3D Motion Estimation with Row-Column Addressed 2D Array Probes

This project presents a practical method of accurately capturing a 3D velocity vector field. The method uses a row-column addressed array (RCA) probe and a synthetic aperture (SA) imaging sequence to perform volumetric imaging with relatively few emissions. The RCA probe’s low channel count reduces significantly the data rate and makes high-quality volumetric imaging viable on available research scanners without the need to synchronize multiple scanners. The project also proposes a new volumetric imaging method, which significantly reduces the computational complexity of the RCA beamformation while yielding a virtually identical output to the conventional approach. The proposed method exploits that the low-resolution volumes (LRVs) from the RCA SA imaging sequence have approximately constant image values along trajectories in volume. The trajectories are the set of positions with constant time-of-flight to the closest position of the receiving aperture. After determining this set it is only necessary to beamform one position to acquire every positions image values. This computational reduction enables much faster volumetric imaging. For comparison, the proposed method was found to beamform an LRV with 192 × 192 × 2000 voxels 10.95 times faster than the conventional approach when the number of receiving channels was N = 128. Furthermore, this speedup was obtained despite comparing a previously published GPU accelerated C++ implementation of the conventional approach to a MATLAB implementation of the proposed method.
From the trajectory models used in the proposed beamformer, it was also possible to derive a simple expression for the grating lobes and a motion artifact that occurs when the imaged object moves axially during the acquisition. These expression are used to design imaging sequences which  avoid grating lobes in the field of view (FoV) and mitigate the motion artifacts.
Motion correction was also proposed as a method of mitigating motion artifacts. By reducing the motion between the LRVs, which combine to form a high resolution volume (HRV), the imaging artifacts can be significantly reduced. It was for instance shown through a flow-rig measurement that the motion correction could reduce the bias from —27.6% to —9.4% when the beam-to-flow angle was 60^◦, the pulse repetition frequency (f_prf ) was 2 kHz, and the peak velocity was 25 cm/s.
The velocity estimation was primarily performed using a transverse oscillation (TO) crosscorrelation estimator. However, a TO auto-correlation estimator was also proposed. The two estimators are evaluated on complex flow simulations performed by coupling computational fluid dynamics (CFD) and Field II. Here the flow was simulated by moving scatterers along a velocity field derived from a CFD simulation of pulsatile flow in the carotid artery. Meanwhile, the corresponding radio frequency (RF) signal from the flow scatterers was simulated using Field II. This complex flow simulation was performed with an fprf of 10 and 20 kHz and from two probe orientations. The cross-correlation estimator yields, from linear regression analysis between the actual and the estimated 3D velocity field, correlation coefficient (R²) values between 0.89 — 0.91, 0.46 —0.77, 0.91 — 0.97 for the x-, y- and z- velocity component respectively. The auto-correlation estimator yields, likewise, R2 values in the range of 0.87 — 0.89, 0.40 — 0.83, 0.91 — 0.96 for the x-, y-and z- velocity component. The two estimators were found to perform similarly, and the most significant difference in root-mean-square error (RMSE) was 0.60 cm/s. This was a relatively small performance difference, considering the largest velocity in the FoV was greater than 60 cm/s.
The cross-correlation estimator was also evaluated from measurements of pulsatile flow in a carotid artery phantom. The pulsatile flow’s average flow rate was set to 2.44 mL/s, and the flow was acquired with an fprf of 8, 10, and 15 kHz. Furthermore, the pulsatile flow was acquired from two measurement sites: one which captures a straight section of the artery and one which captures the artery’s bifurcation. The flow rate was at the artery’s straight section estimated with a bias ranging from —7.99% to 0.10% and a standard deviation ranging from 10.76% to 6.97%. At the bifurcation, the flow rate was estimated with bias and standard deviation ranging between —7.47% to 2.02% and 14.46% to 8.89%.
Overall, the presented motion estimation method has been demonstrated to capture complex flow in 3D accurately and at a high frame rate (between 125 to 417 Hz). However, due to motion artifacts, the accuracy was highly dependent on the magnitude of the axial velocity component. The severity of the motion artifact can be significantly reduced by employing motion correction. However, the presented method still requires a high f_prf to be viable for all flow directions. This suggests that the method is more suitable for superficial vessels, where the flow also is generally easier to acquire at an angle, yielding a small axial velocity component.
Future research should focus on reducing motion artifacts, which can be achieved by further improving the SA imaging sequence and the motion correction procedure or potentially by developing new non-linear RCA imaging methods.