Data-driven bifurcation handling in physics-based reduced-order vascular hemodynamic models

Three-dimensional (3D) computational fluid dynamics simulations of cardiovascular flows provide high-fidelity hemodynamic predictions to support cardiovascular medicine, but require substantial computational resources, limiting their clinical applicability. Reduced-order models (ROMs) offer computationally efficient alternatives but suffer from significant accuracy losses, particularly at vessel bifurcations where complex flow physics are inadequately captured by standard Poiseuille flow assumptions. This work presents an enhanced numerical framework that integrates machine learning-predicted bifurcation coefficients into 0D hemodynamic solvers to improve accuracy while maintaining computational efficiency.

We develop a resistor-resistor-inductor (RRI) model that uses neural networks to predict pressure-flow relationships from bifurcation geometry, incorporating both linear and quadratic resistance terms along with inductive effects. The method employs physics-based non-dimensionalization to reduce training data requirements and includes flow split prediction for improved geometric characterization. We incorporate the RRI model into a zero-dimensional (0D) cardiovascular flow model using an optimization-based solution strategy. We validate the approach in isolated bifurcations and vascular trees containing up to 40 junctions across Reynolds numbers ranging from 0 to 5500, defining ROM accuracy by comparison to high-fidelity 3D finite element simulation results.

Results demonstrate substantial accuracy improvements: averaged across all trees and all Reynolds numbers, the RRI method reduces inlet pressure errors from 54 mmHg (45%) for standard 0D models to 25 mmHg (17%), while a simplified resistor-inductor (RI) variant achieves 31 mmHg (26%) error. The enhanced 0D models show particular effectiveness at high Reynolds numbers and in extensive vascular networks.

This hybrid numerical approach enables accurate, real-time hemodynamic modeling suitable for clinical decision support, uncertainty quantification, and digital twin applications in cardiovascular biomedical engineering.