HUG-VAS: A Hierarchical NURBS-Based Generative Model for Aortic Geometry Synthesis and Controllable Editing

HUG-VAS is a novel hierarchical generative framework that combines NURBS parameterization with diffusion-based modeling to synthesize realistic, CFD-ready aortic geometries and enable training-free, zero-shot conditional editing from sparse clinical imaging data.

The Gist

Imagine you are an architect trying to design a custom house for a specific family. You have a few photos of their current home, but the photos are blurry, some walls are missing, and you don't have the blueprints. You need to create a perfect, watertight 3D model of their house so you can test how the wind blows through it or how a new roof would look.

Doing this manually is slow, tedious, and prone to errors. Doing it with old computer methods often results in a "house" that looks like a blocky video game character—full of holes and impossible to build.

HUG-VAS is a new, super-smart AI tool that solves this problem, but instead of houses, it designs human aortas (the main artery that carries blood from the heart).

Here is how it works, broken down into simple concepts:

1. The "Skeleton and Skin" Trick

Most old AI models try to learn the shape of an artery all at once, like trying to memorize a whole sculpture in one go. HUG-VAS is smarter. It breaks the artery down into two parts:

• The Skeleton (Centerline): Think of this as the wire frame or the "spine" of the artery. It decides where the artery goes, how it curves, and where it branches off.
• The Skin (Radius): This is the thickness of the artery wall at every point along that spine.

HUG-VAS uses a hierarchical approach. First, it generates the "skeleton" using a powerful AI called a Diffusion Model (think of it as an artist who starts with a cloud of static noise and slowly sculpts it into a clear shape). Once the skeleton is decided, a second AI looks at that skeleton and generates the "skin," deciding how thick or thin the artery should be at each spot.

Why is this cool? In real life, two people can have the exact same "spine" for their artery but very different thicknesses due to health or genetics. By separating the two, HUG-VAS captures this natural variety much better than older methods.

2. The "Magic Clay" (NURBS)

Once the AI generates the shape, it doesn't just spit out a messy pile of pixels or a jagged 3D mesh. It uses something called NURBS.

Imagine you are sculpting with digital clay.

• Old methods: Like trying to build a smooth sphere out of Lego bricks. It's blocky, and if you try to cut a piece off, the whole thing falls apart.
• HUG-VAS: Like sculpting with smooth, perfect clay. The result is a watertight surface (no holes), perfectly smooth, and easy to edit. If a doctor wants to change the curve of the artery slightly, they can just pull a control point, and the whole shape stretches smoothly, just like real clay.

This is crucial because these models are often used for CFD (Computational Fluid Dynamics)—simulating how blood flows. You can't run a blood flow simulation on a Lego-block artery; it has to be smooth and sealed. HUG-VAS gives you a "simulation-ready" model instantly.

3. The "Guessing Game" (Conditional Generation)

Sometimes, doctors don't have a full MRI scan. Maybe the image is blurry, or only a small part of the artery is visible.

• Old AI: Would get confused and probably fail or guess a random shape.
• HUG-VAS: Uses a technique called Diffusion Posterior Sampling. Think of it as a game of "Hot and Cold."
  • The doctor gives the AI a few clues: "Here are three dots where the artery passes," or "Here is a slice of the artery from the middle."
  • The AI starts with a random shape and slowly "denoises" it, constantly checking: "Does this shape pass through the dots the doctor gave me?"
  • It keeps adjusting until it finds a shape that fits the clues perfectly but still looks like a real, healthy human artery.

This allows doctors to do semi-automatic segmentation. Instead of spending hours tracing an artery on a screen, they just click a few points, and the AI fills in the rest, even if the original image was terrible quality.

4. Why Does This Matter?

• For Doctors: It turns a 4-hour manual drawing task into a 2-minute click-and-edit task. It helps them plan surgeries or design custom stents (tiny mesh tubes) that fit a specific patient perfectly.
• For Researchers: It can create thousands of "fake" but realistic patient arteries. This helps them train other AI models or test new medical devices without needing thousands of real patients.
• For Patients: It leads to better, more personalized treatments because the computer models are actually accurate and smooth enough to simulate real blood flow.

The Bottom Line

HUG-VAS is like a generative architect for your blood vessels. It takes a few messy clues from a medical scan, uses a smart two-step process to figure out the shape and size, and builds a perfect, smooth, digital twin of your aorta that is ready for doctors to use for surgery planning or for scientists to study. It bridges the gap between a blurry medical image and a perfect, usable 3D model.

Technical Summary

1. Problem Statement

Accurate, patient-specific vascular geometry is essential for diagnosis, treatment planning, and computational fluid dynamics (CFD) simulations. However, existing approaches face significant limitations:

• Statistical Shape Modeling (SSM) Limitations: Traditional SSMs rely on Principal Component Analysis (PCA) with linear priors. This constrains shape variation to a linear subspace, failing to capture the complex, nonlinear, and multimodal nature of anatomical variability. Furthermore, they often require labor-intensive preprocessing to establish point-to-point correspondence.
• Representation Issues: Many existing methods output unstructured meshes or voxel grids, which are difficult to edit, lack watertightness, and are not directly compatible with CFD solvers or CAD tools.
• Deterministic Assumptions: Current generative models often treat vessel centerlines and cross-sectional radii as a deterministic pair, ignoring the fact that a single centerline can correspond to multiple plausible radial distributions due to hemodynamic and tissue constraints.
• Segmentation Challenges: Manual segmentation is slow and labor-intensive, while automated deep learning methods often produce noisy, discontinuous outputs that require extensive manual repair before simulation.

2. Methodology: HUG-VAS Framework

The authors propose HUG-VAS (Hierarchical NURBS Generative framework for Vascular models), which unifies NURBS parameterization with hierarchical diffusion modeling.

A. NURBS-Based Parameterization

Instead of using raw meshes, the framework encodes vascular geometry into a compact, interpretable latent space using Non-Uniform Rational B-Splines (NURBS).

• Decomposition: The aorta with supra-aortic branches is modeled as a vascular graph.
• Latent Representation: Each vessel is encoded into two components:
  1. Centerline Control Points ($C$): A set of 3D points defining the vessel trajectory.
  2. Cross-Sectional Radii ($R$): A matrix of radii sampled along the centerline at specific angular discretizations.
• Advantages: This ensures smooth, watertight surfaces that are inherently editable and simulation-ready (CFD-compatible) without post-processing.

B. Hierarchical Diffusion Modeling

The generation process is decoupled into two stages to preserve stochastic variability:

1. Centerline Generation: A standard Denoising Diffusion Probabilistic Model (DDPM) generates the vessel centerline control points ($C$) from random noise.
2. Radius Generation: A Classifier-Free Guided (CFG) diffusion model generates the radial profiles ($R$) conditioned on the generated centerline ($C$).
   • This hierarchical design allows for diverse radius configurations for a fixed centerline, capturing inter-patient variability more realistically than joint generation.
   • The CFG scale factor ($\gamma$) controls the strength of the dependency between the centerline and radius.

C. Training-Free Conditional Generation (DPS)

HUG-VAS supports zero-shot conditional generation without retraining, utilizing Diffusion Posterior Sampling (DPS).

• Mechanism: The model treats the generation as a Bayesian inference problem ($p(z|y) \propto p(y|z)p(z)$), where $y$ is a user-provided prompt (e.g., sparse 3D points, 2D contours, or partial surface patches).
• Implementation: During the reverse diffusion process, the sampling trajectory is guided by the gradient of the log-likelihood of the prompt with respect to the latent variables. This is computed via Automatic Differentiation (AD).
• Workflow:
  1. Centerline Conditioning: User points/contours guide the centerline diffusion.
  2. Surface Conditioning: The generated centerline and user contours guide the radius diffusion.
  3. Assembly: Vessels are assembled using statistical bifurcation locations and Boolean operations to create a complete, watertight multi-branch geometry.

3. Key Contributions

1. First Unified SSM Framework: To the authors' knowledge, this is the first framework to bridge image-derived priors with generative shape synthesis using a unified combination of NURBS, hierarchical diffusion, and DPS.
2. Hierarchical Decoupling: By separating centerline and radius generation, the model captures the stochastic variability of radial profiles for a given topology, improving anatomical realism.
3. Simulation-Ready Output: The use of NURBS ensures that generated geometries are watertight, smooth, and directly usable in CFD solvers, eliminating the need for manual mesh repair.
4. Zero-Shot Controllability: The integration of DPS enables interactive, semi-automatic segmentation and editing based on sparse inputs (points, contours, patches) without retraining the model.
5. Differentiable Pipeline: The framework is fully differentiable, enabling gradient-based optimization for tasks like surgical implant design and hemodynamic tuning.

4. Results

The model was trained on 21 patient-specific MRA cases (including healthy, aneurysm, and congenital heart disease cases) and evaluated on unseen test cases.

• Unconditional Generation:

  • Successfully synthesized diverse, anatomically plausible multi-branch aortas (including LSA, LCCA, RSA, RCCA).
  • Generated biomarker distributions (e.g., length, tortuosity, radius variation) closely matched the source cohort, outperforming PCA-based baselines which often produced non-physical shapes.
  • The generated geometries were directly meshed and used in CFD simulations, yielding valid velocity and pressure fields.

• Conditional Generation (Semi-Automatic Segmentation):

  • Point Prompts: Generating centerlines from sparse 3D points reduced the Chamfer distance to ground truth from 1.71 (unconditional) to 0.33 (with 5 points).
  • Contour Prompts: Reconstructing surfaces from 2D slice contours reduced uncertainty significantly. With 4 contours, the mean Chamfer distance dropped to 0.26 with a standard deviation of 0.052.
  • Robustness: The model successfully reconstructed high-quality surfaces from low-resolution CT scans and generalized to an unseen rabbit CT dataset despite being trained only on human data.

• Comparison with Baselines:

  • Compared against PCA + Gaussian and PCA + Gaussian (Decoupled), HUG-VAS produced samples with higher anatomical fidelity and multimodal distribution characteristics, avoiding the "blurry" or non-physical outputs common in linear PCA methods.

5. Significance and Future Impact

• Clinical Workflow Integration: HUG-VAS offers a practical path from limited clinical imaging data (sparse points or partial scans) to high-fidelity, simulation-ready vascular models, significantly reducing the time and expertise required for segmentation.
• Personalized Medicine: The ability to generate diverse synthetic cohorts supports the training of machine learning surrogates and the design of patient-specific medical devices.
• Optimization: The differentiable nature of the framework opens new avenues for inverse design, such as optimizing stent grafts or surgical implants to achieve specific hemodynamic goals (e.g., minimizing wall shear stress).
• Scalability: While currently focused on the thoracic aorta with fixed topology, the framework's principles (NURBS + Hierarchical Diffusion) provide a robust foundation for extending to more complex, variable vascular trees in the future.

In summary, HUG-VAS represents a significant advancement in medical image analysis by combining the geometric precision of CAD (NURBS) with the generative power of modern AI (Diffusion Models), solving critical bottlenecks in realism, editability, and CFD compatibility.