AA5 – Variational Problems in Data-Driven Applications

Project

AA5-10

Robust Data-Driven Reduced-Order Models for Cardiovascular Imaging of Turbulent Flows

Project Heads

Alfonso Caiazzo, Jia-Jie Zhu, Leonid Goubergrits

Project Members

Collaborators

Project Duration

01.10.2024 − 30.09.2026

Located at

WIAS

Description

Cardiovascular imaging supports physicians in staging the severity of cardiovascular diseases non-invasively and in monitoring postoperative progress. For coarctation of the aorta (CoA), a congenital heart defect with a localized narrowing in the aorta, image-based diagnosis relies on measuring patient anatomy, blood velocities, and ow rates in the narrowed area, to identify abnormal ow conditions and increased pressure gradient across the narrowing.

Due to the limited spatial resolution, MRI and echocardiography images do not allow to measure these quantities directly. Computed tomography (CT) scans can provide higher details, but they require radiation exposure and the use of contrast agents. Blood flow simulations play therefore an important role to obtain quantitative estimation of relevant biomarkers using limited measurements.

This project focuses on data assimilation based on a parametrized background data-weak (PBDW) method. This approach seeks a reconstruction of the numerical solution of a target PDE from limited measurements by minimizing the discrepancy between the reconstructed solution and a physics-informed reduced-order model (ROM), i.e., a subspace spanned by solutions of the target PDE. One main limitation of this method is that it relies on linear reduced-order subspaces (constructed, e.g., via proper orthogonal decomposition (POD). In the context of coarctation, turbulence modeling plays a relevant role and it is well known that linear ROMs are no longer suitable for building efficient and accurate approximations of the fluid dynamics.

To robustly support the cardiovascular imaging of turbulent flows, this project aims at designing and implementing new data assimilation methods combining linear reduced-order modeling and non-linear data-driven components.

The first goal will be the robust extension of the PBDW data assimilation taking into account physics-informed subspaces built from numerical simulations on different shapes. The second goal of the project will be to extend the PDBW with active learning. The third goal will be to derive learning-theoretical generalizations to enable further applications of digital shapes linked to shape optimization problems.

External Website

Selected Publications

Selected Pictures