SynapseTDA: A High-Throughput Phase-Space Topological Framework for Interpretable Seizure Biomarker Extraction and Clinical Decision Support in Multi-Channel Neurophysiology

SynapseTDA is a high-throughput computational framework and Clinical Decision Support System (CDSS) that converts multi-channel raw EEG signals into dynamic phase-space topological manifolds via Takens' delay embedding and Vietoris–Rips persistent homology (H0 connected components and H1 cycles). To overcome the combinatorial complexity that historically hindered clinical TDA adoption, SynapseTDA introduces four key innovations: Stochastic Anti-Collapse Micro-Perturbation (ξ = 1.0 × 10-6): Prevents simplicial matrix degeneracies during isoelectric flatlines without distorting topological persistence. Topology-Preserving Level-of-Detail (LOD): Decimates quiescent background data by 80% while strictly preserving 100% of simplex vertices constructing persistent H1 representative cycles. Dynamic Multi-Channel Cluster Auto-Tracker (≥ 60% peak persistence): Autonomously isolates seizure epicenters and propagation vectors across multi-lead montages. Decoupled Zero-Localhost WebGL (Ploty.js) Architecture: Pre-computes time-sliced modular payloads in multithreaded Julia and renders interactive 3D diagnostics within offline client browsers at up to 119 FPS, strictly upholding HIPAA/GDPR boundaries without network reliance. Clinical & Benchmark Validation: Evaluated on pediatric continuous scalp EEG from the PhysioNet CHB-MIT repository (Children's Hospital Boston / Harvard), SynapseTDA reliably detects generalized tonic-clonic seizures (chb13_40.edf), brief focal paroxysms (chb16_18.edf), and discovers unannotated sub-clinical focal paroxysms (chb01_04.edf), achieving an overall ROC-AUC of 0.974 (95% CI: 0.958–0.987). Multi-domain validations across full-night polysomnography (7.95M samples/ch), BCI motor imagery, fetal-maternal ECG separation (r01.edf), and turbomachinery vibration confirm universal scalability without memory leaks. Nota em Português: Este registo contém o manuscrito científico completo, bem como o vídeo demonstrativo da consola interativa VCR ("SynapseTDA_Technical_Demo_Supplementary.mp4") e resultados finais num ZIP a operar de forma 100% offline num ambiente clínico.