Synthetic Vascular Model for Aneurysm Detection

• The paper presents a synthetic vascular model that integrates controlled geometric vessel modeling, aneurysm embedding, and statistical noise simulation to generate realistic 3D MRA-like imaging volumes.
• The methodology utilizes 3D spline interpolation and U-Net architectures with combo loss functions, where synthetic patches boost lesion sensitivity and improve small aneurysm detection.
• The research underscores the clinical impact by providing scalable data augmentation for robust deep learning training, ultimately enhancing non-invasive aneurysm risk stratification.

A synthetic vascular model for aneurysm detection is a computational construct that emulates key anatomical, hemodynamic, and imaging properties of the human cerebrovascular system—including vessels, bifurcations, and aneurysmal sacs—with the specific intent of enabling the development, validation, and augmentation of detection algorithms, particularly deep learning (DL) or computational fluid dynamics (CFD)-based methods. Recent research has demonstrated that such models can be constructed using controlled geometric deformations, physiologically inspired noise modeling, advanced generative architectures, and domain-informed constraints to provide high-fidelity, dataset-scale examples for training and assessment.

1. Synthetic Vascular Model Construction: Geometry, Bifurcations, and Aneurysm Embedding

The construction of a synthetic vascular model commences with precise geometric modeling of the cerebral arterial tree, especially the Circle of Willis (CoW), which is the predominant location for intracranial aneurysms (Nader et al., 4 Nov 2024, Nader et al., 27 Mar 2024). The methodology typically involves:

• Arterial graph and centerline extraction: Centerlines are obtained from segmented clinical images or prior templates, forming a graph structure encoding vessel topology (nodes at bifurcations).
• 3D spline interpolation: Centerlines are fit using 3D spline functions, where control points (knots) and B-spline coefficients are tuned to adjust vessel tortuosity and maintain anatomical plausibility. Only spline coefficients are variably altered, preserving endpoints associated with bifurcation anatomy.
• Vessel "thickening": For each branch, the extracted diameter is used to perform a convolution operation (often kernel-based) that utilizes slightly deformed spherical (not idealized circular) cross-sectional kernels, yielding realistic non-tubular, anatomically variable vessel appearances.

Aneurysm embedding is performed with a parameterized approach. A 3D aneurysm shape (initially a sphere) undergoes elastically constrained deformation. Its placement at bifurcations is governed by geometric relationships: $$D = r \times \gamma + \sqrt{\left(\frac{R}{\tan(\Theta/2)}\right)^2 + R^2}$$ where $r$ is aneurysm radius, $R$ is average parent vessel radius, $\Theta$ is branch angle, and $\gamma$ is a growth/development parameter. This formula allows precise control over anatomical positioning and simulation of aneurysm growth stages.

Background and noise modeling for imaging realism includes the generation of high-frequency Gaussian noise filtered by a Gaussian kernel, with variance propagation derived analytically (see below). The process targets the statistical properties (standard deviation, frequency) empirically measured in real MRA-TOF volumes: $$\sigma_f \approx \frac{\sigma_0}{2 \sigma_G \sqrt{\pi}}$$ Here, $\sigma_0$ is the standard deviation of initial noise, $\sigma_G$ the filter's standard deviation, and $\sigma_f$ the desired final noise level (Nader et al., 4 Nov 2024, Nader et al., 27 Mar 2024).

This workflow produces synthetic 3D MRA-like volumes with realistic vasculature, bifurcation topologies, and background, suitable for direct downstream neural network training or simulation studies.

2. Deep Neural Network Architectures for Synthetic Data

Modern synthetic vascular models enable data augmentation for 3D convolutional neural networks tailored for aneurysm segmentation and detection.

• Patch-based 3D U-Net architectures: Networks ingest 3D patches ($64\times64\times64$ voxels) centered on bifurcations. The encoder path consists of stacked 3D convolutions, ReLU activations, batch normalization, and aggressive max pooling. The decoder employs upsampling and skip connections for resolution recovery (Nader et al., 4 Nov 2024, Nader et al., 27 Mar 2024).
• Combo loss functions: Multi-objective training employs a weighted sum of Dice and cross-entropy losses to robustly optimize both overlap (segmentation fidelity) and pixel/voxel-level accuracy.
• Data mixture: The best performance gains are observed when jointly training on real and synthetic data patches. For example, augmentation with 998 synthetic patches raised lesion-level sensitivity from ~75.6% to ~89%, markedly improving detection of small aneurysms (≤2 mm radius) from ~51% to ~76% (Nader et al., 4 Nov 2024).
• Elastic deformations and randomization: Synthetic patches expose models to a broad spectrum of anatomical and pathologic variation, which cannot be easily captured with classical augmentation schemes.

3. Imaging Modality Emulation and Statistical Noise Modeling

Synthetic vascular models specifically target the emulation of Magnetic Resonance Angiography—Time of Flight (MRA-TOF) imaging for several reasons:

• TOF principles: Flowing blood appears as heightened intensity due to unsaturated spins, providing excellent vessel-to-tissue contrast without contrast agents or radiation (Nader et al., 27 Mar 2024, Nader et al., 4 Nov 2024).
• Imaging realism: Accurate modeling of vessel signal, partial voluming, and anisotropic background noise ensures that synthetic images exhibit statistical properties matched to real scans, a necessity for transferability of learned neural representations.

The statistical fidelity of noise is maintained through the analytical variance formula extracted from convolution with a Gaussian filter, as above, and the background label set is modeled via threshold-based segmentation reflecting gray and white brain matter distributions.

4. Data Augmentation, Evaluation, and Performance Gains

Augmenting real datasets with synthetic vascular patches improves the performance and robustness of aneurysm detection systems:

Method	Lesion-level Sensitivity	Small Aneurysm Sensitivity	False Positive Rate
Real data only	~75.6%	~51%	0.22/patient
Synthetic augmentation (proposed model)	~89%	~76%	0.40/patient
Geometric augmentation	Lower than synthetic	Lower than synthetic	N/A

Data trace: (Nader et al., 4 Nov 2024, Nader et al., 27 Mar 2024)

While there is a moderate increase in FPs with synthetic augmentation, the reduction in missed aneurysms (especially small lesions) outweighs this drawback. Synthetic data is especially valuable where real examples are rare or annotation is costly.

5. Anatomical and Clinical Context: Circle of Willis and Aneurysm Distribution

The Circle of Willis (CoW) is the anatomical locus of highest aneurysm prevalence. Synthetic vascular models ensure high-fidelity emulation of CoW bifurcations and vessel-to-vessel transitions:

• Bifurcation variability: Geometric and spline-based parameterizations enable the generation of arterial configurations found in the CoW, covering key branches and anatomical labels (A–O in schematic representations).
• Clinical risk localization: By focusing on realistic CoW representations and varying geometric parameters (e.g., bifurcation angle, vessel diameter), models can reproduce patient-specific risk landscapes and regional aneurysm incidence statistics (Nader et al., 4 Nov 2024).

6. Methodological Limitations and Future Directions

Despite progress, several challenges persist in synthetic vascular modeling for aneurysm detection:

• Anatomical fidelity: Perfectly modeling micro-variability in vessel wall texture and geometry, as well as plausibly capturing arterial/aneurysmal interface features, remains difficult; excessive deformation can result in unrealistic topology (e.g., disconnected branches).
• Noise model adequacy: Simulated background noise may not capture local spatial correlation structures or rare image artifacts found in-particular acquisition protocols.
• Dataset balance: Purely synthetic datasets tend to increase FP rates, suggesting a mixture with real clinical data is optimal (Nader et al., 4 Nov 2024).
• Realism of aneurysm shapes: Spherical base shapes, even when deformed, may not fully reflect the morphological spectrum observed in large clinical datasets.

Future work is expected to pursue more granular vessel wall modeling, multi-physics data fusion (combining synthetic imaging with CFD-derived hemodynamics), and integration of domain priors—such as those derived from automated anatomy-based post-processing or advanced anatomical atlases—to enhance the interpretability and clinical applicability of synthetic vascular data.

7. Implications for Detection, Clinical Practice, and Dataset Generation

Synthetic vascular models, when well-constructed, play a critical role in:

• Training DL models for rare events: Providing scale and diversity beyond what is feasible with clinical data alone, reducing annotation bottlenecks.
• Robustness to anatomical variation: Exposing classifiers to anatomical diversity ensures improved generalizability to novel patient populations and scanner protocols.
• Non-invasive risk stratification: High-resolution, parametric synthetic data enables in silico experiments to relate geometry and flow to aneurysm risk, potentially informing new biomarkers.
• Transfer to real data: Proper noise and shape modeling is essential for the transferability of detection algorithms trained on synthetic data to clinical scenarios.

The integration of synthetic modeling with post-processing schemes that exploit anatomical priors (e.g., artery–vein masks, brain/skull segmentation (Kim et al., 1 Jul 2025)) increases interpretability and further enhances specificity by reducing false positive rates, supporting eventual clinical acceptance.

---

References:

(Nader et al., 27 Mar 2024): "A vascular synthetic model for improved aneurysm segmentation and detection via Deep Neural Networks" (Nader et al., 4 Nov 2024): "Building a Synthetic Vascular Model: Evaluation in an Intracranial Aneurysms Detection Scenario" (Kim et al., 1 Jul 2025): "Automated anatomy-based post-processing reduces false positives and improved interpretability of deep learning intracranial aneurysm detection"