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

Zeyu Jia; Xin Ming

cs.CVOct 5, 2026

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

Authors: Zeyu Jia, Xin Ming

Organizations: School of Biomedical Engineering and Technology, Tianjin Medical University, Tianjin 300070, China

Abstract

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.

Figures & tables

Fig. 1 : End-to-End Autonomous Recursive Arborescence Flow and Non-Linear Hemodynamics Framework: (a) 3D Feature Pyramid Backbone querying continuous multi-scale contrast context via trilinear sampling without grid discretization; (b) Autonomous Dual-Sinus Ostium Landmark Detection Head and scale-space cavity gating repelling ventricular divergence; (c) Continuous Spatially-Grounded Deformable Step Flow and Top-Down Recursive Arborescence State Machine guaranteeing single connected acyclic directed tree topology ( $\beta_{0}\equiv 1.0,\beta_{1}\equiv 0.0$ ); (d) Iterative Picard Non-Linear Kirchhoff Solver modeling quadratic inertial dissipation ( $\Delta P=R_{p}Q+R_{t}Q^{2}$ ), capturing functional ischemia under hyperemic flow.

Model Architecture / Evaluated Baseline	Params (M) $\downarrow$	Time (s) $\downarrow$	$\beta_{0}\downarrow$	$\beta_{1}\downarrow$	Dice (%) $\uparrow$	clDice (%) $\uparrow$	HD95 (mm) $\downarrow$	$\text{F1}_{\text{CL}}$ (%) $\uparrow$	$\text{CD}_{\text{CL}}$ (mm) $\downarrow$	Stratified $\text{Rec}_{\text{CL}}$ [Prox / Mid / Dist] (%) $\uparrow$	KCL Res (mL/s) $\downarrow$
nnU-Net (Isensee et al. [ 13 ] )	31.2	8.40	14.50 $\pm$ 5.20	28.00 $\pm$ 12.00	79.80 $\pm$ 3.40	81.50 $\pm$ 3.90	14.20 $\pm$ 4.80	74.20 $\pm$ 3.80	3.82 $\pm$ 0.95	86.4 $\pm$ 3.2 / 72.5 $\pm$ 4.1 / 42.1 $\pm$ 5.8	N/A
SegResNet (Myronenko [ 14 ] )	18.5	6.10	18.20 $\pm$ 6.10	34.00 $\pm$ 15.00	78.40 $\pm$ 3.90	80.20 $\pm$ 4.20	16.80 $\pm$ 5.50	72.80 $\pm$ 4.10	4.15 $\pm$ 1.10	84.2 $\pm$ 3.5 / 70.1 $\pm$ 4.4 / 38.5 $\pm$ 6.2	N/A
CorSegRec (Qiu et al. [ 21 ] )	24.6	12.30	4.80 $\pm$ 2.10	6.00 $\pm$ 4.00	83.20 $\pm$ 2.80	85.60 $\pm$ 2.50	9.80 $\pm$ 3.10	81.50 $\pm$ 2.60	2.45 $\pm$ 0.65	89.5 $\pm$ 2.5 / 80.2 $\pm$ 3.0 / 58.4 $\pm$ 4.5	N/A
DeformCL (Zhao et al. [ 28 ] )	22.8	5.20	2.10 $\pm$ 1.20	0.00 $\pm$ 0.00	84.10 $\pm$ 2.50	86.70 $\pm$ 2.20	7.60 $\pm$ 2.40	83.60 $\pm$ 2.10	2.10 $\pm$ 0.52	90.1 $\pm$ 2.2 / 81.8 $\pm$ 2.6 / 64.0 $\pm$ 3.8	N/A
Baseline 1: Point-Set Oracle ( $k$ -NN + MST)	—	14.50	1.00 $\pm$ 0.00	$3997\pm 842^{\lx@sectionsign}$	N/A	76.40 $\pm$ 4.50	24.50 $\pm$ 6.20	68.20 $\pm$ 4.50	5.20 $\pm$ 1.40	82.5 $\pm$ 4.1 / 69.4 $\pm$ 4.8 / 45.2 $\pm$ 6.5	N/A
Baseline 2: Centerline Trajectory Oracle (GT Centerlines)	—	—	1.00 $\pm$ 0.00	0.00 $\pm$ 0.00	87.50 $\pm$ 1.80	91.20 $\pm$ 1.40	3.39 $\pm$ 0.72	96.50 $\pm$ 1.10	0.65 $\pm$ 0.15	98.5 $\pm$ 0.8 / 96.2 $\pm$ 1.1 / 92.4 $\pm$ 1.5	$4.77\times 10^{-13}$

TABLE I : Volumetric 3D Coronary Arborescence Generation, Centerline Quality, and Anatomical Caliber Stratification on Held-Out Development Cohort (

N=14

Independent Patients: Cases 129–140, 142, 143 on ImageCAS). Evaluated under deterministic forward inference without test-time adaptation. External baselines include state-of-the-art volumetric segmenters (nnU-Net, SegResNet) and topological centerline architectures (CorSegRec [ 21 ] , DeformCL [ 28 ] ). Baseline 1 is Point-Set Oracle (

k

-NN + MST). Baseline 2 is Trajectory Oracle from ground-truth centerlines. Proposed Semi-Autonomous is initialized at ground-truth ostia; Proposed Autonomous utilizes blind 3D ostium localization and scale-space cavity gating. Anatomical Caliber Stratification reports centerline recall across Proximal (

>2.0

mm), Intermediate (

1.0-2.0

mm), and Distal (

<1.0

mm) divisions.

Fig. 2 : High-Resolution Multi-Model 3D Coronary Centerline Comparison across Three Representative Anatomies on ImageCAS (Case 129: LAD/LCx bifurcation; Case 135: tortuous circumflex with acute curvature; Case 140: dominant RCA main trunk). Columns: (a) Ground Truth Reference ( $\beta_{0}\equiv 1.00,\beta_{1}\equiv 0.00$ ); (b) nnU-Net ( $\beta_{0}=14.50\pm 5.20$ , severe distal vessel severance); (c) CorSegRec ( $\beta_{0}=4.80\pm 2.10$ , DPC walk reconnection with persistent stubs); (d) DeformCL ( $\beta_{0}=2.10\pm 1.20$ , deformable tracking with distal truncation); (e) Proposed Autonomous Flow ( $\beta_{0}\equiv 1.00,\beta_{1}\equiv 0.00,\text{F1}_{\text{CL}}=85.20\%$ , complete 5-generation arborescence).

Part A: Progressive Framework Ablation
Module / Configuration	$\beta_{0}\downarrow$	$\beta_{1}\downarrow$	clDice (%) $\uparrow$	$\text{F1}_{\text{CL}}$ (%) $\uparrow$	Time (s) $\downarrow$
(1) Voxel Thinning Baseline	14.50 $\pm$ 5.20	28.00 $\pm$ 12.00	81.50 $\pm$ 3.90	74.20 $\pm$ 3.80	8.40
(2) + Continuous Flow Matching	8.20 $\pm$ 3.10	14.50 $\pm$ 6.20	83.40 $\pm$ 2.60	78.90 $\pm$ 2.70	2.10
(3) + Ostium Cavity Gating	5.40 $\pm$ 2.20	9.20 $\pm$ 4.10	84.90 $\pm$ 2.30	81.70 $\pm$ 2.20	2.40
(4) + Tree State Machine ( $p_{k}<k$ )	1.00 $\pm$ 0.00	0.00 $\pm$ 0.00	85.90 $\pm$ 2.10	84.50 $\pm$ 1.90	2.65
(5) Full Proposed Framework	1.00 $\pm$ 0.00	0.00 $\pm$ 0.00	86.40 $\pm$ 2.20	85.20 $\pm$ 1.90	2.80

TABLE II : Systematic Component Ablation, Fine-Grained Module Profiling, and Hyperparameter Sensitivity Sweeps on ImageCAS (

N=14

Dataset / Method	Post-Proc.	$\beta_{0}$ (Fragments) $\downarrow$	sAPLS $\uparrow$	Murray MRE $\downarrow$
DRIVE ( $N=20$ )
U-Net + Thinning	None	80.75 $\pm$ 15.10	0.4238 $\pm$ 0.1024	0.3714 $\pm$ 0.0450
U-Net + clDice [ 8 ]	None	64.85 $\pm$ 12.77	0.4095 $\pm$ 0.1137	0.3680 $\pm$ 0.0420
VesselTok [ 26 ]	MST	1.00 $\pm$ 0.00	0.8223 $\pm$ 0.1060	1.0180 $\pm$ 0.0331
Continuous Flow (Ours)	MST	1.00 $\pm$ 0.00	0.8295 $\pm$ 0.0842	0.0465 $\pm$ 0.1987
HRF ( $N=30$ )

TABLE III : Cross-Domain 2D Retinal Microvascular Benchmark on DRIVE (

N=20

) and HRF (

N=30

) Demonstrating Continuous Flow Topological Generalization.

Fig. 3 : CPR Luminal Profiling and Non-Linear Hemodynamics: (a) Curved Planar Reformation radial lumen area profiling across eccentric plaques; (b) Non-linear Young-Tsai quadratic dissipation vs linear Poiseuille flow, capturing trans-lesional kinetic drops ( $\Delta P_{\text{disparity}}=32.89$ mmHg, $p=6.10\times 10^{-5}$ ).

Metric / Hemodynamic Property	Healthy (0% Stenosis)	Mild (30% Stenosis)	Moderate (50% Stenosis)	Severe (70% Stenosis)	Severe (75% Stenosis)	Critical (80% Stenosis)
Linear Poiseuille Mean Distal FFR	0.9995 $\pm$ 0.0003	0.9934 $\pm$ 0.0012	0.9812 $\pm$ 0.0035	0.9385 $\pm$ 0.0084	0.9152 $\pm$ 0.0098	0.8156 $\pm$ 0.0182
Non-Linear Young-Tsai Mean Distal FFR	0.9995 $\pm$ 0.0003	0.9654 $\pm$ 0.0041	0.8420 $\pm$ 0.0125	0.6842 $\pm$ 0.0210	0.5864 $\pm$ 0.0245	0.4240 $\pm$ 0.0312
Mean Lesion Disparity $\Delta P_{\text{disparity}}$ (mmHg)	0.0000 $\pm$ 0.0000	2.80 $\pm$ 0.35	13.92 $\pm$ 1.15	25.43 $\pm$ 1.82	32.89 $\pm$ 2.15	39.16 $\pm$ 2.45
Hodges-Lehmann Median Disparity [95% CI] (mmHg)	0.0000 [0.00, 0.00]	2.81 [2.62, 3.01]	13.95 [13.25, 14.65]	25.48 [24.35, 26.55]	32.99 [32.15, 33.71]	39.22 [37.85, 40.50]
Paired Wilcoxon Signed-Rank Test	N/A	$W=0.0,p=6.1\times 10^{-5}$	$W=0.0,p=6.1\times 10^{-5}$	$W=0.0,p=6.1\times 10^{-5}$	$\mathbf{W=0.0,p=6.10\times 10^{-5}}$	$W=0.0,p=6.1\times 10^{-5}$
Linear Flow False-Negative Rate ( $\text{FFR}>0.80$ )	0.0% (0/14)	0.0% (0/14)	0.0% (0/14)	100.0% (14/14)	100.0% (14/14)	71.4% (10/14)

TABLE IV : In-silico physical sensitivity stress testing of non-linear quadratic hemodynamics vs linear Poiseuille flow across 14 development patients under hyperemic flow (

Q_{0}=4.0

mL/s,

P_{\text{aorta}}=100.0

mmHg) across stenosis severities (

0\%

–

80\%

) evaluating convective kinetic losses and functional diagnostic discordance (FFR

\leq 0.80

Pipeline Stage	Params	GFLOPs	Peak VRAM	Latency (s)
3D Ostium Localization Head	1.8 M	8.4	1.2 GB	$0.12\pm 0.02$
Deformable Step Flow Matching	11.6 M	36.2	3.2 GB	$1.85\pm 0.14$
Recursive Tree-NMS State Machine	0.8 M	4.0	1.4 GB	$0.28\pm 0.04$
Picard Non-Linear Kirchhoff Solver	0.0 M	0.0	0.4 GB	$0.55\pm 0.08$
Full Autonomous Pipeline	14.2 M	48.6	3.2 GB	2.80 $\pm$ 0.22

TABLE V : Computational complexity and hardware profiling across pipeline stages on NVIDIA RTX 4080 Laptop GPU.

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