Nonlinear modeling of therapeutic ultrasound

Wojcik, G.; Mould, John; Abboud, Najib N.; Ostromogilsky, M.; Vaughan, David K.

doi:10.1109/ultsym.1995.495865

Cited by 48 publications

(40 citation statements)

References 17 publications

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“…The results of the SPECTRALFLEX were also in good agreement with the measurements up to the third harmonic, even with only 30 grid points per wavelength, which is consistent with the validation study done by Wojcik. 23 The PZFLEX FEM solver was also able to capture the distributions of harmonics of the HIFU pressure field fairly well when a dense spatial discretization with 160 points per wavelength was applied, but at a relatively high computational cost: the axisymmetric simulation took 155 GB memory and 10 days of run time. Employing PZFLEX for a full 3D problem is likely prohibitively computationally expensive for the foreseeable future.…”

Section: Discussionmentioning

confidence: 99%

“…Although this approximation will result in errors that accrue through the solution, 25 it has been suggested that propagation on the order of hundreds of wavelengths is practical for PZFLEX and that SPECTRALFLEX should be much less sensitive to dispersion errors. 23,24,26 The propagation of a 1D plane wave was simulated in PZFLEX first to find the optimal spatial discretisation for the simulation. The analytical solution for finite amplitude plane wave propagation was used as the benchmark.…”

Section: Methodsmentioning

confidence: 99%

“…The corresponding shock formation distance in water is x shock ¼ 20.5 mm and the computational domain extended to r ¼ x/x shock ¼ 3. The developers of PZFLEX suggest that at least 15 elements per wavelength are necessary for "negligible" numerical dispersion 23 and here the value was varied from 60 (which should give sufficient accuracy at the third harmonic) to 240 points per wavelength.…”

Section: Methodsmentioning

confidence: 99%

“…20,21 Finite element methods (FEM) have also been adopted to simulate nonlinear wave propagation and they are well suited to handling complex geometries such as occur in the body. 22,23 The commercial FEM software PZFLEX (Weidlinger Associates, Inc., Mountain View, CA) is one such full solver that is widely used in industrial and biomedical applications of ultrasound, because it provides a convenient platform with a graphical user interface and optimised computing kernel. The developers demonstrated that the solution for a focused high intensity focused ultrasound (HIFU) source matches the growth of harmonics to within 10%, 24 and that an alternative pseudo-spectral method can model nonlinear pulses from imaging transducers.…”

Section: Introductionmentioning

confidence: 99%

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Simulation of nonlinear propagation of biomedical ultrasound using pzflex and the Khokhlov-Zabolotskaya-Kuznetsov Texas code

Qiao¹,

Jackson²,

Coussios³

et al. 2016

The Journal of the Acoustical Society of America

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Nonlinear acoustics plays an important role in both diagnostic and therapeutic applications of biomedical ultrasound and a number of research and commercial software packages are available. In this manuscript, predictions of two solvers available in a commercial software package, pzflex, one using the finite-element-method (FEM) and the other a pseudo-spectral method, spectralflex, are compared with measurements and the Khokhlov-Zabolotskaya-Kuznetsov (KZK) Texas code (a finite-difference time-domain algorithm). The pzflex methods solve the continuity equation, momentum equation and equation of state where they account for nonlinearity to second order whereas the KZK code solves a nonlinear wave equation with a paraxial approximation for diffraction. Measurements of the field from a single element 3.3 MHz focused transducer were compared with the simulations and there was good agreement for the fundamental frequency and the harmonics; however the FEM pzflex solver incurred a high computational cost to achieve equivalent accuracy. In addition, pzflex results exhibited non-physical oscillations in the spatial distribution of harmonics when the amplitudes were relatively low. It was found that spectralflex was able to accurately capture the nonlinear fields at reasonable computational cost. These results emphasize the need to benchmark nonlinear simulations before using codes as predictive tools.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simulation of nonlinear propagation of biomedical ultrasound using pzflex and the Khokhlov-Zabolotskaya-Kuznetsov Texas code

Qiao¹,

Jackson²,

Coussios³

et al. 2016

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

show abstract

“…Although the adiabatic hypothesis is justified in most biological media due to negligible thermal conductivity, the linear assumption is not justified in many biomedical applications where large amplitude effects occur. 57 However, most nonlinear models, such as Burgers equation and Westervelt's equation, assume a thermoviscous dissipation mechanism, resulting in an attenuation coefficient with frequency-squared dependence. In order to combine the effects of power law attenuation with nonlinearity, several authors have formulated nonlinear FPDEs.…”

Section: Inhomogeneous Media and Nonlinear Mediamentioning

confidence: 99%

Fractal ladder models and power law wave equations

Kelly

McGough

2009

The Journal of the Acoustical Society of America

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The ultrasonic attenuation coefficient in mammalian tissue is approximated by a frequency-dependent power law for frequencies less than 100 MHz. To describe this power law behavior in soft tissue, a hierarchical fractal network model is proposed. The viscoelastic and self-similar properties of tissue are captured by a constitutive equation based on a lumped parameter infinite-ladder topology involving alternating springs and dashpots. In the low-frequency limit, this ladder network yields a stress-strain constitutive equation with a time-fractional derivative. By combining this constitutive equation with linearized conservation principles and an adiabatic equation of state, a fractional partial differential equation that describes power law attenuation is derived. The resulting attenuation coefficient is a power law with exponent ranging between 1 and 2, while the phase velocity is in agreement with the Kramers-Kronig relations. The fractal ladder model is compared to published attenuation coefficient data, thus providing equivalent lumped parameters.

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Lagrangian finite element treatment of transient vibration/acoustics of biosolids immersed in fluids

Krysl

Cranford

Hildebrand

2007

Numerical Meth Engineering

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SUMMARYSuperposition principle is used to separate the incident acoustic wave from the scattered and radiated waves in a displacement-based finite element model. An absorbing boundary condition is applied to the perturbation part of the displacement. Linear constitutive equation allows for inhomogeneous, anisotropic materials, both fluids and solids. Displacement-based finite elements are used for all materials in the computational volume. Robust performance for materials with limited compressibility is achieved using assumed-strain nodally integrated simplex elements or incompatible-mode brick elements. A centereddifference time-stepping algorithm is formulated to handle general damping accurately and efficiently. Verification problems (response of empty steel cylinder immersed in water to a step plane wave, and scattering of harmonic plane waves from an elastic sphere) are discussed for assumed-strain simplex and for voxel-based brick finite element models. A voxel-based modeling scheme for complex biological geometries is described, and two illustrative results are presented from the bioacoustics application domain: reception of sound by the human ear and simulation of biosonar in beaked whales.

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Nonlinear modeling of therapeutic ultrasound

Cited by 48 publications

References 17 publications

Simulation of nonlinear propagation of biomedical ultrasound using pzflex and the Khokhlov-Zabolotskaya-Kuznetsov Texas code

Simulation of nonlinear propagation of biomedical ultrasound using pzflex and the Khokhlov-Zabolotskaya-Kuznetsov Texas code

Fractal ladder models and power law wave equations

Lagrangian finite element treatment of transient vibration/acoustics of biosolids immersed in fluids

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