L1 ⚛ L1-516 ⊙ Testnet

MR Spectroscopy Tumor Grading (PWDR)

Medical Imaging · Brain / prostate / breast tumor metabolite-ratio threshold classification from MR spectroscopy

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⬇ L1-516.md

# ⚛ L1 Principle — MR Spectroscopy Tumor Grading (PWDR) **ID:** `L1-516` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Brain / prostate / breast tumor metabolite-ratio threshold classification from MR spectroscopy* > **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D tumor grade > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553373 --- ## 🧠 1. Introduction **MR Spectroscopy Tumor Grading (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D tumor grade** space, within the **Brain / prostate / breast tumor metabolite-ratio threshold classification from MR spectroscopy** sub-domain of **Medical Imaging**. Measurements consist of radio-frequency electromagnetic waves via a **mrs chemical shift with grade threshold** sensing mechanism. The forward operator applies, in order: Bloch-equation tip of the magnetisation vector; L · gradient echo operator; L · chemical shift select operator; L · metabolite quantification operator; L · ratio threshold classifier operator; detector sums all spectral bands; pixel-level spatial averaging on the detector. Observations are corrupted by additive Gaussian noise. 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). ## ⚙ 2. Forward Model Physical chain: **x** → RF excitation pulse → L · gradient echo → L · chemical shift select → L · metabolite quantification → L · ratio threshold classifier → Spectral integration → Spatial integration → **y** (detector). ``` y = ∫_A dA Σ_λ `L.ratio_threshold_classifier` `L.metabolite_quantification` `L.chemical_shift_select` `L.gradient_echo` B₁(t) x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.rf_excitation` | Bloch-equation tip of the magnetisation vector | | `L.gradient_echo` | L · gradient echo operator | | `L.chemical_shift_select` | L · chemical shift select operator | | `L.metabolite_quantification` | L · metabolite quantification operator | | `L.ratio_threshold_classifier` | L · ratio threshold classifier operator | | `int.spectral` | Detector sums all spectral bands | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Brain / prostate / breast tumor metabolite-ratio threshold classification from MR spectroscopy | | Carrier | radio_wave | | Problem class | linear_inverse_with_categorical_readout | | Solution space | 1D_tumor_grade | | Noise model | gaussian | | Integration axis | spectral_spatial | | Difficulty delta | 3 | | L dag | 5.9 | ## 📡 4. Measurement Model 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). | Metric | Value | |---|---| | Metric | categorical_accuracy | | Secondary | weighted_kappa_grade | ## 📏 5. Operating Range (Ω) **Center problem class:** `mrs_brain_tumor_grading_pwdr` · **Forward operator:** `mrs_grade_pwdr_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Te ms | ms | 35 | | Tr ms | ms | 2000 | | Snr db | dB | 20 | | H voxels | — | 16 | | W voxels | — | 16 | | Z voxels | — | 8 | | B0 field t | — | 3 | | Voxel size mm | mm | 8 | | Spectral points | — | 1024 | | B0 inhomogeneity | — | 0 | | Partial volume csf | — | 0 | | Voxel lipid contamination | — | 0 | | Water suppression residual | — | 0 | | Threshold calibration age effect | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Te ms | ms | 20 – 144 | | H voxels | — | 4 – 64 | | W voxels | — | 4 – 64 | | Z voxels | — | 1 – 32 | | B0 field t | — | 1.5 – 7.0 | | Voxel size mm | mm | 3 – 20 | | Spectral points | — | 256 – 4096 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 0.80_accuracy | Metric | Range | |---|---| | Categorical accuracy | 0.5 – 0.95 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **categorical_accuracy**, with κ = `120` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xd90de40fb6c4b8108d2c99e0497106abf5f24dfb4043a816f1b419791809f0e3` - **Chain tx hash:** `0x3a2fe31113268dd36ab28f8e6dc824a30a6ab7606211529a395deecb669a1ebc` - **Chain block:** `41553373` --- ## File Mapping This bundle consists of: `L1-516.md`, `L1-516.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-516.md` | Source of truth — edit this | Human or LLM | | `L1-516.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-516`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-516.md).
Regenerate L1-516.json so every field matches the Markdown.
Preserve the schema documented in the File Mapping footer at the bottom of the MD.
Output each file in its own fenced code block tagged with the filename.

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L2-516-001 MR Spectroscopy Tumor Grading (PWDR) — Spec Skeleton

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📋 JSON metadata

{
  "artifact_id": "L1-516",
  "chain_block": 41553373,
  "chain_hash": "0xd90de40fb6c4b8108d2c99e0497106abf5f24dfb4043a816f1b419791809f0e3",
  "chain_tx_hash": "0x3a2fe31113268dd36ab28f8e6dc824a30a6ab7606211529a395deecb669a1ebc",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 120,
    "metric": "categorical_accuracy",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "categorical_accuracy",
    "regime": "Existence and uniqueness inherited from L1-044 MRS. Stability inherits L1-044\u0027s kappa_eff plus additive contribution from voxel_lipid_contamination (dominant at TE\u003c35 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).",
    "secondary": "weighted_kappa_grade"
  },
  "physics_fingerprint": {
    "L_DAG": 5.9,
    "carrier": "radio_wave",
    "difficulty_delta": 3,
    "domain": "Medical Imaging",
    "integration_axis": "spectral_spatial",
    "noise_model": "gaussian",
    "primitives": [
      "L.rf_excitation",
      "L.gradient_echo",
      "L.chemical_shift_select",
      "L.metabolite_quantification",
      "L.ratio_threshold_classifier",
      "int.spectral",
      "int.spatial"
    ],
    "problem_class": "linear_inverse_with_categorical_readout",
    "sensing_mechanism": "mrs_chemical_shift_with_grade_threshold",
    "solution_space": "1D_tumor_grade",
    "sub_domain": "Brain / prostate / breast tumor metabolite-ratio threshold classification from MR spectroscopy",
    "title": "MR Spectroscopy Tumor Grading (PWDR)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "mrs_grade_pwdr_forward",
      "mrs_brain_grade_forward",
      "mrs_prostate_grade_forward",
      "mrs_breast_grade_forward"
    ],
    "allowed_omega_dimensions": [
      "H_voxels",
      "W_voxels",
      "Z_voxels",
      "spectral_points",
      "B0_field_T",
      "TE_ms",
      "TR_ms",
      "voxel_size_mm",
      "SNR_dB",
      "voxel_lipid_contamination",
      "B0_inhomogeneity",
      "water_suppression_residual",
      "partial_volume_csf",
      "threshold_calibration_age_effect"
    ],
    "allowed_problem_classes": [
      "mrs_brain_tumor_grading_pwdr",
      "mrs_prostate_grade_pwdr",
      "mrs_breast_grade_pwdr"
    ],
    "center_spec": {
      "epsilon_fn_center": "0.80_accuracy",
      "forward_operator": "mrs_grade_pwdr_forward",
      "input_format": "mrsi_dataset_with_grade_label",
      "omega": {
        "B0_field_T": 3.0,
        "B0_inhomogeneity": 0.0,
        "H_voxels": 16,
        "SNR_dB": 20,
        "TE_ms": 35,
        "TR_ms": 2000,
        "W_voxels": 16,
        "Z_voxels": 8,
        "partial_volume_csf": 0.0,
        "spectral_points": 1024,
        "threshold_calibration_age_effect": 0.0,
        "voxel_lipid_contamination": 0.0,
        "voxel_size_mm": 8.0,
        "water_suppression_residual": 0.0
      },
      "problem_class": "mrs_brain_tumor_grading_pwdr"
    },
    "epsilon_bounds": {
      "categorical_accuracy": [
        0.5,
        0.95
      ]
    },
    "omega_bounds": {
      "B0_field_T": [
        1.5,
        7.0
      ],
      "H_voxels": [
        4,
        64
      ],
      "TE_ms": [
        20,
        144
      ],
      "W_voxels": [
        4,
        64
      ],
      "Z_voxels": [
        1,
        32
      ],
      "spectral_points": [
        256,
        4096
      ],
      "voxel_size_mm": [
        3,
        20
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Brain / prostate / breast tumor metabolite-ratio threshold classification from MR spectroscopy",
  "title": "MR Spectroscopy Tumor Grading (PWDR)"
}

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