Paper Detail
Breno C. Bispo, Stefania Sardellitti, Juliano B. Lima, Fernando A. N. Santos
Brain connectomics is still largely dominated by pairwise-based models, such as graphs, which cannot represent circulatory or higher-order functional interactions. In this paper, we propose a multimodal framework based on Topological Signal Processing (TSP) that models the brain as a higher-order topological domain and treats functional interactions as discrete vector fields. We integrate diffusion MRI and resting-state fMRI to learn subject-specific brain cell complexes, where statistically validated structural connectivity defines a sparse scaffold and phase-coupling functional edge signals drive the inference of higher-order interactions (HOIs). Using Hodge-theoretic tools, spectral filtering, and sparse signal representations, our framework disentangles brain connectivity into divergence (source-sink organization), gradient (potential-driven coordination), and curl (circulatory HOIs), enabling the characterization of temporal dynamics through the lens of discrete vector calculus. Across 100 healthy young adults from Human Connectome Project, node-based HOIs are highly individualized, yet robust mesoscale structure emerges under functional-system aggregation. We identify a distributed default mode network-centered gradient backbone and limbic-centered rotational flows; divergence polarization and curl profiles defining circulation regimes with insightful occupancy and dwell-time statistics. These topological signatures yield significant brain-behavior associations, revealing a relevant higher-order organization intrinsic to edge-based models. By making divergence, circulation, and recurrent mesoscale coordination directly measurable, this work enables a principled and interpretable topological phenotyping of brain function.
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@article{bispo2026multimodal,
title = {Multimodal Higher-Order Brain Networks: A Topological Signal Processing Perspective},
author = {Breno C. Bispo and Stefania Sardellitti and Juliano B. Lima and Fernando A. N. Santos},
year = {2026},
abstract = {Brain connectomics is still largely dominated by pairwise-based models, such as graphs, which cannot represent circulatory or higher-order functional interactions. In this paper, we propose a multimodal framework based on Topological Signal Processing (TSP) that models the brain as a higher-order topological domain and treats functional interactions as discrete vector fields. We integrate diffusion MRI and resting-state fMRI to learn subject-specific brain cell complexes, where statistically val},
url = {https://arxiv.org/abs/2603.29903},
keywords = {q-bio.NC, eess.SP},
eprint = {2603.29903},
archiveprefix = {arXiv},
}
{}