Machine-learning-based intraventricular flow and pressure mapping with moving boundaries for color doppler

Background Color Doppler echocardiography provides real-time measurements of intraventricular flow velocity along the ultrasound beam, which is the most commonly used clinical assessment method. However, it only captures the radial component of velocity, resulting in incomplete flow information. Accurate reconstruction of the two-dimensional velocity field and corresponding pressure distribution from such partial measurements remains a challenging inverse problem. Existing vector flow mapping (VFM) approaches only enforce the continuity equation to reconstruct two-dimensional velocity fields from Doppler data. However, the absence of momentum equation constraints limits their ability to recover pressure fields. A physics-constrained framework capable of reconstructing continuous intraventricular velocity and pressure fields from routine clinical Doppler data is therefore highly desirable. Purpose The intraventricular flow shows a strong coupling with the motion of the wall of the left ventricle. This study aims to reconstruct full two-dimensional velocity and pressure fields from clinical Color Doppler echocardiography, considering the moving boundaries, using a novel Euler-Lagrangian physics-informed neural network (EL-PINN). The pressure fields enable subsequent quantitative hemodynamic analysis, including evaluation of intraventricular hemodynamic force (HDF). Methods EL-PINN is developed to tackle the flow–structure interaction problem, enforcing kinematic consistency at the moving ventricular boundary while incorporating the incompressible Navier–Stokes equations. Four cases were evaluated. Cases I and II used synthetic datasets to assess sensitivity to spatial and temporal resolution and to probe rotation. Case III and Case IV used clinical data from a healthy subject and three patients with hypertrophic cardiomyopathy (HCM), respectively. Reconstructed velocity and pressure fields were subsequently used for intraventricular hemodynamic force computation. Results In synthetic validation, the dynamic EL-PINNs achieved stable reconstruction with relative errors of 2–3% for radial velocity, 3-8% for transverse velocity, and approximately 5% for pressure, demonstrating robustness under degraded spatial–temporal resolution. Compared with a kinematic-only formulation (relative errors of 2–3% for radial velocity, and 5-12% for transverse velocity), the dynamic model significantly improved transverse velocity stability. Clinical reconstructions produced physiologically consistent velocity and pressure distributions in both healthy and HCM subjects, enabling meaningful evaluation of intraventricular flow dynamics and force patterns. Conclusions The proposed EL-PINNs framework enables physics-consistent reconstruction of two-dimensional intraventricular velocity and pressure fields from routine Color Doppler echocardiography. This approach provides a robust and clinically applicable tool for quantitative cardiac flow analysis.