Discrete Approximations of Acoustic Source Distributions.

Area of Science:

• Medical Imaging
• Computational Ultrasound
• Numerical Modeling

Background:

• Accurate modeling of finite spatial extent sources is crucial for ultrasound and medical imaging applications.
• Existing time-domain methods (e.g., finite-difference time-domain, pseudospectral) often use Cartesian grids, leading to artifacts like staircasing errors.
• Efficient and precise representation of source distributions over computational grids remains a significant challenge.

Purpose of the Study:

• To introduce a novel optimization-based approach for representing source distributions in numerical simulations.
• To address the limitations of traditional grid-based methods in accurately capturing source geometries.
• To enhance the fidelity of ultrasound and medical imaging simulations by minimizing representation artifacts.

Main Methods:

• Framing the source distribution representation as an optimization problem in the Fourier domain.
• Utilizing a preselected set of grid points to control computational cost.
• Fine-tuning the optimization to specific wavenumber ranges relevant to numerical methods.

Main Results:

• Demonstrated a method to represent source distributions over a grid by solving an optimization problem in the Fourier domain.
• Successfully applied the method to the specific case of a spherical cap or bowl source.
• The proposed Fourier domain optimization offers improved control over computational cost and accuracy.

Conclusions:

• The Fourier domain optimization approach provides a robust alternative for modeling source distributions with finite spatial extent.
• This method effectively mitigates artifacts commonly encountered in Cartesian grid representations.
• The technique is adaptable and can be optimized for specific numerical methods and frequency ranges in medical imaging.