CARS: a centerline-anchored attention surrogate for coronary blood flow on skeleton-generated lumen geometries
Abstract
When the parameter of a PDE surrogate is the flow domain itself, the key/value set of an attention model must encode that domain. We present CARS (Coronary Artery Rapid Surrogate), a learned surrogate for the finite-volume solution map of the steady incompressible Navier-Stokes equations on coronary lumens built from image-derived centerlines. CARS maps a centerline with per-point lumen radius and a scalar inlet flow rate to pressure and velocity at arbitrary query points. The attention focal set is the case's own centerline, so geometry fusion costs O(N nf) rather than O(N2) in the number of evaluation points. Trained per territory on 2,700 OpenFOAM solutions with synthetic focal lesions, CARS reaches relative ℓ2 errors of $0.120/0.149$ (pressure/velocity) on left-coronary and $0.063/0.119$ on right-coronary test sets, in $87$~ms per case against a solver wall-clock of $572−1{,}063$~s. It outperforms four parameter-matched neural operators, and accuracy saturates eightfold below the operating focal count. Fractional flow reserve derived from the predicted pressure matches the CFD label at Pearson r = 0.941/0.993 and reproduces the FFR≤ 0.8 decision in 97.7%/96.3% of held-out cases. The predicted velocity does not satisfy continuity closely enough for derived quantities, and the weights are territory-specific.
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BibTeX
@misc{bafghi2026cars,
title = {{CARS: a centerline-anchored attention surrogate for coronary blood flow on skeleton-generated lumen geometries}},
author = {Reza Akbarian Bafghi and Sukirt Thakur and Maziar Raissi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30498},
eprint = {2610.30498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30498},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - CARS: a centerline-anchored attention surrogate for coronary blood flow on skeleton-generated lumen geometries
AU - Reza Akbarian Bafghi
AU - Sukirt Thakur
AU - Maziar Raissi
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30498
UR - https://arxiv.org/abs/2610.30498
AB - When the parameter of a PDE surrogate is the flow domain itself, the key/value set of an attention model must encode that domain. We present CARS (Coronary Artery Rapid Surrogate), a learned surrogate for the finite-volume solution map of the steady incompressible Navier-Stokes equations on coronary lumens built from image-derived centerlines. CARS maps a centerline with per-point lumen radius and a scalar inlet flow rate to pressure and velocity at arbitrary query points. The attention focal set is the case's own centerline, so geometry fusion costs O(N n_f) rather than O(N^2) in the number of evaluation points. Trained per territory on 2,700 OpenFOAM solutions with synthetic focal lesions, CARS reaches relative ℓ_2 errors of $0.120/0.149$ (pressure/velocity) on left-coronary and $0.063/0.119$ on right-coronary test sets, in $87$~ms per case against a solver wall-clock of $572−1{,}063$~s. It outperforms four parameter-matched neural operators, and accuracy saturates eightfold below the operating focal count. Fractional flow reserve derived from the predicted pressure matches the CFD label at Pearson r = 0.941/0.993 and reproduces the FFR≤ 0.8 decision in 97.7%/96.3% of held-out cases. The predicted velocity does not satisfy continuity closely enough for derived quantities, and the weights are territory-specific.
ER -