A Review of Equation-Based and Data-Driven Reduced Order Models featuring a Hybrid cardiovascular application

TL;DR

This work addresses the need for fast yet accurate simulations of patient-specific cardiovascular flows. It proposes a hybrid reduced-order modeling approach that combines POD-Galerkin projection with data-driven neural network components, using lifting functions to handle non-homogeneous boundary conditions and a Windkessel model to supply outlet pressures. The reduced framework yields a low-dimensional dynamical system for velocity and pressure, with a neural network predicting time-varying outflow pressures to enable online evaluation beyond stored data. The approach achieves substantial speedups (up to $O(10^5)$) while preserving accuracy in velocity and pressure fields on a 3D patient-specific aortic arch, and offers clear avenues for extension to multiparametric and clinically calibrated settings.

Abstract

Cardiovascular diseases are a leading cause of death in the world, driving the development of patient-specific and benchmark models for blood flow analysis. This chapter provides a theoretical overview of the main categories of Reduced Order Models (ROMs), focusing on both projection-based and data-driven approaches within a classical setup. We then present a hybrid ROM tailored for simulating blood flow in a patient-specific aortic geometry. The proposed methodology integrates projection-based techniques with neural network-enhanced data-driven components, incorporating a lifting function strategy to enforce physiologically realistic outflow pressure conditions. This hybrid methodology enables a substantial reduction in computational cost while mantaining high fidelity in reconstructing both velocity and pressure fields. We compare the full- and reduced-order solutions in details and critically assess the advantages and limitations of ROMs in patient-specific cardiovascular modeling.

Figures (9)

• Figure 1: Time evolution of the boundary condition for the velocity $\bm u_D(t)$ (a) and sketch of the computational domain $\Omega$ (b).
• Figure 2: Sketch of the three-element Windkessel model.
• Figure 3: Decay of the eigenvalues (a) and cumulative energy (b) for the velocity and pressure fields.
• Figure 4: Time-averaged reconstruction and projection error for velocity (a) and pressure (b) as the number of modes $N$ increases.
• Figure 5: Comparison between reconstruction error and projection error for velocity and pressure with $N = 6$. The supremizer approach is adopted and $N$ is the same for pressure, velocity and supremizers.