L1 ⚛ L1-403 ⊙ Testnet

Physiologically Based PK (PBPK)

Computational Biology · Systems pharmacology

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⬇ L1-403.md

# ⚛ L1 Principle — Physiologically Based PK (PBPK) **ID:** `L1-403` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Computational Biology — *Systems pharmacology* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** PBPK parameter vector > **📡 Carrier:** N/A · **🌫 Noise:** lognormal > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555218 --- ## 🧠 1. Introduction **Physiologically Based PK (PBPK)** is a **parameter-estimation problem** whose unknown lives in **PBPK parameter vector** space, within the **Systems pharmacology** sub-domain of **Computational Biology**. Measurements consist of N/A via a **tissue concentration measurement** sensing mechanism. The forward operator applies, in order: time evolution of the state; S · qsr · tissue binding operator; O · nlme · pbpk fit operator. Observations are corrupted by log-normal multiplicative noise. Existence of the recovered PBPK_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 ~= 500); in_vitro_in_vivo_extrapolation_IVIVE_bias dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Time derivative → S · qsr · tissue binding → O · nlme · pbpk fit → **y** (detector). ``` y = `O.nlme.pbpk_fit` `S.qsr.tissue_binding` ∂_t x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.time` | Time evolution of the state | | `S.qsr.tissue_binding` | S · qsr · tissue binding operator | | `O.nlme.pbpk_fit` | O · nlme · pbpk fit operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Computational Biology | | Sub domain | Systems pharmacology | | Carrier | N/A | | Problem class | parameter_estimation | | Solution space | PBPK_parameter_vector | | Noise model | lognormal | | Integration axis | organ_system | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered PBPK_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 ~= 500); in_vitro_in_vivo_extrapolation_IVIVE_bias dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | plasma_RMSE_fold_error | | Secondary | tissue_Kp_RMSE_log | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `tissue_concentration_measurement` **Center point:** | Parameter | Unit | Value | |---|---|---| | Cl int l hr | — | 20 | | Species bw kg | kg | 70 | | N organs modeled | — | 15 | | Fu fraction unbound | — | 0.1 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Cl int l hr | — | 0.1 – 1000 | | Species bw kg | kg | 0.02 – 500 | | N organs modeled | — | 5 – 25 | | Fu fraction unbound | — | 0.001 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 2 plasma_RMSE_fold_error | Metric | Range | |---|---| | Plasma rmse fold error | 1.0 – 10.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **plasma_RMSE_fold_error**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x01a1cd45de8d4c7fffff836b170d1e55dc5e0d7886115b617875f91fae49aa8b` - **Chain tx hash:** `0x3413d775b5969bb353b1f6a4ebc170167950d11d98a7eac9217ed5de6acf3831` - **Chain block:** `41555218` --- ## File Mapping This bundle consists of: `L1-403.md`, `L1-403.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-403.md` | Source of truth — edit this | Human or LLM | | `L1-403.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 `L1-403`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-403.md).
Regenerate L1-403.json so every field matches the Markdown.
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L2-403-001 Physiologically Based PK (PBPK) — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555218,
  "chain_hash": "0x01a1cd45de8d4c7fffff836b170d1e55dc5e0d7886115b617875f91fae49aa8b",
  "chain_tx_hash": "0x3413d775b5969bb353b1f6a4ebc170167950d11d98a7eac9217ed5de6acf3831",
  "domain": "Computational Biology",
  "hardness_fn": {
    "delta": 5,
    "kappa": 10000.0,
    "metric": "plasma_RMSE_fold_error",
    "type": "epsilon_fn"
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  "initiator_dataset": [
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      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
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  "layer": "L1",
  "observable_profile": {
    "metric": "plasma_RMSE_fold_error",
    "regime": "Existence of the recovered PBPK_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 ~= 500); in_vitro_in_vivo_extrapolation_IVIVE_bias dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Lognormal sets the irreducible data-fidelity floor.",
    "secondary": "tissue_Kp_RMSE_log"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "N/A",
    "difficulty_delta": 5,
    "domain": "Computational Biology",
    "integration_axis": "organ_system",
    "noise_model": "lognormal",
    "primitives": [
      "D.time",
      "S.qsr.tissue_binding",
      "O.nlme.pbpk_fit"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "tissue_concentration_measurement",
    "solution_space": "PBPK_parameter_vector",
    "sub_domain": "Systems pharmacology",
    "title": "Physiologically Based PK (PBPK)"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "tissue_concentration_measurement"
    ],
    "allowed_omega_dimensions": [
      "N_organs_modeled",
      "CL_int_L_hr",
      "fu_fraction_unbound",
      "species_BW_kg"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "2 plasma_RMSE_fold_error",
      "forward_operator": "tissue_concentration_measurement",
      "input_format": "measurement_only",
      "omega": {
        "CL_int_L_hr": 20,
        "N_organs_modeled": 15,
        "fu_fraction_unbound": 0.1,
        "species_BW_kg": 70
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "plasma_RMSE_fold_error": [
        1.0,
        10.0
      ]
    },
    "omega_bounds": {
      "CL_int_L_hr": [
        0.1,
        1000
      ],
      "N_organs_modeled": [
        5,
        25
      ],
      "fu_fraction_unbound": [
        0.001,
        1.0
      ],
      "species_BW_kg": [
        0.02,
        500
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Systems pharmacology",
  "title": "Physiologically Based PK (PBPK)"
}

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