| Accurately estimating the strain is one of the fundamental challenges in ultrasound (US) elastography. Yet, most of the techniques used in elastography remain mono- or bi-dimensional and may lead to noisy elastograms if significant lateral or out-of-plane motion occurs. Moreover, the recent development of 2D transducer arrays to acquire 3D US RF data provides new prospects for medical US applications and in particular for elastography. In this paper, a 3D technique, able to accurately estimate biological soft tissue deformation under load, is presented. It is based on a 3D deformation model of the tissues and locally computes axial strains while considering lateral and elevational motions. Unlike most of other techniques, this model locally considers an axial scaling factor in addition to a 3D translation. Parameter estimation, formulated as an optimization problem under constraints, is performed through a sequential quadratic programming methodology. The performance of the algorithm is both assessed with simulated and experimental data. Simulations reproduce the case of a basic homogeneous medium subjected to increasing levels of compression. A comparison between our 3D method and its 2D counterpart is led to study the advantage of considering a 3D approach. The ability of our algorithm to process real data is then considered with US volumes acquired during freehand scanning of a phantom dedicated to elastographic studies. |