Wave envelopes method for description of nonlinear acoustic wave propagation

Area of Science:

• Acoustics and Ultrasonics
• Computational Physics
• Biomedical Engineering

Background:

• Nonlinear acoustic wave propagation is crucial for medical ultrasound imaging and therapy.
• Accurate prediction of 4D acoustic fields requires computationally intensive methods.
• Existing models often rely on approximations like the paraxial approximation.

Purpose of the Study:

• To introduce a novel, computationally efficient numerical algorithm for predicting 4D acoustic fields.
• To model nonlinear acoustic propagation in lossy media from arbitrary sources.
• To overcome the computational limitations of conventional methods for nonlinear wave modeling.

Main Methods:

• Developed the Wave Envelopes (WE) approach based on the second-order nonlinear differential wave equation.
• Employed an incremental stepping scheme for forward wave propagation.
• Utilized operator-splitting to independently handle diffraction, absorption, and nonlinear harmonic interactions.

Main Results:

• The WE method, specifically the Time-Averaged Wave Envelopes (TAWE) variant, reduces computational time by at least an order of magnitude.
• Achieved significant speedups (e.g., 10-15 minutes vs. 2-8 hours) compared to conventional methods for complex source geometries.
• Demonstrated accurate prediction of spatial field distributions for pulsed acoustic waves.

Conclusions:

• The WE/TAWE method offers a computationally efficient and accurate solution for 4D nonlinear acoustic field prediction.
• This advancement is highly relevant for optimizing medical ultrasonic imaging and therapeutic systems.
• The model's validity extends to lossy media, arbitrary sources, and both continuous and pulsed waves.