Counterfactual Analysis of Brain Network Dynamics.

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.