A 2D least square differentiation filter for tensorial elastography

In this paper, a 2D least square FIR differentiation filter method is proposed in the context of tensorial elastography. Displacements are estimated from ultrasonic images obtained during freehand compression. Two 2D filters are used for providing all partial derivative maps according to the estimated motion obtained with a Bilinear Deformable Block Matching method. From these results, several strain tensor images are built, revealing the tissue´s elasticity properties. Among these tensors, the infinitesimal strains, the rigid rotation and principal strains tensors are retained, thus improving the contrast between the tumor and the background tissue. The 2D filters were first applied to displacement maps estimated from simulated data and two experimental RF data sets and then compared to the 1D differentiation filter LSQSE used in elastography. The first experimental data set was collected from a homogeneous phantom with a cylindrical hard inclusion and the second data set was collected from a thyroid gland with a malignant tumor. For all studied RF data sets, the contrast between the tumor and the background tissue calculated on strain tensor maps was increased up to a factor of 3 with our method compared to the LSQSE method. We also observed that the rigid rotation tensor and principal strains tensor were well adapted to thyroid elastography.