## 5 Discussion  
This investigation evaluates the performance of four commonly used tissue displacement estimation methods developed for US elastography. The methods are, namely, AM2D, GLUE, OVERWIND, and SOUL. They were evaluated both as stand-alone methods and in combination with the STREAL method, which was recently developed to enhance tissue displacement fields aimed at US elastography applications. The assessment was performed using datasets consisting of data pertaining to in silico and tissue mimicking phantoms undergoing US imaging in addition to clinical data. When applied to synthetic data, compared with the other measures, the AM2D displacement estimator, by far, provides the best quality of Young's modulus reconstruction with much higher computational efficiency compared to other estimators. This estimator has the added benefit of substantially improving the inclusion-to-background Young's modulus ratio when combined with the STREAL enhancement method founded on tissue mechanics regularization. The other displacement estimators tend to blur the edges of the inclusion, which may be the source of the ratio error as it leads to the underestimation of the inclusion's Young's modulus. The in-silico phantoms results indicate that both OVERWIND and SOUL estimators provide minimal improvements over GLUE but take much longer to compute compared to AM2D. This makes them difficult to recommend in a real-time scenario where run-time is of the utmost importance. Tissue mechanics-based regularization applied through the STREAL enhancement method provides the most improvement when applied to the AM2D estimator. This may be partially due to the displacement field over-smoothing effect applied in other methods, which can lead to excessive loss of actual displacement information. Furthermore, the more advanced and complicated displacement estimators have increasingly many parameters, which makes it more difficult to accurately tune the algorithm for maximum performance. Moreover, the sophisticated window-based approach in OVERWIND was designed to handle large changes in displacement and preserve value; however, it is possible that this same mechanism can sometimes allow artifacts and issues in the displacement field to pass through where they otherwise should be smoothed. SOUL, on the other hand, provides a much smoother image than GLUE; however, the former risks excessive smoothing, while the potential benefit is not worth the increased runtime and should be reconsidered if its algorithm implementation is optimized. When applied to the tissue mimicking phantom, the AM2D estimator performed very well relative to the other estimator as it produces high-quality images for a very low runtime requirement. The quality of the reconstructed images measured by CNR and SNR is comparable, while the STREAL enhancement led to little change in these measures except for OVERWIND, where the enhancement led to substantial improvement. For strain  
Figure 16: Segmented Young’s modulus images computed from displacements estimated through the AM2D estimator with STREAL enhancement overlayed on top of B-mode images of **(a)** Patient 1, **(b)** Patient 2, and **(c)** Patient 3. Highlighted regions have [PERSON]’s modulus values larger than 1.5 times the median of [PERSON]’s modulus of respective background tissue. Apart from artifacts at the top of the images, the stiffness elevation in the tumor area is consistent with their respective ROIs. images, the STREAL enhancement led to only a little improvement of axial strain with all four displacement estimators, whereas the improvement achieved with the lateral strain was highly remarkable, especially with the AM2D estimator. This observation is consistent with [19]. Overall, the difference in reconstruction quality with and without STREAL is quite subtle and, in some cases, seems to decrease CNR and SNR. The decrease in metrics is of relatively trivial magnitude compared to the overall CNR and SNR and could be attributed to subtle changes in the noise content.