G) Average difference
of the spectra of unit j ≠ i when unit i is excited and in the baseline condition, where the average is over all units j ≠ i. For reference, the light gray vertical lines denote the minimum and maximum peak frequency across units in the baseline state, and the dark gray line indicates the peak frequency acquired by the stimulated region i. Shaded boxes denote two frequency bands of interest: (1) the baseline band (purple) consisting of the main oscillation frequencies of brain areas under baseline conditions, and (2) the excited band (green) centered around the peak frequency that the stimulated region inherits. In subsequent analyses, we assess perturbation-induced changes in the PLV between brain areas in the baseline band,
(purple), and in the excited band
(green).
Fig 5.
Phase-locking changes at WP1 are driven by local excitations of neural activity, differ between excited and baseline frequency bands, and are differentially related to structural and functional network properties.
(A) Pairwise changes in the PLV inside the baseline band Δρbase when region i (Left) or region j ≠ i (Right) is perturbed. In this figure, regions i and j correspond to regions 4 (R–Medial Orbitofrontal) and 23 (R–Lateral Occipital), respectively. (B) Network-averaged absolute PLV changes in the baseline band caused by stimulation of different brain areas. (C) Pairwise changes in the PLV inside the excited band Δρexc when region i (Left) or region j ≠ i (Right) is perturbed. (D) Network-averaged absolute PLV changes in the excited band
induced by stimulation of different brain areas. (E) The quantity
vs. structural node strength
(Left), and the quantity
vs. structural node strength
(Right). (F) The quantity
vs. functional node strength
(Left), and the quantity
vs. functional node strength
(Right). In panels (E) and (F), insets indicate Spearman correlation coefficients between the plotted quantities and their associated p-values).
Fig 6.
Effects of local excitations on power spectra are more restricted at the high background drive working point (WP3).
(A) Schematic of a brain network depicting the stimulated site i in brightest red. The black arrows point to two other regions j and k that lie at progressively further topological distances from the perturbed area in the structural network. In this figure, regions i, j, and k correspond to brain areas 1 (R–Lateral Orbitofrontal), 4 (R–Medial Orbitofrontal), and 10 (R–Precentral), respectively. (B) Left: A segment of region i’s activity time-course in the baseline condition. Right: A segment of region i’s activity time-course when it is stimulated. (C) Power spectra of area i and two other downstream regions j and k. In all three panels, the lighter curves correspond to the baseline condition, and the darker curves correspond to the state in which i is driven with additional input. The gray vertical lines indicate the peak frequency of region i in the excited condition. (D) Histogram of the shift in peak frequency
induced by exciting unit i, plotted over all choices of the perturbed area. (E) The average shift in the peak frequency of the stimulated region
for WP1, WP2, and WP3 (error bars indicate the standard deviation over all choices of the excited unit). (F) Distribution of peak frequencies of all units in the baseline condition
(light gray) and distribution of the peak frequency units acquire when directly excited
(dark gray). (G) Average power spectra 〈psd〉j≠i over all units j ≠ i at baseline (light gray) and when unit i is perturbed with additional input (dark gray). Because stimulation does not induce a well-separated excited frequency band, we only assess perturbation-induced changes in the PLV between brain areas for a single baseline frequency band (purple area).
Fig 7.
Phase-locking modulations induced by regional stimulation at WP3 and their associations with network properties.
(A) Pairwise changes in the PLV inside the baseline band Δρbase when region i (Left) or region j ≠ i (Right) is perturbed. In this figure, regions i and j correspond to regions 10 (R–Precentral) and 15 (R–Isthmus), respectively. (B) Network-averaged absolute PLV changes in the baseline band induced by stimulation of different brain areas. (C) The quantity
vs. structural node strength
(Left) and vs. functional node strength
(Right). Insets indicate Spearman correlation coefficients between the plotted quantities and their associated p-values).
Fig 8.
Dependence of global phase-locking changes on the baseline state of the brain network model.
(A) The left axis (gray) shows the network-averaged baseline PLV ρglobal as a function of background drive for a coupling C = 2.5. The right axis (purple) shows the grand average 〈|Δρbase|〉 of the perturbation-induced absolute changes in baseline band PLVs as a function of
. (B) The left axis (gray) shows the network-averaged baseline PLV ρglobal as a function of background drive
for a coupling C = 2.5. The right axis (purple) shows the coefficient of variation of the perturbation-induced average absolute changes in baseline band PLVs,
, as a function of
. (C) The left axis (gray) shows the network-averaged baseline PLV ρglobal as a function of background drive
for a coupling C = 2.5. The right axis (green) shows the grand average 〈|Δρexc|〉 of the perturbation-induced absolute changes in excited band PLVs as a function of
. (D) The left axis (gray) shows the network-averaged baseline PLV ρglobal as a function of background drive
for a coupling C = 2.5. The right axis (green) shows the standard deviation of the perturbation-induced average absolute changes in excited band PLVs,
, as a function of
. (Note that here we consider the standard deviation rather than the coefficient of variation since the mean response in the excited band eventually drops to zero.).
Fig 9.
Relationships between phase-locking modulations and the structural or functional connectivity of the stimulated site vary with working point.
(A) Difference Δrs in the strength of the correlation between the average absolute baseline band PLV changes and structural (
) or functional (
) node strength, plotted as a function of the baseline drive
for a coupling C = 2.5. The difference is defined such that when the curve is positive, overall coherence modulations exhibit a stronger correlation with functional rather than structural strength. The arrows mark the locations of the different working points studied in detail in the main or SI Text. (B) A schematic summarizing how structural sstruc or functional sfunc strength are related to either baseline or excited band PLV changes for different dynamical regimes. As the background drive varies from low (WP1) to medium (WP2) to high (WP3), the oscillatory state of the system changes, and so does the association of different phase-locking modulations to structural or functional network properties.