Axial acoustic radiation force on a sphere embedded in a gel phantom within a focused ultrasound field: simulation...

Acoustic radiation force (ARF) is a distinctive nonlinear phenomenon generated by acoustic wave propagation, primarily driven by acoustic effects including scattering, reflection, shear coupling, and thermo-viscous interactions, which collectively induce motion of medium. To investigate these effects and gain deeper insight into ARF generation mechanisms, this study establishes axial ARF models based on second-order, quasi-plane wave, and attenuated plane wave approximations from the linear solution of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, applied to a concave focused transducer. The second-order model shows high stability and accuracy across focusing angles, closely matching finite element method (FEM) predictions with < 10% error at small angles. Next, the second-order ARF model is integrated with FEM and compared to an analytical model related to sphere interface scattering and shear coupling from sphere interface, enabling parametric analysis of ARF in tissue-mimicking phantoms. It is proved that ARF peaks and standing wave oscillations intensify with larger sphere radius, density, and wave velocities, driven by enhanced acoustic effects. And, increased specific acoustic impedance of sphere and phantom enhances and weaken acoustic effects, leading to increases or decreases in ARF peaks. Besides, as the phantom's acoustic absorption increases, the absorbed energy governing energy transfer exhibits a non-monotonic trend, with ARF peaks mirroring this behavior. Finally, ARF results from laser Doppler vibrometry (LDV) confirms that ARF variations with sphere parameters align with simulations, validating the numerical approach. In summary, the proposed framework and protocol accurately characterize ARF distributions and sphere dynamics, enabling broader exploitation in biomedical engineering. Deeper insights into ARF will advance its applications in biomedical engineering.