Quadrilateral Segmental Analysis (QSA): A Calibration-Free Geometric Method for Detecting Lumbar Spondylolisthesis

Background/Objectives: Degenerative lumbar spondylolisthesis is first assessed on standing lateral radiographs, yet the slip is still measured in millimeters or graded semi-quantitatively, both dependent on magnification, calibration and reader experience. We introduce quadrilateral segmental analysis (QSA), a calibration-free geometric method for detecting anterolisthesis. Methods: In 50 patients from the PROGRES cohort, a blinded observer drew the L1–S1 superior endplate lines on standing radiographs; an automated pipeline computed the diagonal ratio K for each quadrilateral formed by adjacent lines. The reference standard was adjudicated two-radiologist classification (κ = 0.916). After excluding 90 retrolisthetic segments, 160 segments were analyzed by receiver operating characteristic analysis with patient-cluster bootstrap, a 61-threshold sweep of K and cross-validated logistic models. Results: Anterolisthesis was present in 54 segments (33.8%). K discriminated well (area under the curve [AUC] 0.892, 95% CI 0.841–0.937): K ≤ 0.85 confirmed a slip (specificity 99.1%, positive predictive value [PPV] 96.0%) and K > 0.95 excluded it (sensitivity 100%, negative predictive value [NPV] 100%). Rounded to one decimal, K defined three tiers that classified 46.9% of segments without error (K < 0.9: PPV 100%; K = 1.0: NPV 100%). Conclusions: Quadrilateral segmental analysis (QSA) converts vertebral translation into an angular signature readable from a single standing lateral radiograph without calibration. K (the diagonal ratio) translates the radiologist's assessment of anterolisthesis into a single number. QSA is simple enough for routine reporting and fully automatable. Reliability testing, external validation and extension to dynamic image pairs are the next steps.