L1 ⚛ L1-051 ⊙ Testnet

Proton Therapy (proton-beam radiation dose imaging)

Medical Imaging · Dose-deposition imaging for Bragg-peak therapy

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⬇ L1-051.md

# ⚛ L1 Principle — Proton Therapy (proton-beam radiation dose imaging) **ID:** `L1-051` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Dose-deposition imaging for Bragg-peak therapy* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D dose distribution > **📡 Carrier:** photon · **🌫 Noise:** shot poisson > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553372 --- ## 🧠 1. Introduction **Proton Therapy (proton-beam radiation dose imaging)** is a **nonlinear inverse problem** whose unknown lives in **3D dose distribution** space, within the **Dose-deposition imaging for Bragg-peak therapy** sub-domain of **Medical Imaging**. Measurements consist of photons collected by an optical detector via a **proton therapy dose** sensing mechanism. The forward operator applies, in order: L · proton accelerator operator; L · bragg peak energy deposition operator; D · dose meter operator; pixel-level spatial averaging on the detector. Observations are corrupted by Poisson shot noise from quantum-limited detection. Existence of the recovered 3D dose distribution is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 15); range_uncertainty dominates the stability cliff; organ_motion and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. ## ⚙ 2. Forward Model Physical chain: **x** → L · proton accelerator → L · bragg peak energy deposition → D · dose meter → Spatial integration → **y** (detector). ``` y = ∫_A dA `D.dose_meter` `L.bragg_peak_energy_deposition` `L.proton_accelerator` x, measurements ~ Poisson(αy) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.proton_accelerator` | L · proton accelerator operator | | `L.bragg_peak_energy_deposition` | L · bragg peak energy deposition operator | | `D.dose_meter` | D · dose meter operator | | `int.spatial` | Pixel-level spatial averaging on the detector | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Dose-deposition imaging for Bragg-peak therapy | | Carrier | photon | | Problem class | nonlinear_inverse | | Solution space | 3D_dose_distribution | | Noise model | shot_poisson | | Integration axis | spatial | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered 3D dose distribution is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 15); range_uncertainty dominates the stability cliff; organ_motion and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `proton_therapy` · **Forward operator:** `proton_therapy_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 256 | | W | px | 256 | | Z | — | 128 | | Snr db | dB | 30 | | N beams | — | 3 | | Organ motion | — | 0 | | Proton energy mev | — | 150 | | Range uncertainty | — | 0.01 | | Tissue heterogeneity | — | 0.05 | | Ct hu calibration error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 32 – 512 | | Snr db | dB | 10.0 – 40.0 | | N beams | — | 1 – 16 | | Organ motion | — | 0.0 – 0.3 | | Proton energy mev | — | 70 – 250 | | Range uncertainty | — | 0.0 – 0.05 | | Tissue heterogeneity | — | 0.0 – 0.3 | | Ct hu calibration error | — | 0.0 – 0.1 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 27.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `300` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x90a75deafb0a2ddf854fb59b7604011ab4e09f02d0650a2ebc7854a2a65e5020` - **Chain tx hash:** `0x900ff579a09bed5d80545525bac5238b8bca3a498a8476966153d190cd62b60a` - **Chain block:** `41553372` --- ## File Mapping This bundle consists of: `L1-051.md`, `L1-051.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-051.md` | Source of truth — edit this | Human or LLM | | `L1-051.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 `L1-051`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-051.md).
Regenerate L1-051.json so every field matches the Markdown.
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L2-051-001 Proton Therapy (proton-beam radiation dose imaging) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553372,
  "chain_hash": "0x90a75deafb0a2ddf854fb59b7604011ab4e09f02d0650a2ebc7854a2a65e5020",
  "chain_tx_hash": "0x900ff579a09bed5d80545525bac5238b8bca3a498a8476966153d190cd62b60a",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 5,
    "kappa": 300,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
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    "regime": "Existence of the recovered 3D dose distribution is guaranteed within the declared Omega bounds. Uniqueness is local rather than global (non-convex landscape); convergence depends on initialisation and priors. Stability is moderately conditioned (kappa_eff ~= 15); range_uncertainty dominates the stability cliff; organ_motion and the remaining mismatch parameters contribute higher-order bias terms. Photon-shot-noise-limited (poisson counting) sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "photon",
    "difficulty_delta": 5,
    "domain": "Medical Imaging",
    "integration_axis": "spatial",
    "noise_model": "shot_poisson",
    "primitives": [
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      "L.bragg_peak_energy_deposition",
      "D.dose_meter",
      "int.spatial"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "proton_therapy_dose",
    "solution_space": "3D_dose_distribution",
    "sub_domain": "Dose-deposition imaging for Bragg-peak therapy",
    "title": "Proton Therapy (proton-beam radiation dose imaging)"
  },
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      "organ_motion",
      "tissue_heterogeneity",
      "CT_hu_calibration_error",
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      "organ_motion",
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    ],
    "allowed_problem_classes": [
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        "N_beams": 3,
        "SNR_dB": 30,
        "W": 256,
        "Z": 128,
        "organ_motion": 0.0,
        "proton_energy_MeV": 150,
        "range_uncertainty": 0.01,
        "tissue_heterogeneity": 0.05
      },
      "problem_class": "proton_therapy"
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      "H": 128,
      "N_beams": [
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        16
      ],
      "SNR_dB": [
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        40.0
      ],
      "W": 128,
      "Z": [
        32,
        512
      ],
      "organ_motion": [
        0.0,
        0.3
      ],
      "proton_energy_MeV": [
        70,
        250
      ],
      "range_uncertainty": [
        0.0,
        0.05
      ],
      "tissue_heterogeneity": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Dose-deposition imaging for Bragg-peak therapy",
  "title": "Proton Therapy (proton-beam radiation dose imaging)"
}

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