[Paper Review] Pressure dependence of the ultrasound attenuation and speed in bubbly media: Theory and experiment

Amin Jafari Sojahrood, Q. Li+4 more|arXiv (Cornell University)|Nov 19, 2018

Ultrasound and Cavitation PhenomenaMaterials Science5 references18 citations

TL;DR

This paper proposes a nonlinear model for predicting ultrasound attenuation and sound speed in bubbly media that accounts for pressure-dependent, nonlinear microbubble oscillations without linear approximations. The model, validated experimentally, shows strong agreement with data and enables accurate characterization of microbubble shell properties using simultaneous measurements of sound speed and attenuation.

ABSTRACT

Results of the measurements of sound speed and attenuation in a bubbly medium are reported. Monodisperse bubble solutions are sonicated with broadband ultrasound pulses with pressure amplitudes ranging between 12.5-100 kPa. Fundamental relationships between the frequency dependent attenuation, sound speed and pressure are established. A new model for the estimation of sound speed and attenuation is derived that incorporates the effect of nonlinear bubble oscillations on the wave propagation in the bubbly media. Model predictions are in good agreement with experimental results.

Motivation & Objective

• To develop a comprehensive nonlinear model for predicting pressure-dependent ultrasound attenuation and sound speed in bubbly media.
• To address the limitations of linear approximations in existing models, which fail under typical biomedical ultrasound exposure conditions.
• To experimentally measure and validate the pressure dependence of sound speed and attenuation in monodisperse microbubble suspensions.
• To demonstrate that simultaneous measurement of sound speed and attenuation improves accuracy in characterizing microbubble shell parameters.
• To provide a framework free from the $\frac{dP}{dV}$ term issues common in prior models, enabling robust prediction in highly nonlinear regimes.

Proposed method

• Derives a theoretical model based on the Caflisch equation for wave propagation in a bubbly medium, incorporating full nonlinear dynamics of microbubble radial oscillations.
• Uses the radial oscillation of microbubbles as the sole input, avoiding complex analytical expressions for energy loss terms.
• Introduces a pressure-dependent scattering cross-section to account for nonlinear bubble behavior under varying ultrasound pressure amplitudes (12.5–100 kPa).
• Employs a nonlinear approach to calculate both the real (sound speed) and imaginary (attenuation) parts of the wave number without linearization.
• Validates the model against experimental data from broadband ultrasound pulses in monodisperse microbubble suspensions.
• Fits shell parameters (surface tension, elasticity, viscosity) by simultaneously matching predicted and measured attenuation and sound speed curves.

Experimental results

Research questions

• RQ1 How does ultrasound pressure amplitude influence the sound speed and attenuation in a bubbly medium with microbubbles?
• RQ2 Can a nonlinear model that avoids linear approximations accurately predict both attenuation and sound speed in bubbly media under high-pressure ultrasound exposure?
• RQ3 What is the experimental relationship between ultrasound pressure and changes in sound speed in microbubble suspensions?
• RQ4 How do simultaneous measurements of sound speed and attenuation improve the accuracy of microbubble shell parameter characterization?
• RQ5 Can the model overcome the limitations of prior approaches that rely on $\frac{dP}{dV}$ and fail in nonlinear oscillation regimes?

Key findings

• The model predicts both attenuation and sound speed with high accuracy across a wide range of ultrasound pressures (12.5–100 kPa), outperforming linear and semi-linear models at higher pressures.
• Experimental results confirm a measurable, pressure-dependent change in sound speed in bubbly media, which had not been previously experimentally investigated.
• The model shows good agreement with experimental data, particularly in capturing nonlinear trends in attenuation and sound speed that linear models fail to reproduce.
• Simultaneous fitting of sound speed and attenuation data enables more accurate determination of microbubble shell parameters than fitting attenuation alone.
• The model does not rely on the $\frac{dP}{dV}$ term, avoiding known difficulties in nonlinear regimes and enabling robust predictions for complex shell behaviors.
• Even at low microbubble concentrations and small bubble sizes, the model successfully captures and predicts small but measurable changes in sound speed, validating its sensitivity and reliability.