  Higher-order properties of functional magnetic resonance imaging (fMRI)
induced connectivity have been shown to unravel many exclusive topological and
dynamical insights beyond pairwise interactions. Nonetheless, whether these
fMRI-induced higher-order properties play a role in disentangling other
neuroimaging modalities' insights remains largely unexplored and poorly
understood. In this work, by analyzing fMRI data from the Human Connectome
Project Young Adult dataset using persistent homology, we discovered that the
volume-optimal persistence homological scaffolds of fMRI-based functional
connectomes exhibited conservative topological reconfigurations from the
resting state to attentional task-positive state. Specifically, while
reflecting the extent to which each cortical region contributed to functional
cycles following different cognitive demands, these reconfigurations were
constrained such that the spatial distribution of cavities in the connectome is
relatively conserved. Most importantly, such level of contributions covaried
with powers of aperiodic activities mostly within the theta-alpha (4-12 Hz)
band measured by magnetoencephalography (MEG). This comprehensive result
suggests that fMRI-induced hemodynamics and MEG theta-alpha aperiodic
activities are governed by the same functional constraints specific to each
cortical morpho-structure. Methodologically, our work paves the way toward an
innovative computing paradigm in multimodal neuroimaging topological learning.
