Physics-informed vessel characterization and compliance scoring in ultrasound localization microscopy

: Ultrasound Localization Microscopy (ULM) enables vascular imaging and blood velocity measurements at micrometer resolution, but its high sensitivity makes the resulting measurements difficult to validate, limiting their interpretability and hindering clinical translation. This work aims to provide a vessel level framework that extracts robust hemodynamic biomarkers from ULM data while quantifying the physical reliability of the measurements. Approach: We propose a physics informed vessel reconstruction framework that integrates analytical fluid dynamics models directly into the ULM processing pipeline. Vessel geometry and flow profiles are reconstructed from velocity maps by locally fitting a Poiseuille model, justified by the low Reynolds, quasi steady laminar regime characterized across the data. We further introduce a physics compliance score that aggregates four constraints (model coverage, model to measurement similarity, flow conservation, and temporal consistency) into a single reliability metric. The method was applied to 325 manually segmented vessels from four publicly available preclinical datasets, spanning rat brain, rat kidney, and mouse tumor acquisitions. Main results: The reconstructed biomarkers (radius, centerline velocity, volumetric flow rate, wall shear stress, and pressure drop) are consistent with reported rodent microcirculation and exhibit power law scaling in agreement with network level predictions. The compliance score provides a consistent vessel level characterization, varying in agreement with the expected determinants of measurement quality (acquisition time, frame rate, and insonified vessel area), while a convergence analysis shows that physically meaningful flow can be recovered even from sparse, short acquisition data. Significance: The proposed framework offers a quantitative approach to vessel level hemodynamic characterization, combining biomarker extraction with a principled reliability assessment tool, and supports more interpretable and clinically translatable ULM outcomes.