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. 2020 Jun;101(6-1):062301.
doi: 10.1103/PhysRevE.101.062301.

Control of brain network dynamics across diverse scales of space and time

Evelyn Tang  1   2 , Harang Ju  1   3 , Graham L Baum  1   3 , David R Roalf  4 , Theodore D Satterthwaite  4 , Fabio Pasqualetti  5 , Danielle S Bassett  1   4   6   7   8   9
Affiliations

Control of brain network dynamics across diverse scales of space and time

Evelyn Tang et al. Phys Rev E. 2020 Jun.

Abstract

The human brain is composed of distinct regions that are each associated with particular functions and distinct propensities for the control of neural dynamics. However, the relation between these functions and control profiles is poorly understood, as is the variation in this relation across diverse scales of space and time. Here we probe the relation between control and dynamics in brain networks constructed from diffusion tensor imaging data in a large community sample of young adults. Specifically, we probe the control properties of each brain region and investigate their relationship with dynamics across various spatial scales using the Laplacian eigenspectrum. In addition, through analysis of regional modal controllability and partitioning of modes, we determine whether the associated dynamics are fast or slow, as well as whether they are alternating or monotone. We find that brain regions that facilitate the control of energetically easy transitions are associated with activity on short length scales and slow timescales. Conversely, brain regions that facilitate control of difficult transitions are associated with activity on long length scales and fast timescales. Built on linear dynamical models, our results offer parsimonious explanations for the activity propagation and network control profiles supported by regions of differing neuroanatomical structure.

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Figures

FIG. 1.
FIG. 1.
Controllability and synchronizability in brain networks. (a) While the brain displays nonlinear dynamics (top left), linear models (top right) have shown great utility in predicting such dynamics across spatial scales [13,14,37]. We study two such metrics: Average controllability provides an intuitive measure of the structural support for moving the brain to easy-to-reach states (short red transition), whereas modal controllability provides an intuitive measure of the structural support for moving the brain to difficult-to-reach states (long blue transition). (b) Diffusion tensor imaging measures the direction of water diffusion in the brain. From this data, white matter streamlines can be reconstructed that connect brain regions in a structural network. (c.i) Regional average controllability ranked on N = 234 brain regions of a group-averaged network for visualization purposes. (c.ii) Regions with high average controllability tend to display low modal controllability: ρ = −0.76, df = 233, p < 1 × 10−16. (d) We operationalize a synchronous state as a state in which all nodes have the same activity magnitude. Such a state is stable when the master stability function is negative for all positive eigenvalues of the graph Laplacian [38]. Following Ref. [39], we use the inverse spread of the Laplacian eigenvalues 1/σ2({λi}) as a measure of global synchronizability. Adapted with permission from Ref. [39].
FIG. 2.
FIG. 2.
Synchronizability and the spatial extent of predicted harmonic waves. (a) Spatial distribution of the eigenvector ϕ1 for the smallest Laplacian eigenvalue λ1, showing which regions on a group-averaged brain network most strongly contribute to this large-scale mode. (b) Spatial distribution of the eigenvector ϕN−1 for the largest Laplacian eigenvalue λN−1, showing which regions most strongly contribute to this small-scale mode. (c) Regions most relevant for this large-scale mode |ϕ1j| are positively correlated with regions of high modal controllability: ρ = 0.27, df = 233, p < 1 × 10−4. (d) Regions most relevant for this small-scale mode |ϕN−1j| are positively correlated with regions of high average controllability: ρ = 0.95, df = 233, p < 1 × 10−5. Note that the color in panels (a, b) is recapitulated by values along the vertical axis in panels (c, d), simply for ease of identifying relevant brain regions with the given results.
FIG. 3.
FIG. 3.
Extracting fast or slow, and alternating or monotone modes of network dynamics. Here we show the histogram of N = 234 eigenvalues of the group representative brain network, constructed by averaging all 190 subject-specific brain networks. Given the trimodal distribution of eigenvalues, we partition them into a densely populated cluster of |ξj| < 0.2, a lightly populated cluster of 0.2 < |ξj| < 0.6, and the remaining |ξj| > 0.6 eigenvalues that are separated from the other modes with a clear gap. This partitioning can be done for both positive and negative eigenvalues, respectively, which correspond to the monotone and alternating modes of the system. From left to right, these groups are ξj < −0.6 (slow alternating), −0.2 < ξj < 0 (fast alternating), 0 < ξj < 0.2 (fast monotone), and ξj > 0.6 (slow monotone), respectively.
FIG. 4.
FIG. 4.
Monotone modes and their control profiles across the brain. (a) Spatial distribution of the controllability of slow monotone modes (ξj > 0.6), showing which regions on a group-representative brain network most strongly contribute. (b) Spatial distribution of the controllability of fast monotone modes (0 < ξj < 0.2), showing which regions on a group-representative network most strongly contribute. (c) Regions most relevant for control of slow monotone modes tended to be regions of high average controllability: ρ = 0.99, df = 233, p < 1 × 10−4. (d) Regions most relevant for control of fast monotone modes tended to be regions of high modal controllability: ρ = 0.59, df = 233, p < 1 × 10−4. Note that the color in panels (a, b) is recapitulated by values along the vertical axis in panels (c, d), simply for ease of identifying relevant brain regions with the given results.
FIG. 5.
FIG. 5.
Alternating modes and their control profiles across the brain. (a) Spatial distribution of the controllability of slow alternating modes (ξj < −0.6), showing which regions on a group-representative brain network most strongly contribute. (b) Spatial distribution of the controllability of fast alternating modes (−0.2 < ξj < 0), showing which regions on a group-representative network most strongly contribute. (c) Regions most relevant for the control of slow alternating modes tended to be regions of high average controllability: ρ = 0.83, df = 233, p < 1 × 10−4. (d) Regions most relevant for the control of fast alternating modes tended to be regions of high modal controllability: ρ = 0.24, df = 233, p < 2 × 10−4. Note that the color in panels (a, b) is recapitulated by values along the vertical axis in panels (c, d), simply for ease of identifying relevant brain regions with the given results.
FIG. 6.
FIG. 6.
Histogram of N = 234 eigenvalues of a Barabasi-Albert preferential attachment network. As we had done for the group-representative brain network, we make partitions of |ξj| < 0.2, 0.2 < |ξj| < 0.6, and |ξj| > 0.6 for positive and negative eigenvalues, respectively, which correspond to the monotone and alternating modes of the system.
FIG. 7.
FIG. 7.
Different results from the group-representative brain network and a Barabasi-Albert network. Study of the alternating dynamical modes for the two different networks shows that while controllers of fast modes are positively correlated with modal controllers in the brain network (left), the same controllers are negatively correlated in a Barabasi-Albert network (right), ρ = −0.91, df = 233, p < 1 × 10−4. [The color in the left image simply corresponds to the strength of control of fast alternating modes, for consistency with Fig. 5(d).]
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