L1 ⚛ L1-508 ⊙ Testnet

Optical Coherence Elastography (OCE)

Medical Imaging · Sub-resolution displacement-tracked tissue mechanical property recovery (multi-physics joint inverse)

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⬇ L1-508.md

# ⚛ L1 Principle — Optical Coherence Elastography (OCE) **ID:** `L1-508` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Sub-resolution displacement-tracked tissue mechanical property recovery (multi-physics joint inverse)* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** 3D lame parameter map > **📡 Carrier:** photon_with_mechanical_load · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553373 --- ## 🧠 1. Introduction **Optical Coherence Elastography (OCE)** is a **nonlinear inverse problem** whose unknown lives in **3D lame parameter map** space, within the **Sub-resolution displacement-tracked tissue mechanical property recovery (multi-physics joint inverse)** sub-domain of **Medical Imaging**. Measurements consist of photon with mechanical load via a **phase sensitive oct with elasticity wave** sensing mechanism. The forward operator applies, in order: L · oct acquisition operator; L · phase extraction operator; L · displacement tracking operator; L · elasticity wave operator; L · constitutive law operator; L · applied loading operator; pixel-level spatial averaging on the detector; detector accumulates flux over the exposure window. Observations are corrupted by additive Gaussian noise. Existence of recovered Lame parameter maps (mu, lambda)(r) is guaranteed within the declared Omega bounds. Uniqueness holds for shear-wave-mode loading at multiple frequencies (2D-3D shear-wave dispersion analysis); compression-mode and surface-wave OCE are conditionally unique requiring boundary-condition specification and density assumption. Stability is moderately conditioned (kappa_eff ~ 35 after physics-informed wave-equation regularization) — oct_phase_noise dominates displacement-tracking precision; tissue_anisotropy contributes off-diagonal Lame-tensor bias; density_uncertainty contributes a scaling factor of order rho^(-1/2). Joint Hadamard well-posedness for the coupled OCT-elasticity forward is established by Schmitt 1998 (foundational), Wang-Kirkpatrick-Hinds 2007 (phase-sensitive OCE), Kennedy-Wijesinghe-Sampson 2014 (compression OCE), Larin-Sampson 2017 (review), Kirby et al. 2017 (shear-wave OCE methods), and Wijesinghe et al. 2019 (computational OCE). ## ⚙ 2. Forward Model Physical chain: **x** → L · oct acquisition → L · phase extraction → L · displacement tracking → L · elasticity wave → L · constitutive law → L · applied loading → Spatial integration → Temporal integration → **y** (detector). ``` y = ∫_t dt ∫_A dA `L.applied_loading` `L.constitutive_law` `L.elasticity_wave` `L.displacement_tracking` `L.phase_extraction` `L.oct_acquisition` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.oct_acquisition` | L · oct acquisition operator | | `L.phase_extraction` | L · phase extraction operator | | `L.displacement_tracking` | L · displacement tracking operator | | `L.elasticity_wave` | L · elasticity wave operator | | `L.constitutive_law` | L · constitutive law operator | | `L.applied_loading` | L · applied loading operator | | `int.spatial` | Pixel-level spatial averaging on the detector | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Medical Imaging | | Sub domain | Sub-resolution displacement-tracked tissue mechanical property recovery (multi-physics joint inverse) | | Carrier | photon_with_mechanical_load | | Problem class | nonlinear_inverse | | Solution space | 3D_lame_parameter_map | | Noise model | gaussian | | Integration axis | spatial_temporal | | Difficulty delta | 5 | | L dag | 8.4 | ## 📡 4. Measurement Model Existence of recovered Lame parameter maps (mu, lambda)(r) is guaranteed within the declared Omega bounds. Uniqueness holds for shear-wave-mode loading at multiple frequencies (2D-3D shear-wave dispersion analysis); compression-mode and surface-wave OCE are conditionally unique requiring boundary-condition specification and density assumption. Stability is moderately conditioned (kappa_eff ~ 35 after physics-informed wave-equation regularization) — oct_phase_noise dominates displacement-tracking precision; tissue_anisotropy contributes off-diagonal Lame-tensor bias; density_uncertainty contributes a scaling factor of order rho^(-1/2). Joint Hadamard well-posedness for the coupled OCT-elasticity forward is established by Schmitt 1998 (foundational), Wang-Kirkpatrick-Hinds 2007 (phase-sensitive OCE), Kennedy-Wijesinghe-Sampson 2014 (compression OCE), Larin-Sampson 2017 (review), Kirby et al. 2017 (shear-wave OCE methods), and Wijesinghe et al. 2019 (computational OCE). | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | RMSE_log_modulus | ## 📏 5. Operating Range (Ω) **Center problem class:** `oce_shear_wave` · **Forward operator:** `oce_joint_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | H | px | 512 | | W | px | 512 | | Z | — | 256 | | Snr db | dB | 25 | | N frames | — | 100 | | Loading mode | — | shear_wave | | Wavelength nm | nm | 1300 | | Oct phase noise | — | 0 | | Loading amplitude | — | 1e-07 | | Tissue anisotropy | — | 0 | | Axial resolution um | µm | 10 | | Density uncertainty | — | 0 | | Loading frequency hz | Hz | 1000 | | Lateral resolution um | µm | 15 | | Scatter decorrelation | — | 0 | | Loading calibration error | — | 0 | | Boundary condition uncertainty | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | H | px | 128 – 2048 | | W | px | 128 – 2048 | | Z | — | 64 – 1024 | | Snr db | dB | 5.0 – 40.0 | | N frames | — | 10 – 1000 | | Wavelength nm | nm | 800 – 1700 | | Oct phase noise | — | 0.0 – 0.3 | | Loading amplitude | — | 1e-09 – 0.0001 | | Tissue anisotropy | — | 0.0 – 0.4 | | Axial resolution um | µm | 1 – 50 | | Density uncertainty | — | 0.0 – 0.2 | | Loading frequency hz | Hz | 10 – 20000 | | Lateral resolution um | µm | 2 – 50 | | Scatter decorrelation | — | 0.0 – 0.4 | | Loading calibration error | — | 0.0 – 0.3 | | Boundary condition uncertainty | — | 0.0 – 0.3 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 8.0 – 42.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `250` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x1eb90e1a535c5f6a2303cfe383613dd03b4fcefd22920aa0128c23ba2fc2207e` - **Chain tx hash:** `0x6ed0c8272521e923e97f12b2a4fcc23a6b91eced8fa9a77aa67a0071fe517008` - **Chain block:** `41553373` --- ## File Mapping This bundle consists of: `L1-508.md`, `L1-508.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-508.md` | Source of truth — edit this | Human or LLM | | `L1-508.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 `L1-508`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-508-001 Optical Coherence Elastography (OCE) — Spec Skeleton

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📋 JSON metadata

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  "domain": "Medical Imaging",
  "hardness_fn": {
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    "regime": "Existence of recovered Lame parameter maps (mu, lambda)(r) is guaranteed within the declared Omega bounds. Uniqueness holds for shear-wave-mode loading at multiple frequencies (2D-3D shear-wave dispersion analysis); compression-mode and surface-wave OCE are conditionally unique requiring boundary-condition specification and density assumption. Stability is moderately conditioned (kappa_eff ~ 35 after physics-informed wave-equation regularization) \u2014 oct_phase_noise dominates displacement-tracking precision; tissue_anisotropy contributes off-diagonal Lame-tensor bias; density_uncertainty contributes a scaling factor of order rho^(-1/2). Joint Hadamard well-posedness for the coupled OCT-elasticity forward is established by Schmitt 1998 (foundational), Wang-Kirkpatrick-Hinds 2007 (phase-sensitive OCE), Kennedy-Wijesinghe-Sampson 2014 (compression OCE), Larin-Sampson 2017 (review), Kirby et al. 2017 (shear-wave OCE methods), and Wijesinghe et al. 2019 (computational OCE).",
    "secondary": "RMSE_log_modulus"
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    "carrier": "photon_with_mechanical_load",
    "difficulty_delta": 5,
    "domain": "Medical Imaging",
    "integration_axis": "spatial_temporal",
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    "solution_space": "3D_lame_parameter_map",
    "sub_domain": "Sub-resolution displacement-tracked tissue mechanical property recovery (multi-physics joint inverse)",
    "title": "Optical Coherence Elastography (OCE)"
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      "wavelength_nm": [
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    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Sub-resolution displacement-tracked tissue mechanical property recovery (multi-physics joint inverse)",
  "title": "Optical Coherence Elastography (OCE)"
}

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