L1 ⚛ L1-057 ⊙ Testnet

Arterial Spin Labeling (ASL) MRI

Medical Imaging · Non-contrast brain perfusion via magnetically tagged blood

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⬇ L1-057.md

# ⚛ L1 Principle — Arterial Spin Labeling (ASL) MRI **ID:** `L1-057` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Non-contrast brain perfusion via magnetically tagged blood* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** 3D perfusion map > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41552302 --- ## 🧠 1. Introduction **Arterial Spin Labeling (ASL) MRI** is a **linear inverse problem** whose unknown lives in **3D perfusion map** space, within the **Non-contrast brain perfusion via magnetically tagged blood** sub-domain of **Medical Imaging**. Measurements consist of radio-frequency electromagnetic waves via a **mri perfusion** sensing mechanism. The forward operator applies, in order: Bloch-equation tip of the magnetisation vector; L · arterial labeling pulse operator; L · difference image operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered 3D perfusion map is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 15); arterial_transit_time dominates the stability cliff; labeling_efficiency and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise 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** → RF excitation pulse → L · arterial labeling pulse → L · difference image → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.difference_image` `L.arterial_labeling_pulse` 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.arterial_labeling_pulse` | L · arterial labeling pulse operator | | `L.difference_image` | L · difference image operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Non-contrast brain perfusion via magnetically tagged blood | | Carrier | radio_wave | | Problem class | linear_inverse | | Solution space | 3D_perfusion_map | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Existence of the recovered 3D perfusion map is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 15); arterial_transit_time dominates the stability cliff; labeling_efficiency and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise 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:** `asl_mri` · **Forward operator:** `asl_mri_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 96 | | W | px | 96 | | Z | — | 16 | | Pld ms | ms | 1800 | | Snr db | dB | 15 | | Motion | — | 0 | | Labeling efficiency | — | 0.9 | | N label control pairs | — | 30 | | Arterial transit time | — | 1500 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 | | W | px | 32 | | Z | — | 4 – 64 | | Pld ms | ms | 500 – 3500 | | Snr db | dB | 0.0 – 30.0 | | Motion | — | 0.0 – 0.5 | | Labeling efficiency | — | 0.5 – 1.0 | | Noise amplification | — | 0.0 – 0.3 | | N label control pairs | — | 5 – 200 | | Arterial transit time | — | 500 – 3000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 14.0 | 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:** `0xc3701d48a3f5cc81e706f8c3921d4d727dbb2f58e41d399c1f0b3e2b7ceb28b6` - **Chain tx hash:** `0xe9c61e1eb30c1788afb6e0fe256c067317875d0f28a83d376a4f051ad0bf50b4` - **Chain block:** `41552302` --- ## File Mapping This bundle consists of: `L1-057.md`, `L1-057.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-057.md` | Source of truth — edit this | Human or LLM | | `L1-057.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 `L1-057`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-057.md).
Regenerate L1-057.json so every field matches the Markdown.
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L2-057-001 Arterial Spin Labeling (ASL) MRI Mismatch-Only Spec

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📋 JSON metadata

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  "chain_tx_hash": "0xe9c61e1eb30c1788afb6e0fe256c067317875d0f28a83d376a4f051ad0bf50b4",
  "domain": "Medical Imaging",
  "hardness_fn": {
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  "physics_fingerprint": {
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    "integration_axis": "temporal",
    "noise_model": "gaussian",
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    "sensing_mechanism": "mri_perfusion",
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      "motion",
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        "Z": 16,
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      "SNR_dB": [
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      ],
      "W": 32,
      "Z": [
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        64
      ],
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        3000
      ],
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        1.0
      ],
      "motion": [
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        0.5
      ],
      "noise_amplification": [
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        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Non-contrast brain perfusion via magnetically tagged blood",
  "title": "Arterial Spin Labeling (ASL) MRI"
}

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