Dependence of the subharmonic signal from contrast agent microbubbles on ambient pressure: A theoretical analysis

Impact of Microbubble Degradation and Flow Velocity on Subharmonic-aided Pressure Estimation (SHAPE): An Experimental Investigation

OBJECTIVE

This study aimed to investigate the impact of microbubble degradation and flow velocity on Sub-Harmonic Aided Pressure Estimation (SHAPE), and to explore the correlation between subharmonic amplitude and pressure as a single factor.

METHODS

We develop an open-loop vascular phantom platform system and utilize a commercial ultrasound machine and microbubbles for subharmonic imaging. Subharmonic amplitude was measured continuously at constant pressure and flow velocity to assess the impact of microbubble degradation. Flow velocity was varied within a range of 4-14 cm/s at constant pressure to investigate its relationship to subharmonic amplitude. Furthermore, pressure was varied within a range of 10-110 mm Hg at constant flow velocity to assess its isolated effect on subharmonic amplitude.

RESULTS

Under constant pressure and flow velocity, subharmonic amplitude exhibited a continuous decrease at an average rate of 0.221 dB/min, signifying ongoing microbubble degradation during the experimental procedures. Subharmonic amplitude demonstrated a positive correlation with flow velocity, with a variation ratio of 0.423 dB/(cm/s). Under controlled conditions of microbubble degradation and flow velocity, a strong negative linear correlation was observed between pressure and subharmonic amplitude across different Mechanical Index (MI) settings (all R2 > 0.90). The sensitivity of SHAPE was determined to be 0.025 dB/mmHg at an MI of 0.04.

CONCLUSION

The assessment of SHAPE sensitivity is affected by microbubble degradation and flow velocity. Excluding the aforementioned influencing factors, a strong linear negative correlation between pressure and subharmonic amplitude was still evident, albeit with a sensitivity coefficient lower than previously reported values.

Collective nonlinear behavior of interacting polydisperse microbubble clusters

Acoustically excited microbubbles (MBs) have shown to exhibit rich dynamics, enabling them to be employed in various applications ranging from chemistry to medicine. Exploiting the full potential of MBs for applications requires a good understanding of their complex dynamics. Improved understanding of MB oscillations can lead to further enhancement in optimizing their efficacy in many applications and also invent new ones. Oscillating MBs have been shown to generate secondary pressure waves that modify the dynamics of the MBs in their proximity. A modified Keller-Miksis equation is used to account for inter-bubble interactions. The oscillatory dynamics of each MB within clusters was computed by numerically solving the resulting system of coupled nonlinear second order differential equations in potential fluid flow. Frequency response analysis and bifurcation diagrams were employed to track the dynamics of interacting MBs. We start with investigating the effect of inter-bubble interactions for cases of three and four MBs over a wide range of acoustic and geometric parameters. Emergent collective behavior was observed which are dominated by the dynamics of the largest MB within the cluster. The emergent dynamics of smaller MBs within clusters can be characterized by constructive and destructive inter-bubble interactions. In constructive interactions, the radial oscillations of smaller MBs matched those of the largest MB and their oscillations are amplified. In destructive interactions, the oscillations of smaller bubbles are suppressed so that their oscillations match those of the largest MB. Furthermore, a special case of constructive interactions is presented where dominant MB (largest) can force smaller MBs into period doubling and subharmonic oscillations. The collective behavior is further investigated in large MB cluster and it is shown that largest MBs, even in small numbers can force smaller ones into period doubling and subharmonic oscillations.

Improvement of Detection Sensitivity of Microbubbles as Sensors to Detect Ambient Pressure

Microbubbles are considered a promising tool for noninvasive estimation of local blood pressure. It is reported that the subharmonic scattering amplitude of microbubbles decreases by 9 to 12 dB when immersed in the media under an ambient pressure variation from 0 to 180 mmHg. However, the pressure sensitivity still needs to be improved to satisfy clinical diagnostic requirements. Here, we investigated the effects of acoustic parameters on the pressure sensitivity of microbubbles through measuring the acoustic attenuation and scattering properties of commercially available SonoVue microbubbles. Our results showed that the first harmonic, subharmonic, and ultraharmonic amplitudes of microbubbles were reduced by 6.6 dB, 10.9 dB, and 9.3 dB at 0.225 mechanical index (MI), 4.6 dB, 19.8 dB, and 12.3 dB at 0.25 MI, and 18.5 dB, 17.6 dB, and 12.6 dB at 0.3 MI, respectively, when the ambient pressure increased from 0 to 180 mmHg. Our finding revealed that a moderate MI (0.25–0.4) exciting microbubbles could significantly improve their sensitivities to detect ambient pressure.