MR Spectroscopy Tumor Grading (PWDR) L1-516

Medical ImagingBrain / prostate / breast tumor metabolite-ratio threshold classification from MR spectroscopyδ=3 · standardL_DAG = 5.9📋 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.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

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Forward model E

S t a g e 1 (L 1 - 044) : c h e mi c a l - s hi f t - r eso l v e d a c q u i s i t i o n \to m e t ab o l i t eco n ce n t r a t i o nma p . S t a g e 2 : r a t i os = (C h o / N AA, C h o / C r, (C h o + C r) / C i t); g r a d e = s t e p (r a t i os a t or g an - s p ec i f i c t a u) . B r ain : 4 - g r a d e W H O c l a ss i f i c a t i o n; p r os t a t e : Gl e a so n - e q u i v a l e n t g r a d in g; b r e a s t : b e ni g n - ma l i g nan t bina r y .

MR Spectroscopy Tumor Grading (PWDR): wraps L1-044 MRS analytical core with established metabolite-ratio threshold rules from neuro-oncology, prostate cancer, and breast cancer literature. Stage 1 (analytical, from L1-044): voxel-resolved 1H-MRS recovers metabolite concentrations (NAA, Cho, Cr, Cit, lactate, lipid, mI) from chemical-shift-resolved acquisition. Stage 2 (deterministic threshold): per-organ rule applies metabolite-ratio thresholds (Cho/NAA, Cho/Cr, (Cho+Cr)/Cit, Cho/water) to assign tumor grade. Difficulty tier delta = 3. Mismatch parameters: voxel_lipid_contamination, B0_inhomogeneity, water_suppression_residual, partial_volume_csf, threshold_calibration_age_effect.

L-DAG

L.rf_excitation -> L.gradient_echo -> L.chemical_shift_select -> L.metabolite_quantification -> L.ratio_threshold_classifier -> int.spectral -> int.spatial

L.rf_excitationL.gradient_echoL.chemical_shift_selectL.metabolite_quantificationL.ratio_threshold_classifierint.spectralint.spatial

Well-posedness W

Existence:: true
Uniqueness:: conditional
Stability:: conditional
κ:: 120

Existence and uniqueness inherited from L1-044 MRS. Stability inherits L1-044's kappa_eff plus additive contribution from voxel_lipid_contamination (dominant at TE<35 ms) and partial_volume_csf. Joint Hadamard well-posedness for the coupled MRS + metabolite-ratio threshold forward established by Howe 2003, Tate 2003, McKnight 2002, Kurhanewicz 2002 (prostate), Bolan 2003 (breast), Provencher 1993 (LCModel).

Solvability C

Solver class:: linear-operator + convex optimisation [LCModel / jMRUI / TARQUIN metabolite quantification] + categorical-readout [organ-specific ratio threshold] | end-to-end deep neural [DeepMRS]
Convergence rate q:: 2
Complexity:: O(H_voxels * W_voxels * Z_voxels * spectral_points) for stage 1; O(H W Z * N_grades) for stage 2

Specs (0)

No L2 specs registered yet for this principle.