The short-pulse subharmonic response of microbubbles based on a two-frequency approximation

The subharmonic response due to the nonlinear behavior of microbubbles can be used to provide good discrimination between microbubble and surrounding tissue, especially in the deep region. In this work, we extend the 2-frequency approximated analytic solution of Newhouse et al. to derive the subharmonic response of a microbubble under band-limited insonification. Based on Fourier theory, a band-limited signal can be synthesized by multiple sinusoids, with a 2-frequency approximation being the simplest case. Our theoretical analysis illustrates that the amplitude of the subharmonics decreases with the transmitted fractional bandwidth (FB). Moreover, under an applied pressure of 514 kPa, it approaches zero when the FB is increased to 8 %. In other words, this proves theoretically that only narrowband transmission can excite the microbubble to generate the subharmonics. The amplitude of the low-frequency response can be derived to increase with the FB, which is different from that of subharmonics. Experimental data from free gas were used to verify the theoretical predictions.