The multiscale self-similarity of the weighted human brain connectome

TL;DR

This paper uncovers multiscale self-similarity in the weighted human brain connectome, revealing consistent structural patterns across scales and proposing a unified geometric model that captures this fractal organization.

Contribution

It introduces a novel multiscale analysis of weighted brain connectomes, demonstrating self-similarity and proposing a hyperbolic embedding model that unifies weights across scales.

Findings

Multiscale self-similarity in weighted connectomes

A hyperbolic embedding model captures the multiscale structure

Symmetry indicates criticality in brain connectivity

Abstract

Anatomical connectivity between different regions in the brain can be mapped to a network representation, the connectome, where the intensities of the links, the weights, influence its structural resilience and the functional processes it sustains. Yet, many features associated with the weights in the human brain connectome are not fully understood, particularly their multiscale organization. In this paper, we elucidate the architecture of weights, including weak ties, in multiscale hierarchical human brain connectomes reconstructed from empirical data. Our findings reveal multiscale self-similarity in the weighted statistical properties, including the ordering of weak ties, that remain consistent across the analyzed length scales of every individual and the group representatives. This phenomenon is effectively captured by a renormalization of the weighted structure applied to hyperbolic embeddings of the connectomes, based on a unique weighted geometric model that integrates links of all weights across all length scales. This eliminates the need for separate generative weighted connectivity rules for each scale or to replicate weak and strong ties at specific scales in brain connectomes. The observed symmetry represents a distinct signature of criticality in the weighted connectivity of human brain connectomes, aligning with the fractality observed in their topology, and raises important questions for future research, like the existence of a resolution threshold where the observed symmetry breaks, or whether it is preserved in cases of neurodegenerative disease or psychiatric disorder.