Dynamic Reconstruction of Ultrasound-Derived Flow Fields With Physics-Informed Neural Fields

TL;DR

This paper tackles the challenge of reconstructing physiologically plausible blood flow fields from ultrasound, which is hampered by attenuation and partial velocity measurements. It introduces physics-informed neural fields (PINNs) enhanced with multi-scale Fourier features to denoise and inpaint EchoPIV data without ground-truth supervision, enforcing Navier–Stokes-like residuals via automatic differentiation. The authors compare vanilla, random, trainable, and multi-scale Fourier feature encodings, and propose a branched architecture to inpaint occluded regions, validated on synthetic Womersley-flow data and real ultrasound phantom scans through a multi-modal verification pipeline. The approach yields consistently lower mean squared errors in denoising and inpainting across synthetic and real datasets, with Branched and MSFF models showing robustness to noise and depth-related attenuation, highlighting the potential for clinically useful, data-efficient flow reconstruction in ultrasound.

Abstract

Blood flow is sensitive to disease and provides insight into cardiac function, making flow field analysis valuable for diagnosis. However, while safer than radiation-based imaging and more suitable for patients with medical implants, ultrasound suffers from attenuation with depth, limiting the quality of the image. Despite advances in echocardiographic particle image velocimetry (EchoPIV), accurately measuring blood velocity remains challenging due to the technique's limitations and the complexity of blood flow dynamics. Physics-informed machine learning can enhance accuracy and robustness, particularly in scenarios where noisy or incomplete data challenge purely data-driven approaches. We present a physics-informed neural field model with multi-scale Fourier Feature encoding for estimating blood flow from sparse and noisy ultrasound data without requiring ground truth supervision. We demonstrate that this model achieves consistently low mean squared error in denoising and inpainting both synthetic and real datasets, verified against reference flow fields and ground truth flow rate measurements. While physics-informed neural fields have been widely used to reconstruct medical images, applications to medical flow reconstruction are mostly prominent in Flow MRI. In this work, we adapt methods that have proven effective in other imaging modalities to address the specific challenge of ultrasound-based flow reconstruction.

Figures (18)

• Figure 1: Schematic of EchoPIV process patelCreatedBioRender2026. The transducer captures an ultrasound image of the blood vessel at different time steps. Interrogation windows are overlaid in the same location of consecutive frames, the cross-correlation is evaluated to infer displacement. These displacements are used to construct a flow field.
• Figure 2: Architecture of the neural fields that used Fourier Features. In the first layer, the spatiotemporal coordinates were projected into a Fourier space so that the subsequent layer of the model had $2d$ input features. For RFF neural fields, $B$ is chosen from a normal distribution with 0 mean and standard deviation 10. For TFF neural fields, $B$ is initiated in this way but was treated as a trainable parameter by the model.
• Figure 3: The occlusion map was found by calculating the difference between the velocity at each point along a streamline and the average velocity along that streamline, preserving no-slip boundary conditions. This difference was input into a sigmoid function to produce a probability of a point belonging to the occluded region.
• Figure 4: For inpainting occluded regions, the spatiotemporal coordinates were separately fed into two neural field branches: the MSFF model (top) and the Vanilla model (bottom). For the first 100 epochs, these branches were trained to separately optimise data fidelity and total variation. After this, a combining neural network was trained to select the correct branch depending on the coordinate based on the occlusion map $\Lambda$.
• Figure 5: The percentage reduction in flow field MSE, cycle MSE, and profile MSE when the RFF architecture was applied to a synthetic dataset with a moderate level noise (exp12) for different values of $\lambda_\text{phys}$. The model provides no improvement after $\lambda_\text{phys} \sim 10^{-6}$