Noninvasive pressure difference mapping by integrating ultrasonic vector flow imaging and physics-informed conditional variational learning

Pressure differences across the circulatory system provide valuable insights into many cardiovascular diseases, including arterial stenosis. Catheterization is used clinically to measure intravascular pressure, but it is invasive, costly, and carries risks. As a noninvasive alternative, physics-informed deep learning combined with measured flow data can estimate intravascular pressure by embedding physical laws, such as the Navier–Stokes equations, into the learning process. However, this approach is still vulnerable to data noise, which can disrupt the balance between data fidelity and physical consistency, leading to unstable predictions. This study proposes a physics-informed conditional variational learning method that integrates ultrasonic vector flow data, probabilistic latent representation, and computational fluid dynamics principles for robust pressure difference estimation. The method is validated using both in-vitro and in-vivo experiments with high-frame-rate ultrasound imaging. For in-vitro experiments, compared to the conventional fully-connected network approach, the proposed method demonstrates improved accuracy, leading to a root mean square error reduction from 23.5 pascals to 13.1 pascals (a 9.3% reduction relative to the peak pressure difference), and demonstrates robustness in the presence of dark regions and across various network sizes, while the conventional fully-connected network method fails under certain conditions. In in-vivo experiments, the proposed method provides stable predictions across different training data volumes, with a peak pressure difference discrepancy of 1.8 pascals, compared to 12.1 pascals for the conventional fully-connected network method. This work demonstrates advances in deep learning strategies for robust pressure difference estimation using practical flow imaging measurements, particularly when incorporating noisy, sparse, or missing data.