Precision estimation and imaging of normal and shear components of the 3D strain tensor in elastography.

In elastography we have previously developed a tracking and correction method that estimates the axial and lateral strain components along and perpendicular to the compressor/scanning axis following an externally applied compression. However, the resulting motion is a three-dimensional problem. Therefore, in order to fully describe this motion we need to consider a 3D model and estimate all three principal strain components, i.e. axial, lateral and elevational (out-of-plane), for a full 3D tensor description. Since motion is coupled in all three dimensions, the three motion components have to be decoupled prior to their estimation. In this paper, we describe a method that estimates and corrects motion in three dimensions, which is an extension of the 2D motion tracking and correction method discussed before. In a similar way as in the 2D motion estimation, and by assuming that ultrasonic frames are available in more than one parallel elevational plane, we used methods of interpolation and cross-correlation between elevationally displaced RF echo segments to estimate the elevational displacement and strain. In addition, the axial, lateral and elevational displacements were used to estimate all three shear strain components that, together with the normal strain estimates, fully describe the full 3D normal strain tensor resulting from the uniform compression. Results of this method from three-dimensional finite-element simulations are shown.