Numerical investigation of the nonlinear attenuation and dissipation of acoustic waves in a medium containing ultrasound contrast agents

The presence of microbubble ultrasound contrast agents (UCAs) in path of an ultrasound beam increases the attenuation of the medium. A detailed knowledge about the medium attenuation in the presence of UCAs is critical for optimizing ultrasound applications. In this study, a model incorporating the nonlinear attenuation of microbubbles is developed by deriving the complex and real part of the wave number from the Calfish model. Results showed that when UCAs are sonicated by their linear resonance frequency (fr), the effective attenuation of the medium can potentially decrease as the pressure increases, in agreement with experimental observations of the attenuation of monodisperse microbubbles. When sonicated with their pressure dependent resonance frequency (fs), the effective attenuation of the medium is smaller than the case of sonication with fr, but only below a pressure threshold (Ps). Above Ps, the effective attenuation increases abruptly (e.g. ~3 fold) and becomes significantly more than the attenuation during sonication with fr. The attenuation in the subharmonic (SH) regimes of oscillations (sonication with n*fr where n = 2, 3.) are considerably smaller compared to the cases of sonication with fr and fs (~10 times). The attenuation undergoes a sharp increase concomitant with the generation of SH oscillations.