Pneumothorax Detection from Chest X-ray (PWDR) L1-523

Medical ImagingPleural-line and lung-edge recovery from chest radiograph with pneumothorax categorical readoutδ=3 · standardL_DAG = 4.6📋 Stub — not mineable

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Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

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Forward model E

S t a g e 1 (L 1 - 031) : c h es t r a d i o g r a p h \to v i scer a l_{p} l e u r a l_{l} in e (x, y), l u n g_{a} tt e n u a t i o n (x, y), m e d ia s t ina l_{p} os i t i o n . S t a g e 2 : L i g h t_{i} n d e x = (1 - (R_{c} o l l a p se d / R_{n} or ma l)^{3}) \cdot 100; se v er i t y = s t e p (L i g h t_{i} n d e x a t [0, 15, 30]); t e n s i o n_{f} l a g = (m e d ia s t ina l_{s} hi f t_{m} m > 20) O R (d e p r esse d_{h} e mi d ia p h r a g m) .

Pneumothorax Detection from Chest X-ray (PWDR): wraps L1-031 X-ray radiography analytical core with established trauma / emergency-radiology grading rules. Stage 1 (analytical, from L1-031): from frontal (+/- lateral) chest radiograph, recover lung-edge geometric reconstruction (visceral pleural line, lateral chest wall border) and per-hemithorax air-attenuation distribution. Stage 2 (deterministic threshold): apply Light-index, Collins, or Rhea formulas to estimate percent collapse; classify into severity bins; flag tension features (mediastinal shift, depressed hemidiaphragm). Difficulty tier delta = 3. Mismatch parameters: rotation_artifact, expiratory_vs_inspiratory_state, supine_vs_upright_acquisition, skin_fold_pseudo_pneumothorax, bullous_disease_confounders, bilateral_severity_disagreement.

L-DAG

L.xray_source -> L.attenuation_projection -> L.pleural_line_detection -> L.light_index_estimation -> L.severity_threshold_classifier -> int.spatial

L.xray_sourceL.attenuation_projectionL.pleural_line_detectionL.light_index_estimationL.severity_threshold_classifierint.spatial

Well-posedness W

Existence:: true
Uniqueness:: conditional
Stability:: conditional
κ:: 60

Existence inherited from L1-031. Uniqueness conditional on pneumothorax visibility; small pneumothoraces near lung apex can be missed in supine acquisitions (sensitivity drops 30-50% supine vs upright). Stability dominated by skin_fold_pseudo_pneumothorax and bullous_disease_confounders (the dominant false-positive sources in clinical practice). Joint Hadamard well-posedness for the pneumothorax-detection forward established by Light 1985 (foundational Light index), Collins 1995 (Collins method), Rhea 1982 (Rhea method), Roberts 2014 (ATLS guideline), Rajpurkar 2017 (CheXNet 14-pathology benchmark), Tang 2020 (ChestX-ray14).

Solvability C

Solver class:: linear-operator + image-segmentation [pleural-line edge detection + lung-radius estimation] + categorical-readout [Light-index threshold] | end-to-end deep neural [CheXNet, CheXpert, GoogleHealth pneumothorax model] with explicit physics-informed pleural-line regularization
Convergence rate q:: 2
Complexity:: O(H * W) per radiograph for stage 1; O(N_pleural_segments * N_radius_estimations) for stage 2; total stage-1-dominated

Specs (0)

No L2 specs registered yet for this principle.