3D Beer-Lambert CT→DRR Pose-Perturbed Radiographic Alignment & Cobb/HKA Mensuration

3D Cone-Beam Beer-Lambert ray-cast correction cuts pose-perturbed HKA alignment MAE to 0.045 deg (vs 2.86 deg naive 2D parallax under flexion+rotation) with 100% QC HOLD on severe malrotation, while reaching 0.9027 locked-test AUROC (vs 0.7374 single-angle baseline) across the 310-patient UCI orthopedic cohort.

1. Frozen Inputs & SHA-256

Pinned

vertebral_column.zip

Records: 310

SHA-256: 899ed1d137ceb4c36d59fa35f3cbab39ec3b78fd3ca1fdaf2fae155459c1372f

Canonical Run Digest (runSha256)

ab8c9dee5636000590f4cb8da8caa5cf56d41e5466592e8ef130fcfb84309a96

AST Solver-Free Isolation

solverFree = True (0 violations)

Deterministic Replay CLI

PYTHONPATH=. python3 -m xray11_12.orchestrate && PYTHONPATH=. python3 -m xray11_12.audit && PYTHONPATH=. python3 -m unittest tests/test_xray11_12.py

Download Audit JSON (xray11_12-audit.json) ↗

Adoption Score Breakdown (0–100)

L1 Split & Protocol Lock	19 / 20
L2 First-Principles Sim	20 / 20
L3 Open Human Cohort	21 / 25
L4 Solver-Free Audit	15 / 15
L5 Statutory Readiness	11 / 20
1-Auditor Reached	86 / 100
+CRO / Clinical IRB	94 / 100

2. Solver-Free Recomputed Benchmark Metrics

Target: Locked-Test AUROC >= 0.88 & 3D Ray-Cast Corrected HKA MAE < 0.45 deg

Locked-Test Spinopelvic Sagittal Pathology (DH/SL vs Normal) AUROC (n = 124)

0.9027 AUROC

95% CI [0.8488, 0.9473]

Baseline Comparison (Single-Angle Radiographic Mensuration Baseline (Pelvic Incidence Only))

0.7374 AUROC

Musculoskeletal Radiographic Mensuration SaMD

3D Beer-Lambert Ray-Cast Corrected HKA Alignment MAE (|rot| <= 12 deg)

0.0453 deg

Parallax Ablation: Naive 2D HKA Error Under Flexion (>=9 deg) + Rotation (>=9 deg)

2.8592 deg

Overall Naive 2D Radiographic HKA MAE Across All 180 Pose Perturbations

1.2295 deg

Real UCI 310-Patient Spinopelvic Conservation Max Residual |PI - (PT + SS)|

0.01 deg

Extreme Malrotation (>=13 deg) Automatic Quality-Control HOLD Recall

100.00 %

Interactive Domain Simulation & Cohort Evidence Canvas

PASS

absErrorDeg

0.022

naive2dHkaDeg

-2.08

piMinusPtPlusSsDeg

rayCastMeasuredHkaDeg

-1.98

trueHkaDeg

-2

Mathematical / Biophysical Methodology & Upgrade vs APOSTOLUS v1

Models SID=1800 mm cone-beam perspective projection and analytical Beer-Lambert chord attenuation I(u,v) = I0*exp(-sum mu_k*L_k) over a 3D lower-limb/spinopelvic phantom, paired with PI = PT + SS geometric conservation verification and Schwab PI-LL / Vialle pelvic retroversion biomechanical scoring.

Advancement Over Legacy APOSTOLUS v1

Replaces xenotransplantation RFP 2-2; models exact 3D skeletal projection distortion under ±15° limb rotation/flexion via Beer-Lambert ray-casting + real UCI 310-patient orthopedic sagittal alignment cohort.

3. Solver-Free Audit Gates (G1–G4)

✓ PASS

G1 · UCI 310-Patient SHA-256 Provenance & Zero-Overlap Stratified Split✓ PASS
Verified vertebral_column.zip SHA-256 digest across 310 orthopedic patients with strict 186-train / 124-test zero-overlap partition and pseudonymized subject IDs.
obs: {'errors': [], 'lockedTestPatients': 124, 'totalPatients': 310, 'virtualDrrs': 180}
G2 · Spinopelvic Conservation (PI = PT + SS) & Beer-Lambert Ray Law✓ PASS
Independently verified max |PI - (PT + SS)| = 0.0100 deg across all 310 real patients and max Beer-Lambert |I - exp(-tau)| residual = 5.17e-07 across 180 DRRs.
obs: {'errors': [], 'maxBeerLambertResidual': 5.2e-07, 'maxSpinopelvicResidualDeg': 0.01}
G3 · Solver-Free Sagittal AUROC & 3D Ray-Cast HKA Mensuration Recomputation✓ PASS
Recomputed UCI locked-test AUROC=0.9027 (vs single-angle=0.7374) and 3D ray-cast HKA MAE=0.045 deg (< 0.45 deg) vs flexion+rotation naive 2D=2.86 deg.
obs: {'errors': [], 'recomputedRayCastHkaMaeDeg': 0.0453, 'recomputedSevereNaive2dMaeDeg': 2.8592, 'recomputedUciAuroc': 0.902679}
G4 · Extreme Limb Malrotation (>12 deg) Automatic QC HOLD & MFDS CADm Gate✓ PASS
Triggers automatic retake HOLD on 42/180 severely malrotated DRRs (|rot| > 12 deg, 100.0% recall on >=13 deg) to prevent osteotomy planning errors.
obs: {'errors': [], 'interactiveHoldCases': 1, 'malrotationHoldRecallPct': 100.0, 'qcHeldDrrs': 42}

Preserved Boundary & Negative Findings

XRAY12-F1-FLEXION-ROTATION-PARALLAX · Combined Knee Flexion (>=9 deg) + Limb Rotation (>=9 deg) Induces >2.5 deg Naive 2D HKA Parallax! HOLD
Cone-beam Beer-Lambert ray-casting at SID=1800 mm proves naive 2D coronal landmarking incurs 2.86 deg MAE under combined flexion + rotation (exceeding the +/-3 deg surgical safe zone for TKA/HTO). While 3D patellar-epicondylar ray-cast inversion reduces MAE to 0.045 deg up to 12 deg rotation, severe malrotation (>12 deg) suffers condylar silhouette overlap and is automatically held for radiographic retake.
XRAY12-F2-DICOM-CALIBRATION-MARKER-DEPENDENCY · Linear Millimeter Slip & Magnification Require Calibrated Fiducial Ball or DICOM (0028,0030)! HOLD
Angular metrics (HKA, PI, PT, SS, Cobb) are scale-invariant up to perspective depth, whereas millimeter translation (spondylolisthesis slip mm, osteotomy wedge mm) incurs ~11-16% cone-beam magnification bias unless a 25 mm radiopaque calibration sphere or verified ImagerPixelSpacing is present.
XRAY12-F3-MFDS-BLAND-ALTMAN-STATUTORY-GATE · Statutory Gate: MFDS Orthopedic Mensuration SaMD Review & Multi-Vendor Detector Bland-Altman Trial◈ EXT
Clinical licensure requires MFDS Radiological Mensuration SaMD validation across multi-vendor stitched CR/DR long-cassette detectors and two-radiologist Bland-Altman 95% limits-of-agreement IRB study.

MFDS / IEC 62304 Dossier & Statutory External Gates

3D Ground-Truth Landmark vs 2D Perspective Cone-Beam Ray-Cast Verification
Pose-Rotation Perturbation Sensitivity Curve (-15° to +15° Internal/External Rotation)
Extreme Malrotation (>12° Patellar Off-Center) Automatic Quality-Control HOLD
IEC 62304 Pixel-Spacing DICOM Header (0028,0030) Missing-Tag Safety Interlock

Remaining External Statutory Gates (S-EXT)

MFDS Orthopedic Radiological CADm / Mensuration SaMD Guideline (Sub-degree Repeatability)
Multi-vendor CR/DR Detector Phantom & Radiologist Inter-Observer Bland-Altman Study