4D Left Ventricular Vector Flow Mapping by Physics-Informed Neural Networks

Despite major advances in medical imaging, current methods for measuring intracardiac blood flow remain limited. 4D Flow MRI provides time-resolved, three-directional velocity data across a full 3D volume, but it requires long scan times, has relatively low spatial and temporal resolution, and is not widely accessible. In contrast, color Doppler ultrasound offers real-time imaging with high temporal resolution, but is restricted to 2D planes and measures only the velocity component along the ultrasound beam, making it highly angle-dependent. Vector Flow Mapping (VFM) reduces this angle dependence through physics-based reconstruction but remains constrained to 2D acquisitions.

To overcome these limitations, we present 4D AI-VFM, a physics-informed deep learning framework that reconstructs volumetric three-directional intracardiac flow fields from standard tri-plane color Doppler echocardiography. The model incorporates physical constraints, including mass conservation, the Navier--Stokes equations, and phase unwrapping, using a physics-informed neural network that interpolates flow in space and time and also estimates relative intracardiac pressure fields (up to an undetermined constant).

We validate 4D AI-VFM using synthetic CFD-generated datasets as ground truth and compare its performance against a prior 3D VFM approach, which uses Fourier interpolation on tri-plane data and infers missing velocity components from continuity. We also demonstrate proof-of-concept application to clinical scans. Together, these results highlight the potential of 4D AI-VFM for noninvasive, physics-aware cardiovascular flow assessment using widely available echocardiographic data.