Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles
To facilitate practical medical applications such as cancer treatment utilizing focused ultrasound and bubbles, a mathematical model that can describe the soft viscoelasticity of human body, the nonlinear propagation of focused ultrasound, and the nonlinear oscillations of multiple bubbles is theore...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-07-01
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| Series: | Ultrasonics Sonochemistry |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1350417723001670 |
| _version_ | 1797801777996759040 |
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| author | Shunsuke Kagami Tetsuya Kanagawa |
| author_facet | Shunsuke Kagami Tetsuya Kanagawa |
| author_sort | Shunsuke Kagami |
| collection | DOAJ |
| description | To facilitate practical medical applications such as cancer treatment utilizing focused ultrasound and bubbles, a mathematical model that can describe the soft viscoelasticity of human body, the nonlinear propagation of focused ultrasound, and the nonlinear oscillations of multiple bubbles is theoretically derived and numerically solved. The Zener viscoelastic model and Keller–Miksis bubble equation, which have been used for analyses of single or few bubbles in viscoelastic liquid, are used to model the liquid containing multiple bubbles. From the theoretical analysis based on the perturbation expansion with the multiple-scales method, the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, which has been used as a mathematical model of weakly nonlinear propagation in single phase liquid, is extended to viscoelastic liquid containing multiple bubbles. The results show that liquid elasticity decreases the magnitudes of the nonlinearity, dissipation, and dispersion of ultrasound and increases the phase velocity of the ultrasound and linear natural frequency of the bubble oscillation. From the numerical calculation of resultant KZK equation, the spatial distribution of the liquid pressure fluctuation for the focused ultrasound is obtained for cases in which the liquid is water or liver tissue. In addition, frequency analysis is carried out using the fast Fourier transform, and the generation of higher harmonic components is compared for water and liver tissue. The elasticity suppresses the generation of higher harmonic components and promotes the remnant of the fundamental frequency components. This indicates that the elasticity of liquid suppresses shock wave formation in practical applications. |
| first_indexed | 2024-03-13T04:55:39Z |
| format | Article |
| id | doaj.art-7cb84595b23f4775a9f96004319affd6 |
| institution | Directory Open Access Journal |
| issn | 1350-4177 |
| language | English |
| last_indexed | 2024-03-13T04:55:39Z |
| publishDate | 2023-07-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ultrasonics Sonochemistry |
| spelling | doaj.art-7cb84595b23f4775a9f96004319affd62023-06-18T05:01:13ZengElsevierUltrasonics Sonochemistry1350-41772023-07-0197106455Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubblesShunsuke Kagami0Tetsuya Kanagawa1Department of Engineering Mechanics and Energy, Degree Programs in Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, JapanDepartment of Engineering Mechanics and Energy, Institute of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Japan; Corresponding author.To facilitate practical medical applications such as cancer treatment utilizing focused ultrasound and bubbles, a mathematical model that can describe the soft viscoelasticity of human body, the nonlinear propagation of focused ultrasound, and the nonlinear oscillations of multiple bubbles is theoretically derived and numerically solved. The Zener viscoelastic model and Keller–Miksis bubble equation, which have been used for analyses of single or few bubbles in viscoelastic liquid, are used to model the liquid containing multiple bubbles. From the theoretical analysis based on the perturbation expansion with the multiple-scales method, the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, which has been used as a mathematical model of weakly nonlinear propagation in single phase liquid, is extended to viscoelastic liquid containing multiple bubbles. The results show that liquid elasticity decreases the magnitudes of the nonlinearity, dissipation, and dispersion of ultrasound and increases the phase velocity of the ultrasound and linear natural frequency of the bubble oscillation. From the numerical calculation of resultant KZK equation, the spatial distribution of the liquid pressure fluctuation for the focused ultrasound is obtained for cases in which the liquid is water or liver tissue. In addition, frequency analysis is carried out using the fast Fourier transform, and the generation of higher harmonic components is compared for water and liver tissue. The elasticity suppresses the generation of higher harmonic components and promotes the remnant of the fundamental frequency components. This indicates that the elasticity of liquid suppresses shock wave formation in practical applications.http://www.sciencedirect.com/science/article/pii/S1350417723001670Focused ultrasoundViscoelastic mediaBubbly liquidWeakly nonlinear waveKZK equationHIFU |
| spellingShingle | Shunsuke Kagami Tetsuya Kanagawa Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles Ultrasonics Sonochemistry Focused ultrasound Viscoelastic media Bubbly liquid Weakly nonlinear wave KZK equation HIFU |
| title | Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles |
| title_full | Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles |
| title_fullStr | Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles |
| title_full_unstemmed | Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles |
| title_short | Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles |
| title_sort | weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles |
| topic | Focused ultrasound Viscoelastic media Bubbly liquid Weakly nonlinear wave KZK equation HIFU |
| url | http://www.sciencedirect.com/science/article/pii/S1350417723001670 |
| work_keys_str_mv | AT shunsukekagami weaklynonlinearfocusedultrasoundinviscoelasticmediacontainingmultiplebubbles AT tetsuyakanagawa weaklynonlinearfocusedultrasoundinviscoelasticmediacontainingmultiplebubbles |