Analysis of 2-D motion tracking in ultrasound with dual transducers

Hadamard-Encoded Synthetic Transmit Aperture Imaging for Improved Lateral Motion Estimation in Ultrasound Elastography

Lateral motion estimation has been a challenge in ultrasound elastography mainly due to the low resolution, low sampling frequency, and lack of phase information in the lateral direction. Synthetic transmit aperture (STA) can achieve high resolution due to two-way focusing and can beamform high-density image lines for improved lateral motion estimation with the disadvantages of low signal-to-noise ratio (SNR) and limited penetration depth. In this study, Hadamard-encoded STA (Hadamard-STA) is proposed for the improvement of lateral motion estimation in elastography, and it is compared with STA and conventional focused wave (CFW) imaging. Simulations, phantom, and in vivo experiments were conducted to make the comparison. The normalized root mean square error (NRMSE) and the contrast-to-noise ratio (CNR) were calculated as the evaluation criteria in the simulations. The results show that, at a noise level of -10 dB and an applied strain of -1% (compression), Hadamard-STA decreases the NRMSEs of lateral displacements by 46.92% and 35.35%, decreases the NRMSEs of lateral strains by 52.34% and 39.75%, and increases the CNRs by 9.70 and 9.75 dB compared with STA and CFW, respectively. In the phantom experiments performed on a heterogeneous tissue-mimicking phantom, the sum of squared differences (SSD) between the reference and the motion-compensated RF data, and the CNR were calculated as the evaluation criteria. At an applied strain of -1.80%, Hadamard-STA is found to decrease the SSDs by 20.91% and 30.99% and increase the CNRs by 14.15 and 24.66 dB compared with STA and CFW, respectively. In the experiments performed on a breast phantom, Hadamard-STA achieves better visualization of the breast inclusion with a clearer boundary between the inclusion and the background than STA and CFW. The in vivo experiments were performed on a patient with a breast tumor, and the tumor could also be better visualized with a more homogeneous background in the strain image obtained by Hadamard-STA than by STA and CFW. These results demonstrate that Hadamard-STA achieves a substantial improvement in lateral motion estimation and maybe a competitive method for quasi-static elastography.

Recovering vector displacement estimates in quasistatic elastography using sparse relaxation of the momentum equation

We consider the problem of estimating the 2D vector displacement field in a heterogeneous elastic solid deforming under plane stress conditions. The problem is motivated by applications in quasistatic elastography. From precise and accurate measurements of one component of the 2D vector displacement field and very limited information of the second component, the method reconstructs the second component quite accurately. No a priori knowledge of the heterogeneous distribution of material properties is required. This method relies on using a special form of the momentum equations to filter ultrasound displacement measurements to produce more precise estimates. We verify the method with applications to simulated displacement data. We validate the method with applications to displacement data measured from a tissue mimicking phantom, and in-vivo data; significant improvements are noticed in the filtered displacements recovered from all the tests. In verification studies, error in lateral displacement estimates decreased from about 50% to about 2%, and strain error decreased from more than 250% to below 2%.

Calibration for position tracking of swept motor 3-D ultrasound

Tracking the position and orientation of a 3-D ultrasound transducer has many clinical applications. Tracking requires calibration to find the transformation between the tracking sensor and the ultrasound coordinates. Typically the set of image slice data are scan converted to a Cartesian volume using assumed motor geometry and a single transformation to the sensor. We propose, instead, the calibration of individual slices using a 2-D calibration technique. A best fit to a subset of slices is performed to decrease data collection time compared with that for calibration of all slices, and to reduce the influence of random errors in individual calibrations. We compare our technique with four scan conversion-based techniques: 2-D N-wire on the center slice, N-wire using a 3-D volume, N-wire using a 3-D volume including the edge points and a new closed-form planar method using a 3-D volume. The proposed multi-slice technique produced the smallest point reconstruction error (0.82 mm using a tracked stylus).