## 4 Discussion  
The aim of this study was to find a set of imaging parameters that provides a good image quality using an aperture-shifting matrix array, within the boundary condition of a limited number of transmissions (20), such that a volume frame rate of 1000 per second could be reached. We aimed for such high volume rate to facilitate CPWI (seeing the 4.5 m/s pulse wave pass laterally within a few volumes [8]). Depths of evaluation were 10, 15, and 20 mm as the anterior and posterior walls are expected at these depths [8]. The effects of receive aperture size (Nr), the aperture shifting distance per pitch (Ns), and transmit aperture size (Nt) were studied. Improving the quality of B-mode images helps in CPWI as it facilitates the motion estimation algorithms to track the axial displacement of the arterial walls [8,13]. This is essential for accurate local pulse wave velocity estimation required to generate an elasticity map. Our assessment and parameters selection priority were as follows: (1) the size of effective aperture; as it indicates whether we can have a comprehensive view on the carotid artery or not [37], (2) suppression of grating lobes; the lower the level of grating lobes, the higher the contrast, which is important for motion estimation algorithms to better estimate the axial displacement of carotid walls [8], and (3) resolution/sidelobes. Both Ns of 3 and 4 could provide sufficiently large effective aperture. Due to the lower grating lobes achieved with Ns = 3, compared to Ns = 4, Ns = 3 was selected. Selection of Nr imposed a trade-off between FWHM and grating lobes. The rate of decrement of grating lobes and increment of FWHM in Ns = 3 led to a Nr of 5. Almost the same trends happened in all the three depths of interest for CPWI [8], which led us to Ns = 3 and Nr = 5. The finalized imaging sequence, with a boundary condition of 20 transmit-receive shots, consists of a full-aperture transmission (Nt = 80), Nr = 5, Ns = 3 and using the angular weighting (AW) technique in the image reconstruction procedure. Signal-to-noise ratio (SNR) is also an important criterion in the performance of motion estimation techniques. However, it is not included in our study since in previous studies, an acceptable SNR in CPWI was achievable with both 1D or 2D arrays [8,13], and it is expected that this is the case with our  
Figure 11: (**a–c**) The maximum intensity projection (MIP) of the reconstructed 3D images of Figure 10 using the data obtained with the two-needle phantom. (**d**) The clutter pattern in azimuth direction measured on the dashed black line in (**b**). 2D matrix array as well [34]. If SNR is not good enough (either for CPWI or other applications which need the same effective aperture size) to perform a reliable motion estimation, a larger Nr can be used. However, it would cause a larger FWHM as a consequence of relatively more direct receive apertures and applying the dynamic focusing in reception. Therefore, in the case of using a large Nr (i.e., 20), a more sophisticated image reconstruction method, which takes the narrow directivity of a large Nr into account, should be used in the elevation direction to form a 3D volume [42]. The final version of our 2D transducer will have 10 tiles in the azimuth (row) direction and two tiles in the elevation (column) direction, making \(120\times 80\) (row \(\times\) column) elements available to form a 3D image. Having an azimuth pitch of 300 \(\upmu\)m, the size of our 2D transducer in azimuth direction will be 36 mm, thus providing an aperture size big enough to track the carotid pulse wave velocity (estimated to be around 4.5 m/s [8]). All the evaluations and decisions in this paper were conducted using static imaging phantoms while in CPWI, there are several types of motion, i.e., carotid wall movement caused by pulse wave propagation, overall movement by breathing, and patient/transducer movement. Motion of the object might lead to unwanted decorrelation of the signals recorded by the sequentially switched apertures, leading to lower image quality.