OPTIMAL CONTROL MODELING OF RESTING STATE DYNAMIC FUNCTIONAL CONNECTIVITY

Large-scale functional connectivity (FC) reconfigures rapidly at rest, yet most approaches to dynamic FC (dFC) either neglect temporal dependencies or rely on black-box sequence models. We ask whether brain-wide FC trajectories can be understood as the evolution of a low-dimensional dynamical system governed by optimal control, and whether subject-specific control costs relate to depressive symptom burden. Resting-state fMRI from 2,770 adults (823 with major depressive disorder; MACS dataset) was transformed into framewise FC estimates among 32 cortical regions using instantaneous phase differences of BOLD signals. K-means clustering identified four recurrent FC states, and each time point was represented as a four-dimensional mixture over these states. We modeled the temporal evolution of these embeddings using an inverse Linear–Quadratic Regulator (LQR), estimating per-subject feedback dynamics and control penalties. As a benchmark, gated recurrent unit (GRU) models were trained on the same embeddings. Both approaches predicted next-time-point states with high accuracy (median held-out Pearson r ≈ 0.90), with the interpretable control-theoretic model matching the deep sequence model. Prediction accuracy decreased with the number of inter-state transitions, indicating reduced predictability in subjects with richer switching dynamics. Critically, transition rates were behaviorally relevant: higher Beck Depression Inventory (BDI-II) scores were associated with fewer transitions, consistent with “stickier,” harder-to-steer FC dynamics. These continuous symptom relationships were stronger than categorical comparisons between healthy controls and MDD patients. Together, our findings show that dynamic FC can be parsimoniously described as an optimal-control process, providing interpretable parameters that link large-scale brain dynamics to individual variation in depressive symptoms.