L1 ⚛ L1-045 ⊙ Testnet

Diffusion MRI (DWI / DTI / HARDI)

Medical Imaging · Water-diffusion-weighted MRI for microstructure/tractography

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⬇ L1-045.md

# ⚛ L1 Principle — Diffusion MRI (DWI / DTI / HARDI) **ID:** `L1-045` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Water-diffusion-weighted MRI for microstructure/tractography* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 4D diffusion tensor or ODF > **📡 Carrier:** radio_wave · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41552301 --- ## 🧠 1. Introduction **Diffusion MRI (DWI / DTI / HARDI)** is a **nonlinear inverse problem** whose unknown lives in **4D diffusion tensor or ODF** space, within the **Water-diffusion-weighted MRI for microstructure/tractography** sub-domain of **Medical Imaging**. Measurements consist of radio-frequency electromagnetic waves via a **mri fourier encoding** sensing mechanism. The forward operator applies, in order: Bloch-equation tip of the magnetisation vector; L · diffusion gradient operator; L · gradient encoding operator; integration over the solid angle of incidence/emission. Observations are corrupted by additive Gaussian noise. Existence of the recovered 4D diffusion tensor or ODF 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 ~= 18); eddy_currents dominates the stability cliff; motion 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 · diffusion gradient → L · gradient encoding → Angular integration → **y** (detector). ``` y = ∫dΩ `L.gradient_encoding` `L.diffusion_gradient` 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.diffusion_gradient` | L · diffusion gradient operator | | `L.gradient_encoding` | L · gradient encoding operator | | `int.angular` | Integration over the solid angle of incidence/emission | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Water-diffusion-weighted MRI for microstructure/tractography | | Carrier | radio_wave | | Problem class | nonlinear_inverse | | Solution space | 4D_diffusion_tensor_or_ODF | | Noise model | gaussian | | Integration axis | angular | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered 4D diffusion tensor or ODF 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 ~= 18); eddy_currents dominates the stability cliff; motion 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:** `dmri` · **Forward operator:** `dmri_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 128 | | W | px | 128 | | Z | — | 64 | | Snr db | dB | 20 | | Motion | — | 0 | | N directions | — | 32 | | B0 distortion | — | 0 | | Eddy currents | — | 0 | | B max s per mm2 | — | 1000 | | Partial volume csf | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 64 | | W | px | 64 | | Z | — | 16 – 256 | | Snr db | dB | 0.0 – 35.0 | | Motion | — | 0.0 – 0.5 | | N directions | — | 6 – 256 | | B0 distortion | — | 0.0 – 0.3 | | Eddy currents | — | 0.0 – 0.3 | | B max s per mm2 | — | 100 – 5000 | | Partial volume csf | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `360` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x86eda8fa6529b40c56bdcd45721d0f846b0e76b9d5a8f82f08800d56b1b062c1` - **Chain tx hash:** `0xae0121d4d4c450e698d264aa07d0cf545572f1c42e70b0f483a4a3c3ea2da7b9` - **Chain block:** `41552301` --- ## File Mapping This bundle consists of: `L1-045.md`, `L1-045.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-045.md` | Source of truth — edit this | Human or LLM | | `L1-045.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 `L1-045`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-045.md).
Regenerate L1-045.json so every field matches the Markdown.
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L2-045-001 Diffusion MRI (DWI / DTI / HARDI) Mismatch-Only Spec

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📋 JSON metadata

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  "status": "testnet",
  "sub_domain": "Water-diffusion-weighted MRI for microstructure/tractography",
  "title": "Diffusion MRI (DWI / DTI / HARDI)"
}

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