Detection and characterization of higher order nonlinearities in the oscillations of Definity at higher frequencies and very low acoustic pressures

Abstract

The oscillation dynamics of phospholipid shell microbubbles (MBs) (e.g. Definity) exhibiting subharmonic (SH) oscillations has been widely investigated for high frequency ultrasonic imaging of the vascular bed. However, many aspects of the behavior of these MBs have remained unexplored, partly due to an extra degree of complexity imposed by the nonlinear behavior of the shell, leading to behavior. Full understanding of the dynamics of these MBs at higher frequencies will aid in the design of optimal ultrasonic exposure parameters and MB properties to improve the current SH imaging protocols. The dynamics of Definity MBs were investigated both numerically and experimentally. Polydisperse dilute solutions of Definity were sonicated separately at frequencies of 25 and 55 MHz using pulse trains of 30 cycles with a Vev0770 ultrasonic machine. For each sonication the driving pressure was varied between 100 kPa to 3.8 MPa. The backscatter signals from single MBs were iso la ted and analyzed. The Marmottant model for lipid shell MBs was numerically solved for a wide range of MB sizes and driving acoustic pressures at frequencies of 25 and 55 MHz. The results of the numerical simulations were visualized using bifurcations diagrams (MB expansion ratio versus MB size and acoustic pressure and buckling radius). Analysis of the signals extracted from the oscillations of single Definity MBs revealed, for the first time, that in addition to the conventional SH of order 1/2, SHs of the higher order of 1/3, 1/4 and 1/5 can be observed at very low acoustic pressures (~200 kPa) at both frequencies (25 and 55 MHz). These results contradict the predictions of the viscoelastic models (e.g. Hoff) which require very high acoustic pressures (~2.5 MPa) for the generation of higher order SHs at high frequencies (e.g. 55MHz). In order to investigate the origin of these oscillations, the bifurcation structure of the Marmottant model was generated. In very good agreement with experimental results, numerical results reveal the generation of higher order subharmonics in the dynamics of lipid shell MBs at pressure levels as low as 200kPa. Depending on the initial size of the MBs, simulations predict the generation of the oscillations including period 2 (P2), P3 and up to PS. Results of the simulations using the bifurcation diagrams showed that compression only behavior is the most probable reason for the occurrence of higher order SHs at very small pressure values. These results suggest that the value for the buckling radius is of great importance in the generation and order of higher order SHs. To our best knowledge, this is the first time that the numerical classification and experimental observation of the higher order SHs in the dynamics of MBs undergoing buckling and rupture is shown.