Understanding the pressure dependence of the nonlinear behavior of ultrasonically excited phospholipid-stabilized nanobubbles (NBs) is important for optimizing ultrasound exposure parameters for implementations of contrast enhanced ultrasound, critical to molecular imaging. The viscoelastic properties of the shell can be controlled by the introduction of membrane additives, such as propylene glycol as a membrane softener or glycerol as a membrane stiffener. We report on the production of high-yield NBs with narrow dispersity and different shell properties. Through precise control over size and shell structure, we show how these shell components interact with the phospholipid membrane, change their structure, affect their viscoelastic properties, and consequently change their acoustic response. A two-photon microscopy technique through a polarity-sensitive fluorescent dye, C-laurdan, was utilized to gain insights on the effect of membrane additives to the membrane structure. We report how the shell stiffness of NBs affects the pressure threshold (P_t) for the sudden amplification in the scattered acoustic signal from NBs. For narrow size NBs with 200 nm mean size, we find P_t to be between 123 and 245 kPa for the NBs with the most flexible membrane as assessed using C-Laurdan, 465–588 kPa for the NBs with intermediate stiffness, and 588–710 kPa for the NBs with stiff membranes. Numerical simulations of the NB dynamics are in good agreement with the experimental observations, confirming the dependence of acoustic response to shell properties, thereby substantiating further the development in engineering the shell of ultrasound contrast agents. The viscoelastic-dependent threshold behavior can be utilized for significantly and selectively enhancing the diagnostic and therapeutic ultrasound applications of potent narrow size NBs.

In many applications, microbubbles (MBs) are encapsulated by a lipid coating to increase their stability. However, the complex behavior of the lipid coating including buckling and rupture sophisticates the dynamics of the MBs and as a result the dynamics of the lipid coated MBs (LCMBs) are not well understood. Here, we investigate the nonlinear behavior of the LCMBs by analyzing their bifurcation structure as a function of acoustic pressure. We show that, the LC can enhance the generation of period 2 (P2), P3, higher order subharmonics (SH), superharmonics and chaos at very low excitation pressures (e.g. 1 kPa). For LCMBs sonicated by their SH resonance frequency and in line with experimental observations with increasing pressure, P2 oscillations exhibit three stages: generation at low acoustic pressures, disappearance and re-generation. Within non-destructive oscillation regimes and by pressure amplitude increase, LCMBs can also exhibit two saddle node (SN) bifurcations resulting in possible abrupt enhancement of the scattered pressure. The first SN resembles the pressure dependent resonance phenomenon in uncoated MBs and the second SN resembles the pressure dependent SH resonance. Depending on the initial surface tension of the LCMBs, the nonlinear behavior may also be suppressed for a wide range of excitation pressures.

The problem of attenuation and sound speed of bubbly media has remained partially unsolved. Comprehensive data regarding pressure-dependent changes of the attenuation and sound speed of a bubbly medium are not available. Our theoretical understanding of the problem is limited to linear or semi-linear theoretical models, which are not accurate in the regime of large amplitude bubble oscillations. Here, by controlling the size of the lipid coated bubbles (mean diameter of ≈5.4μm), we report the first time observation and characterization of the simultaneous pressure dependence of sound speed and attenuation in bubbly water below, at and above microbubbles resonance (frequency range between 1-3 MHz). With increasing acoustic pressure (between 12.5-100 kPa), the frequency of the peak attenuation and sound speed decreases while maximum and minimum amplitudes of the sound speed increase. We propose a nonlinear model for the estimation of the pressure dependent sound speed and attenuation with good agreement with the experiments. The model calculations are validated by comparing with the linear and semi-linear models predictions. One of the major challenges of the previously developed models is the significant overestimation of the attenuation at the bubble resonance at higher void fractions (e.g. 0.005). We addressed this problem by incorporating bubble-bubble interactions and comparing the results to experiments. Influence of the bubble-bubble interactions increases with increasing pressure. Within the examined exposure parameters, we numerically show that, even for low void fractions (e.g. 5.1×10^-6) with increasing pressure the sound speed may become 4 times higher than the sound speed in the non-bubbly medium.

The bubble oscillator is a highly nonlinear system, which makes it difficult to generate a comprehensive understanding of its oscillatory behavior. One method used to investigate such complex dynamical systems is the bifurcation analysis. Numerous investigations have employed the method of bifurcation diagrams to study the effect of different control parameters on the bubble behavior. These studies, however, focused mainly on investigating the subharmonic (SH) and chaotic oscillations of the bubbles. Super-harmonic (SuH) and ultra-harmonic (UH) bubble oscillations remain under-investigated. One reason is that the conventional method used for generating bifurcation diagrams cannot reliably identify features that are responsible for the identification of SuH and UH oscillations. Additionally, the conventional method cannot distinguish between the UHs and SHs. We introduce a simple procedure to address this shortcoming. In this method, the maxima of the bubble oscillatory response were selected and plotted alongside the traditional bifurcation points for the corresponding control parameter. Results show that depending on the control parameters the conventional method or the method of maxima may miss intricate details of the oscillations. In order to have a comprehensive knowledge on the rich dynamics of the system, the two methods should be employed side by side. Through plotting the two bifurcation structures in tandem, the oscillatory behavior of the bubble was analyzed with more detail, and stable SuH and UH bubble oscillations were investigated. Based on this new analysis, the conditions for the generation and amplification of UH and SuH regimes are discussed.