Analysis of the modulated acoustic radiation-force profile for a dual-beam confocal geometry

A localized modulated radiation force can be produced when two confocal ultrasound beams of nearly equal frequencies interfere in an attenuating medium such as tissue. It is well-established that this force generates both shear and longitudinal waves. By scanning the focal point over a plane and observing the propagation of these waves, the mechanical properties of the medium can be imaged. In this paper, the modulated radiation force is analytically derived in the case of attenuating media, by expanding on the theory of ultrasound-stimulated-vibro-acoustography (USVA) for lossless media. Furthermore, weak nonlinearities are considered in the formulation, since higher source pressures may prove to be necessary to improve the radiation-force profile - only the fundamental component is, however, studied in this paper. An analysis of the generated radiation force is performed and the effects of various parameters are investigated on its amplitude and spatial distribution. It will be shown that by carefully selecting the confocal geometry of the beams, as well as, the source pressure and center frequency, the spatial profile of the radiation force can be optimized. This, subsequently, could improve not only the resolution of the point-spread-function in USVA, but also, the profile of the shear waves in elastography applications.