L1 ⚛ L1-507 ⊙ Testnet

Joint MEG-EEG Source Imaging

Medical Imaging · Multi-modal bioelectromagnetic neural source localization (multi-physics joint inverse)

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⬇ L1-507.md

# ⚛ L1 Principle — Joint MEG-EEG Source Imaging **ID:** `L1-507` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Medical Imaging — *Multi-modal bioelectromagnetic neural source localization (multi-physics joint inverse)* > **🎯 Problem class:** linear inverse underdetermined · **🧮 Solution space:** 5D neural source spatiotemporal > **📡 Carrier:** neural_current · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553359 --- ## 🧠 1. Introduction **Joint MEG-EEG Source Imaging** is a **linear inverse underdetermined** whose unknown lives in **5D neural source spatiotemporal** space, within the **Multi-modal bioelectromagnetic neural source localization (multi-physics joint inverse)** sub-domain of **Medical Imaging**. Measurements consist of neural current sources reconstructed from external sensors via a **joint magnetic and electric with volume conductor** sensing mechanism. The forward operator applies, in order: L · neural source operator; L · cortical mesh constraint operator; L · head volume conductor operator; L · maxwell magnetostatic operator; L · poisson electrostatic operator; L · megsensor detection operator; L · eegsensor detection 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 neural source distribution J(r, t) is guaranteed within the cortical-mesh constraint and the declared Omega bounds. Uniqueness is fundamentally conditional — the joint inverse problem is underdetermined (~15000 source dipoles with constrained orientation vs ~400 sensors typical), so unique solutions require regularization (minimum-norm, sLORETA, beamformer, sparse priors, dynamical / temporal constraints). Stability is moderately conditioned (kappa_eff ~ 100 after L2 regularization) — head_segmentation_error dominates source-localization bias; conductivity_uncertainty contributes scaling factor; sensor_position_error contributes a few-millimeter localization shift; source_orientation_assumption (free vs cortically-constrained vs surface-normal) contributes prior bias. Joint Hadamard well-posedness for the coupled MEG+EEG forward (with regularization) is established by Mosher et al. 1992, Hamalainen-Ilmoniemi 1994, Pascual-Marqui 2002 (sLORETA), Sharon et al. 2007, Henson et al. 2009, and Huang et al. 2014. ## ⚙ 2. Forward Model Physical chain: **x** → L · neural source → L · cortical mesh constraint → L · head volume conductor → L · maxwell magnetostatic → L · poisson electrostatic → L · megsensor detection → L · eegsensor detection → Spatial integration → Temporal integration → **y** (detector). ``` y = ∫_t dt ∫_A dA `L.eegsensor_detection` `L.megsensor_detection` `L.poisson_electrostatic` `L.maxwell_magnetostatic` `L.head_volume_conductor` `L.cortical_mesh_constraint` `L.neural_source` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.neural_source` | L · neural source operator | | `L.cortical_mesh_constraint` | L · cortical mesh constraint operator | | `L.head_volume_conductor` | L · head volume conductor operator | | `L.maxwell_magnetostatic` | L · maxwell magnetostatic operator | | `L.poisson_electrostatic` | L · poisson electrostatic operator | | `L.megsensor_detection` | L · megsensor detection operator | | `L.eegsensor_detection` | L · eegsensor detection 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 | Multi-modal bioelectromagnetic neural source localization (multi-physics joint inverse) | | Carrier | neural_current | | Problem class | linear_inverse_underdetermined | | Solution space | 5D_neural_source_spatiotemporal | | Noise model | gaussian | | Integration axis | spatial_temporal | | Difficulty delta | 5 | | L dag | 10 | ## 📡 4. Measurement Model Existence of recovered neural source distribution J(r, t) is guaranteed within the cortical-mesh constraint and the declared Omega bounds. Uniqueness is fundamentally conditional — the joint inverse problem is underdetermined (~15000 source dipoles with constrained orientation vs ~400 sensors typical), so unique solutions require regularization (minimum-norm, sLORETA, beamformer, sparse priors, dynamical / temporal constraints). Stability is moderately conditioned (kappa_eff ~ 100 after L2 regularization) — head_segmentation_error dominates source-localization bias; conductivity_uncertainty contributes scaling factor; sensor_position_error contributes a few-millimeter localization shift; source_orientation_assumption (free vs cortically-constrained vs surface-normal) contributes prior bias. Joint Hadamard well-posedness for the coupled MEG+EEG forward (with regularization) is established by Mosher et al. 1992, Hamalainen-Ilmoniemi 1994, Pascual-Marqui 2002 (sLORETA), Sharon et al. 2007, Henson et al. 2009, and Huang et al. 2014. | Metric | Value | |---|---| | Metric | PSNR_dB | | Secondary | spatial_localization_error_mm | ## 📏 5. Operating Range (Ω) **Center problem class:** `meg_eeg_joint_source_imaging` · **Forward operator:** `meg_eeg_joint_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 20 | | N dipoles | — | 8000 | | T samples | — | 1000 | | N eeg channels | — | 64 | | N meg channels | — | 306 | | Head layer count | — | 3 | | Sampling rate hz | Hz | 1000 | | Sensor position error | — | 0 | | Head segmentation error | — | 0 | | Conductivity uncertainty | — | 0 | | Reference electrode drift | — | 0 | | Source orientation assumption | — | cortically_constrained | | Magnetic artifact contamination | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0.0 – 35.0 | | N dipoles | — | 1000 – 30000 | | T samples | — | 100 – 100000 | | N eeg channels | — | 0 – 256 | | N meg channels | — | 0 – 306 | | Head layer count | — | 3 – 7 | | Sampling rate hz | Hz | 256 – 5000 | | Sensor position error | — | 0.0 – 0.2 | | Head segmentation error | — | 0.0 – 0.3 | | Conductivity uncertainty | — | 0.0 – 0.5 | | Reference electrode drift | — | 0.0 – 0.3 | | Magnetic artifact contamination | — | 0.0 – 0.4 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 20.0 | Metric | Range | |---|---| | Psnr db | 3.0 – 38.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `1000` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xc5b5823cf02645ff781e015fc071cd01cb138c2ec39adf26564ee8f0716fc417` - **Chain tx hash:** `0xdebc47053da2a66ee606952ad7d1f1115aa01f0e65e5d73470794d4ce0f74263` - **Chain block:** `41553359` --- ## File Mapping This bundle consists of: `L1-507.md`, `L1-507.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-507.md` | Source of truth — edit this | Human or LLM | | `L1-507.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 `L1-507`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-507-001 Joint MEG-EEG Source Imaging — Spec Skeleton

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📋 JSON metadata

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  "chain_tx_hash": "0xdebc47053da2a66ee606952ad7d1f1115aa01f0e65e5d73470794d4ce0f74263",
  "domain": "Medical Imaging",
  "hardness_fn": {
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    "kappa": 1000,
    "metric": "PSNR_dB",
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  "observable_profile": {
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    "regime": "Existence of recovered neural source distribution J(r, t) is guaranteed within the cortical-mesh constraint and the declared Omega bounds. Uniqueness is fundamentally conditional \u2014 the joint inverse problem is underdetermined (~15000 source dipoles with constrained orientation vs ~400 sensors typical), so unique solutions require regularization (minimum-norm, sLORETA, beamformer, sparse priors, dynamical / temporal constraints). Stability is moderately conditioned (kappa_eff ~ 100 after L2 regularization) \u2014 head_segmentation_error dominates source-localization bias; conductivity_uncertainty contributes scaling factor; sensor_position_error contributes a few-millimeter localization shift; source_orientation_assumption (free vs cortically-constrained vs surface-normal) contributes prior bias. Joint Hadamard well-posedness for the coupled MEG+EEG forward (with regularization) is established by Mosher et al. 1992, Hamalainen-Ilmoniemi 1994, Pascual-Marqui 2002 (sLORETA), Sharon et al. 2007, Henson et al. 2009, and Huang et al. 2014.",
    "secondary": "spatial_localization_error_mm"
  },
  "physics_fingerprint": {
    "L_DAG": 10.0,
    "carrier": "neural_current",
    "difficulty_delta": 5,
    "domain": "Medical Imaging",
    "integration_axis": "spatial_temporal",
    "noise_model": "gaussian",
    "primitives": [
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      "L.cortical_mesh_constraint",
      "L.head_volume_conductor",
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      "L.megsensor_detection",
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      "int.spatial",
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    "solution_space": "5D_neural_source_spatiotemporal",
    "sub_domain": "Multi-modal bioelectromagnetic neural source localization (multi-physics joint inverse)",
    "title": "Joint MEG-EEG Source Imaging"
  },
  "size_tiers": {
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      "SNR_dB",
      "head_segmentation_error",
      "conductivity_uncertainty",
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    ],
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        "head_layer_count": 3,
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        "sampling_rate_Hz": 1000,
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      ],
      "N_dipoles": [
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        30000
      ],
      "SNR_dB": [
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      "T_samples": [
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        100000
      ],
      "conductivity_uncertainty": [
        0.0,
        0.5
      ],
      "head_layer_count": [
        3,
        7
      ],
      "head_segmentation_error": [
        0.0,
        0.3
      ],
      "magnetic_artifact_contamination": [
        0.0,
        0.4
      ],
      "reference_electrode_drift": [
        0.0,
        0.3
      ],
      "sampling_rate_Hz": [
        256,
        5000
      ],
      "sensor_position_error": [
        0.0,
        0.2
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Multi-modal bioelectromagnetic neural source localization (multi-physics joint inverse)",
  "title": "Joint MEG-EEG Source Imaging"
}

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