# Data-Driven Bifurcation Handling in Physics-Based Reduced-Order Vascular Hemodynamic Models

## TL;DR

This paper introduces a machine learning-enhanced reduced-order model for cardiovascular flow simulations that significantly improves accuracy at vessel bifurcations while maintaining computational efficiency, enabling real-time clinical applications.

## Contribution

The authors develop a novel hybrid 0D model integrating neural network-predicted bifurcation coefficients, improving accuracy over standard models in vascular hemodynamics simulations.

## Key findings

- Reduces pressure error from 45% to 17% in vascular models.
- Improves accuracy especially at high Reynolds numbers.
- Maintains computational efficiency suitable for real-time applications.

## Abstract

Three-dimensional (3D) finite-element simulations of cardiovascular flows provide high-fidelity predictions to support cardiovascular medicine, but their high computational cost limits clinical practicality. Reduced-order models (ROMs) offer computationally efficient alternatives but suffer reduced accuracy, particularly at vessel bifurcations where complex flow physics are inadequately captured by standard Poiseuille flow assumptions. We present an enhanced numerical framework that integrates machine learning-predicted bifurcation coefficients into zero-dimensional (0D) hemodynamic ROMs 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 linear and quadratic resistances along with inductive effects. The method employs non-dimensionalization to reduce training data requirements and apriori flow split prediction for improved bifurcation characterization. We incorporate the RRI model into a 0D model using an optimization-based solution strategy. We validate the approach in isolated bifurcations and vascular trees, across Reynolds numbers from 0 to 5,500, defining ROM accuracy by comparison to 3D finite element simulation. Results demonstrate substantial accuracy improvements: averaged across all trees and 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 for clinical decision support, uncertainty quantification, and digital twins in cardiovascular biomedical engineering.