Journal ArticleDOI
Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian
Bradley E. Treeby,Ben T. Cox +1 more
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TLDR
In this paper, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived, which can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts.Abstract:
The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many three-dimensional problems of interest. Here, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived. These operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts. A framework for encoding the developed wave equation using three coupled first-order constitutive equations is discussed, and the model is demonstrated through several one-, two-, and three-dimensional simulations.read more
Citations
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Journal ArticleDOI
Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method
TL;DR: The k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations of nonlinear ultrasound propagation through tissue realistic media, and increases the accuracy of the gradient calculation and relaxes the requirement for dense computational grids compared to conventional finite difference methods.
Journal ArticleDOI
Photoacoustic tomography in absorbing acoustic media using time reversal
TL;DR: In this article, a method to compensate for the effect of acoustic absorption on the measured time domain signals is described, where the reconstruction is regularized by filtering the absorption and dispersion terms in the spatial frequency domain using a Tukey window.
Journal ArticleDOI
What is the fractional Laplacian? A comparative review with new results
Anna Lischke,Guofei Pang,Mamikon Gulian,Fangying Song,Christian A. Glusa,Xiaoning Zheng,Zhiping Mao,Wei Cai,Mark M. Meerschaert,Mark Ainsworth,George Em Karniadakis +10 more
TL;DR: A comparison of several commonly used definitions of the fractional Laplacian theoretically, through their stochastic interpretations as well as their analytical properties, and a collection of benchmark problems to compare different definitions on bounded domains using a sample of state-of-the-art methods.
Journal ArticleDOI
Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians
Tieyuan Zhu,Jerry M. Harris +1 more
TL;DR: In this article, a wave equation was derived from Kjartansson's constant-Q constitutive stress-strain relation in combination with the mass and momentum conservation equations for modeling acoustic wave propagation in attenuating media.
Journal ArticleDOI
Analytical solutions for the multi-term time–space Caputo–Riesz fractional advection–diffusion equations on a finite domain
TL;DR: In this article, the authors derived analytical solutions of three types of the MT-TSCR-FADE with Dirichlet boundary conditions, which are called respectively the multi-term time-fractional diffusion terms, the multiscale time fractional wave terms, and the multiiscale mixed diffusion-wave terms.
References
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