Mapping individualized multi-scale hierarchical brain functional networks from fMRI by self-supervised deep learning.

The brain's multi-scale hierarchical organization supports functional segregation and integration. Characterizing the hierarchy of individualized multi-scale functional networks (FNs) is crucial for understanding these fundamental brain processes. It provides promising opportunities for both basic neuroscience and translational research in neuropsychiatric illness. However, current methods typically compute individualized FNs at a single scale and are not equipped to quantify any possible hierarchical organization. To address this limitation, we present a self-supervised deep learning (DL) framework that simultaneously computes multi-scale FNs and characterizes their across-scale hierarchical structure at the individual level. Our method learns intrinsic representations of fMRI data in a low-dimensional latent space to effectively encode multi-scale FNs and their hierarchical structure by optimizing functional homogeneity of FNs across scales jointly in an end-to-end learning manner. A DL model trained on fMRI scans from the Human Connectome Project successfully identified individualized multi-scale hierarchical FNs for unseen individuals and generalized to two external cohorts. Furthermore, the individualized hierarchical structure of FNs was significantly associated with biological phenotypes, including sex, brain development, and brain health. Our framework provides an effective method to compute multi-scale FNs and to characterize the inter-scale hierarchy of FNs for individuals, facilitating a comprehensive understanding of brain functional organization and its inter-individual variation.