An Open, Reproducible Gamma-Variate Pipeline for CT-Perfusion Time-Attenuation Curve Analysis, with Standardized (ASIST-Japan) Map Visualization

Technical Summary: An Open, Reproducible Gamma-Variate Pipeline for CT-Perfusion

Problem Statement
CT perfusion (CTP) is critical for acute stroke and oncologic imaging, yet its quantitative reliability is compromised by a lack of reproducibility across commercial vendor software. Identical source data processed by different packages yield significantly different perfusion maps and values due to variations in deconvolution algorithms, implementations, and thresholds. Furthermore, the visualization of these maps suffers from cross-site variability caused by non-standardized lookup tables (LUTs), where identical quantitative values can appear visually distinct depending on the color scale used. This "black box" opacity prevents clinicians and researchers from auditing or inspecting the underlying processing steps.

Methodology
The authors present ctp-core (v0.1.0), a pure Python (>=3.9) open-source library designed to provide a transparent, parameter-exposed pipeline for CTP analysis. The methodology focuses on two primary components:

1. Gamma-Variate (GV) Fitting and Analytic Index Derivation:

   • Model: First-pass time–attenuation curves are modeled using the gamma-variate function $C(t) = K (t −t_0)^\alpha \exp(-\frac{t - t_0}{\beta})$, where $t_0$ is onset, $\alpha$ is shape, $\beta$ is scale, and $K$ is a coefficient.
   • Fitting: Curves are fitted using nonlinear least squares (Trust Region Reflective algorithm) with physically motivated bounds. Initialization is data-driven (e.g., $t_0$ placed before the 10% peak crossing).
   • Analytic Derivation: Instead of re-optimizing, perfusion indices are derived analytically from the fitted parameters ($K, t_0, \alpha, \beta$):
     • Peak Time ($t_{peak}$): $t_0 + \alpha\beta$
     • Peak Amplitude ($y_{peak}$): $K (\alpha\beta)^\alpha e^{-\alpha}$
     • Area Under Curve (AUC): $K \beta^{\alpha+1} \Gamma(\alpha + 1)$
     • Bolus-Arrival Time (BAT): $t_0$
   • Robustness: The pipeline includes a "fit-free" raw path for cases where fitting fails, returning NaN rather than exceptions. Failures are explicitly flagged with error messages (e.g., shape mismatch, optimizer failure).

2. Standardized Visualization (ASIST-Japan a-LUT):

   • The pipeline implements the ASIST-Japan standardized lookup table (a-LUT), a 256-level RGB table mapping values through a black–blue–cyan–green–yellow–red spectrum.
   • Scalars are linearly windowed to standard display ranges (e.g., CBF 0–80 mL/100 g/min) and indexed deterministically.
   • Crucially, the color mapping affects visualization only; the underlying quantitative voxel values remain unchanged and are stored separately.

3. Scope and Implementation:

   • The open core (ctp-core) is standalone, containing no GUI, DICOM I/O, or patient data handling.
   • Full parametric mapping (CBF, CBV, MTT, Tmax) via deconvolution and Arterial Input Function (AIF) detection is documented and implemented but resides in a separate private application; the open core's reproducible claims are limited to the GV fitting and synthetic validation.

Validation and Results
The pipeline was validated exclusively on synthetic Monte-Carlo data with known ground truth, avoiding the use of confidential or patient data.

• Experimental Setup: 200 independent runs were performed at Signal-to-Noise Ratio (SNR) levels ranging from 5 to 100.
• Performance:
  • At a representative SNR of 20, the pipeline recovered peak time within 0.13 s, peak amplitude within 2.0%, and BAT within 0.51 s (Mean Absolute Error).
  • Fit quality achieved an $R^2$ of 0.98.
  • Errors degraded monotonically with noise; at SNR 5, peak time error was ~0.52 s and amplitude error ~8.1%.
  • The fit-derived peak was consistently closer to ground truth than the raw maximum (fit-free path).
• Reproducibility: The code is deterministic (fixed seeds), and the test suite (34 tests) confirms bit-stable metrics. The synthetic data generator and evaluation scripts are released alongside the core.

Key Contributions

1. Transparency: A fully open, parameter-transparent pipeline where every parameter, bound, and processing step is exposed, contrasting with commercial "black box" solutions.
2. Standardization: Integration of the ASIST-Japan a-LUT ensures that parametric map visualization is comparable across sites without altering quantitative values.
3. Reproducibility: The entire workflow, including synthetic data generation and validation benchmarks, is released under the MIT license, allowing independent audit and reuse.
4. Validation: Demonstration of recovery accuracy against known ground truth across a wide SNR range, with explicit handling of fit failures.

Significance and Claims
The authors position ctp-core not as a clinical or regulatory-grade tool, but as a research reference and a reproducible benchmark. The paper claims that by providing a transparent gamma-variate fitting engine combined with standardized visualization, it addresses the reproducibility crisis in CTP post-processing. The work allows others to audit the mathematical foundations of perfusion analysis, reuse the code for independent verification, and build upon a known, validated baseline. The authors explicitly state that no clinical validation on real patient data is claimed in this preprint, and external validation on public datasets (e.g., ISLES) is planned for future work.