Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media

Yuan, Jinsha; Cleveland, Robin O.

doi:10.1121/1.2767420

Cited by 41 publications

(33 citation statements)

References 28 publications

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“…[25][26][27]46 Power-law attenuation can be modeled by adding relaxation processes to the PDE model, 14,47,48 and several preliminary tests of an axisymmetric piston transducer have been able to recover the correct attenuation curve efficiently using three to four relaxation processes.…”

Section: B Advanced Tissue Modelsmentioning

confidence: 99%

Fourier continuation methods for high-fidelity simulation of nonlinear acoustic beams

Albin

Bruno

Cheung

et al. 2012

The Journal of the Acoustical Society of America

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On the basis of recently developed Fourier continuation (FC) methods and associated efficient parallelization techniques, this text introduces numerical algorithms that, due to very low dispersive errors, can accurately and efficiently solve the types of nonlinear partial differential equation (PDE) models of nonlinear acoustics in hundred-wavelength domains as arise in the simulation of focused medical ultrasound. As demonstrated in the examples presented in this text, the FC approach can be used to produce solutions to nonlinear acoustics PDEs models with significantly reduced discretization requirements over those associated with finite-difference, finite-element and finite-volume methods, especially in cases involving waves that travel distances that are orders of magnitude longer than their respective wavelengths. In these examples, the FC methodology is shown to lead to improvements in computing times by factors of hundreds and even thousands over those required by the standard approaches. A variety of one-and two-dimensional examples presented in this text demonstrate the power and capabilities of the proposed methodology, including an example containing a number of scattering centers and nonlinear multiple-scattering events.

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Section: B Advanced Tissue Modelsmentioning

confidence: 99%

Fourier continuation methods for high-fidelity simulation of nonlinear acoustic beams

Albin

Bruno

Cheung

et al. 2012

The Journal of the Acoustical Society of America

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“…Simplifying assumptions have been needed in the past for modeling beam patterns from ultrasound transducers, as one-way parabolic approximations, most based on the Khokhlov-ZabolotskayaKuznetsov equation (KZK) [1][2][3][4][5][6][7][8] . To overcome the validity limitations of the parabolic approximations, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Tissue inhomogeneity can be modeled in these oneway models 6 , like transmission though tissue layers with refraction, but they do not take into account backscattering and multiple reflections. More realistic models, e.g.…”

Section: Introductionmentioning

confidence: 99%

Time-Domain Simulation of Ultrasound Propagation in a Tissue-Like Medium Based on the Resolution of the Nonlinear Acoustic Constitutive Relations

Jiménez¹,

Camarena²,

Redondo³

et al. 2016

Acta Acustica united with Acustica

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A time-domain numerical code based on the constitutive relations of nonlinear acoustics for simulating ultrasound propagation is presented. To model frequency power law attenuation, such as observed in biological media, multiple relaxation processes are included and relaxation parameters are fitted to both exact frequency power law attenuation and empirically measured attenuation of a variety of tissues that does not fit an exact power law. A computational technique based on artificial relaxation is included to correct the non-negligible numerical dispersion of the numerical method and to improve stability when shock waves are present. This technique avoids the use of high order finite difference schemes, leading to fast calculations. The numerical code is especially suitable to study high intensity and focused axisymmetric acoustic beams in tissue-like medium, as it is based on the full constitutive relations that overcomes the limitations of the parabolic approximations, while some specific effects not contemplated by the Westervelt equation can be also studied. The accuracy of the method is discussed by comparing the proposed simulation solutions to one-dimensional analytical ones, to k-space numerical solutions and also to experimental data from a focused beam propagating in a frequency power law attenuation media.

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“…There have been recent developments, however, that allow for the modeling of weak range-dependence, that is, small variations in medium properties (Jing & Cleveland, 2007), but these methods cannot handle sloping bottoms where variations in medium properties are large.…”

Section: List Of Figures and Tablesmentioning

confidence: 99%

Nonlinear acoustic pulse propagation in range-dependent underwater environments

Maestas

Collis

2012

The Journal of the Acoustical Society of America

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The nonlinear progressive wave equation (NPE) is a time-domain formulation of Eulers fluid equations designed to model low angle wave propagation using a wave-following computational domain. The standard formulation consists of four separate mathematical quantities that physically represent refraction, nonlinear steepening, radial spreading, and diffraction. The latter two of these effects are linear whereas the steepening and refraction are nonlinear. This formulation recasts pressure, density, and velocity into a single variable a dimensionless pressure perturbation which allows for greater efficiency in calculations.The wave-following frame of reference permits the simulation of long-range propagation that is useful in modeling the effects of blast waves in the ocean waveguide. Nonlinear effects such as weak shock formation are accurately captured with the NPE. The numerical implementation is a combination of two numerical schemes: a finite-difference Crank-Nicholson algorithm for the linear terms of the NPE and a flux-corrected transport algorithm for the nonlinear terms. In this work, an existing implementation is extended to allow for a penetrable fluid bottom. Range-dependent environments, characterized by sloping bathymetry, are investigated and benchmarked using a rotated coordinate system approach.

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Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media

Cited by 41 publications

References 28 publications

Fourier continuation methods for high-fidelity simulation of nonlinear acoustic beams

Fourier continuation methods for high-fidelity simulation of nonlinear acoustic beams

Time-Domain Simulation of Ultrasound Propagation in a Tissue-Like Medium Based on the Resolution of the Nonlinear Acoustic Constitutive Relations

Nonlinear acoustic pulse propagation in range-dependent underwater environments

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