Topological Effective Connectivity Modeling in Brain Networks

2026-06-06

AI Summary

This study addresses a key limitation in existing effective connectivity methods for brain networks, which typically assume acyclic structures and thus fail to capture directed cyclic information flows arising from feedback loops. To overcome this, the authors introduce discrete Hodge decomposition into brain network modeling for the first time, integrating lead-lag mutual information with nonparametric permutation testing. This approach orthogonally decomposes edge-wise information flow into gradient (feedforward), curl (recurrent feedback), and harmonic components, explicitly disentangling cyclic dependencies associated with triangular motifs and topological cavities. The method’s validity is demonstrated on synthetic data, and its application to a rat model of focal cerebral ischemia reveals a significant post-stroke shift in information flow—from a balanced feedforward–feedback regime toward one predominantly driven by hierarchical sources.

Abstract

Characterizing directed information flow in brain networks is difficult because neural circuits are full of recurrent feedback loops. Many existing tools for directed dependence assume a directed acyclic graph (DAG) structure to resolve directional ambiguity, and therefore cannot represent these loops. We present a nonparametric, information-theoretic framework that addresses this by coupling the discrete Hodge decomposition with lead-lag mutual information, splitting the resulting edge flow into three orthogonal components: a gradient term capturing hierarchical, feed-forward relationships; a curl term isolating triangle-level feedback loops; and a harmonic term capturing cyclic flow around topological holes. This separation makes it possible to disentangle feed-forward drive from recurrent circulation, which conventional measures conflate. We further develop a permutation-based hypothesis-testing layer that identifies nodes and triangular motifs whose information-flow signatures change significantly between conditions. We validate the framework on simulations with known ground-truth structure and apply it to local field potential recordings from a rodent model of focal ischemic stroke. In three of four animals, we find a post-stroke shift toward hierarchical, source-driven propagation at the expense of recurrent feedback, while the fourth shows no significant change.

Problem

• topological effective connectivity
• directed information flow
• recurrent feedback loops
• brain networks
• directed acyclic graph

Innovation

• Hodge decomposition
• lead-lag mutual information
• topological effective connectivity
• recurrent feedback loops
• nonparametric information-theoretic framework