###### Abstract
First, due to longitudinal wall motion, 2D transverse US acquisitions will suffer from out of plane motion reducing the strain estimation accuracy. A second limitation of 2D scanning is that it is more difficult to find the optimal cross-section needed for appropriate assessment of carotid disease, i.e., the most vulnerable spot might be missed. Also, inter- and intra-operator variability in skill and experience could hamper a reliable judgement about the best response to the therapy of the plaques [26]. Three-dimensional B-mode-based US of the carotid artery [27; 28] has been described before and has been shown to improve the visualization of the intima-media thickness. It complements Intima Media Thhickness (IMT), which is a typical 2D US-based biomarker [29] with a measurement of the Total Plaque Volume (TPV) [30] and the Vessel Wall Volume (VWV) [31]. However, the implementation of 3D ultrasound in these studies did not allow measurement of 3D tissue motion or strain. The main aim of the present study is to develop a 3D ultrasound technique that enables 3D vascular strain estimation of the carotid artery. As aforementioned, adding this functionality could possibly lead to a significant improvement of the prediction of plaque vulnerability. A few studies have investigated 3D strain imaging for vascular applications. In vitro studies have shown a 3D representation of the 2D strain tensor derived from multi-slice 2D displacement estimations [32; 33]. In this approach, the dominant tissue motion in radial direction was aligned with the US beam direction due to the rotational acquisition protocol using the longitudinal axis for rotation. However, the rotation applied in this approach cannot be performed noninvasively, and therefore translation towards clinical practice is not realistic. Furthermore, in reality, the vessel wall tends to deform in three orthogonal directions due to the arterial pressure pulse, and the vessel wall dynamics are affected by the heterogeneous composition and complex geometry in the presence of a stenosis or a plaque [24]. Volumetric 2D strain tensor estimation based on 3D motion estimation showed the capability of handling out of plane motion, i.e., the direction perpendicular to the transversal image plane [23]. However, measurement of the complete 3D strain tensor for the entire vessel wall of the carotid artery in 3D is desirable in the pursuit of better understanding the underlying true deformation encompassing the horizontal, vertical, and longitudinal directions. This requires 3D tracking of the 3D tissue deformation and the derivation of the full 3D strain tensor. To our knowledge, only one study reporting 3D strain tensors for arteries using intravascular B-mode US was presented in cylindrical coordinates [34], resulting in radial, circumferential, and longitudinal strain distributions. However, predefining the coordinate space to be cylindrical assumes an equal cylindrical geometry of the vessel wall to relate to the dominant strain direction. In the case of a geometry such as the bifurcation, this relation does not hold. Principal strains based on the principles of continuum mechanics have the intrinsic characteristic of coordinate system independence and are therefore more suitable to report the full 3D strain distribution at the bifurcation. 2D principal strains were reported for vascular applications based on 2D strain tensor in previous studies [35; 36]. In this paper we implemented the acquisition method of our previous simulation study in an experimental setup and extended the strain estimation algorithm to full 3D. To evaluate the performance of this implementation experimentally, we constructed a phantom of the same patient-specific geometry as used in the simulation study of PolyVinyl Alcohol (PVA) solutions, subjected it to a pulsating physiological flow, and evaluated the accuracy of our 3D strain estimation. The main benefit of the simulation study was the availability of a ground truth to compare the performance of different strategies.