Multiharmonic Algorithms for Contrast-Enhanced Ultrasound.

Area of Science:

• Acoustics and Ultrasound Physics
• Nonlinear Acoustics
• Computational Physics

Background:

• Harmonic generation is vital for contrast-enhanced ultrasound (CEUS) imaging and therapy.
• Traditional time-domain methods for simulating nonlinear acoustics in CEUS are computationally intensive.
• Accurate modeling of microbubble dynamics is essential for understanding CEUS.

Purpose of the Study:

• To develop computationally efficient algorithms for simulating nonlinear acoustic effects in CEUS.
• To model the coupled dynamics of acoustic pressure and microbubble agents.
• To establish theoretical foundations for time-periodic solutions in acoustic models.

Main Methods:

• Developed a multiharmonic Ansatz applied to a model coupling the Westervelt equation (acoustic pressure) and a volume-based Rayleigh-Plesset equation (microbubble dynamics).
• Established the existence of time-periodic solutions for the Westervelt-ODE system.
• Derived a multiharmonic representation and developed iterative algorithms for real-valued and complex-valued solutions.
• Characterized approximation error based on the number of harmonics and fixed-point iteration.

Main Results:

• Successfully established time-periodic solutions for the coupled Westervelt-ODE system.
• Developed iterative algorithms for computing higher harmonics, improving computational efficiency.
• Quantified approximation error in the real-valued solution setting.
• Numerically demonstrated the influence of harmonic number and microbubbles on acoustic wave propagation.

Conclusions:

• The proposed multiharmonic algorithms offer a computationally efficient alternative to traditional time-domain methods for CEUS.
• The study provides a rigorous mathematical framework and numerical validation for modeling nonlinear acoustics with microbubbles.
• These advancements have the potential to improve both imaging and therapeutic applications of contrast-enhanced ultrasound.