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

Many biomedical applications such as ultrasonic targeted drug delivery, gene therapy, and molecular imaging entail the problems of manipulating microbubbles by means of a high-intensity focused ultrasound (HIFU) pressure field; namely stable cavitation. In high-intensity acoustic field, bubbles demonstrate translational instability, the well-known erratic dancing motion, which is caused by shape oscillations of the bubbles that are excited by their volume oscillations. The literature of bubble dynamics in the HIFU field is mainly centered on experiments, lacking a systematic study to determine the threshold for shape oscillations and translational motion. In this work, we extend the existing multiphysics mathematical modeling platform on bubble dynamics for taking account of (1) the liquid compressibility which allows us to apply a high-intensity acoustic field; (2) the mutual interactions of volume pulsation, shape modes, and translational motion; as well as (3) the effects of nonlinearity, diffraction, and absorption of HIFU to incorporate the acoustic nonlinearity due to wave kinematics or medium—all in one model. The effects of acoustic nonlinearity on the radial pulsations, axisymmetric modes of shape oscillations, and translational motion of a bubble, subjected to resonance and off-resonance excitation and various acoustic pressure, are examined. The results reveal the importance of considering all the involved harmonics and wave distortion in the bubble dynamics, to accurately predict the oscillations, translational trajectories, and the threshold for inertial (unstable) cavitation. This result is of interest for understanding the bubble dynamical behaviors observed experimentally in the HIFU field.

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“…where A depends on the attenuation coefficient. The attenuation follows a power-law dependence on frequency given as [41,42]…”

Section: Nonlinear Acoustic Pressure From Fu Transducermentioning

confidence: 99%

Effects of Nonlinear Propagation of Focused Ultrasound on the Stable Cavitation of a Single Bubble

Bakhtiari-Nejad

Shahab

2018

Acoustics

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“…Marquet et al [20] predicted and corrected the defocusing effect of the skull using a full 3D finite-difference simulation code together with stereotactic CT images. The full wave simulation method is computationally costly [21]. Therefore, another CT-or MRI-guided method, the ray-tracing method, was also introduced to correct phase aberrations [22], [23].…”

Section: Introductionmentioning

confidence: 99%

Ray Theory-Based Transcranial Phase Correction for Intracranial Imaging: A Phantom Study

Jiang

et al. 2019

IEEE Access

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Ultrasonic imaging provides a non-invasive way to diagnose brain disease. However, due to imaging degradation effects from the phase-aberration and reverberation, it is still challenging to achieve an accurate transcranial imaging. The objective of this work is to improve the quality of transcranial imaging. To this end, a ray theory based transcranial phase correction method was proposed to correct the phase abberation induced by cranial bones. With the pre-knowledge of the shape and longitudinal velocity of the cranial bones, the corrected phases are derived by solving eikonal equation (ray-theory). The Ideal Synthetic Aperture Focusing Technique (I-SAFT) is applied for signal acquisitions in simulations and in-vitro phantom experiment with one-element transmitting and all-element receiving method. Dynamic focusing is achieved at each imaging position with I-SAFT and the transcranial imaging distortion is modified with the proposed phase correction method. Simulations and experiments show that the imaging distortion of target circular phantoms was corrected, and the imaging quality is improved after the phase correction. With the proposed method, the average error of the central position of target phantoms decreases from 1.98 mm to 0.21 mm, the eccentricity of fitted ellipse averagely decreases from 0.63 to 0.19, and the average maximum luminance contrast of phantoms improves from 37.36dB to 42.41dB. It is illustrated that the proposed ray-theory based phase correction method might be useful for intracranial imaging.

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“…The use of ADE formalism in 3-D-FDTD, for non-linear and dispersive material, is widely used for electromagnetic waves propagation and particularly for photonics and active plasmonics applications where Lorentz-Drude, Raman and Kerr non-linear terms are incorporated (Taflove & Hagness 2005;Greene & Taflove 2006;Taflove et al 2013). This approach is very uncommon (almost inexistant) in seismic wave propagation despite its great potential, except in rare modelling studies in 1-D dispersive and attenuated fluid/acoustic biophysical media (Jiménez et al 2016) or nondestructive testing (Lombard & Piraux 2011). The only mention of ADE formalism concerns the implementation of ADE-perfectly matched layer (PML) absorbing boundary conditions (Martin et al 2010;Zhang & Shen 2010;Moczo et al 2014).…”

Section: Introductionmentioning

confidence: 99%

Seismic wave propagation in nonlinear viscoelastic media using the auxiliary differential equation method

Martin

Bodet

Tournat

et al. 2018

Geophysical Journal International

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In previous studies, the auxiliary differential equation (ADE) method has been applied to 2-D seismic-wave propagation modelling in viscoelastic media. This method is based on the separation of the wave propagation equations derived from the constitutive law defining the stress-strain relation. We make here a 3-D extension of a finite-difference (FD) scheme to solve a system of separated equations consisting in the stress-strain rheological relation, the strain-velocity and the velocity-stress equations. The current 3-D FD scheme consists in the discretization of the second order formulation of a non-linear viscoelastic wave equation with a time actualization of the velocity and displacement fields. Compared to the usual memory variable formalism, the ADE method allows flexible implementation of complex expressions of the desired rheological model such as attenuation/viscoelastic models or even non-linear behaviours, with physical parameters that can be provided from dispersion analysis. The method can also be associated with optimized perfectly matched layers-based boundary conditions that can be seen as additional attenuation (viscoelastic) terms. We present the results obtained for a non-linear viscoelastic model made of a Zener viscoelastic body associated with a non-linear quadratic strain term. Such non-linearity is relevant to define unconsolidated granular model behaviour. Thanks to a simple model, but without loss of generality, we demonstrate the accuracy of the proposed numerical approach.

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

Cited by 23 publications

References 43 publications

Effects of Nonlinear Propagation of Focused Ultrasound on the Stable Cavitation of a Single Bubble

Effects of Nonlinear Propagation of Focused Ultrasound on the Stable Cavitation of a Single Bubble

Ray Theory-Based Transcranial Phase Correction for Intracranial Imaging: A Phantom Study

Seismic wave propagation in nonlinear viscoelastic media using the auxiliary differential equation method

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