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Multiharmonic Algorithms for Contrast-Enhanced Ultrasound.

Vanja Nikolić1, Teresa Rauscher2

  • 1Department of Mathematics, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.

Journal of Scientific Computing
|March 27, 2026
PubMed
Summary
This summary is machine-generated.

New algorithms improve contrast-enhanced ultrasound by efficiently modeling nonlinear acoustic effects. This approach enhances imaging and therapeutic applications by accurately capturing microbubble dynamics and wave propagation.

Keywords:
Contrast-enhanced ultrasoundHelmholtz equationIterative algorithmsMicrobubblesMultiharmonic expansionsNonlinear acousticsWestervelt’s equation

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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.