## 4 Discussion  
In this study, compressive and tensile 3D principal strain estimation in a pulsating carotid artery bifurcation phantom was performed using a compounding and zero-degree displacement estimation method in a dual probe setup. Previous experimental studies have been performed using straight-forward phantoms (i.e., single tube shaped phantoms) and simulations based on 2D and 3D compound strain imaging [19; 23] showing a significant improvement compared to a single angle based strain estimation. Multiple 3D phantoms of the carotid artery have been developed lately [44; 45]. However, to our knowledge, no other paper has reported 3D principal strain estimation in a complex geometry like the CA bifurcation. The principal finding of this study is that 3D compound strain estimation outperforms single angle zero degree 3D strain estimation, even in a complex geometry, when embedded in surrounding tissue. Compared to other methods, this method is the first showing volumetric 3D strain tensor information for vascular applications retrieved in a non-invasive manner. The developed dual probe setup approach, which provided a reference for the estimated deformations, is, to our knowledge, also novel and circumvents requiring exact knowledge of mechanical properties and geometry of the tissue and of boundary conditions, which is normally needed when deriving a finite element, model-based ground truth. Therefore, this setup might also be used in future studies to provide reference deformations for in vitro studies using excised tissue in which the mechanical properties are also not known. To derive the reference strains from the RF data obtained with the dual-probe setup, the RF data acquired with both probes needs to be spatially registered. Since the angle of the probes is set to 90 degrees, only the translation should be resolved, which was performed using a feature-based registration using coherently compounded B-mode images. Although this might seem to be a simple registration, the quality of the registration depends on the choice of registration metric and also on the speed of sound and the assumption of a homogenous speed of sound throughout the phantom. In our case, setting the sound speed to 1540 m/s provided the most optimal registration, which is in line with reported speed of sound values for PVA [37]. In this work, a patient-specific model of the carotid artery at the bifurcation was used to construct a PVA-based phantom. Since the surrounding tissue affects the mechanical behavior of the carotid artery wall [46], the CA was embedded in surrounding PVA instead of water. The addition of surrounding tissue is not only important for obtaining realistic motion and deformation of the carotid artery segment but also resembles realistic in vivo acquisitions, since deterioration of the strain estimates due to side and grating lobes will be present. What was not accounted for in the current phantoms were heterogeneities within the vessel wall and plaque. Especially, the presence of calcifications and induced shadowing is expected to affect strain estimation accuracy. In the experiment, the cardiac pressure cycle was enforced with 60 bpm. This resulted in a cyclic reproducible deformation of the vessel phantom. In the process of accumulation of inter-frame displacements, inaccuracies and interpolation errors led to an overall progressive displacement error over time, which explains the observed residual strain for all methods at the end of the pressure cycle (Figure 9). The longitudinal progression of the strain distribution (5 th-95 th percentile strain) over time shows a divergent trend for the full cardiac cycle. Since a ground truth strain distribution in the longitudinal direction is absent, this indicates the lack of a cyclic strain progression for each cardiac cycle. The elevational ultrasound beam width is one order of magnitude larger than the step-size in elevational direction. This results in redundant ultrasound RF data in the elevational direction.