## 2 Materials and Methods  
### Imaging Schemes  
For CPWI, the lateral direction in our 2D assessment (the elevation direction in 3D imaging) lies perpendicular to the carotid artery. For people of age over 60 years, the carotid diameter is \(7.4\pm 0.7\) mm and \(8.2\pm 0.8\) mm and over 70, it is \(7.6\pm 0.8\) mm and \(9\pm 0.7\) mm, for females and males, respectively [37]. The effective covered aperture size is calculated as \((\text{Nr}+19\text{Ns})\times\text{Pitch}\), where Nr is the receive aperture size, \(\text{Ns}\) is the shift of the receiving aperture between sequential shots, and Nt is transmit aperture size. With \(\text{Ns}\) 1 and 2 and with a small Nr, the obtained effective aperture is much less than what is needed to cover the whole carotid artery. As we aim to have an effective covered aperture size big enough for all ages, we neglect \(\text{Ns}\) of 1 and 2 in our study.  
A tile of \(12\times 40\) elements (rows \(\times\) columns) requires 12 channels for transmission and 12 channels for data reception (Figure 1a). The row-level circuitry allows us to put two tiles head-to-head in a row to form an array of \(12\times 80\) elements without increasing the channel count [33]. In this study, the array is fabricated using \(4\times 2\) (rows \(\times\) columns) tiles providing \(48\times 80\) (azimuth \(\times\) elevation) elements (Figure 1b; the carotid has a diameter of 6-9 mm [37]; the array is \(14\times 12\) mm). A single plane wave imaging with full data acquisition can be implemented using a column-by-column (CBC) data acquisition approach which requires 80 transmit/receive shots. In this approach, all the 80 elements are connected to the transmit bus, and only a single element in the elevation direction is connected to the receive bus. For CPWI, we need 1000 V/s which restricts the number of transmit-receive shots to 20 for one volume. These 20 shots can be implemented in different manners; an example is shown in Figure 2b where the transmit aperture of 50 elements is shifted over three elements for each step, co-aligned with the receive aperture of 10 elements.  
Applying dynamic focusing to the received data having an effective element pitch larger than half of a wave length introduces grating lobes [24]. In our study, the 2D matrix transducer has an elevation pitch of 150 \(\upmu\)m, and the operating frequency ranges from 6 to 9 MHz, i.e., the shortest wavelength is 170 \(\upmu\)m in tissue. Therefore, grating lobes in the elevation direction will appear.  
The current ASIC architecture can accommodate 20 arbitrary transmit/receive patterns in the provided memories, which can be used to define sparse patterns (out of the scope of this paper) [34]. In addition to these element level memories, elements can be grouped into a set of transmit/receive apertures with an arbitrary size and shifted along elevation direction with one element per clock cycle [34]. In this study, we use this feature to define regular aperture patterns (see Figure 2b for example). The elements contributing in a receive aperture are interconnected (switched in parallel without further inter-element delays) in practice, and one time series is achieved for the receive aperture.