Reconstructing the source condition for focused shear wave beams in soft elastic media

Abstract

Shear waves are employed in medical ultrasound imaging because they reveal variations in viscoelastic properties of soft tissue. Focused shear waves produced by a longitudinally vibrating piston at several hundred hertz are investigated here experimentally in soft tissue phantoms and using an analytical model for shear wave beam generation and propagation. Experiments employed a spherically concave piston shaped to focus the shear wave beam at a depth of 4 cm in a soft tissue phantom. Analytical modeling of this data provided a good fit, but required treating the focal length and piston diameter as adjustable parameters. The largest source of error in the modeling is suspected to be that the source condition is assumed to exhibit zero displacement surrounding the piston, whereas the actual condition in the source plane is a traction-free surface surrounding the piston. Here, in order to elucidate the actual source condition, numerical back propagation of field measurements is employed. Simulations show that the shear source condition can be accurately recovered with information related only to the shear wave, i.e., without compressional wave information. Back propagation of measured beams is discussed in the context of more accurately modeling the source condition for future device optimization.