Leveraging flow physics to model vessels in ultrasound localization microscopy

Vascular imaging is essential for a wide range of medical applications, including early cancer detection and monitoring of cardiovascular diseases. In recent years, ultrasound localization microscopy (ULM) achieved vasculature reconstruction beyond the diffraction limit by tracking microbubbles (MBs) perfusing an area of interest. However, ULM data are often noisy, hard to interpret, and limited by some critical trade-offs. In particular, achieving sufficient vessel saturation requires either long acquisition times, impractical in clinical settings, or high MB densities, which increase measurement errors. We propose a physics-informed method for vessel reconstruction that estimates both geometry and flow field from MB velocity measurements. By locally fitting a Poiseuille flow profile, we extract vessel radius and peak velocity, then we interpolate these estimates with a smoothing spline weighted by local measurements reliability. This results in a globally consistent representation of the channel. We tested the method on in vitro data from a tube with varying diameter, showing its robustness even in sparse measurements scenarios. This approach improves the interpretability of ULM outcomes, while reducing dependence on long acquisitions and high MB concentrations.