Explaining the correlation between subharmonic amplitude and ambient pressure for subharmonic-aided pressure estimation (SHAPE)

Abstract

Background

Subharmonic aided pressure estimation (SHAPE) is an innovative non-invasive technique that leverages ultrasound subharmonic imaging to estimate pressure. This method exploits the “negative correlation between subharmonic amplitude and ambient pressure” observed in experimental settings. Despite extensive experimental validation and some promising results in clinical studies, the underlying mechanism of SHAPE remains incompletely understood. Although some studies have attempted to provide theoretical explanations, definitive conclusions have yet to be reached. In addition, theoretical investigations have mainly focused on the steady oscillation of bubbles under long pulse excitation, which contrasts with the short pulse excitation required for clinical SHAPE applications. An understanding of the SHAPE principle under short pulse excitation is needed.

Methods

The exponential elasticity model (EEM) was used to simulate Sonazoid bubbles, and a probe-to-probe acoustic propagation model was introduced to mimic a practical SHAPE scenario. The simulated acoustic signals in response to three-cycle sinusoidal pulse excitations were analyzed for spectral composition. The relationship between microbubble oscillation patterns and subharmonic characteristics was identified through detailed investigation.

Results

For the excitation pulse of 2.5 MHz frequency and 350 kPa magnitude, bubbles larger than the resonance radius (2.29 μm) exhibited significant subharmonics in the magnitude spectrum, while bubbles smaller than the subharmonic resonance radius (3.85 μm) showed the activity of scattering subharmonic energy and the sensitivity to ambient pressure. The emergence of subharmonics when increasing excitation power was related to the increasing amplification of the bubble self-oscillation and the period-doubling features in the acoustically forced oscillation. The negative correlation between subharmonic amplitude and ambient pressure was attributed to the reduced self-oscillation caused by increasing ambient pressure and hence bubble size reduction. Microbubbles falling between 2 and 3 μm showed the desired subharmonic sensitivity to ambient pressure under the specified excitation conditions.

Conclusion

The transient oscillatory behavior of microbubbles in response to short pulse excitation, characterized by a ringing down self-oscillation after the acoustic forcing effect has ceased, is crucial for understanding the subharmonic emergence and the observed negative correlation between subharmonic amplitude and ambient pressure. The proposed concepts of subharmonic resonance radius, subharmonic-significant bubbles, and subharmonic-active bubbles provide valuable insights into the diverse subharmonic behavior of microbubbles. The theoretical explanation of this negative correlation highlights the importance of using subharmonic-significant-and-active bubbles for SHAPE applications.