L1 ⚛ L1-056 ⊙ Testnet

Chemical Exchange Saturation Transfer (CEST) MRI

Medical Imaging · Indirect detection of exchangeable metabolite protons

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⬇ L1-056.md

# ⚛ L1 Principle — Chemical Exchange Saturation Transfer (CEST) MRI **ID:** `L1-056` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Indirect detection of exchangeable metabolite protons* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D cest spectrum > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553386 --- ## 🧠 1. Introduction **Chemical Exchange Saturation Transfer (CEST) MRI** is a **nonlinear inverse problem** whose unknown lives in **3D cest spectrum** space, within the **Indirect detection of exchangeable metabolite protons** sub-domain of **Medical Imaging**. Measurements consist of radio-frequency electromagnetic waves via a **mri chemical exchange** sensing mechanism. The forward operator applies, in order: Bloch-equation tip of the magnetisation vector; L · saturation rf pulse operator; L · z spectrum fit operator; detector sums all spectral bands. Observations are corrupted by additive Gaussian noise. Existence of the recovered 3D cest spectrum 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 ~= 17); B0_inhomogeneity dominates the stability cliff; B1_inhomogeneity and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. ## ⚙ 2. Forward Model Physical chain: **x** → RF excitation pulse → L · saturation rf pulse → L · z spectrum fit → Spectral integration → **y** (detector). ``` y = Σ_λ `L.z_spectrum_fit` `L.saturation_rf_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.saturation_rf_pulse` | L · saturation rf pulse operator | | `L.z_spectrum_fit` | L · z spectrum fit operator | | `int.spectral` | Detector sums all spectral bands | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Indirect detection of exchangeable metabolite protons | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 3D_cest_spectrum | | Noise model | gaussian | | Integration axis | spectral | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered 3D cest spectrum 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 ~= 17); B0_inhomogeneity dominates the stability cliff; B1_inhomogeneity and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while TV / wavelet-sparsity / deep priors stabilise recovery at the ill-conditioned end of Omega. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `cest_mri` · **Forward operator:** `cest_mri_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 16 | | B1 ut | — | 2 | | Tr ms | ms | 4000 | | Snr db | dB | 20 | | N offsets | — | 31 | | B0 inhomogeneity | — | 0 | | B1 inhomogeneity | — | 0 | | Mt contamination | — | 0 | | Direct water saturation | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 32 | | W | px | 32 | | Z | — | 4 – 64 | | B1 ut | — | 0.5 – 5.0 | | Tr ms | ms | 1000 – 10000 | | Snr db | dB | 0.0 – 35.0 | | N offsets | — | 10 – 101 | | B0 inhomogeneity | — | 0.0 – 0.3 | | B1 inhomogeneity | — | 0.0 – 0.3 | | Mt contamination | — | 0.0 – 0.3 | | Direct water saturation | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 16.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `340` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x5f6ecefd3ad7a6cd4b0802388c37a29c9f5c2ce9d9406b654dc04ae4603b52b4` - **Chain tx hash:** `0xa732d6e582591baff493cc68415468e56fceb556a2fdbc3fc9b3f03a19a9a6ff` - **Chain block:** `41553386` --- ## File Mapping This bundle consists of: `L1-056.md`, `L1-056.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-056.md` | Source of truth — edit this | Human or LLM | | `L1-056.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 `L1-056`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-056.md).
Regenerate L1-056.json so every field matches the Markdown.
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L2-056-001 Chemical Exchange Saturation Transfer (CEST) MRI Mismatch-Only Spec

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📋 JSON metadata

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  "domain": "Medical Imaging",
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    "sensing_mechanism": "mri_chemical_exchange",
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    "title": "Chemical Exchange Saturation Transfer (CEST) MRI"
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      "H": 32,
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      "TR_ms": [
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      "Z": [
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    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Indirect detection of exchangeable metabolite protons",
  "title": "Chemical Exchange Saturation Transfer (CEST) MRI"
}

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