Analysis of Long-Term Neuronal Dynamics via Ordinal Pattern Quantifiers Following Traumatic Brain Injury and Pharmacological Modulation

Traumatic brain injury (TBI) profoundly disrupts hippocampal network dynamics, triggering persistent alterations in oscillatory activity that underlie cognitive deficits and increased susceptibility to post-traumatic epilepsy. Characterizing these alterations quantitatively remains challenging: the resulting signals are nonlinear, non-stationary, and exhibit complex multiscale structure that conventional spectral metrics fail to resolve. Ordinal-pattern information-theoretic quantifiers offer a principled, model-free alternative for probing such dynamics. In this work we apply permutation entropy (PE), statistical complexity (SC), Fisher information (FI), and permutation Lempel-Ziv complexity (PLZC) to hippocampal local field potentials (LFPs) recorded over 21 days in a rodent controlled cortical impact model of TBI, across five experimental groups under distinct pharmacological conditions. Embedding signal trajectories in the SC-PE, FI-PE, and PLZC-PE information planes reveals group- and time-dependent dynamical signatures in the theta (4-8 Hz) and high-frequency oscillation (80-200 Hz) bands, exposing state transitions invisible to spectral analysis. Unsupervised dimensionality reduction (UMAP) combined with HDBSCAN clustering further delineates distinct regions of dynamical state space associated with injury progression and pharmacological modulation. We additionally applied the Ordinal Modulation Index (OMI), an ordinal-based measure of theta-HFO cross-frequency coupling, which captures treatment-dependent reorganization of phase-amplitude coordination. These results establish ordinal-pattern analysis as a sensitive and interpretable framework for tracking the nonlinear reorganization of hippocampal dynamics following TBI.