Counterfactual Analysis of Brain Network Dynamics

Abstract

Causal inference in brain networks has traditionally relied on regression-based models such as Granger causality, structural equation modeling, and dynamic causal modeling. While effective for identifying directed associations, these methods remain descriptive and acyclic, leaving open the fundamental question of intervention: what would the causal organization become if a pathway were disrupted or externally modulated? We introduce a unified framework for counterfactual causal analysis that models both pathological disruptions and therapeutic interventions as an energy-perturbation problem on network flows. Grounded in Hodge theory, directed communication is decomposed into dissipative and persistent (harmonic) components, enabling systematic analysis of how causal organization reconfigures under hypothetical perturbations. This formulation provides a principled foundation for quantifying network resilience, compensation, and control in complex brain systems.

Figures (3)

• Figure 1: Left: Average fraction of simplices in the Spatial Scaffold relative to the Rips complex (theoretical upper bound) across subjects in rs-fMRI connectivity. Right: Average time-lagged correlation across all time points and subjects. The mean correlation is extremely low (maximum $r = 0.034$), indicating that none of the connections reach statistical significance.
• Figure 2: Minimization of the Dirichlet potential energy of edge flow $X$ converges to the persistent harmonic flow ${\color{red} X_H}$, which captures long-range, stable, and recurrent communication patterns. The residual $X - {\color{red} X_H}$, composed of the gradient ${\color{blue} X_G}$ and curl ${\color{green} X_C}$, represents transient dynamics that dissipate over time.
• Figure 3: Middle: Ten dominant average harmonic flows (${\color{red} X_H}$) across time and 400 healthy subjects, showing strong recurrent interhemispheric and predominantly homotopic organization—most evident in visual (Calcarine, Cuneus, Lingual) and sensorimotor (Postcentral, Paracentral) regions. Left: After counterfactual perturbation of the temporal–limbic feedback loop, pathological hyperrecurrence shifts dominance from interhemispheric sensory pathways toward olfactory–limbic–vermal circuits. Right: After counterfactual simulation of left anterior temporal lobectomy (ATL) on healthy controls, the global topology remains largely preserved, indicating compensatory stabilization through contralateral and midline pathways.