Unveiling subject-specific causal latency in motor imagery: a physiologically transparent BCI via Riemannian tangent space fusion

OBJECTIVE: While deep learning has improved motor imagery (MI) brain-computer interfaces (BCIs), its "black-box" nature lacks physiological interpretability. Building upon our previous findings that cortical state transitions are governed by non-linear network dynamics, this study aims to elucidate subject-specific functional network delays during MI and propose a physiologically transparent BCI architecture incorporating these functional network temporal delays. 
Approach: We analyzed 4-class MI EEG data (sensorimotor μ and β rhythms, 8-30 Hz) from the full cohort of 109 subjects in the PhysioNet dataset. To effectively mitigate instantaneous volume conduction effects, we utilized partial correlation-based True Transfer Entropy (True-TE) to extract the optimal functional causal latency (τopt) of information between the supplementary motor area and the primary motor cortex. We then proposed a Tangent Space Fusion (TSF-PDER) framework, independently projecting the current and delayed spatial covariance matrices into the Riemannian tangent space before fusion to prevent topological degradation.
Main results: Under a strict, leakage-free nested cross-validation where τopt was estimated exclusively within the training folds, the extracted personalized latencies exhibited a wide functional distribution (median: 374.0 ms). Incorporating TSF-PDER significantly outperformed the spatial-only Riemannian baseline (mean accuracy: 47.24% vs. 45.70%, Wilcoxon signed-rank p = 1.577e-04), while a deep learning baseline (EEGNet) achieved only 28.53% under strictly limited data conditions. Furthermore, bidirectional control analysis revealed significantly stronger feedback information flow than feedforward flow. External validation on the BCI Competition IV-2a dataset demonstrated consistent improvements, with TSF-PDER achieving an average accuracy of 61.92% (vs. baseline 59.07%).
Significance: MI execution involves personalized, long-range functional network loops. Fusing these personalized functional delays within the Riemannian tangent space provides a robust decoding boundary without topological degradation. Consequently, TSF-PDER offers a computationally lightweight proof-of-concept for an interpretable BCI, paving the way for personalized neurorehabilitation tailored to patient-specific cortical network dynamics.