Theoretical Study of the Effects of Nanoparticles on the Acoustic Performance of Microbubbles

There are growing investigations on incorporating solid nanoparticles (NPs) into the shell of microbubbles (MBs), because NPs may endow the MBs with other bio-functions, such as multimodality imaging and drug delivery. These novel MBs have been developed as hybrid MBs' contrast agents. Generally, the shell density of hybrid MBs was assumed to be the same as water in the studies of bubble dynamics. In fact, the NPs in the layer of MBs can change the density of the shell, which leads to the change of scattering characteristics of MBs under ultrasonic excitation. Thus, it is necessary to develop a new model to simulate dynamics of the hybrid MBs. Here, we have investigated scattering characteristics of the hybrid MB embedded with NPs based on a modified Rayleigh-Plesset model. The numerical and analytical solutions to this equation are obtained for oscillation response, harmonic components, and scattered cross section of hybrid MBs at small-amplitude oscillations. The results indicated that the shell density had a greater impact on the nonlinear harmonics than fundamental ones. Considering acoustic driving frequency and pulse lengths, the largest ultraharmonic amplitude is 14 times larger than the smallest value. Considering the effects of bubble equilibrium radius, the second scattering cross section of hybrid MBs increased first and then decreased with increasing bubble equilibrium radius. Therefore, the optimal values of shell density for hybrid MBs can be predicted to obtain higher scattered signals. This also offers more accurate assessment of scattering characteristics for hybrid MB contrast agents.