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

Background/Objectives: On standing lateral radiographs, millimetre measurements of vertebral slip depend on magnification and calibration; slip percentage is scale-free but is usually reported in coarse Meyerding grades. In this exploratory derivation study, we introduce quadrilateral segmental analysis (QSA), a calibration-free geometric method for detecting anterolisthesis. Methods: In 50 patients with degenerative spondylolisthesis 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 and the posterior angles of each quadrilateral formed by adjacent lines. The annotation was performed by a single observer; its reproducibility was not assessed, and its sensitivity to annotation error was simulated. The reference standard was an adjudicated two-radiologist classification (κ = 0.916). Segments outside the anterior-translation domain (negative shear; n = 90) were not graded further; the remaining 160 were analysed with patient-cluster bootstrap and leave-one-patient-out validation. Results: Anterolisthesis was present in 54 of 160 segments (33.8%). K discriminated well (area under the curve [AUC] 0.892, 95% CI 0.841-0.937): K ≤ 0.85 supported a slip (specificity 99.1%), and K > 0.95 argued against it (sensitivity 100%; smallest reference-positive slip 9%). Rounded to one decimal, K assigned 46.9% of segments to extreme tiers without observed misclassification. With the lower posterior angle N ≤ 93° in the intermediate tier, the two-step rule reached 94.4% sensitivity and 95.3% specificity, unchanged under nested leave-one-patient-out validation. Simulated endpoint errors of 0.5-1.0 mm changed the two-step classification in 5-13% of segments (ICC 0.74-0.92 for K and 0.85-0.96 for N). Conclusions: Calibration-free QSA parameters discriminated reference-positive from reference-negative segments in patients with degenerative spondylolisthesis. K (the diagonal ratio) translates the radiologist's assessment of anterolisthesis into a single number. These exploratory findings, which do not establish performance for small or borderline slips, require replication in independent cohorts and by other observers before the thresholds can be applied clinically.