A Physics-Informed Neural Network Surrogate for Patient-Specific Hepatic Arterial Hemodynamics in Yttrium-90 Radioembolization: Network Architecture, Boundary-Condition Enforcement, and Data Efficiency

Trans-arterial radioembolization using yttrium-90 (Y-90) microspheres treats unresectable liver cancer with radiation. The tumor-to-parenchyma dose ratio is mainly governed by the patient-specific hepatic arterial flow distribution, which transports the microspheres. Even though computational fluid dynamics (CFD) simulation can predict this flow distribution, its high computational cost and time limit intraprocedural application. To overcome this computational limitation, a physics-informed neural network (PINN) surrogate was developed to provide rapid predictions of flow distribution in a patient-specific hepatic artery model. The surrogate maps spatial coordinates to the velocity vector U with Cartesian components u, v, w and the static pressure p. Reference velocity and pressure fields came from a converged finite-element CFD solve of the same geometry at about 1.05 x 105 nodes; a controlled fraction was used to supervise the training while the remainder was held out for validation. Using the NVIDIA PhysicsNeMo framework, we compared four coordinate networks (MLP, Modified Fourier, Multi-Scale Fourier and SIREN) under soft and hard inlet enforcement across a supervised data sweep (data fraction df = 0 to 0.20) and repeated df = 0.20 at a matched 300,000-step budget. Predicted flow splits were propagated through an established Y-90 dose-kernel pipeline. Accuracy is governed primarily by the supervised-data fraction, not the architecture: at df [≥] 0.10 the backbones agree to within one to two R2 points, and R2(u) rises from {approx} 0 under pure physics (df = 0) to {approx} 0.95 by df = 0.01 for the best backbones, saturating near 0.97 to 0.99 by df = 0.20. At a matched 300,000-step budget the Multi-Scale Fourier network leads (R2(u) = 0.978) ahead of SIREN (R2(u) = 0.976) and the MLP (R2(u) = 0.968); the best value seen (R2(u) = 0.985, Modified Fourier) needed 1.8 times that budget. On the df = 0.20 checkpoint the per-outlet flow split matches CFD (r = 0.999, L1 = 4.4 percentage points) and the derived dosimetry agrees to within 2.4% for perfused volume, mean dose and every isodose volume. At df = 0 training collapses toward the trivial near-zero state, which satisfies continuity, momentum and the zero-pressure outlets exactly and is ruled out only by the inlet and data terms; this, not architecture choice, is the limiting failure mode. Once trained, the network evaluates the full 105,284-node field in about 2 s on a four-core CPU. The supervised-data fraction, with a practical floor between df = 0.05 and 0.10, is the primary design lever for such hepatic-arterial PINN surrogates.