The role of constitutive nonlinearities and sound modulation in the generation of the acoustic radiation force

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This study investigates the acoustic radiation force (ARF) in soft tissues when the generating ultrasound field is modulated with a low-frequency envelope (102-104 Hz range). On approximating the soft tissue as that of a nonlinear elastic material with heat conduction and viscosity, the system of nonlinear balance equations, governing both the ultrasound-scale oscillatory motion and the ARF-induced mean motion, is formulated explicitly. To deal with the effects of ultrasound modulation, a dual-time-scale approach featuring the “fast” (ultrasound-scale) and “slow” (modulation-scale) temporal coordinates is deployed. In this setting the governing equations for the mean motion, featuring the ARF as the body force term, are extracted by taking the “fast” time average of the nonlinear balance laws. The ARF is shown to consist of two distinct terms, namely (i) the potential term, which is proportional to the gradient of the ultrasound intensity and (ii) the axial term, which contains both an attenuation-driven ...