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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\u2013Plesset 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\u2019s acoustic equation to Rayleigh\u2013Plesset 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. Third, we devise and discuss numerical experiments on both single-bubble dynamics and the interaction of microbubbles with ultrasound waves.<\/jats:p>","DOI":"10.1137\/24m1691235","type":"journal-article","created":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T09:04:48Z","timestamp":1745571888000},"page":"961-982","source":"Crossref","is-referenced-by-count":4,"title":["Mathematical Models for Nonlinear Ultrasound Contrast Imaging with Microbubbles"],"prefix":"10.1137","volume":"85","author":[{"given":"Vanja","family":"Nikoli\u0107","sequence":"first","affiliation":[{"name":"Department of Mathematics, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3056-7086","authenticated-orcid":false,"given":"Teresa","family":"Rauscher","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Klagenfurt, Universit\u00e4tsstra\u00dfe 65\u201367, A-9020 Klagenfurt, Austria."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,4,25]]},"reference":[{"key":"ref1","author":"Baratta I. 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