Left ventricular 2D flow pattern estimation of the heart by combining speckle tracking with Navier-Stokes based regularization

The dynamics of the blood flow inside the left ventricle (LV) has an important effect on cardiac performance. Although ultrasound (US) methodologies based on speckle tracking after low-dose contrast injection have been proposed, the fast motion in combination with out-of-plane flow makes the tracking challenging. The aim of this study was therefore to develop a new estimation method by regularizing the speckle tracking results using the Navier-Stokes equations. This method was tested in a Computational Fluid Dynamics (CFD) based ultrasound simulation environment. A dynamic 3D anatomical model of the LV was combined with a realistic inflow velocity profile to build a CFD flow vector field (Fluent 12.1, ANSYS). The motion of injected bubbles (density = 500/ml) was simulated and used as input to an ultrasound simulator (COLE) to obtain a 2D B-mode image sequence (f = 4.5MHz; 50°opening angle; dynamic focusing; frame rate = 227Hz). On this sequence, block-matching was applied (kernel 0.34mm × 0.028rad; search region 15.4mm × 0.078rad; window overlap 40 ± 90%) using normalized cross-correlation as a similarity measure and spline-interpolation for subsample motion estimation. To regularize the velocity estimates, the difference between the measured and regularized velocity field was added as an external force to a finite difference implementation of the Navier-Stokes equations. The RMSE normalized for the maximal velocity (NRMSE) at each frame was calculated using the CFD velocity field as the ground truth. The NRMSE analysis showed that regularization improved the initial estimates mostly in the lateral direction for inflow velocities below 0.25 m/s (axial: 16.37 ± 2.89% vs. 16.67 ± 2.49%; lateral: 18.69 ± 3.57% vs. 23.27 ± 3.38%). However, for larger inflow velocities, regularization did not refine the estimates (axial: 22.83 ± 3.20% vs. 24.00 ± 4.37%; lateral: 17.58 ± 4.73% vs. 18.66 ± 4.32%), since the initial estimates were too noisy to be adequately regularized. In future work, the regularized velocities from low inflow velocity frames will be used as prior to improve the tracking results of the higher velocity frames.