L1 ⚛ L1-401 ⊙ Testnet

Windkessel Cardiac Afterload Model

Computational Biology · Cardiovascular physiology

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⬇ L1-401.md

# ⚛ L1 Principle — Windkessel Cardiac Afterload Model **ID:** `L1-401` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Cardiovascular physiology* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** windkessel parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** measurement gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555217 --- ## 🧠 1. Introduction **Windkessel Cardiac Afterload Model** is a **parameter-estimation problem** whose unknown lives in **windkessel parameter vector** space, within the **Cardiovascular physiology** sub-domain of **Computational Biology**. Measurements consist of N/A via a **aortic pressure flow measurement** sensing mechanism. The forward operator applies, in order: time evolution of the state; O · least squares · pressure fit operator; S · gradient · ode params operator. Observations are corrupted by measurement gaussian. Existence of the recovered windkessel_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); nonlinearity_pressure_compliance dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Time derivative → O · least squares · pressure fit → S · gradient · ode params → **y** (detector). ``` y = `S.gradient.ode_params` `O.least_squares.pressure_fit` ∂_t x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `O.least_squares.pressure_fit` | O · least squares · pressure fit operator | | `S.gradient.ode_params` | S · gradient · ode params operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Cardiovascular physiology | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | windkessel_parameter_vector | | Noise model | measurement_gaussian | | Integration axis | cardiac_cycle | | Difficulty delta | 3 | | L dag | 2.2 | ## 📡 4. Measurement Model Existence of the recovered windkessel_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); nonlinearity_pressure_compliance dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | pressure_waveform_RMSE_mmHg | | Secondary | parameter_identifiability_index | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `aortic_pressure_flow_measurement` **Center point:** | Parameter | Unit | Value | |---|---|---| | Heart rate bpm | — | 70 | | N cardiac cycles | — | 10 | | Systolic pressure mmhg | — | 120 | | Diastolic pressure mmhg | — | 80 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Heart rate bpm | — | 40 – 120 | | N cardiac cycles | — | 3 – 100 | | Systolic pressure mmhg | — | 80 – 200 | | Diastolic pressure mmhg | — | 50 – 100 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 2.0 pressure_waveform_RMSE_mmHg | Metric | Range | |---|---| | Pressure waveform rmse mmhg | 0.2 – 10.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **pressure_waveform_RMSE_mmHg**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x9e264bd4cb29c0c0d2805ff69313eb2d909d79a18da8bfea36b01e6e83ce6b2c` - **Chain tx hash:** `0xbb2f99b0073c1b641d5f7611f14337dc55d81de4da2937f931619f6e60ed9109` - **Chain block:** `41555217` --- ## File Mapping This bundle consists of: `L1-401.md`, `L1-401.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-401.md` | Source of truth — edit this | Human or LLM | | `L1-401.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 `L1-401`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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L2-401-001 Windkessel Cardiac Afterload Model — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555217,
  "chain_hash": "0x9e264bd4cb29c0c0d2805ff69313eb2d909d79a18da8bfea36b01e6e83ce6b2c",
  "chain_tx_hash": "0xbb2f99b0073c1b641d5f7611f14337dc55d81de4da2937f931619f6e60ed9109",
  "domain": "Computational Biology",
  "hardness_fn": {
    "delta": 3,
    "kappa": 500,
    "metric": "pressure_waveform_RMSE_mmHg",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "pressure_waveform_RMSE_mmHg",
    "regime": "Existence of the recovered windkessel_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); nonlinearity_pressure_compliance dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.",
    "secondary": "parameter_identifiability_index"
  },
  "physics_fingerprint": {
    "L_DAG": 2.2,
    "carrier": "N/A",
    "difficulty_delta": 3,
    "domain": "Computational Biology",
    "integration_axis": "cardiac_cycle",
    "noise_model": "measurement_gaussian",
    "primitives": [
      "D.time",
      "O.least_squares.pressure_fit",
      "S.gradient.ode_params"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "aortic_pressure_flow_measurement",
    "solution_space": "windkessel_parameter_vector",
    "sub_domain": "Cardiovascular physiology",
    "title": "Windkessel Cardiac Afterload Model"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "aortic_pressure_flow_measurement"
    ],
    "allowed_omega_dimensions": [
      "heart_rate_bpm",
      "systolic_pressure_mmHg",
      "diastolic_pressure_mmHg",
      "N_cardiac_cycles"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "2.0 pressure_waveform_RMSE_mmHg",
      "forward_operator": "aortic_pressure_flow_measurement",
      "input_format": "measurement_only",
      "omega": {
        "N_cardiac_cycles": 10,
        "diastolic_pressure_mmHg": 80,
        "heart_rate_bpm": 70,
        "systolic_pressure_mmHg": 120
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "pressure_waveform_RMSE_mmHg": [
        0.2,
        10.0
      ]
    },
    "omega_bounds": {
      "N_cardiac_cycles": [
        3,
        100
      ],
      "diastolic_pressure_mmHg": [
        50,
        100
      ],
      "heart_rate_bpm": [
        40,
        120
      ],
      "systolic_pressure_mmHg": [
        80,
        200
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Cardiovascular physiology",
  "title": "Windkessel Cardiac Afterload Model"
}

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