An analytical model of full-field displacement and strain induced by amplitude-modulated focused ultrasound in harmonic motion imaging.

The majority of disease processes involves changes in the micro-structure of the affected tissue, which can translate to changes in the mechanical properties of the corresponding tissue. Harmonic motion imaging (HMI) is an elasticity imaging technique that allows the study of the mechanical parameters of tissue by detecting the tissue response by a harmonic motion field, which is generated by oscillatory acoustic radiation force. HMI has been demonstrated in tumor detection and characterization as well as monitoring of ablation procedures. In this study, an analytical HMI model is demonstrated and compared with a finite element model (FEM), allowing rapid and accurate computation of the displacement, strain, and shear wave velocity (SWV) at any location in a homogenous linear elastic material. Average absolute differences between the analytical model and the FEM were respectively 1.2% for the displacements and 0.5% for the strains for 41 940 force voxels at 0.22 s per displacement evaluation. A convergence study showed that the average difference could be further decreased to 1.0% and 0.15% for the displacements and strains, respectively, if force resolution is increased. SWV fields, as calculated with the FEM and the analytical model, have regional differences in velocities up to 0.57 m s