The nonlinear oscillation of encapsulated microbubbles in ultrasound contrast agents

Subharmonics or ultraharmonics provide better contrast-to-tissue ratio (CTR) in comparison with fundamental or second harmonics, which show prospective applications in medical diagnosis. In this paper, frequency response for the nonlinear oscillation of encapsulated bubbles is presented based on the Church's equation. Frequency shifting problem is explained and optimized frequency for subharmonic or ultraharmonic emissions are discussed. In addition, sound pressure dependences of the subharmonics and ultraharmonics are studied in theory as well as in measurement. Results revealed that the developments of both subharmonics and ultraharmonics have the same trend, i.e. occurrence, growth and saturation. The generation of ultraharmonic is earlier than that of subharmonic, but the component of subharmonic is larger than ultraharmonic while saturating.