L1 ⚛ L1-062 ⊙ Testnet

Contrast-Enhanced Ultrasound (CEUS)

Medical Imaging · Microbubble-contrast harmonic ultrasound

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⬇ L1-062.md

# ⚛ L1 Principle — Contrast-Enhanced Ultrasound (CEUS) **ID:** `L1-062` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Microbubble-contrast harmonic ultrasound* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 2D perfusion map > **📡 Carrier:** acoustic · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553359 --- ## 🧠 1. Introduction **Contrast-Enhanced Ultrasound (CEUS)** is a **nonlinear inverse problem** whose unknown lives in **2D perfusion map** space, within the **Microbubble-contrast harmonic ultrasound** sub-domain of **Medical Imaging**. Measurements consist of acoustic pressure waves recorded by transducers via a **contrast enhanced ultrasound** sensing mechanism. The forward operator applies, in order: L · emit · acoustic pulse operator; L · microbubble oscillate operator; L · harmonic separate operator; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D perfusion map 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 ~= 11); bubble_destruction dominates the stability cliff; nonlinear_tissue_harmonics 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 · emit · acoustic pulse → L · microbubble oscillate → L · harmonic separate → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.harmonic_separate` `L.microbubble_oscillate` `L.emit.acoustic_pulse` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.emit.acoustic_pulse` | L · emit · acoustic pulse operator | | `L.microbubble_oscillate` | L · microbubble oscillate operator | | `L.harmonic_separate` | L · harmonic separate operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Microbubble-contrast harmonic ultrasound | | Carrier | acoustic | | Problem class | nonlinear_inverse | | Solution space | 2D_perfusion_map | | Noise model | gaussian | | Integration axis | temporal | | Difficulty delta | 3 | | L dag | 3.3 | ## 📡 4. Measurement Model Existence of the recovered 2D perfusion map 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 ~= 11); bubble_destruction dominates the stability cliff; nonlinear_tissue_harmonics 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:** `ceus` · **Forward operator:** `ceus_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Mi | — | 0.1 | | F mhz | MHz | 3.5 | | Snr db | dB | 22 | | N frames | — | 200 | | N elements | — | 128 | | Flow artifacts | — | 0 | | Contrast washout | — | 0 | | Bubble destruction | — | 0 | | Nonlinear tissue harmonics | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Mi | — | 0.05 – 0.5 | | F mhz | MHz | 1 – 15 | | Snr db | dB | 0.0 – 35.0 | | N frames | — | 30 – 1000 | | N elements | — | 32 – 256 | | Flow artifacts | — | 0.0 – 0.3 | | Contrast washout | — | 0.0 – 0.5 | | Bubble destruction | — | 0.0 – 0.3 | | Nonlinear tissue harmonics | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 22.0 | Metric | Range | |---|---| | Psnr db | 5.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `220` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xddf77bb62043675b6608359f2eeb22c27d8ce2e85bcc3ce52a7ee495019eedd7` - **Chain tx hash:** `0x2d0baaa87ae0de59896f49d719bfbcee5de4f0685ff3adf4e7137930230cadf8` - **Chain block:** `41553359` --- ## File Mapping This bundle consists of: `L1-062.md`, `L1-062.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-062.md` | Source of truth — edit this | Human or LLM | | `L1-062.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 `L1-062`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-062.md).
Regenerate L1-062.json so every field matches the Markdown.
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L2-062-001 Contrast-Enhanced Ultrasound (CEUS) Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553359,
  "chain_hash": "0xddf77bb62043675b6608359f2eeb22c27d8ce2e85bcc3ce52a7ee495019eedd7",
  "chain_tx_hash": "0x2d0baaa87ae0de59896f49d719bfbcee5de4f0685ff3adf4e7137930230cadf8",
  "domain": "Medical Imaging",
  "hardness_fn": {
    "delta": 3,
    "kappa": 220,
    "metric": "PSNR_dB",
    "type": "epsilon_fn"
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      "name": "primary",
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    "regime": "Existence of the recovered 2D perfusion map 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 ~= 11); bubble_destruction dominates the stability cliff; nonlinear_tissue_harmonics 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": 3.3,
    "carrier": "acoustic",
    "difficulty_delta": 3,
    "domain": "Medical Imaging",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
      "L.emit.acoustic_pulse",
      "L.microbubble_oscillate",
      "L.harmonic_separate",
      "int.temporal"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "contrast_enhanced_ultrasound",
    "solution_space": "2D_perfusion_map",
    "sub_domain": "Microbubble-contrast harmonic ultrasound",
    "title": "Contrast-Enhanced Ultrasound (CEUS)"
  },
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    "allowed_omega_dimensions": [
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      "f_MHz",
      "MI",
      "N_frames",
      "SNR_dB",
      "bubble_destruction",
      "nonlinear_tissue_harmonics",
      "flow_artifacts",
      "contrast_washout",
      "bubble_destruction",
      "nonlinear_tissue_harmonics",
      "flow_artifacts",
      "contrast_washout"
    ],
    "allowed_problem_classes": [
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    ],
    "center_spec": {
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      "forward_operator": "ceus_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_elements": 128,
        "N_frames": 200,
        "SNR_dB": 22,
        "bubble_destruction": 0.0,
        "contrast_washout": 0.0,
        "f_MHz": 3.5,
        "flow_artifacts": 0.0,
        "nonlinear_tissue_harmonics": 0.0
      },
      "problem_class": "ceus"
    },
    "epsilon_bounds": {
      "psnr_db": [
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        45.0
      ]
    },
    "omega_bounds": {
      "MI": [
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        0.5
      ],
      "N_elements": [
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        256
      ],
      "N_frames": [
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        1000
      ],
      "SNR_dB": [
        0.0,
        35.0
      ],
      "bubble_destruction": [
        0.0,
        0.3
      ],
      "contrast_washout": [
        0.0,
        0.5
      ],
      "f_MHz": [
        1,
        15
      ],
      "flow_artifacts": [
        0.0,
        0.3
      ],
      "nonlinear_tissue_harmonics": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Microbubble-contrast harmonic ultrasound",
  "title": "Contrast-Enhanced Ultrasound (CEUS)"
}

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