Reverberant shear wave phase gradients for elastography

Reverberant shear wave fields are produced when multiple sources and multiple reflections establish a complex three-dimensional wave field within an organ. The expected values are assumed to be isotropic across all directions and the autocorrelation functions for velocity are expressed in terms of spherical Bessel functions. These results provide the basis for adroit implementations of elastography from imaging systems that can map out the internal velocity or displacement of tissues during reverberant field excitations. By examining the phase distribution of the reverberant field, additional estimators can be derived. In particular, we demonstrate that the reverberantphase gradientis shown to be proportional to the local value of wavenumber. This phase estimator is less sensitive to imperfections in the reverberant field distribution and requires a smaller support window, relative to earlier estimators based on autocorrelation. Applications are shown in simulations, phantoms, andin vivoliver.