Three-Dimensional Geometric Deformation of the 12-Lead Electrocardiogram in Bundle Branch Block

Background: The 12-lead electrocardiogram (ECG) represents cardiac electrical activity as separate scalar leads, whereas ventricular activation is spatial and time-varying.We evaluated an interpretable experimental three-dimensional (3D) mathematical embedding of the 12-lead ECG, termed the ECG road, and quantified deformation of the ventricular depolarization complex (QRS) relative to a normal reference atlas.Methods: PTB-XL (Physikalisch-Technische Bundesanstalt -Extra Large) version 1.0.3 (National Metrology Institute of Germany, Braunschweig, Germany) was partitioned using its official patient-safe folds (training folds 1-8, validation fold 9, and locked test fold 10).Strict normal ECGs were compared with clean complete left bundle branch block (CLBBB), complete right bundle branch block (CRBBB), and intraventricular conduction delay (IVCD).A QRS-focused normal road atlas was built exclusively from training normals.Four prespecified geometric features measured QRS trajectory scale and normalized Euclidean and Mahalanobis deformation.L2-regularized logistic models using demographics, geometry, or both were frozen before test evaluation.A QRS-duration-only analysis was retained as a secondary sensitivity benchmark.A post hoc morphology-aware conventional 12-lead comparator incorporating QRS duration and prespecified lead-level QRS morphology features was separately specified, trained on the training folds only, and frozen before test performance was evaluated.Confidence intervals (CIs) used 2,000 patient-level stratified bootstrap replicates.Results: All 1,001 test ECGs were processed successfully for the primary geometry analysis.After deterministic selection of one ECG per patient, binary test cohorts contained 33 CLBBB cases among 867 patients, 21 CRBBB cases among 855 patients, and 26 IVCD cases among 860 patients; each comparison included 834 strict normals.The primary combined model achieved an area under the receiver operating characteristic curve (AUROC) of 0.9998 (95% CI 0.9992-1.0000)and average precision (AP) of 0.9951 (0.9833-1.0000) for CLBBB, and an AUROC of 0.9995 (0.9984-1.0000) and AP of 0.9858 (0.9546-1.0000) for CRBBB.IVCD discrimination was limited (AUROC 0.5857, 0.4725-0.6982;AP 0.0443, 0.0311-0.0852).In its own evaluable test cohort, the morphology-aware conventional comparator achieved AUROC/AP values of 1.0000/1.0000for CLBBB, 0.9998/0.9860for CRBBB, and 0.6614/0.0935for IVCD.Conclusions: The experimental 3D ECG representation preserved information sufficient to discriminate canonical CLBBB and CRBBB but not heterogeneous IVCD.Conventional lead-level morphology showed near-ceiling discrimination for canonical bundle branch block, and paired analyses did not demonstrate a clear performance advantage for either representation.These findings support the ECG road as an interpretable proof-of-concept mathematical representation of conduction-pattern information already present in the 12-lead ECG, rather than evidence of clinical superiority over conventional ECG criteria.External validation against independent clinical or imaging endpoints and established ECG-to-XYZ approaches is required before clinical application.