# ⚛  L1 Principle — Stroke Ischemic Core / Penumbra Classification from CT-Perfusion (PWDR)

**ID:** `L1-524` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Medical Imaging — *Cerebral hemodynamics recovery from dynamic CT-perfusion with mismatch-based stroke triage readout*
> **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D stroke triage label
> **📡 Carrier:** x_ray · **🌫 Noise:** poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553360

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## 🧠 1. Introduction

**Stroke Ischemic Core / Penumbra Classification from CT-Perfusion (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D stroke triage label** space, within the **Cerebral hemodynamics recovery from dynamic CT-perfusion with mismatch-based stroke triage readout** sub-domain of **Medical Imaging**.

Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **ct perfusion with stroke triage threshold** sensing mechanism.

The forward operator applies, in order: polyenergetic X-ray emission spectrum; line-integral projection through an attenuation map; L · dynamic reconstruction operator; L · deconvolution aif operator; L · cbf cbv mtt tmax operator; L · ctp threshold classifier operator; int · spatial temporal operator.

Observations are corrupted by Poisson counting noise. Existence inherited from L1-029. Uniqueness conditional on AIF selection (manual or automated) and temporal sampling adequacy. Stability conditional with deconvolution_regularization dominant for noise sensitivity; threshold_calibration_vendor_difference contributes inter-vendor bias (~20% volume estimation difference between RAPID and Olea). Joint Hadamard well-posedness for the coupled dynamic-CTP + perfusion-threshold forward established by Ostergaard 1996 (foundational SVD deconvolution), Konstas 2009 (CTP technical review), Wintermark 2006 (perfusion thresholds), Albers 2018 (DEFUSE-3 trial), Nogueira 2018 (DAWN trial), Goyal 2016 (HERMES meta-analysis).

## ⚙ 2. Forward Model

Physical chain: **x** → X-ray source → Attenuation projection → L · dynamic reconstruction → L · deconvolution aif → L · cbf cbv mtt tmax → L · ctp threshold classifier → int · spatial temporal → **y** (detector).

```
y = `int.spatial_temporal` `L.ctp_threshold_classifier` `L.cbf_cbv_mtt_tmax` `L.deconvolution_aif` `L.dynamic_reconstruction` ∫µ dl I₀(E) x,    measurements ~ Poisson(αy)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.xray_source` | Polyenergetic x-ray emission spectrum |
| `L.attenuation_projection` | Line-integral projection through an attenuation map |
| `L.dynamic_reconstruction` | L · dynamic reconstruction operator |
| `L.deconvolution_aif` | L · deconvolution aif operator |
| `L.cbf_cbv_mtt_tmax` | L · cbf cbv mtt tmax operator |
| `L.ctp_threshold_classifier` | L · ctp threshold classifier operator |
| `int.spatial_temporal` | Int · spatial temporal operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Medical Imaging |
| Sub domain | Cerebral hemodynamics recovery from dynamic CT-perfusion with mismatch-based stroke triage readout |
| Carrier | x_ray |
| Problem class | linear_inverse_with_categorical_readout |
| Solution space | 1D_stroke_triage_label |
| Noise model | poisson |
| Integration axis | spatial_temporal |
| Difficulty delta | 5 |
| L dag | 7.3 |

## 📡 4. Measurement Model

Existence inherited from L1-029. Uniqueness conditional on AIF selection (manual or automated) and temporal sampling adequacy. Stability conditional with deconvolution_regularization dominant for noise sensitivity; threshold_calibration_vendor_difference contributes inter-vendor bias (~20% volume estimation difference between RAPID and Olea). Joint Hadamard well-posedness for the coupled dynamic-CTP + perfusion-threshold forward established by Ostergaard 1996 (foundational SVD deconvolution), Konstas 2009 (CTP technical review), Wintermark 2006 (perfusion thresholds), Albers 2018 (DEFUSE-3 trial), Nogueira 2018 (DAWN trial), Goyal 2016 (HERMES meta-analysis).

| Metric | Value |
|---|---|
| Metric | categorical_accuracy |
| Secondary | RMSE_core_volume_mL |

## 📏 5. Operating Range (Ω)

**Center problem class:** `stroke_ctp_triage_pwdr` · **Forward operator:** `ctp_stroke_pwdr_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 512 |
| W | px | 512 |
| Z | — | 32 |
| Kvp | — | 80 |
| Mas | — | 100 |
| N time frames | — | 60 |
| Voxel size mm | mm | 0.7 |
| Frame period s | s | 1.5 |
| Contrast dose ml | — | 50 |
| Contrast bolus timing | — | 0 |
| Aif selection uncertainty | — | 0 |
| Motion during acquisition | — | 0 |
| Partial volume at arteries | — | 0 |
| Deconvolution regularization | — | 0 |
| Threshold calibration vendor difference | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 256 – 1024 |
| W | px | 256 – 1024 |
| Z | — | 8 – 80 |
| N time frames | — | 20 – 120 |
| Frame period s | s | 1.0 – 3.0 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 0.85_accuracy

| Metric | Range |
|---|---|
| Categorical accuracy | 0.5 – 0.99 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **categorical_accuracy**, with κ = `200` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0xaa563431da0e16ed0eff5ab2b07a375ed2b1d32be1b208ecabb50bb303358a48`
- **Chain tx hash:** `0xb7c16c02abb69d9279620d8ee881383fa07845e9dc2605ba8164b0db37f8e19d`
- **Chain block:** `41553360`

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## File Mapping

This bundle consists of: `L1-524.md`, `L1-524.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-524.md` | Source of truth — edit this | Human or LLM |
| `L1-524.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 `L1-524`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._