Fast Nonlinear Ultrasound Propagation Simulation Using a Slowly Varying Envelope Approximation

Medical systems usually consider linear propagation of ultrasound, an approximation of reality. However, numerous studies have attempted to accurately simulate the nonlinear pressure wave distortion and to evaluate the contribution of harmonic frequencies. In such simulations, the computation time i...

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Published in:	IEEE transactions on ultrasonics, ferroelectrics, and frequency control Vol. 64; no. 6; pp. 1015 - 1022
Main Authors:	Varray, Francois, Toulemonde, Matthieu, Bernard, Adeline, Basset, Olivier, Cachard, Christian
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.06.2017 The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers
Subjects:	Acoustics Approximation Attenuation Bioengineering Coefficient of nonlinearity Computational modeling Computer simulation Deviation Distortion Engineering Sciences Fourier analysis Fourier transforms Graphics processing units harmonic Harmonic analysis Harmonics Imaging Life Sciences Mathematical analysis Mathematical model nonlinear ultrasound (US) propagation Nonlinearity Propagation Simulation slowly varying envelope approximation (SVEA) Ultrasonic imaging
ISSN:	0885-3010, 1525-8955, 1525-8955
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Abstract	Medical systems usually consider linear propagation of ultrasound, an approximation of reality. However, numerous studies have attempted to accurately simulate the nonlinear pressure wave distortion and to evaluate the contribution of harmonic frequencies. In such simulations, the computation time is very large, except for the method based on the angular spectrum scheme where the derivative order is reduced using the Fourier transform. However, the harmonic computation is usually limited to the second harmonic because of quasi-linear approximation. In this paper, a slowly varying envelope approximation (SVEA) is used in the Fourier domain to compute the entire nonlinear distortion induced, including high harmonics and nonlinear mixing frequencies. The simulation by SVEA is evaluated by comparison with other simulation tools. The obtained deviation and difference remain low enough to fully validate such an approximation. Moreover, the simulator is implemented on a GPU to obtain a very fast tool, where the full nonlinear distorted 3-D + t field is computed in less than 10 s.
AbstractList	Medical systems usually consider linear propagation of ultrasound, an approximation of reality. However, numerous studies have attempted to accurately simulate the nonlinear pressure wave distortion and to evaluate the contribution of harmonic frequencies. In such simulations, the computation time is very large, except for the method based on the angular spectrum scheme where the derivative order is reduced using the Fourier transform. However, the harmonic computation is usually limited to the second harmonic because of quasi-linear approximation. In this paper, a slowly varying envelope approximation (SVEA) is used in the Fourier domain to compute the entire nonlinear distortion induced, including high harmonics and nonlinear mixing frequencies. The simulation by SVEA is evaluated by comparison with other simulation tools. The obtained deviation and difference remain low enough to fully validate such an approximation. Moreover, the simulator is implemented on a GPU to obtain a very fast tool, where the full nonlinear distorted 3-D + t field is computed in less than 10 s. Medical systems usually consider linear propagation of ultrasound, an approximation of reality. However, numerous studies have attempted to accurately simulate the nonlinear pressure wave distortion and to evaluate the contribution of harmonic frequencies. In such simulations, the computation time is very large, except for the method based on the angular spectrum scheme where the derivative order is reduced using the Fourier transform. However, the harmonic computation is usually limited to the second harmonic because of quasi-linear approximation. In this paper, a slowly varying envelope approximation (SVEA) is used in the Fourier domain to compute the entire nonlinear distortion induced, including high harmonics and nonlinear mixing frequencies. The simulation by SVEA is evaluated by comparison with other simulation tools. The obtained deviation and difference remain low enough to fully validate such an approximation. Moreover, the simulator is implemented on a GPU to obtain a very fast tool, where the full nonlinear distorted [Formula: see text] field is computed in less than 10 s.Medical systems usually consider linear propagation of ultrasound, an approximation of reality. However, numerous studies have attempted to accurately simulate the nonlinear pressure wave distortion and to evaluate the contribution of harmonic frequencies. In such simulations, the computation time is very large, except for the method based on the angular spectrum scheme where the derivative order is reduced using the Fourier transform. However, the harmonic computation is usually limited to the second harmonic because of quasi-linear approximation. In this paper, a slowly varying envelope approximation (SVEA) is used in the Fourier domain to compute the entire nonlinear distortion induced, including high harmonics and nonlinear mixing frequencies. The simulation by SVEA is evaluated by comparison with other simulation tools. The obtained deviation and difference remain low enough to fully validate such an approximation. Moreover, the simulator is implemented on a GPU to obtain a very fast tool, where the full nonlinear distorted [Formula: see text] field is computed in less than 10 s. Medical systems usually consider linear propagation of ultrasound, an approximation of reality. However, numerous studies have attempted to accurately simulate the nonlinear pressure wave distortion and to evaluate the contribution of harmonic frequencies. In such simulations, the computation time is very large, except for the method based on the angular spectrum scheme where the derivative order is reduced using the Fourier transform. However, the harmonic computation is usually limited to the second harmonic because of quasi-linear approximation. In this paper, a slowly varying envelope approximation (SVEA) is used in the Fourier domain to compute the entire nonlinear distortion induced, including high harmonics and nonlinear mixing frequencies. The simulation by SVEA is evaluated by comparison with other simulation tools. The obtained deviation and difference remain low enough to fully validate such an approximation. Moreover, the simulator is implemented on a GPU to obtain a very fast tool, where the full nonlinear distorted [Formula: see text] field is computed in less than 10 s. Medical systems usually consider linear propagation of ultrasound, an approximation of reality. However, numerous studies have attempted to accurately simulate the nonlinear pressure wave distortion and to evaluate the contribution of harmonic frequencies. In such simulations, the computation time is very large, except for the method based on the angular spectrum scheme where the derivative order is reduced using the Fourier transform. However, the harmonic computation is usually limited to the second harmonic because of quasi-linear approximation. In this paper, a slowly varying envelope approximation (SVEA) is used in the Fourier domain to compute the entire nonlinear distortion induced, including high harmonics and nonlinear mixing frequencies. The simulation by SVEA is evaluated by comparison with other simulation tools. The obtained deviation and difference remain low enough to fully validate such an approximation. Moreover, the simulator is implemented on a GPU to obtain a very fast tool, where the full nonlinear distorted [Formula Omitted] field is computed in less than 10 s.
Author	Cachard, Christian Toulemonde, Matthieu Bernard, Adeline Varray, Francois Basset, Olivier
Author_xml	– sequence: 1 givenname: Francois surname: Varray fullname: Varray, Francois email: francois.varry@creatis.insa-lyon.fr organization: INSERM, Univ. Lyon, Lyon, France – sequence: 2 givenname: Matthieu surname: Toulemonde fullname: Toulemonde, Matthieu organization: INSERM, Univ. Lyon, Lyon, France – sequence: 3 givenname: Adeline surname: Bernard fullname: Bernard, Adeline organization: INSERM, Univ. Lyon, Lyon, France – sequence: 4 givenname: Olivier surname: Basset fullname: Basset, Olivier organization: INSERM, Univ. Lyon, Lyon, France – sequence: 5 givenname: Christian surname: Cachard fullname: Cachard, Christian organization: INSERM, Univ. Lyon, Lyon, France
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SubjectTerms	Acoustics Approximation Attenuation Bioengineering Coefficient of nonlinearity Computational modeling Computer simulation Deviation Distortion Engineering Sciences Fourier analysis Fourier transforms Graphics processing units harmonic Harmonic analysis Harmonics Imaging Life Sciences Mathematical analysis Mathematical model nonlinear ultrasound (US) propagation Nonlinearity Propagation Simulation slowly varying envelope approximation (SVEA) Ultrasonic imaging
Title	Fast Nonlinear Ultrasound Propagation Simulation Using a Slowly Varying Envelope Approximation
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