Bibliographic Details
| Title: |
Mathematical models for nonlinear ultrasound contrast imaging with microbubbles |
| Authors: |
Nikolić, Vanja, Rauscher, Teresa |
| Publication Year: |
2024 |
| Collection: |
Computer Science
Mathematics |
| Subject Terms: |
Mathematics - Analysis of PDEs, Mathematics - Numerical Analysis, 35L05, 35L72, 34A34 |
| More Details: |
Ultrasound contrast imaging is a specialized imaging technique that applies microbubble contrast agents to traditional medical sonography, providing real-time visualization of blood flow and vessels. Gas-filled microbubbles are injected into the body, where they undergo compression and rarefaction and interact nonlinearly with the ultrasound waves. Therefore, the propagation of sound through a bubbly liquid is a strongly nonlinear problem that can be modeled by a nonlinear acoustic wave equation for the propagation of the pressure waves coupled via the source terms to a nonlinear ordinary differential equation of Rayleigh-Plesset type for the bubble dynamics. In this work, we first derive a hierarchy of such coupled models based on constitutive laws. We then focus on the coupling of Westervelt's acoustic equation to Rayleigh-Plesset type equations, where we rigorously show the existence of solutions locally in time under suitable conditions on the initial pressure-microbubble data and final time. Thirdly, we devise and discuss numerical experiments on both single-bubble dynamics and the interaction of microbubbles with ultrasound waves. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2408.06108 |
| Accession Number: |
edsarx.2408.06108 |
| Database: |
arXiv |
