# ⚛  L1 Principle — Intravascular Ultrasound (IVUS)

**ID:** `L1-061` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Medical Imaging — *Catheter-based high-frequency ultrasound of coronary arteries*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** 2D vessel cross section
> **📡 Carrier:** acoustic · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41552303

---

## 🧠 1. Introduction

**Intravascular Ultrasound (IVUS)** is a **linear inverse problem** whose unknown lives in **2D vessel cross section** space, within the **Catheter-based high-frequency ultrasound of coronary arteries** sub-domain of **Medical Imaging**.

Measurements consist of acoustic pressure waves recorded by transducers via a **intravascular ultrasound** sensing mechanism.

The forward operator applies, in order: L · emit · acoustic pulse 40MHz operator; L · catheter rotate operator; L · pulse echo operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Existence of the recovered 2D vessel cross section is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 13); catheter_motion dominates the stability cliff; non_uniform_rotation and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

## ⚙ 2. Forward Model

Physical chain: **x** → L · emit · acoustic pulse 40MHz → L · catheter rotate → L · pulse echo → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.pulse_echo` `L.catheter_rotate` `L.emit.acoustic_pulse_40MHz` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.emit.acoustic_pulse_40MHz` | L · emit · acoustic pulse 40mhz operator |
| `L.catheter_rotate` | L · catheter rotate operator |
| `L.pulse_echo` | L · pulse echo operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Medical Imaging |
| Sub domain | Catheter-based high-frequency ultrasound of coronary arteries |
| Carrier | acoustic |
| Problem class | linear_inverse |
| Solution space | 2D_vessel_cross_section |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 5 |
| L dag | 3.8 |

## 📡 4. Measurement Model

Existence of the recovered 2D vessel cross section is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by the declared priors. Stability is moderately conditioned (kappa_eff ~= 13); catheter_motion dominates the stability cliff; non_uniform_rotation and the remaining mismatch parameters contribute higher-order bias terms. Additive gaussian thermal/electronic noise sets the irreducible data-fidelity floor, while mild Tikhonov or analytic inversion is sufficient at the nominal Omega point.

| Metric | Value |
|---|---|
| Metric | PSNR_dB |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `ivus` · **Forward operator:** `ivus_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| F mhz | MHz | 40 |
| Snr db | dB | 25 |
| N lines | — | 256 |
| Depth mm | mm | 8 |
| Blood speckle | — | 0.1 |
| Catheter motion | — | 0 |
| Guidewire artifact | — | 0 |
| Non uniform rotation | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| F mhz | MHz | 20 – 60 |
| Snr db | dB | 0.0 – 40.0 |
| N lines | — | 64 – 1024 |
| Depth mm | mm | 2 – 20 |
| Blood speckle | — | 0.0 – 0.3 |
| Catheter motion | — | 0.0 – 0.5 |
| Guidewire artifact | — | 0.0 – 0.3 |
| Non uniform rotation | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 24.0

| Metric | Range |
|---|---|
| Psnr db | 5.0 – 45.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `260` and δ = `5`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xd77a0c70a7c0ddf54cffec7f004fea7d31c4f5e2b3fdddb734d84807e9e46cd3`
- **Chain tx hash:** `0x79e52b1fb82037a8fbb2353bc90197a0dfec2717838a1e5d62275f0abeee8e2d`
- **Chain block:** `41552303`

---

## File Mapping

This bundle consists of: `L1-061.md`, `L1-061.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-061.md` | Source of truth — edit this | Human or LLM |
| `L1-061.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 `L1-061`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._