Simulation of Ultrasound Radio-Frequency Signals in Deformed Tissue for Validation of 2D Motion Estimation with Sub-Sample Accuracy

Motion estimation in sequences of ultrasound echo signals is essential for a wide range of applications. In time domain cross correlation, which is a common motion estimation technique, the displacements are typically not integral multiples of the sampling period. Therefore, to estimate the motion with sub-sample accuracy, 1D and 2D interpolation methods such as parabolic, cosine, and ellipsoid fitting have been introduced in the literature. In this paper, a simulation framework is presented in order to compare the performance of currently available techniques. First, the tissue deformation is modeled using the finite element method (FEM) and then the corresponding pre-/post-deformation radio-frequency (RF) signals are generated using Field II ultrasound simulation software. Using these simulated RF data of deformation, both axial and lateral tissue motion are estimated with sub-sample accuracy. The estimated displacements are then evaluated by comparing them to the known displacements computed by the FEM. This simulation approach was used to evaluate three different lateral motion estimation techniques employing (i) two separate 1D sub-sampling, (ii) two consecutive 1D sub-sampling, and (Hi) 2D joint sub-sampling estimators. The estimation errors during two different tissue compression tests are presented with and without spatial filtering. Results show that RF signal processing methods involving tissue deformation can be evaluated using the proposed simulation technique, which employs accurate models.