Three-dimensional motion estimation in elastography

In elastography we are capable of estimating the two in-plane principal strain components following an applied compression, namely the axial and lateral components, along and perpendicular to the compressor/transducer axis, respectively. However, the motion resulting from the compression is three-dimensional. Therefore, in order fully describe the resulting three-dimensional motion we need to also estimate the third strain, or elevational (out-of-plane) component. In this paper, we describe a method that estimates motion, i.e., displacement and strain, in the elevational direction. In a similar way as in the lateral motion estimation, and by assuming that ultrasonic frames are available in more than one parallel elevational planes, we used methods of interpolation and cross-correlation between elevationally displaced RF echo segments. We were thus able to obtain high resolution elevational displacement and strain estimates. An iterative method corrected for motion in the axial and lateral directions. As a result, together with the corrected axial and lateral strain estimates, we obtained the full 3D normal strain tensor resulting from a uniform compression. Results of this method from three-dimensional finite-element simulations are shown