Evaluation of a wave vector frequency domain method for nonlinear wave propagation.

Jing, Yun; Clement, Greg T.

doi:10.1121/1.4783902

Cited by 3 publications

(4 citation statements)

References 36 publications

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“…An implicit solution to Eq. (4) can be derived from the 1-D Green's function in an integral form [22], such that ( 2 )).…”

Section: A Governing Equationmentioning

confidence: 99%

“…Additionally, density, speed of sound, attenuation coefficient, power law exponent and nonlinear coefficient can all be spatially varying functions. The Kramers-Kronig dispersion relation is applied by directly replacing the speed of sound with and = (1/̂+ 0 tan( /2) −1 ) −1 [22],where ̂ is the sound speed at zero frequency, is the power law exponent, 0 is the absorption in Np•MHz -y •m -1 . This model, however, is only accurate for media with weak speed of sound contrast.…”

Section: A Governing Equationmentioning

confidence: 99%

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A Modified Mixed Domain Method for Modeling Wave Propagation in Heterogeneous Media

Jing

2018

2018 IEEE International Ultrasonics Symposium (IUS)

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In this paper, phase correction and amplitude compensation are introduced to a previously developed mixed domain method (MDM), which is only accurate for modeling wave propagation in weakly heterogeneous media. Multiple reflections are also incorporated with the one-way model to improve the accuracy. The resulting model is denoted as the modified mixed-domain method (MMDM) and is numerically evaluated for its accuracy and efficiency using two distinct cases: a layered medium and a human skull. It is found that the MMDM is significantly more accurate than the MDM for strongly heterogeneous media, especially when the phase aberrating layer is roughly perpendicular to the acoustic beam. Additionally, convergence study suggests that the secondorder reflection is sufficient for wave modeling in lossy biological media. The method developed in this work could be used to facilitate therapeutic ultrasound for treating brain-related diseases and disorders. 2 I. IntroductionNumerical modeling of acoustic wave propagation in heterogeneous media is of great importance for medical ultrasound. In therapeutic ultrasound applications, for example, numerical simulations can be used to study the phase aberration in MR-guided focused ultrasound surgery[1], [2] and to improve the treatment outcome. For diagnostic ultrasound, numerical modeling has been used as an important tool for image reconstruction[3], [4], [5] as well as to understand the sources of image degradation in ultrasound imaging[6]. A myriad of wave propagation algorithms that take medium heterogeneities into account have been developed. A vast majority of these algorithms operate in the time-domain. Treeby et al.[7] developed a k-space time-domain (KSTD) method using the coupled nonlinear wave equation. Jing et al.[8] alternatively developed the KSTD from the Westervelt equation. Pinton et al.[9] studied a heterogeneous nonlinear attenuating full-wave model based on the finite-difference timedomain (FDTD) method. Frequency-domain methods have also been investigated. For example, Clement and Hynynen[10] combined the Angular Spectrum Approach (ASA) with ray theory to describe the propagation of ultrasound through randomly oriented, dissipative, layered media. Vyas and Christensen[11] modified the conventional ASA method to model linear wave propagation in inhomogeneous media. Most recently, a mixed domain method (MDM) for modeling linear/nonlinear wave propagation in dissipative, weakly heterogeneous media has been presented[12], [13]. A detailed summary of modern ultrasound modeling algorithms can be found in a review paper[14]. Although there are many existing ultrasound numerical models, none can currently achieve efficient yet sufficiently accurate simulations for linear/nonlinear acoustic wave propagation in large-scale, strongly heterogeneous media. Driven by this motivation, this paper aims to establish 3 and validate an accuracy-efficiency balanced numerical model for simulating acoustic wave propagation in strongly heterogeneous media. Within the realm of biome...

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“…An implicit solution to Eq. (4) can be derived from the 1-D Green's function in an integral form [22], such that ( 2 )).…”

Section: A Governing Equationmentioning

confidence: 99%

Section: A Governing Equationmentioning

confidence: 99%

A Modified Mixed Domain Method for Modeling Wave Propagation in Heterogeneous Media

Jing

2018

2018 IEEE International Ultrasonics Symposium (IUS)

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“…To estimate system behavior under the approximate operating conditions of a focused transducer in air, as well as to simulate the transducer pressure field for comparison with experimental measurement, a nonlinear model was implemented based on a wavevectorfrequency domain solution to the Westervelt equation. This approach, described in detail in [28], was specifically developed for its ability to accurately model both omnidirectional nonlinear waves as well as cases of frequency-dependent attenuation. As such, the approach provides an appropriate model equation [29] and methodology [30] for focused transducers.…”

Section: Nonlinear Field Simulationmentioning

confidence: 99%

Ultrasound field measurement using a binary lens

Clement

Nomura

Kamakura

2015

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Field characterization methods using a scattering target in the absence of a point-like receiver have been well described in which scattering is recorded by a relatively large receiver located outside the field of measurement. Unfortunately, such methods are prone to artifacts due to averaging across the receiver surface. To avoid this problem while simultaneously increasing the gain of a received signal, the present study introduces a binary plate lens designed to focus spherically-spreading waves onto a planar region having a nearly-uniform phase proportional to that of the target location. The lens is similar to a zone plate, but modified to produce a biconvex-like behavior, such that it focuses both planar and spherically spreading waves. A measurement device suitable for characterizing narrowband ultrasound signals in air is designed around this lens by coupling it to a target and planar receiver. A prototype device is constructed and used to characterize the field of a highly-focused 400 kHz air transducer along 2 radial lines. Comparison of the measurements with numeric predictions formed from nonlinear acoustic simulation showed good relative pressure correlation, with mean differences of 10% and 12% over center 3dB FWHM drop and 12% and 17% over 6dB.

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“…Recently, several methods have been proposed to solve the Westervelt equation without such restrictions [15][16][17] . Likewise, the present work investigates a new wave-vector time-domain (k-space) based numerical algorithm [18][19][20][21] that can be applied to a wide range of nonlinear applications.…”

Section: Introductionmentioning

confidence: 99%