Left ventricular 2D flow pattern estimation by combining speckle tracking with Navier-Stokes-based regularization in an iterative way

Ultrasound imaging with low dose contrast injection would be of interest to better characterize the cardiac flow dynamics inside the left ventricle (LV). The aim of this study was to combine speckle tracking (ST) with regularization based on Navier-Stokes (NS) equations in an iterative manner in order to improve the pure ST results when the inflow velocities were high. It was tested in a Computational Fluid Dynamics (CFD) based Ultrasound simulation environment. On two subsequent images in diastasis, block-matching was applied using normalized cross-correlation as a similarity measure and spline-interpolation for subsample motion estimation. During regularization, the difference between the measured and the regularized velocity field was added as an external force to a finite difference implementation of the NS equations. This regularized velocity field was used as prior to the ST procedure between the following pair of images by guiding and reshaping the search region appropriately. This iterative approach was performed in the forward and the backward temporal direction to obtain the flow fields of the whole filling phase. The RMSE of all velocity estimates (amplitude & angle) within each frame was calculated using the CFD velocity vector fields as the ground truth and these findings were contrasted to pure ST. In this study, we could thus show that LV flow tracking by combining ST with NS based regularization in an iterative manner improves the accuracy of the pure ST results even at high inflow velocity.