L1 ⚛ L1-047 ⊙ Testnet

Elastography (Shear-Wave / Strain)

Medical Imaging · Tissue stiffness imaging via shear waves or compression

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⬇ L1-047.md

# ⚛ L1 Principle — Elastography (Shear-Wave / Strain) **ID:** `L1-047` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Tissue stiffness imaging via shear waves or compression* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D tissue stiffness > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553372 --- ## 🧠 1. Introduction **Elastography (Shear-Wave / Strain)** is a **nonlinear inverse problem** whose unknown lives in **2D tissue stiffness** space, within the **Tissue stiffness imaging via shear waves or compression** sub-domain of **Medical Imaging**. Measurements consist of acoustic pressure waves recorded by transducers via a **shear wave elastography** sensing mechanism. The forward operator applies, in order: L · shear wave excitation operator; L · wave tracking operator; L · inverse elasticity operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D tissue stiffness 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); wave_reflections dominates the stability cliff; tissue_anisotropy 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** → L · shear wave excitation → L · wave tracking → L · inverse elasticity → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.inverse_elasticity` `L.wave_tracking` `L.shear_wave_excitation` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.shear_wave_excitation` | L · shear wave excitation operator | | `L.wave_tracking` | L · wave tracking operator | | `L.inverse_elasticity` | L · inverse elasticity operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Tissue stiffness imaging via shear waves or compression | | Carrier | acoustic | | Problem class | nonlinear_inverse | | Solution space | 2D_tissue_stiffness | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 5 | | L dag | 3.8 | ## 📡 4. Measurement Model Existence of the recovered 2D tissue stiffness 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); wave_reflections dominates the stability cliff; tissue_anisotropy 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:** `elastography` · **Forward operator:** `elastography_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Snr db | dB | 22 | | Pre load | — | 0 | | F push hz | Hz | 150 | | N time samples | — | 200 | | Wave reflections | — | 0 | | Tissue anisotropy | — | 0 | | Boundary conditions | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 | | W | px | 128 | | Snr db | dB | 0.0 – 35.0 | | Pre load | — | 0.0 – 0.3 | | F push hz | Hz | 30 – 500 | | N time samples | — | 50 – 1000 | | Wave reflections | — | 0.0 – 0.5 | | Tissue anisotropy | — | 0.0 – 0.3 | | Boundary conditions | — | 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 = `300` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x32bfb5b1d5419d32c63af20f0085e7a909e469699d2554fbe22634cb5bdff4d6` - **Chain tx hash:** `0xcd2bd44cf717eb8346d81d901418c0f9a7781a3807e541b9dea512e9b8609912` - **Chain block:** `41553372` --- ## File Mapping This bundle consists of: `L1-047.md`, `L1-047.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-047.md` | Source of truth — edit this | Human or LLM | | `L1-047.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 `L1-047`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-047.md).
Regenerate L1-047.json so every field matches the Markdown.
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L2-047-001 Elastography (Shear-Wave / Strain) Mismatch-Only Spec

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📋 JSON metadata

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  "artifact_id": "L1-047",
  "chain_block": 41553372,
  "chain_hash": "0x32bfb5b1d5419d32c63af20f0085e7a909e469699d2554fbe22634cb5bdff4d6",
  "chain_tx_hash": "0xcd2bd44cf717eb8346d81d901418c0f9a7781a3807e541b9dea512e9b8609912",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 5,
    "kappa": 300,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "PSNR_dB",
    "regime": "Existence of the recovered 2D tissue stiffness 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); wave_reflections dominates the stability cliff; tissue_anisotropy 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.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.8,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Medical Imaging",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.shear_wave_excitation",
      "L.wave_tracking",
      "L.inverse_elasticity",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "shear_wave_elastography",
    "solution_space": "2D_tissue_stiffness",
    "sub_domain": "Tissue stiffness imaging via shear waves or compression",
    "title": "Elastography (Shear-Wave / Strain)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "elastography_forward"
    ],
    "allowed_omega_dimensions": [
      "H",
      "W",
      "f_push_Hz",
      "N_time_samples",
      "SNR_dB",
      "wave_reflections",
      "tissue_anisotropy",
      "pre_load",
      "boundary_conditions",
      "wave_reflections",
      "tissue_anisotropy",
      "pre_load",
      "boundary_conditions"
    ],
    "allowed_problem_classes": [
      "elastography"
    ],
    "center_spec": {
      "epsilon_fn_center": "20.0",
      "forward_operator": "elastography_forward",
      "input_format": "measurement_only",
      "omega": {
        "H": 512,
        "N_time_samples": 200,
        "SNR_dB": 22,
        "W": 512,
        "boundary_conditions": 0.0,
        "f_push_Hz": 150,
        "pre_load": 0.0,
        "tissue_anisotropy": 0.0,
        "wave_reflections": 0.0
      },
      "problem_class": "elastography"
    },
    "epsilon_bounds": {
      "psnr_db": [
        5.0,
        45.0
      ]
    },
    "omega_bounds": {
      "H": 128,
      "N_time_samples": [
        50,
        1000
      ],
      "SNR_dB": [
        0.0,
        35.0
      ],
      "W": 128,
      "boundary_conditions": [
        0.0,
        0.3
      ],
      "f_push_Hz": [
        30,
        500
      ],
      "pre_load": [
        0.0,
        0.3
      ],
      "tissue_anisotropy": [
        0.0,
        0.3
      ],
      "wave_reflections": [
        0.0,
        0.5
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Tissue stiffness imaging via shear waves or compression",
  "title": "Elastography (Shear-Wave / Strain)"
}

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