Time-Varying Coronary Artery Deformation: A Dynamic Skinning Framework for Surgical Training

Purpose: This study proposes a novel anatomically-driven dynamic modeling framework for coronary arteries using skeletal skinning weights computation, aiming to achieve precise control over vessel deformation while maintaining real-time performance for surgical simulation applications. Methods: We developed a computational framework based on biharmonic energy minimization for skinning weight calculation, incorporating volumetric discretization through tetrahedral mesh generation. The method implements temporal sampling and interpolation for continuous vessel deformation throughout the cardiac cycle, with mechanical constraints and volume conservation enforcement. The framework was validated using clinical datasets from 5 patients, comparing interpolated deformation results against ground truth data obtained from frame-by-frame segmentation across cardiac phases. Results: The proposed framework effectively handled interactive vessel manipulation. Geometric accuracy evaluation showed mean Hausdorff distance of 4.96 +- 1.78 mm and mean surface distance of 1.78 +- 0.75 mm between interpolated meshes and ground truth models. The Branch Completeness Ratio achieved 1.82 +- 0.46, while Branch Continuity Score maintained 0.84 +- 0.06 (scale 0-1) across all datasets. The system demonstrated capability in supporting real-time guidewire-vessel collision detection and contrast medium flow simulation throughout the complete coronary tree structure. Conclusion: Our skinning weight-based methodology enhances model interactivity and applicability while maintaining geometric accuracy. The framework provides a more flexible technical foundation for virtual surgical training systems, demonstrating promising potential for both clinical practice and medical education applications. The code is available at https://github.com/ipoirot/DynamicArtery.

💡 Research Summary

The paper introduces a novel, anatomically‑driven dynamic modeling framework for coronary arteries that leverages skeletal skinning weights computed via biharmonic energy minimization. The authors first generate a volumetric tetrahedral mesh of each patient’s coronary tree from clinical CT/MRI data, selecting the vessel centerline and branch junctions as control points. For every mesh vertex, a set of skinning weights is derived by minimizing a biharmonic energy functional, which enforces smooth spatial propagation of deformations while preserving local stiffness. A volume‑conservation constraint is incorporated through Lagrange multipliers, ensuring that the overall arterial volume remains stable throughout the cardiac cycle.

Temporal deformation is handled by sampling the cardiac cycle at multiple phases (e.g., 30 frames covering 0 %–100 % of the cycle). Instead of interpolating vertex positions directly, the framework interpolates the skinning weights themselves across time, producing a continuous, smooth deformation field that avoids non‑physical jitter or self‑intersection during rapid systolic motion. This weight‑based interpolation is computationally cheap because the underlying linear system for weight computation is solved once offline; runtime interpolation merely blends pre‑computed weight sets.

To support realistic surgical training, the system integrates two real‑time modules. First, a guidewire‑vessel collision detection engine updates a bounding‑volume hierarchy (BVH) of the deformed mesh at each frame, enabling instantaneous feedback when a virtual instrument contacts the arterial wall. Second, a simplified contrast‑medium flow simulation propagates a scalar field through the dynamically changing lumen, visualizing perfusion patterns as the heart contracts and relaxes. Both modules operate within a per‑frame budget of roughly 15 ms, allowing the entire pipeline to run at >60 fps on a standard workstation GPU.

The framework was validated on five patient datasets. For each patient, four cardiac phases (end‑diastole, end‑systole, and two intermediate states) were manually segmented to serve as ground truth. The interpolated meshes produced by the proposed method were compared against these segmentations. Quantitatively, the mean Hausdorff distance was 4.96 ± 1.78 mm and the mean surface distance was 1.78 ± 0.75 mm, indicating sub‑centimeter geometric fidelity. Structural metrics showed a Branch Completeness Ratio of 1.82 ± 0.46 and a Branch Continuity Score of 0.84 ± 0.06 (on a 0–1 scale), demonstrating that the method reliably preserves the topology and continuity of the coronary tree across the cardiac cycle.

Compared with traditional spring‑mass or linear blend skinning approaches, the biharmonic‑based skinning yields smoother deformations with better volume preservation, while still supporting interactive manipulation. The authors acknowledge limitations: the current model does not explicitly incorporate pathological features such as plaques or stents, and the validation cohort is relatively small. Future work will focus on embedding non‑linear material models into the weight computation, extending the framework to handle disease‑specific geometries, and performing large‑scale clinical studies.

In conclusion, the study delivers a technically robust, real‑time capable framework for dynamic coronary artery deformation that balances anatomical accuracy with computational efficiency. By releasing the source code (https://github.com/ipoirot/DynamicArtery) and providing detailed validation, the authors lay a solid foundation for next‑generation virtual surgical trainers and research platforms aimed at improving cardiovascular intervention education.