Subharmonic response of encapsulated microbubbles: conditions for existence and amplification

The response of encapsulated microbubbles at half the ultrasound insonation frequency, termed subharmonic response, may have potential applications in diagnosis and therapy. The subharmonic signal, emitted by Definity microbubble cloud sonicated by ultrasound was studied theoretically and experimentally. The size distribution of the microbubbles was optically analyzed and resonance frequency of 2.7 MHz was determined. An asymptotic model has been developed that generates subharmonic response of a single and of a cloud of bubbles of various sizes. Threshold conditions for existence and the intensity of the subharmonic signal are predicted to depend on microbubbles size distribution and shell properties, as well as on the driving field frequency and pressure. Thin tubes filled with Definity solution were insonated at acoustic pressures from 100 to 630 kPa. The intensities of the emitted fundamental harmonics and subharmonics were measured. At frequency 5.5MHz, twice the resonance frequency, the subharmonic signals were observed only at pressures greater than 190 kPa. The subharmonic to fundamental harmonics intensity ratio was within -12 to -1 dB. The experimental results showed good correlation with the theoretical results in the range of validity of the asymptotic solution, thus supporting the model assumptions.