Modelling power-law ultrasound absorption using a time-fractional, static memory, Fourier pseudo-spectral method.

Area of Science:

• Biomedical Engineering
• Computational Physics
• Acoustics

Background:

• Ultrasound absorption in biological tissues exhibits frequency-dependent power-law behavior.
• Modeling this phenomenon accurately is crucial for applications like medical imaging and therapy.
• Existing models often use approximations or computationally intensive methods.

Purpose of the Study:

• To develop and implement an efficient numerical method for simulating frequency-dependent power-law ultrasound absorption in tissue.
• To model ultrasound propagation using first-order linear wave equations with fractional time derivative loss.
• To compare the proposed method with existing fractional-Laplacian models.

Main Methods:

• A numerical method based on the Caputo fractional time derivative is implemented.
• The method incorporates full problem history within an iterative procedure, achieving static memory cost.
• The spatial domain is discretized using the Fourier spectral method.

Main Results:

• The numerical method effectively models frequency-dependent power-law ultrasound absorption.
• The fractional time derivative approach demonstrates computational efficiency with fixed memory requirements.
• Comparisons show the fractional time derivative model allows for spatially varying power-law absorption, unlike the fractional-Laplacian operator.

Conclusions:

• The developed numerical method provides an efficient and accurate tool for modeling ultrasound absorption in tissues.
• The use of fractional time derivatives offers advantages in handling spatially varying absorption properties.
• This method has potential implications for improving ultrasound-based medical technologies.