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Lang Xia

Publications and source records attributed to Lang Xia.

11 recordsLinked to original sources
arXiv2021

On the Prediction of the Subharmonic Threshold of an Ultrasound Contrast Agent

Subharmonics emitted from microbubble-based ultrasound contrast agents (UCA) are considered as a noninvasive indicator for diagnostic applications in medical fields. Contrast ultrasound imaging using the modality of subharmonics could be also better than that of using harmonics. Unlike the harmonics of an UCA that increase with increasing the amplitude of excitation pressure, subharmonics occur only when the excitation pressure exceeds a threshold value. The excitation pressure inducing the onset of subharmonic components from the UCA during nonlinear oscillations is known as the subharmonic threshold. Although numerous studies on the subharmonics of free bubbles or UCAs have been carried out for decades, several experimental observations, such as the shift of the subharmonic resonance and subharmonic threshold at low excitation pressures, cannot be well characterized by existing theories. An analytical method for resolving these inconsistencies remains incomplete. The present article theoretically investigates the subharmonic threshold of an UCA through the techniques of energy balancing in the phase plane and instability analysis of subharmonic-free oscillations. The influence of shell parameters of the UCA on the subharmonic threshold is studied. Those experimental observations are explained by the amplitude-dependent nonlinear resonance and damping. The effect of nonspherical oscillations on subharmonic emissions is also discussed.

physics.med-ph↗
arXiv2020

Theoretical Estimation of Attenuation Coefficient of Resonant Ultrasound Contrast Agents

Acoustic characterization of ultrasound contrast agents (UCAs, coated microbubbles) relies on the attenuation theory that assumes the UCAs oscillate linearly at sufficiently low excitation pressures. Effective shell parameters of the UCAs can be estimated by fitting a theoretical attenuation curve to experimentally measured attenuation data. Depending on the excitation frequency and properties of the shell, however, an UCA may oscillate nonlinearly even at sufficiently low excitation pressures violating the assumption in the linear attenuation theory. Notably, the concern on the estimation of the attenuation coefficient of a microbubble at resonance using linearized approximation has long been addressed. In this article, we investigated the attenuation phenomenon through analyzing the energy dissipation of a single UCA and propagating waves in an UCA suspension, both of which employed a nonlinear Rayleigh-Plesset equation. Analytical formulae capable of estimating the attenuation coefficient due to the weakly nonlinear oscillations of the UCA were obtained with a relatively rigorous mathematical analysis. The computed results that were verified by numerical simulations showed the attenuation coefficient of the UCA at resonance was pressure-dependent and could be significantly smaller than that predicted by the linear attenuation theory. Polydispersity of the UCA population enlarged the difference in the estimation of attenuation between the linear and present second-order nonlinear theories.

physics.flu-dyn↗
arXiv2019

A Note on the Nonlinear Attenuation of an Ultrasound Contrast Agent Calculated by Rayleigh-Plesset Equation

The attenuation of small-amplitude acoustic waves in a suspension containing ultrasound contrast agents (UCAs, coated microbubbles) is determined by the linear oscillation of the UCAs in the medium, which can be estimated via a linear attenuation theory. Recently, several nonlinear phenomena of energy attenuation at very low-intensity of acoustic pressures have been observed experimentally, raising concerns on the validity of the linear attenuation theory. Explanations of the nonlinear phenomenon are still lacking. Particularly, the interpretation of the pressure-dependent attenuation phenomenon is still under debate. In this note, we investigated the energy dissipation of a single UCA via a nonlinear Rayleigh-Plesset equation and used a formula capable of estimating attenuation coefficient due to the nonlinear oscillation of the UCA. The simulation results show the linear oscillation of an UCA at low excitation pressures does not always guarantee the linearity in the energy attenuation. Although nonlinear oscillation of the UCA contributes to the occurrence of nonlinear attenuation phenomena, it is not the only trigger.

physics.flu-dyn↗
arXiv2019

Attenuation of an Ultrasound Contrast Agent Estimated from Transient Solution of Linearized Rayleigh-Plesset Equation

The attenuation of low-intensity acoustic waves in the suspension of ultrasound contrast agents (UCAs, microbubbles) is determined by the oscillation of the microbubbles in the medium. This bubble-induced attenuation is a linear phenomenon and can be estimated via a linearized Rayleigh-Plesset equation (RPE). In the material characterization, theoretical attenuation is estimated from steady state oscillation of an UCA and immediately compared with experimental attenuation data that are usually measured by shot-pulse ultrasound. However, discrepancy could exist in the characterization if the UCA does not ring up to steady state oscillation. In this article, we investigate the situation where the transient solution of the RPE is not negligible and discuss its impact on the modeling of the shell parameters of an UCA. We provide a formula for attenuation estimation considering the contribution due to transient oscillation.

physics.flu-dyn↗
arXiv2019

Acoustic Nonlinearity Parameter B/A in the Suspension of Ultrasound Contrast Agents Part I: A Thermodynamic Approach

The acoustic nonlinearity parameter B/A plays a significant role in the characterization of acoustic properties of various biomaterials and biological tissues. It has the potential to be a favorable imaging modality in contrast ultrasound imaging with coated microbubbles. However, the development of effective means for evaluating the nonlinearity parameter of suspensions of ultrasound contrast agents (UCAs, also known as bubbly liquids) remains open. The present paper formulates a new equation based on the thermodynamic method that correlates both attenuation and phase velocity of linear ultrasound. The simplicity of the present method makes the B/A estimation possible with a relatively rigorous mathematical derivation. The calculated nonlinearity parameter contains the contribution of dynamic effects of bubbles, and its low-frequency limit agrees with B/A estimated by the method of mixture law when the volume fraction is below 10-4. Furthermore, the maximum B/A in bubbly liquids can reach up to105, while the minimum can be as low as -105. The negative nonlinearity parameter indicates significantly different thermodynamic properties of bubbly liquids.

physics.flu-dyn↗
arXiv2018

Propagation of Nonlinear Acoustic Waves in the Suspension of Ultrasound Contrast Agents Part I: Equation for Counting Resonance Effects and Revealing Acoustic Localization

The oscillations of ultrasound contrast agents are of particular importance to the understanding of the propagation of acoustic waves in the bubbly liquids (suspensions of ultrasound contrast agents). Acoustic waves propagating in bubbly liquids have been investigated extensively. Little has been dedicated to the resonance effects of the microbubbles on the propagating waves. Here a nonlinear partial differential equation for describing one-dimensional acoustic waves propagating near the resonance frequency of the microbubbles in bubbly liquids is obtained. The present equation recovers classical results for propagating acoustic waves with finite amplitudes in liquids and interprets the acoustic localization in bubbly liquids explicitly.

physics.flu-dyn↗
arXiv2018

Analysis on the Integrability of the Rayleigh-Plesset Equation with Painlevé Test and Lie Symmetry Groups

The Rayleigh-Plesset equation (RPE) is a nonlinear ordinary differential equation (ODE) of second order that governs the dynamics of a spherical bubble and plays an essential role in interpreting many real-world phenomena involving the presence of bubbles in engineering and medical fields. In the present paper, we present a relatively comprehensive analysis of the analytical solutions of the RPE. The integrability of the Rayleigh-Plesset equation is investigated and discussed using the Painlevé test. Lie symmetry groups are employed subsequentially to obtain several exact solutions to the simplified Rayleigh-Plesset equations.

math-ph↗
arXiv2018

Morphology of Flow Patterns Generated by Viscous Fingering from Miscible Fluids

A rest fluid displaced by a less viscous fluid in a porous medium triggers the so-called Saffman-Taylor instability at their contact front and hence forms complicated finger-like patterns. When the two fluids are miscible, the surface tension at their contact front vanishes, leaving the variation in viscosity dominant the contribution to the instability. The phenomena, named viscous fingering, can be studied by the analogy of a single-phase flow in the Hele-Shaw cell, a quasi-two-dimensional rectilinear plane. Viscous fingering produces complex geometrical patterns. They are important not only in industry but also in mathematics. Theoretical analyses on the evolution of the finger-like patterns in miscible fluids are still expanding (it is referred to the morphology of the flow patterns). Here we study the morphology of the finger-like patterns within some simple concepts in differential geometry, in which surfaces and curves are analog to the profiles of the concentration and its contours, respectively. We thus can investigate the fingering phenomena through the geometrical perspective in which various results in differential geometry are immediately applicable.

physics.flu-dyn↗
arXiv2018

Characterizing two-dimensional incompressible flows through traveling wave and symmetry solutions of the vorticity transportation equation

We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These traveling wave solutions, including both continuous and solitary waves, also recover the results existing in the theory of potential flows. We further analyze the flow patterns regarding symmetry solutions generated by Lie transformation groups. Some of the symmetry solutions have not been discussed in the current literature. They could display flow patterns very different from that of the original exact solutions, suggesting the symmetry solutions are not trivial. Particularly, the symmetry solutions to Lame-Oseen vortex and doublet exhibit more complicated dynamics.

math-ph↗
arXiv2018

Lie Subalgebras and Invariant Solutions to the Equation of Fluid Flows in Toroidal Field

In the present report, by using the Stokes-Helmholtz decomposition theorem the 3-dimensional Navier-Stokes equation (NSE) is uncoupled and transformed into a scalar equation for the velocity potential when the flow field is toroidal. The dynamics of the velocity potential is independent of the vector potential. The reduction and invariant solutions to the equation are analyzed by the Lie symmetry method subsequently. The Lie subalgebras for the equation are discussed and the corresponding invariant solutions are also presented.

math.DG↗