Numerical and experimental classification of the oscillations of single isolated microbubbles: Occurrence of higher order subharmonics

Abstract

Imaging and therapeutic applications of micro bubbles (MBs) in medical ultrasound are rapidly increasing. Despite the many theoretical and experimental investigations of MB dynamics, the MB behavior is considered to be very complex and difficult to control. The optimization of microbubble composition and ultrasound exposure parameters requires detailed knowledge of the behavior of MBs over a large range of the control parameters of the system (e.g. pressure, frequency, MB size, MB shell composition). In this work, the dynamics of microbubbles consisting of viscoelastic shells were studied both numerically and experimentally. Polydisperse dilute solutions of Artenga MBs (Artenga Inc.) were sonicated at the frequency of 25 MHz using pulse trains of 30 cycles with a Vev0770 ultrasonic machine. For each sonication the driving pressure were varied between 100 kPa to 3.8 MPa. The backscatter signals from single MBs were isolated and analyzed further. The Hoff model for viscoelastic shell MBs was numerically solved for a wide range of MB sizes and driving acoustic pressures at 25 and 55 MHz. The results of the numerical simulations were visualized using bifurcations diagrams (MB expansion ratio versus MB size and acoustic pressure). The bifurcation structure of the viscoelastic MBs, to our best knowledge for the first time, classified the dynamics over a large range of exposure parameters, predicting the existence of higher order subharmonics. In agreement with experimental observations, simulations predict the generation of oscillations including period 2, period 3, period 4 and period 5 in the case of the sonication of polydisperse MB sizes at pressure values above specific thresholds. Another interesting finding is the differentiation between different regimes of period 4 oscillations, observed both experimentally and numerically. Numerical simulations reveal that depending on the MB size, an increase in acoustic pressure can result in oscillations that can undergo two successive period doublings from period two to period 4 or directly from period one to period 4. The dynamic characteristics of these two types of oscillations are for the first time studied in detail. In addition, frequency analysis of the ring-down oscillations of the MBs in experiments is in good agreement with the size predictions of the numerical simulations. The higher period oscillations from bigger MBs at higher frequencies may provide significant advantages for imaging, drug delivery and clot lysis ultrasound applications. These include stronger SHs or UHs signals which are closer to the transducer resonant frequency and higher and longer lasting shear stresses on the nearby cells.