Multiharmonic algorithms for contrast-enhanced ultrasound
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908834889465856 |
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| author | Nikolić, Vanja Rauscher, Teresa |
| author_facet | Nikolić, Vanja Rauscher, Teresa |
| contents | Harmonic generation plays a crucial role in contrast-enhanced ultrasound, both for imaging and therapeutic applications. However, accurately capturing these nonlinear effects is computationally very demanding when using traditional time-domain approaches. To address this issue, in this work, we develop algorithms based on a time discretization that uses a multiharmonic Ansatz applied to a model that couples the Westervelt equation for acoustic pressure with a volume-based approximation of the Rayleigh--Plesset equation for the dynamics of microbubble contrast agents. We first rigorously establish the existence of time-periodic solutions for this Westervelt-ODE system. We then derive a multiharmonic representation of the system under time-periodic excitation and develop iterative algorithms that rely on the successive computation of higher harmonics under the assumption of real-valued or complex solution fields. In the real-valued setting, we characterize the approximation error in terms of the number of harmonics and a contribution owing to the fixed-point iteration. Finally, we investigate these algorithms numerically and illustrate how the number of harmonics and presence of microbubbles influence the propagation of acoustic waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13335 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiharmonic algorithms for contrast-enhanced ultrasound Nikolić, Vanja Rauscher, Teresa Numerical Analysis Analysis of PDEs 35L05, 35L72, 34A34, 35J05 Harmonic generation plays a crucial role in contrast-enhanced ultrasound, both for imaging and therapeutic applications. However, accurately capturing these nonlinear effects is computationally very demanding when using traditional time-domain approaches. To address this issue, in this work, we develop algorithms based on a time discretization that uses a multiharmonic Ansatz applied to a model that couples the Westervelt equation for acoustic pressure with a volume-based approximation of the Rayleigh--Plesset equation for the dynamics of microbubble contrast agents. We first rigorously establish the existence of time-periodic solutions for this Westervelt-ODE system. We then derive a multiharmonic representation of the system under time-periodic excitation and develop iterative algorithms that rely on the successive computation of higher harmonics under the assumption of real-valued or complex solution fields. In the real-valued setting, we characterize the approximation error in terms of the number of harmonics and a contribution owing to the fixed-point iteration. Finally, we investigate these algorithms numerically and illustrate how the number of harmonics and presence of microbubbles influence the propagation of acoustic waves. |
| title | Multiharmonic algorithms for contrast-enhanced ultrasound |
| topic | Numerical Analysis Analysis of PDEs 35L05, 35L72, 34A34, 35J05 |
| url | https://arxiv.org/abs/2504.13335 |