Dynamic Functional Connectome Harmonics

Abstract

Functional connectivity (FC) "gradients" enable investigation of connection topography in relation to cognitive hierarchy, and yield the primary axes along which FC is organized. In this work, we employ a variant of the "gradient" approach wherein we solve for the normal modes of FC, yielding functional connectome harmonics. Until now, research in this vein has only considered static FC, neglecting the possibility that the principal axes of FC may depend on the timescale at which they are computed. Recent work suggests that momentary activation patterns, or brain states, mediate the dominant components of functional connectivity, suggesting that the principal axes may be invariant to change in timescale. In light of this, we compute functional connectome harmonics using time windows of varying lengths and demonstrate that they are stable across timescales. Our connectome harmonics correspond to meaningful brain states. The activation strength of the brain states, as well as their inter-relationships, are found to be reproducible for individuals. Further, we utilize our time-varying functional connectome harmonics to formulate a simple and elegant method for computing cortical flexibility at vertex resolution and demonstrate qualitative similarity between flexibility maps from our method and a method standard in the literature.

Keywords: dynamic functional connectivity; flexibility; harmonics.

Fig. 1.

Group-level most-prevalent harmonics ${\stackrel{-}{\mathit{\Psi }}}_k$ derived from 2 min window for test cohort mapped to the cortical surface. Matrix below each ${\stackrel{-}{\mathit{\Psi }}}_k$ is cosine similarity between group-level harmonics computed for different window lengths and test or retest cohort. Matrix labels are window length in minutes, with $\text{R}$ denoting retest cohort. ${\stackrel{-}{\mathit{\Psi }}}_1$ differentiates the default mode network from the rest of the brain, ${\stackrel{-}{\mathit{\Psi }}}_2$ differentiates regions in the task positive network from the rest of the brain. Color bar ranges from cosine similarity of 0.70 to 1.00.

Fig. 2.

Group average flexibility computed using a) dynamic functional connectome harmonic method (Eq. 3) and b) conventional community detection based method. Note that both flexibility maps are computed using 2 min window length.