Mesh-Free Blood Flow Simulation for Liver Cancer Therapy Using Physics-Informed Neural Networks
Abstract
Purpose
To develop and validate a Physics-Informed Neural Network (PINN) framework for simulating blood flow in hepatic arteries, serving as a proof-of-concept for modeling Y-90 microsphere distribution for liver cancer radioembolization. This study aims to demonstrate that PINNs can accurately solve traditional computational fluid dynamics (CFD) Navier-Stokes equations without finite element meshing, establishing a workflow that will ultimately accommodate real 3D patient geometries reconstructed from contrast-enhanced CT (CECT) images.
Methods
A deep neural network was constructed to solve the steady, incompressible Navier-Stokes equations for blood flowing in a two-dimensional bifurcating channel. The network takes spatial coordinates as inputs to predict velocity components and pressure. The training process minimizes a composite loss function comprising the residuals of the momentum and continuity equations, along with boundary conditions (parabolic inlet profile, no-slip walls, and zero-pressure outlets). A reference solution generated using COMSOL Multiphysics was used to validate the PINN’s accuracy.
Results
The PINN successfully reconstructed the velocity and pressure fields throughout the bifurcation, demonstrating excellent agreement with the reference CFD. Quantitative analysis yielded a Mean Absolute Error (MAE) of approximately 3.8 mm/s for the streamwise velocity and 2.5 mm/s for the transverse velocity (corresponding to a ~0.6% error). The pressure field was recovered with an MAE of approximately 1.11 Pa (~0.3% error). Visual comparisons confirmed that the model accurately captured the flow physics across the entire domain.
Conclusion
PINNs provide a robust, mesh-free alternative to traditional numerical solvers for hemodynamic simulations and can drastically reduce computational time while maintaining high accuracy. By eliminating the preprocessing burden of mesh generation, this method holds significant potential for clinical radioembolization treatment planning. Future work will extend this framework to 3D patient-specific models derived from CECT that will be incorporated in a digital twin for personalized dosimetry and treatment planning for liver cancer.