Nonlinear ultrasound simulation in an axisymmetric coordinate system using a k-space pseudospectral method.

Area of Science:

• Computational physics
• Acoustics
• Biomedical engineering

Background:

• Accurate modeling of nonlinear ultrasound propagation is crucial for advanced medical imaging and therapeutic applications.
• Heterogeneous and absorbing media present significant challenges for existing ultrasound models.
• Axisymmetric coordinate systems are often used to simplify complex geometries in acoustic simulations.

Purpose of the Study:

• To develop and validate a robust full-wave computational model for nonlinear ultrasound propagation.
• To simulate ultrasound behavior in complex, heterogeneous, and absorbing media.
• To demonstrate the model's utility in realistic scenarios, such as transcranial ultrasound imaging.

Main Methods:

• Developed a full-wave model in an axisymmetric coordinate system.
• Employed a k-space pseudospectral time domain method for solving model equations.
• Utilized Fourier collocation spectral method and discrete trigonometric transforms for spatial gradients, and a k-space corrected finite difference scheme for time integration.

Main Results:

• The model accurately simulates linear and nonlinear ultrasound propagation, including absorption and dispersion.
• Validation against analytical solutions for plane waves, transducer fields, and scattering by a sphere confirmed model accuracy.
• Successful simulation of nonlinear transcranial ultrasound using a simplified head model demonstrated practical applicability.

Conclusions:

• The developed full-wave model provides accurate and efficient simulation of nonlinear ultrasound propagation in complex media.
• The k-space pseudospectral time domain method effectively handles spatial gradients and time integration, reducing numerical dispersion.
• This model is a valuable tool for advancing research and applications in medical ultrasound, particularly for transcranial imaging.