High-resolution hemodynamic estimation from ultrafast ultrasound image velocimetry using a physics-informed neural network

<i>Objective.</i>Estimating the high-resolution (HR) blood flow velocity and pressure fields for the diagnosis and treatment of vascular diseases remains challenging.<i>Approach</i>. In this study, a physics-informed neural network (PINN) with a refined mapping capability was combined with ultrafast ultrasound image velocimetry (u-UIV) to predict HR hemodynamic parameters. Specifically, the Navier-Stokes equations were encoded into the PINN to dynamically optimize the network performance under physical constraints, and a refined mapping network was added at the input to achieve data refinement. During the prediction of HR ultrasound hemodynamic parameters, only the sparse spatial coordinates in the time series were input into the PINN, and the velocity vectors generated from the u-UIV were used together with physical residuals to enhance the physical correctness of HR predictions during the iterative process.<i>Main results.</i>The performance of the refined mapping network was validated via simulations, with a 1.9-fold increase in the radial resolution and a 2.5-fold increase in the axial resolution. HR velocity field estimation from<i>in vitro</i>and<i>in vivo</i>data showed good agreement with theoretical values and u-UIV measurements, with micrometer-level spatial resolution (88<i>µ</i>m×115<i>µ</i>m for straight vessel, 75<i>µ</i>m×120<i>µ</i>m for stenotic vessel and 63<i>µ</i>m × 79<i>µ</i>m for<i>in vivo</i>data), while the pressure field could be inferred from physical laws.<i>Significance.</i>The proposed method performs well when few data samples are available and has the potential to assist in the clinical diagnosis of vascular diseases.