Geometry-Aware Abdominal Aortic Aneurysm Digital Twin for Patient-Specific Wall Stress Mapping

Technical Summary: Geometry-Aware Abdominal Aortic Aneurysm Digital Twin for Patient-Specific Wall Stress Mapping

Problem Statement
Accurate estimation of wall stress distributions in Abdominal Aortic Aneurysms (AAAs) is essential for improving rupture risk prediction beyond traditional maximum diameter criteria. While high-fidelity Finite Element Analysis (FEA) provides precise patient-specific stress estimates, its reliance on laborious preprocessing (segmentation, mesh generation, material assumptions) and substantial computational time limits its utility in real-time clinical decision-making. Furthermore, uncertainties in material properties and boundary conditions can propagate to stress predictions, complicating clinical translation. The authors propose a data-driven alternative to bridge the gap between image-derived anatomy and biomechanical stress endpoints, aiming to create a "geometry-aware digital twin" that enables rapid, patient-specific wall stress mapping.

Methodology
The study introduces a pipeline that converts Computed Tomography Angiography (CTA) images into standardized graph representations to predict wall stress using Deep Learning.

1. Data Acquisition and Preprocessing:

   • Cohort: Retrospective CTA data from 202 AAA patients across three clinical centers.
   • Segmentation: An in-house U-Net pipeline, refined by experts, generated binary masks for the outer wall, inner wall, lumen, and intraluminal thrombus (ILT).
   • Standardization: Outer wall surfaces were remeshed to a uniform target of approximately 150,000 nodes to ensure comparable graph statistics and consistent batching.
   • Ground Truth Generation: Patient-specific FEA simulations were performed in Abaqus using a Mooney–Rivlin hyperelastic material model for the wall and ILT. First principal wall stresses were computed and projected back onto the standardized outer wall surface to serve as ground truth labels.

2. Feature Engineering:
   Node-specific geometric and biomechanical descriptors were calculated for each vertex on the surface mesh, including:

   • Thicknesses: Wall thickness (WallTHK) and ILT thickness (ILTTHK).
   • Curvatures: Principal curvatures ($k_1, k_2$), Gaussian curvature ($K$), and mean curvature ($M$).
   • Geometry: Distance to the lumen centerline ($r_L$), normalized local diameter (NORD), and the ILT-to-wall thickness ratio ($\rho_{ILT}$).
   • Biomechanics: A surrogate for wall strength ($\sigma_{ult}$) derived from a regression model incorporating local thrombus burden, diameter, family history, and sex.
   • Local Context: Features were augmented with statistics (mean, std, max, delta) computed from the six nearest neighbors (kNN-6) to capture local interactions.
   • Global Attributes: Graph-level attributes (e.g., maximum diameter, sex, ILT class) were broadcast to nodes.

3. Graph-Based Surrogate Models:
   The AAA surface was treated as a graph $G=(V, E)$ where nodes represent mesh vertices and edges represent mesh connectivity. Three distinct Graph Neural Network (GNN) architectures were benchmarked:

   • Gated Graph Convolutional Network (GGCN): A residual architecture using gated message passing (inspired by Gated Graph Sequence Neural Networks) to propagate information along the mesh. It utilizes GRU-style updates to regulate information integration, stabilizing optimization on large, irregular graphs.
   • Equivariant Graph Neural Network (EGNN): Explicitly encodes Euclidean symmetries (invariance to translation and rotation) by updating node features and coordinates simultaneously using distance-based messages. This reduces reliance on arbitrary coordinate frames.
   • Graph Transformer (GT): Replaces standard message passing with multi-head self-attention conditioned on graph structure and geometry. It utilizes relative and positional encodings to model long-range, biomechanically coupled interactions (e.g., sac-to-neck) and handle anisotropic stress patterns.

4. Training Strategy:

   • Objective: The models were trained to predict the full node-specific wall stress field.
   • Loss Function: A composite, tail-aware loss function was employed, combining:
     • Stress-weighted Mean Squared Error (MSE) to up-weight high-stress nodes.
     • Penalties on the discrepancy of global summaries: Mean Wall Stress ($\bar{\sigma}$) and the 99th percentile Wall Stress ($\sigma_{99}$).
     • A pinball (quantile) loss term to specifically emphasize the high-stress tail.
   • Augmentation: Techniques included stress-stratified node subsampling, geometric data augmentation, and focal-style reweighting of complex cases.

Key Contributions

1. Digital Twin Pipeline: A reproducible workflow converting CTA images into standardized graph representations with node-specific geometric and biomechanical descriptors.
2. Systematic Benchmark: A comparative evaluation of GGCN, EGNN, and GT architectures for estimating $\bar{\sigma}$, $\sigma_{99}$, and full-field wall stress in a multi-institution AAA cohort.
3. Tail-Aware Training: Implementation of training and readout strategies designed to enhance sensitivity to clinically critical high-stress regions without sacrificing overall accuracy.
4. Comprehensive Evaluation: Reporting of graph-level errors, node-specific accuracy, spatial correlations, and agreement between predicted and ground-truth FEA stress maps.

Results

• Performance: All three GNN architectures achieved high fidelity in reproducing patient-specific FEA wall stress fields.
• Best Model: The Graph Transformer (GT) demonstrated the best overall agreement. It achieved node-specific $R^2 > 0.97$ and graph-level $R^2 > 0.98$.
• Capabilities: The GT model successfully captured spatial stress patterns, preserved biomechanical trends, and enabled near real-time inference.
• Efficiency: The framework reduced per-case inference time from hours (required for a complete FEA simulation) to a few seconds on a single GPU.
• Comparison: While the GGCN and EGNN delivered strong performances, the GT's ability to model global receptive fields and long-range interactions via attention mechanisms provided superior accuracy in reproducing the stress distribution and high-stress tail.

Significance and Claims
The paper posits that framing wall stress estimation as a geometry-aware digital twin enables fast, scalable, and patient-specific wall stress mapping. The authors claim that with further refinement and larger cohorts, this graph-based framework has the potential to strengthen rupture risk assessment and facilitate the integration of routine, patient-specific biomechanical analyses into clinical workflows. The study emphasizes that the goal is not necessarily the perfect reproduction of every nodal value, but rather the adequate reproduction of the general stress distribution and high-stress tail to accurately derive clinically salient global summaries ($\bar{\sigma}$ and $\sigma_{99}$) for individual risk assessment. The framework is presented as a complementary path to traditional FEA, offering a data-driven surrogate that can be applied to other vascular pathologies representable by surface meshes.