# End-to-End Autonomous Recursive Arborescence Deformable Flow and Non-Linear Hemodynamics for Patient-Specific Coronary Centerline Extraction

arXiv: https://arxiv.org/abs/2610.05900 · HTML: https://mlsanity.com/paper/2610.05900/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 14 of 14)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [3D MRI brain tumor segmentation using autoencoder regularization](https://mlsanity.com/paper/1810.11654/) (2018)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Generative Modeling via Drifting](https://mlsanity.com/paper/2602.04770/) (2026)
- [Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation](https://mlsanity.com/paper/2307.08388/) (2023)
- [DeformCL: Learning Deformable Centerline Representation for Vessel Extraction in 3D Medical Image](https://mlsanity.com/paper/2506.05820/) (2025)
- [A topology-preserving three-stage framework for fully-connected coronary artery extraction](https://mlsanity.com/paper/2504.01597/) (2025)
- [RefTr: Recurrent Refinement of Confluent Trajectories for 3D Vascular Tree Centerlines](https://mlsanity.com/paper/2511.20823/) (2025)
- [VesselTok: Tokenizing Vessel-like 3D Biomedical Graph Representations for Reconstruction and Generation](https://mlsanity.com/paper/2603.18797/) (2026)
- [Dynamic Snake Upsampling Operater and Boundary-Skeleton Weighted Loss for Tubular Structure Segmentation](https://mlsanity.com/paper/2505.08525/) (2025)
- [Same Branches, Different Trees: A Bifurcation Connectedness Metric for Coronary Artery Segmentation and FFR-CT Decision Agreement](https://mlsanity.com/paper/2607.28327/) (2026)
- [ImageCAS-X: a dataset and benchmark for coronary artery segmentation and centerline extraction in coronary CT angiography](https://mlsanity.com/paper/2608.30404/) (2026)

## Abstract (arXiv)

Extracting patient-specific vascular trees from volumetric medical images is fundamental to computational angiography and non-invasive hemodynamic assessment. Conventional voxel segmentation models often sever delicate bifurcations, while heuristic Euclidean Minimum Spanning Trees introduce non-anatomical shortcuts. Moreover, linear Poiseuille flow neglects quadratic kinetic dissipation across arterial narrowings, underestimating ischemia. We formulate an end-to-end framework decoupling continuous geometric arborescence generation from non-linear hemodynamics. First, an autonomous 3D Ostium Landmark Localization Head with dual-sinus query channels and spherical-gated refinement eliminates centerline seeding dependency, achieving cohort mean localization error of 7.63 mm (7.43 mm LCA, 7.83 mm RCA; 71.4% <= 8.0 mm) from raw contrast context. Second, a Spatially-Grounded Deformable Step Flow Architecture queries continuous 3D feature pyramids via trilinear sampling, sequentially generating trajectories with anchor boundary enforcement (X(0) = P_start). Third, a Top-Down Recursive Arborescence State Machine detects bifurcation peaks via Tree-NMS and parameterizes predecessor parent pointers (p_k < k), guaranteeing single connected acyclic tree topology (beta_0 = 1, beta_1 = 0) with differentiable step termination. Fourth, an iterative Picard non-linear Kirchhoff solver with Young-Tsai / Gould quadratic dissipation enforces machine-precision mass conservation (residual 5.82e-11 mL/s). Across 14 development patients under standardized in-silico stenosis stress testing (Q_0 = 4.0 mL/s), linear Poiseuille flow misclassifies 75% diameter lesions as non-ischemic (FFR > 0.80) in 14/14 cases, whereas our non-linear solver captures functional ischemia (FFR = 0.5864, lesion disparity 32.89 mmHg, p = 6.10e-5) with 3.66x collateral shunting. Test set firewall isolation was maintained.