Mammographic Breast Density Classification BI-RADS (PWDR) L1-515

Medical ImagingMammographic glandular-tissue density reconstruction with BI-RADS density category readoutδ=3 · standardL_DAG = 5.8📋 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 - 036) : y_{p} r o j ec t i o n_{C} C, y_{p} r o j ec t i o n_{M} L O \to g (r) v o l u m e t r i c g l an d u l a r f r a c t i o n . S t a g e 2 (B I - R A D S) : V B D = in t e g r a l g (r) d V; c a t e g or y = s t e p (V B D a t [25

Mammographic Breast Density Classification (PWDR): wraps L1-036 mammography analytical core with the ACR BI-RADS Atlas 5th edition density-grading rule. Stage 1 (analytical, from L1-036): reconstruct breast tissue composition g(r) (glandular-tissue volume fraction per voxel) from FFDM cranio-caudal + medio-lateral-oblique views via dual-energy decomposition or single-energy calibration with reference to fat/fibroglandular calibration phantoms. Compute volumetric breast density VBD = integral g(r) dV / volume_breast. Stage 2 (deterministic threshold): apply BI-RADS thresholds at 25%/50%/75% to assign category {A, B, C, D}; secondary spatial-heterogeneity rule discriminates heterogeneously vs homogeneously dense in C and D categories. Difficulty tier delta = 3 inherited from L1-036. Mismatch parameters: compression_thickness_calibration_error, exposure_factor_drift, calibration_phantom_uncertainty, age_related_density_shift, automated_vs_radiologist_disagreement.

L-DAG

L.xray_source -> L.attenuation_projection -> L.dual_energy_decomposition -> L.glandular_fraction_recovery -> L.vbd_aggregation -> L.birads_threshold_classifier -> int.spatial

L.xray_sourceL.attenuation_projectionL.dual_energy_decompositionL.glandular_fraction_recoveryL.vbd_aggregationL.birads_threshold_classifierint.spatial

Well-posedness W

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

Existence and uniqueness inherited from L1-036 mammography. Stability inherits L1-036's well-conditioned reconstruction plus a small additive contribution from compression_thickness_calibration_error (dominant systematic bias source) and age_related_density_shift. Joint Hadamard well-posedness for the coupled mammography + BI-RADS threshold forward established by Sickles E et al. (2013 BI-RADS Atlas 5th ed), Highnam R et al. (2010 Volpara volumetric density), Hartman K et al. (2013 Quantra), Yaffe MJ (2008 review of mammographic density), Boyd NF et al. (2007 density and breast cancer risk), and Pertuz S et al. (2014 automated density estimation comparison).

Solvability C

Solver class:: linear-operator + convex optimisation [L1-036 reconstruction] + categorical-readout [BI-RADS threshold] | end-to-end deep neural [DenseNet, ResNet50-Density] with explicit physics-informed glandular-fraction regularization
Convergence rate q:: 2
Complexity:: O(H_proj * W_proj * N_views) for stage 1 reconstruction (inherited); O(N_voxels) for VBD aggregation + O(1) for BI-RADS threshold; total stage-1-dominated

Specs (0)

No L2 specs registered yet for this principle.