\section{Methods}
\label{sec:methods}

\subsection{Datasets}

PaSAL is trained and evaluated on three datasets whose structural characteristics directly motivate several components of our pipeline. A key limitation across all training datasets is the absence of the smallest peripheral vessels in the provided artery/vein annotations. Addressing this gap is a central contribution of our pipeline, motivating the early presentation of the datasets.

For artery/vein segmentation we use the HiPaS dataset \cite{chu2025deep}, which provides 250 chest CT volumes with artery and vein masks that cover vessels approximately up to mid-level branches. For anatomical labeling we use the Pulmonary Tree Labeling (PTL) dataset \cite{xie2025efficient}, containing 799 vascular and airway trees labeled with 19 anatomical classes, again limited to central and mid-peripheral vessels. Clinical generalization is assessed on an Amsterdam UMC cohort of 63 CT scans from 12 lung cancer patients imaged pre- and post-radiotherapy; predictions were scored by a radiation oncologist.

\begin{table}[ht]
    \centering
    \scriptsize
    \renewcommand{\arraystretch}{1.15}
    \caption{Summary of datasets. ``Annotation extent'' describes the availability and depth of vessel labels; neither public dataset includes the smallest peripheral branches. 
    \textsuperscript{*}The 63 scans in the clinical evaluation dataset come from 12 distinct patients.}
    \label{tab:dataset_info}
    \begin{tabular}{l l c l l}
        \toprule
        \textbf{Task} & \textbf{Source} & \textbf{Count} & \textbf{Usage} & \textbf{Annotation extent} \\
        \midrule
        A/V segmentation & HiPaS & 250 & Training/validation & Central--mid vessels; no distal branches \\
        Anatomical labeling & PTL & 799 & Training/validation & Central--mid vessels; no distal branches \\
        Clinical evaluation & AUMC & 63\textsuperscript{*} & Clinical testing & No vessel annotations available \\
        \bottomrule
    \end{tabular}
\end{table}

All datasets contain scans of patients with pulmonary pathologies. The training datasets (HiPaS and PTL) include patients with diverse pathologies such as emboli and lung tumors. The clinical evaluation dataset (Amsterdam UMC) contains only lung cancer patients and includes scans acquired both before and after receiving radiotherapy. Because the public training datasets were provided in NIfTI/NPZ formats, DICOM metadata, including slice thickness and contrast phase, was unavailable. However, it is known from the original publications that the HiPaS dataset contains scans acquired with both contrast-enhanced (CECT) and non-contrast (NCCT) protocols. This prevents protocol-stratified training and analysis of whether performance disparities exist between these protocols, which is a key consideration given that contrast enhancement varies significantly between NCCT and CECT. For the in-house Amsterdam UMC clinical evaluation cohort, protocol information was available from DICOM headers. Additional dataset characteristics are summarized in Appendix~\ref{appendix:data-details}.


\subsection{PaSAL pipeline overview}

PaSAL produces anatomically labeled trees through four integrated stages. Unlike standard out-of-the-box implementations, we introduce non-trivial integration strategies: (i) hierarchical segmentation using extended Level-4 targets to capture peripheral vessels; (ii) a deterministic graph-extraction pipeline involving MST-inspired skeleton reconnection; (iii) orientation-standardized IPGN labeling; and (iv) a watershed-based label propagation module to bridge the gap between central labels and distal anatomy. A schematic overview of the full prediction pipeline is provided in Figure~\ref{fig:prediction-pipeline} in the Introduction.


\subsection{Hierarchical artery--vein segmentation}
\label{sec:meth_segmentation_short}

We adopt the hierarchical Salience-Transmission Segmentation (STS) framework of~\citet{chu2025deep}, which predicts artery and vein masks across four vessel levels
\[
[A^1, V^1], [A^2, V^2], [A^3, V^3], [A^4, V^4],
\]
ranging from central to distal branches. HiPaS only provides a single vessel mask corresponding to Level~3, so we reconstruct the missing proximal (Levels~1--2) and distal (Level~4) targets using the provided vessel mask.


\paragraph{Extended distal supervision (Level~4).}
Level~3 corresponds to the original HiPaS annotations, which omit the smallest peripheral vessels. To expose the network to distal vessel morphology and reduce under-segmentation near the vascular periphery, we construct extended Level~4 targets by merging the HiPaS masks with TotalSegmentator vessel predictions and refining distal branches via constrained region growing seeded inside the predicted vessels (Fig.~\ref{fig:extended-targets-hipas}).

These extended targets are used exclusively during training to provide distal supervision and are excluded from all quantitative evaluation. They were reviewed by a clinical expert and deemed to be of sufficient quality, although minor localized inconsistencies may be present due to their partially automatic construction. As these inconsistencies are not systematic across the dataset, their influence during training is expected to be limited. All reported segmentation metrics are computed solely on the original HiPaS annotations, and Level~4 predictions are considered only in qualitative clinical assessment, where no distal ground truth is available.



\begin{figure}[ht]
    \centering
    \includegraphics[width=0.75\linewidth]{Figures/Methodology/Extended targets.PNG}
    \caption{Construction of extended Level~4 targets on HiPaS by fusing the original labels with TotalSegmentator predictions and refining distal branches via region growing.}
    \label{fig:extended-targets-hipas}
\end{figure}

\paragraph{Skeleton-based hierarchy construction (Levels~1-2).}
To recover the missing proximal levels required by STS, we derive Levels~1 and~2 directly from the topology of the Level~3 vessel tree. We first extract vessel skeletons from the HiPaS masks using 3D medial-axis thinning~\cite{lee1994building}, since skeletons explicitly encode branch order, path length, and bifurcations and are therefore a natural basis for hierarchical targets. However, raw skeletons often contain multiple disconnected components due to gaps and annotation inconsistencies. We address this by introducing a two-phase MST-inspired reconnection strategy (see Figure~\ref{fig:mst-postprocessing}). First, in the mask-validated phase, nearest-neighbor nodes are linked only if the connecting edge lies predominantly ($\geq 90\%$) within the vessel mask. Second, a fallback phase ensures a single globally connected tree by adding shortest edges regardless of mask constraints. This deterministic process allows us to derive branch-order labels based on the distance from the largest average radius edge, which acts as the tree root.

\begin{figure}[ht]
    \centering
    \includegraphics[width=0.75\linewidth]{Figures/MST postprocessing.PNG}
    \caption{MST-style skeleton reconnection merges disconnected components into a single connected vascular tree.}
    \label{fig:mst-postprocessing}
\end{figure}

\paragraph{Hierarchical target assignment.}
From the connected skeleton, voxels are assigned to Levels~1-3 using simple radius- and distance-based rules, producing the coarse-to-fine vessel priors required by STS. Combined with the extended Level~4 supervision, this yields the complete hierarchy used during training (Figure~\ref{fig:hierarchical-targets-case}).

\begin{figure}[ht]
    \centering
    \includegraphics[width=0.75\linewidth]{Figures/Methodology/Data_case_1.PNG}
    \caption{Four-level artery--vein target hierarchy for one HiPaS case. Levels~1--3 are evaluated; Level~4 provides distal supervision during training only.}
    \label{fig:hierarchical-targets-case}
\end{figure}

At each level $i \geq 2$, the model receives the CT volume, a Frangi vesselness map~\cite{frangi1998multiscale}, and predictions from the preceding level; Level~1 uses only CT and the Frangi vesselness map. We employ the standard 3D full-resolution nnU-Net~\cite{isensee2021nnu}, training separate artery and vein models for each level.

\subsection{Anatomical labeling}
\label{sec:meth_labeling_short}

Anatomical labeling is performed by transforming the Level-3 vessel segmentations into connected trees suitable for graph-based learning. Vessel centerlines are extracted using 3D medial-axis thinning, followed by the MST-inspired reconnection strategy described in Section~\ref{sec:meth_segmentation_short} to enforce global connectivity. The resulting graphs are deterministically reoriented by standardizing axis permutations and rotations to match the PTL coordinate convention.

We use the Implicit Point-Graph Network (IPGN) \citet{xie2025efficient} as the anatomical labeling backbone. IPGN combines point-based features with graph topology to predict 19 anatomical classes. We employ the publicly released pre-trained artery and vein models without architectural modification to produce graph-, point-, and voxel-level labels; as IPGN itself is not a contribution of this work, we do not revisit its internal design. Because the PTL training data is limited to Level-3 vessels, labeling is consistently restricted to Level-3 segmentations across all datasets to ensure prediction reliability. A schematic overview of the IPGN framework is provided in Appendix~\ref{appendix:label-implementation} (Figure~\ref{appendix:IPGN-framework}).


\subsection{Label propagation to peripheral vessels}
\label{sec:meth_label-propagation}

Because the IPGN training dataset is limited to targets corresponding to level 3 targets and therefore do not contain the distal peripheral vessels, we introduce a marker-based watershed algorithm to propagate these labels to the Level-4 peripheral segmentations. This step is essential for producing complete vascular trees, bridging the gap in existing datasets where ground truth for distal branches is unavailable. IPGN voxel predictions act as seed markers and the watershed operates within the union of Level~4 artery and vein masks \cite{van2014scikit}. This post hoc propagation step enables PaSAL to produce fully labeled vascular trees despite the lack of ground truth for peripheral branches. Propagated labels are used only for qualitative assessment, since no ground truth exists for these regions. Implementation details are given in Appendix~\ref{appendix:label-propagation}.

\subsection{Training and evaluation}
\label{sec:training-eval}

All segmentation models follow the default 3D full-resolution nnU-Net training pipeline \cite{isensee2021nnu} with a combined Dice and cross-entropy loss and standard 3D augmentations. Artery and vein models are trained separately for each hierarchical level.

For anatomical labeling, we use the publicly released IPGN artery and vein models \cite{xie2025efficient} without modification, but integrate them into our CT-based pipeline via the custom preprocessing and graph-construction steps described above.

Segmentation performance on HiPaS is evaluated using Dice, HD95, Sensitivity, and Precision, while anatomical labeling accuracy on PTL is assessed using voxel-, node-, and edge-level micro-averaged Dice following \cite{xie2025efficient}.

Beyond quantitative metrics, we assess clinical usefulness on the in-house radiotherapy cohort using a structured 0--5 scoring protocol completed by a radiation oncologist. For segmentation, scores reflect overall accuracy/robustness, peripheral branch completeness, and diagnostic usefulness; for labeling, they assess label consistency, proximal-distal correctness, and clinical interpretability (full criteria in Appendix~\ref{appendix:clinical-evaluation}). We report mean expert scores and compute Spearman correlations between quantitative metrics and expert ratings to study how well overlap-based measures reflect perceived clinical utility. Given that the primary goal of the clinical evaluation was to establish clinical utility and practical applicability rather than protocol-specific performance analysis, differences in performance between NCCT and CECT protocols were not explicitly analyzed in the clinical cohort.
