# ⚛  L1 Principle — Pulmonary Embolism Detection from CT Pulmonary Angiography (PWDR)

**ID:** `L1-525` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Medical Imaging — *Pulmonary vascular contrast-enhanced reconstruction with embolism location + RV-strain severity readout*
> **🎯 Problem class:** linear inverse with categorical readout · **🧮 Solution space:** 1D pe severity
> **📡 Carrier:** x_ray · **🌫 Noise:** poisson
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41553374

---

## 🧠 1. Introduction

**Pulmonary Embolism Detection from CT Pulmonary Angiography (PWDR)** is a **linear inverse with categorical readout** whose unknown lives in **1D pe severity** space, within the **Pulmonary vascular contrast-enhanced reconstruction with embolism location + RV-strain severity readout** sub-domain of **Medical Imaging**.

Measurements consist of X-ray photons transmitted through (or scattered by) the sample via a **ctpa with pe severity 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 · pulmonary artery segmentation operator; L · filling defect detection operator; L · rv lv measurement operator; L · pe severity classifier operator; pixel-level spatial averaging on the detector.

Observations are corrupted by Poisson counting noise. Existence inherited from L1-029. Uniqueness conditional on adequate contrast bolus timing (peak pulmonary-arterial enhancement). Stability conditional with contrast_bolus_timing dominant for false-negative rate at subsegmental level (~15-25% miss rate for isolated subsegmental PE). Joint Hadamard well-posedness for the CTPA + PE-detection forward established by Wittram 2007 (foundational PE imaging review), Quanadli 2001 (Qanadli obstruction index), Mastora 2003 (Mastora score), Konstantinides 2019 (ESC 2019 PE guidelines), Jaff 2011 (AHA scientific statement), Stein 2006 (PIOPED II).

## ⚙ 2. Forward Model

Physical chain: **x** → X-ray source → Attenuation projection → L · dynamic reconstruction → L · pulmonary artery segmentation → L · filling defect detection → L · rv lv measurement → L · pe severity classifier → Spatial integration → **y** (detector).

```
y = ∫_A dA `L.pe_severity_classifier` `L.rv_lv_measurement` `L.filling_defect_detection` `L.pulmonary_artery_segmentation` `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.pulmonary_artery_segmentation` | L · pulmonary artery segmentation operator |
| `L.filling_defect_detection` | L · filling defect detection operator |
| `L.rv_lv_measurement` | L · rv lv measurement operator |
| `L.pe_severity_classifier` | L · pe severity classifier operator |
| `int.spatial` | Pixel-level spatial averaging on the detector |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Medical Imaging |
| Sub domain | Pulmonary vascular contrast-enhanced reconstruction with embolism location + RV-strain severity readout |
| Carrier | x_ray |
| Problem class | linear_inverse_with_categorical_readout |
| Solution space | 1D_pe_severity |
| Noise model | poisson |
| Integration axis | spatial |
| Difficulty delta | 5 |
| L dag | 7 |

## 📡 4. Measurement Model

Existence inherited from L1-029. Uniqueness conditional on adequate contrast bolus timing (peak pulmonary-arterial enhancement). Stability conditional with contrast_bolus_timing dominant for false-negative rate at subsegmental level (~15-25% miss rate for isolated subsegmental PE). Joint Hadamard well-posedness for the CTPA + PE-detection forward established by Wittram 2007 (foundational PE imaging review), Quanadli 2001 (Qanadli obstruction index), Mastora 2003 (Mastora score), Konstantinides 2019 (ESC 2019 PE guidelines), Jaff 2011 (AHA scientific statement), Stein 2006 (PIOPED II).

| Metric | Value |
|---|---|
| Metric | categorical_accuracy |
| Secondary | sensitivity_for_central_lobar_PE |

## 📏 5. Operating Range (Ω)

**Center problem class:** `pe_ctpa_severity_pwdr` · **Forward operator:** `ctpa_pe_pwdr_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| H | px | 512 |
| W | px | 512 |
| Z | — | 300 |
| Kvp | — | 100 |
| Mas | — | 250 |
| Voxel size mm | mm | 0.7 |
| Slice thickness mm | mm | 1 |
| Contrast bolus timing | — | 0 |
| Rv lv measurement axis | — | 0 |
| Beam hardening artifact | — | 0 |
| Ai threshold calibration | — | 0 |
| Motion during breath hold | — | 0 |
| Partial volume at subsegmental | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| H | px | 256 – 1024 |
| W | px | 256 – 1024 |
| Z | — | 100 – 800 |
| Slice thickness mm | mm | 0.5 – 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 = `100` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0x780048ef357a05ccae93b61f5fe224347236960a9bdefd76d890ff79084a3622`
- **Chain tx hash:** `0x10b7f926211a1f4fd1a41b8c2ee7ee59bb6f15dfc9b267bd5c554bb3bedde6c7`
- **Chain block:** `41553374`

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## File Mapping

This bundle consists of: `L1-525.md`, `L1-525.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-525.md` | Source of truth — edit this | Human or LLM |
| `L1-525.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 `L1-525`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._