VesselTok: Tokenizing Vessel-like 3D Biomedical Graph Representations for Reconstruction and Generation

1. Problem Statement

Biomedical structures such as blood vessels, lung airways, and neuronal networks are naturally represented as 3D spatial graphs (centerlines with connectivity). Accurately modeling these graphs is vital for clinical research and disease diagnosis. However, existing approaches face significant challenges:

• Computational Complexity: High-resolution networks contain massive numbers of nodes and edges, making them computationally intractable for standard graph algorithms and generative models.
• Limitations of Current Tokenizers: Existing graph tokenizers (e.g., VQ-VAE) often operate at native resolution, retaining the original node count, which prevents efficient compression and generation of large-scale graphs.
• Limitations of Shape Tokenizers: General 3D shape tokenizers (e.g., 3DShape2VecSet) rely on surface point sampling. This is suboptimal for tubular structures which have a high surface-to-volume ratio; sampling the surface is computationally expensive and fails to capture the intrinsic 1D topology efficiently.
• Radius Variability: Explicitly modeling varying radii adds complexity. While radii vary, they often follow smooth anatomical constraints that can be inferred later, suggesting a focus on topology and geometry first.

Goal: To develop a framework that learns compact, high-fidelity latent representations (tokens) of complex, large-scale 3D spatial graphs, enabling efficient reconstruction, generative modeling, and the solution of inverse problems.

2. Methodology: VesselTok

VesselTok is a tokenizer framework designed specifically for tubular, vessel-like structures. It departs from surface-centric methods by operating on centerline points and modeling the structure as a continuous 3D occupancy field.

Core Concepts

• Pseudo-Radius & Occupancy Field: Instead of treating the graph as a set of discrete points, VesselTok thickens each edge of the graph with a fixed pseudo-radius ($r$). This converts the graph into a continuous 3D occupancy field $\phi_r$, where a point is "occupied" if its distance to the nearest edge is $\le r$. This representation is invariant to the specific number of centerline points used to define the graph.
• Centerline-Centric Processing: Unlike methods that sample surface points, VesselTok uses the sparse centerline points as structural primitives. This drastically reduces computational load while preserving the high surface-to-volume characteristics of vessels.

Architecture (VAE-style)

The model consists of an Encoder ($\mathcal{T}$) and a Decoder ($\mathcal{D}$) based on Transformer blocks:

1. Encoder:
   • Takes a pre-processed centerline point cloud $P$.
   • Uses Farthest Point Sampling (FPS) to select a fixed set of query points $Q_{in}$.
   • Employs Cross-Attention between the input points and query points, followed by Self-Attention layers.
   • Outputs a continuous latent token sequence $Z \in \mathbb{R}^{l \times c}$ (mean and variance for a VAE).
2. Decoder:
   • Takes the latent $Z$ and a set of query points $Q_{out}$ sampled from a 3D grid.
   • Uses Cross-Attention to predict the continuous occupancy field $\tilde{\phi}_\theta$ at these query points.
3. Graph Reconstruction:
   • The continuous occupancy field is thresholded to create a binary mask.
   • A skeletonization algorithm extracts the centerline points from the mask.
   • A deterministic neighborhood-based connectivity prediction reconstructs the final graph edges.

Training Objective

The model is trained using a reconstruction loss (Binary Cross Entropy between predicted and ground-truth occupancy) and a KL-divergence term to regularize the latent space. An imbalance-aware query selection strategy emphasizes points near the vessel boundaries to handle the sparsity of the occupancy field.

3. Key Contributions

1. VesselTok Framework: A novel tokenizer that leverages implicit neural representations of tubular shapes, operating on centerlines rather than surfaces. It generalizes across diverse curvilinear anatomies (airways, brain vessels, pulmonary vessels).
2. Generative Modeling: Demonstrates that the learned latent tokens support both unconditional and conditional generative modeling (using Diffusion Models) to synthesize plausible, complex 3D anatomical graphs.
3. Inverse Problem Solving: Shows that the generative prior in the token space can solve downstream tasks like link prediction (repairing incomplete or broken vessel structures) effectively.
4. Generalization: The model generalizes to unseen anatomies (e.g., renal vasculature, Circle of Willis) and scales to graph sizes an order of magnitude larger than the training data.

4. Experimental Results

The authors evaluated VesselTok on diverse datasets including airways (ATM, AIIB), cerebral vasculature (COSTA), and pulmonary vessels (HiPas, PARSE).

• Reconstruction Performance:
  • Outperformed strong baselines (Hunyuan3D 2.0, 3DShape2VecSet) across all metrics.
  • clDice: Significantly higher (e.g., 94.85 vs. 87.22 on AIIB), indicating better preservation of centerline connectivity.
  • Chamfer Distance (CD): Lower geometric error (e.g., 0.66 vs. 2.74 on AIIB).
  • Topological Accuracy: Reduced errors in Betti numbers ($|\Delta\beta_0|$ and $|\Delta\beta_1|$), meaning fewer broken components and spurious loops.
• Generalization:
  • Successfully reconstructed renal vasculature (graphs with >100k nodes, 10x larger than training) and Circle of Willis structures.
  • Maintained high fidelity on synthetic "half-lung" and "half-brain" data, proving robustness to topological breaks.
• Generative Quality:
  • Achieved lower Fréchet Inception Distance (FID) and better coverage metrics (COV) compared to baselines, indicating generated graphs are more realistic and diverse.
  • Generated graphs matched the distribution of connected components and loops in the training data.
• Downstream Tasks:
  • In link prediction (inpainting missing vessel segments), VesselTok outperformed a strong autodecoder baseline, achieving higher clDice and lower topological errors.

5. Significance and Impact

• Scalability: VesselTok solves the computational bottleneck of processing large-scale biomedical graphs by compressing them into a fixed-length latent space, enabling the use of powerful generative models (like Diffusion) on complex anatomical networks.
• Topology Preservation: By focusing on the centerline and using an occupancy field, the method prioritizes topological connectivity over exact surface meshing, which is crucial for functional analysis (e.g., blood flow simulation).
• Clinical Utility: The ability to generate plausible anatomical graphs and repair incomplete data (e.g., from low-quality imaging) opens new avenues for disease diagnosis, surgical planning, and the creation of synthetic training data for medical AI.
• Paradigm Shift: It challenges the notion that explicit radius modeling is necessary for learning compact representations, showing that structural topology can be learned first, with radius inferred as a post-hoc step.

In summary, VesselTok provides a robust, scalable, and topology-aware framework for representing and generating complex 3D biomedical graphs, bridging the gap between high-resolution anatomical data and modern generative AI.