## 4 Discussion
In a previous study, we showed the ability to resolve sub-plane elevational displacement estimation [23], but still it remains the direction with the relatively lowest displacement estimation resolution. Furthermore, the geometrical shape of the lumen in combination with this elevational beam overlap between slices might also lead to displacement estimation errors. Inter-slice geometrical lumen changes might dominate the normalized cross-correlation-process, which is supposed to detect inter-frame displacement changes. Three methods for each probe should yield similar results for the strain estimation in the elevational direction. Figure 8 confirms that, in general, this is the case, since equal strain distributions between the zero-degree and compounding based methods are observed. Nevertheless, local strain differences were found between probe A and B. These were found especially at the inlet side and outlet side, and might be due to different displacement estimation kernel orientations and filter effects. To calculate the 3D strain components, a 3D Least Square (LSQ) strain estimator was applied. The kernel size determines the tradeoff between outlier suppression and true value detection. Large kernels sizes result in smooth global strain estimates but also in underestimation of the local strain differences. Especially at the edges, underestimation might occur, since the displacement gradient of the true deformation in the vessel wall is the highest at the vessel wall-lumen transition. To compare the performance across the methods, the LSQ kernel size for the single probe compounding and zero degree method was kept equal to that of the reference method. Application of larger kernel sizes for these methods might be favorable to smoothen results without losing essential strain map features. This will be investigated in future studies. Further research needs to be carried out to fully translate the single probe compounding technique into the clinic. The practical setup needs to be supportive to actually acquire multi-slice US data from the CA in vivo. Due to the curved neck and jaw skin surface, maintaining acoustic contact will be challenging during the complete acquisition range in the elevational direction. A possible solution to this might be to create a thick, pre-shaped layer of ultrasound transparent material, ensuring constant acoustic contact between the transducer and skin surface. Another challenge for in vivo acquisition is related to the data acquisition. The trigger originating from the pump driver at the start of each systolic phase initiated data acquisition for the complete cardiac cycle. Since the acquisition took 1 second at each position, thus several minutes for the entire acquisition, the phantom motion had to be very reproducible. In vivo, this multi-slice technique might become more difficult to achieve due to heart rate and blood pressure variability and motion artifacts due to, for example, breathing. However, it is already known that heart rate variability in general only affects the diastolic phase and not the systolic phase of the pressure cycle [47], and only one phase of the pressure cycle is required to obtain maximum strain contrast. Thus, for in vivo application we recommend to apply this technique on the systolic phase while the subject is in resting position to minimize blood pressure variations. ECG-triggering will then need to be incorporated to enable synchronization in vivo, and probably the head and neck region should be fixated to minimize motion artefact. Finally, for in vivo application a reduction in overall acquisition time is favored. The acquisition time can already be halved compared to the acquisition sequence used in this paper, because, as aforementioned, it is not necessary to acquire data for the diastolic phase. With the development of matrix probes with a sufficient footprint, pitch, and number of elements, it might even become possible to acquire volumetric ultrasound and strain data within one cardiac cycle.